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decNumber.c

/* Decimal number arithmetic module for the decNumber C Library.
   Copyright (C) 2005, 2007, 2009 Free Software Foundation, Inc.
   Contributed by IBM Corporation.  Author Mike Cowlishaw.

   This file is part of GCC.

   GCC is free software; you can redistribute it and/or modify it under
   the terms of the GNU General Public License as published by the Free
   Software Foundation; either version 3, or (at your option) any later
   version.

   GCC is distributed in the hope that it will be useful, but WITHOUT ANY
   WARRANTY; without even the implied warranty of MERCHANTABILITY or
   FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module                         */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for General Decimal Arithmetic  */
/* as defined in the specification which may be found on the            */
/* http://www2.hursley.ibm.com/decimal web pages.  It implements both */
/* the full ('extended') arithmetic and the simpler ('subset')          */
/* arithmetic.                                              */
/*                                                    */
/* Usage notes:                                             */
/*                                                    */
/* 1. This code is ANSI C89 except:                         */
/*                                                    */
/*       If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and         */
/*     uint64_t types may be used.  To avoid these, set DECUSE64=0  */
/*     and DECDPUN<=4 (see documentation).                        */
/*                                                    */
/* 2. The decNumber format which this library uses is optimized for   */
/*    efficient processing of relatively short numbers; in particular */
/*    it allows the use of fixed sized structures and minimizes copy  */
/*    and move operations.  It does, however, support arbitrary         */
/*    precision (up to 999,999,999 digits) and arbitrary exponent     */
/*    range (Emax in the range 0 through 999,999,999 and Emin in the  */
/*    range -999,999,999 through 0).  Mathematical functions (for     */
/*    example decNumberExp) as identified below are restricted more   */
/*    tightly: digits, emax, and -emin in the context must be <=      */
/*    DEC_MAX_MATH (999999), and their operand(s) must be within      */
/*    these bounds.                                         */
/*                                                    */
/* 3. Logical functions are further restricted; their operands must   */
/*    be finite, positive, have an exponent of zero, and all digits   */
/*    must be either 0 or 1.  The result will only contain digits     */
/*    which are 0 or 1 (and will have exponent=0 and a sign of 0).    */
/*                                                    */
/* 4. Operands to operator functions are never modified unless they   */
/*    are also specified to be the result number (which is always     */
/*    permitted).  Other than that case, operands must not overlap.   */
/*                                                    */
/* 5. Error handling: the type of the error is ORed into the status   */
/*    flags in the current context (decContext structure).  The         */
/*    SIGFPE signal is then raised if the corresponding trap-enabler  */
/*    flag in the decContext is set (is 1).                       */
/*                                                    */
/*    It is the responsibility of the caller to clear the status      */
/*    flags as required.                                    */
/*                                                    */
/*    The result of any routine which returns a number will always    */
/*    be a valid number (which may be a special value, such as an     */
/*    Infinity or NaN).                                     */
/*                                                    */
/* 6. The decNumber format is not an exchangeable concrete        */
/*    representation as it comprises fields which may be machine-     */
/*    dependent (packed or unpacked, or special length, for example). */
/*    Canonical conversions to and from strings are provided; other   */
/*    conversions are available in separate modules.              */
/*                                                    */
/* 7. Normally, input operands are assumed to be valid.      Set DECCHECK */
/*    to 1 for extended operand checking (including NULL operands).   */
/*    Results are undefined if a badly-formed structure (or a NULL    */
/*    pointer to a structure) is provided, though with DECCHECK         */
/*    enabled the operator routines are protected against exceptions. */
/*    (Except if the result pointer is NULL, which is unrecoverable.) */
/*                                                    */
/*    However, the routines will never cause exceptions if they are   */
/*    given well-formed operands, even if the value of the operands   */
/*    is inappropriate for the operation and DECCHECK is not set.     */
/*    (Except for SIGFPE, as and where documented.)               */
/*                                                    */
/* 8. Subset arithmetic is available only if DECSUBSET is set to 1.   */
/* ------------------------------------------------------------------ */
/* Implementation notes for maintenance of this module:                 */
/*                                                    */
/* 1. Storage leak protection:      Routines which use malloc are not     */
/*    permitted to use return for fastpath or error exits (i.e.,      */
/*    they follow strict structured programming conventions).           */
/*    Instead they have a do{}while(0); construct surrounding the     */
/*    code which is protected -- break may be used to exit this.      */
/*    Other routines can safely use the return statement inline.      */
/*                                                    */
/*    Storage leak accounting can be enabled using DECALLOC.            */
/*                                                    */
/* 2. All loops use the for(;;) construct.  Any do construct does     */
/*    not loop; it is for allocation protection as just described.    */
/*                                                    */
/* 3. Setting status in the context must always be the very last      */
/*    action in a routine, as non-0 status may raise a trap and hence */
/*    the call to set status may not return (if the handler uses long */
/*    jump).  Therefore all cleanup must be done first.      In general,  */
/*    to achieve this status is accumulated and is only applied just  */
/*    before return by calling decContextSetStatus (via decStatus).   */
/*                                                    */
/*    Routines which allocate storage cannot, in general, use the     */
/*    'top level' routines which could cause a non-returning            */
/*    transfer of control.  The decXxxxOp routines are safe (do not   */
/*    call decStatus even if traps are set in the context) and should */
/*    be used instead (they are also a little faster).                  */
/*                                                    */
/* 4. Exponent checking is minimized by allowing the exponent to      */
/*    grow outside its limits during calculations, provided that      */
/*    the decFinalize function is called later.  Multiplication and   */
/*    division, and intermediate calculations in exponentiation,      */
/*    require more careful checks because of the risk of 31-bit         */
/*    overflow (the most negative valid exponent is -1999999997, for  */
/*    a 999999999-digit number with adjusted exponent of -999999999). */
/*                                                    */
/* 5. Rounding is deferred until finalization of results, with any    */
/*    'off to the right' data being represented as a single digit     */
/*    residue (in the range -1 through 9).  This avoids any double-   */
/*    rounding when more than one shortening takes place (for           */
/*    example, when a result is subnormal).                       */
/*                                                    */
/* 6. The digits count is allowed to rise to a multiple of DECDPUN    */
/*    during many operations, so whole Units are handled and exact    */
/*    accounting of digits is not needed.  The correct digits value   */
/*    is found by decGetDigits, which accounts for leading zeros.     */
/*    This must be called before any rounding if the number of digits */
/*    is not known exactly.                                 */
/*                                                    */
/* 7. The multiply-by-reciprocal 'trick' is used for partitioning     */
/*    numbers up to four digits, using appropriate constants.  This   */
/*    is not useful for longer numbers because overflow of 32 bits    */
/*    would lead to 4 multiplies, which is almost as expensive as     */
/*    a divide (unless a floating-point or 64-bit multiply is           */
/*    assumed to be available).                                   */
/*                                                    */
/* 8. Unusual abbreviations that may be used in the commentary:         */
/*    lhs -- left hand side (operand, of an operation)            */
/*    lsd -- least significant digit (of coefficient)             */
/*    lsu -- least significant Unit (of coefficient)              */
/*    msd -- most significant digit (of coefficient)              */
/*    msi -- most significant item (in an array)                  */
/*    msu -- most significant Unit (of coefficient)               */
/*    rhs -- right hand side (operand, of an operation)           */
/*    +ve -- positive                                       */
/*    -ve -- negative                                       */
/*    **  -- raise to the power                             */
/* ------------------------------------------------------------------ */

#include <stdlib.h>              /* for malloc, free, etc. */
#include <stdio.h>               /* for printf [if needed] */
#include <string.h>              /* for strcpy */
#include <ctype.h>               /* for lower */
#include "dconfig.h"             /* for GCC definitions */
#include "decNumber.h"           /* base number library */
#include "decNumberLocal.h"      /* decNumber local types, etc. */

/* Constants */
/* Public lookup table used by the D2U macro */
const uByte d2utable[DECMAXD2U+1]=D2UTABLE;

#define DECVERB       1          /* set to 1 for verbose DECCHECK */
#define powers        DECPOWERS        /* old internal name */

/* Local constants */
#define DIVIDE        0x80       /* Divide operators */
#define REMAINDER   0x40         /* .. */
#define DIVIDEINT   0x20         /* .. */
#define REMNEAR       0x10       /* .. */
#define COMPARE       0x01       /* Compare operators */
#define COMPMAX       0x02       /* .. */
#define COMPMIN       0x03       /* .. */
#define COMPTOTAL   0x04         /* .. */
#define COMPNAN       0x05       /* .. [NaN processing] */
#define COMPSIG       0x06       /* .. [signaling COMPARE] */
#define COMPMAXMAG  0x07         /* .. */
#define COMPMINMAG  0x08         /* .. */

#define DEC_sNaN     0x40000000        /* local status: sNaN signal */
#define BADINT    (Int)0x80000000      /* most-negative Int; error indicator */
/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
#define BIGEVEN (Int)0x80000002
#define BIGODD    (Int)0x80000003

static Unit uarrone[1]={1};   /* Unit array of 1, used for incrementing */

/* Granularity-dependent code */
#if DECDPUN<=4
  #define eInt    Int         /* extended integer */
  #define ueInt uInt          /* unsigned extended integer */
  /* Constant multipliers for divide-by-power-of five using reciprocal */
  /* multiply, after removing powers of 2 by shifting, and final shift */
  /* of 17 [we only need up to **4] */
  static const uInt multies[]={131073, 26215, 5243, 1049, 210};
  /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
  #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
#else
  /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
  #if !DECUSE64
    #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
  #endif
  #define eInt    Long        /* extended integer */
  #define ueInt uLong         /* unsigned extended integer */
#endif

/* Local routines */
static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
                        decContext *, uByte, uInt *);
static Flag    decBiStr(const char *, const char *, const char *);
static uInt    decCheckMath(const decNumber *, decContext *, uInt *);
static void    decApplyRound(decNumber *, decContext *, Int, uInt *);
static Int     decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
static decNumber * decCompareOp(decNumber *, const decNumber *,
                        const decNumber *, decContext *,
                        Flag, uInt *);
static void    decCopyFit(decNumber *, const decNumber *, decContext *,
                        Int *, uInt *);
static decNumber * decDecap(decNumber *, Int);
static decNumber * decDivideOp(decNumber *, const decNumber *,
                        const decNumber *, decContext *, Flag, uInt *);
static decNumber * decExpOp(decNumber *, const decNumber *,
                        decContext *, uInt *);
static void    decFinalize(decNumber *, decContext *, Int *, uInt *);
static Int     decGetDigits(Unit *, Int);
static Int     decGetInt(const decNumber *);
static decNumber * decLnOp(decNumber *, const decNumber *,
                        decContext *, uInt *);
static decNumber * decMultiplyOp(decNumber *, const decNumber *,
                        const decNumber *, decContext *,
                        uInt *);
static decNumber * decNaNs(decNumber *, const decNumber *,
                        const decNumber *, decContext *, uInt *);
static decNumber * decQuantizeOp(decNumber *, const decNumber *,
                        const decNumber *, decContext *, Flag,
                        uInt *);
static void    decReverse(Unit *, Unit *);
static void    decSetCoeff(decNumber *, decContext *, const Unit *,
                        Int, Int *, uInt *);
static void    decSetMaxValue(decNumber *, decContext *);
static void    decSetOverflow(decNumber *, decContext *, uInt *);
static void    decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
static Int     decShiftToLeast(Unit *, Int, Int);
static Int     decShiftToMost(Unit *, Int, Int);
static void    decStatus(decNumber *, uInt, decContext *);
static void    decToString(const decNumber *, char[], Flag);
static decNumber * decTrim(decNumber *, decContext *, Flag, Int *);
static Int     decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
                        Unit *, Int);
static Int     decUnitCompare(const Unit *, Int, const Unit *, Int, Int);

#if !DECSUBSET
/* decFinish == decFinalize when no subset arithmetic needed */
#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
#else
static void    decFinish(decNumber *, decContext *, Int *, uInt *);
static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
#endif

/* Local macros */
/* masked special-values bits */
#define SPECIALARG  (rhs->bits & DECSPECIAL)
#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)

/* Diagnostic macros, etc. */
#if DECALLOC
/* Handle malloc/free accounting.  If enabled, our accountable routines */
/* are used; otherwise the code just goes straight to the system malloc */
/* and free routines. */
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#define DECFENCE 0x5a            /* corruption detector */
/* 'Our' malloc and free: */
static void *decMalloc(size_t);
static void  decFree(void *);
uInt decAllocBytes=0;            /* count of bytes allocated */
/* Note that DECALLOC code only checks for storage buffer overflow. */
/* To check for memory leaks, the decAllocBytes variable must be */
/* checked to be 0 at appropriate times (e.g., after the test */
/* harness completes a set of tests).  This checking may be unreliable */
/* if the testing is done in a multi-thread environment. */
#endif

#if DECCHECK
/* Optional checking routines.      Enabling these means that decNumber */
/* and decContext operands to operator routines are checked for */
/* correctness.    This roughly doubles the execution time of the */
/* fastest routines (and adds 600+ bytes), so should not normally be */
/* used in 'production'. */
/* decCheckInexact is used to check that inexact results have a full */
/* complement of digits (where appropriate -- this is not the case */
/* for Quantize, for example) */
#define DECUNRESU ((decNumber *)(void *)0xffffffff)
#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
#define DECUNCONT ((decContext *)(void *)(0xffffffff))
static Flag decCheckOperands(decNumber *, const decNumber *,
                       const decNumber *, decContext *);
static Flag decCheckNumber(const decNumber *);
static void decCheckInexact(const decNumber *, decContext *);
#endif

#if DECTRACE || DECCHECK
/* Optional trace/debugging routines (may or may not be used) */
void decNumberShow(const decNumber *);    /* displays the components of a number */
static void decDumpAr(char, const Unit *, Int);
#endif

/* ================================================================== */
/* Conversions                                              */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* from-int32 -- conversion from Int or uInt                      */
/*                                                    */
/*  dn is the decNumber to receive the integer                    */
/*  in or uin is the integer to be converted                      */
/*  returns dn                                              */
/*                                                    */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
  uInt unsig;
  if (in>=0) unsig=in;
   else {                     /* negative (possibly BADINT) */
    if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
     else unsig=-in;                /* invert */
    }
  /* in is now positive */
  decNumberFromUInt32(dn, unsig);
  if (in<0) dn->bits=DECNEG;        /* sign needed */
  return dn;
  } /* decNumberFromInt32 */

decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
  Unit *up;                   /* work pointer */
  decNumberZero(dn);                /* clean */
  if (uin==0) return dn;            /* [or decGetDigits bad call] */
  for (up=dn->lsu; uin>0; up++) {
    *up=(Unit)(uin%(DECDPUNMAX+1));
    uin=uin/(DECDPUNMAX+1);
    }
  dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
  return dn;
  } /* decNumberFromUInt32 */

/* ------------------------------------------------------------------ */
/* to-int32 -- conversion to Int or uInt                    */
/*                                                    */
/*  dn is the decNumber to convert                          */
/*  set is the context for reporting errors                       */
/*  returns the converted decNumber, or 0 if Invalid is set       */
/*                                                    */
/* Invalid is set if the decNumber does not have exponent==0 or if    */
/* it is a NaN, Infinite, or out-of-range.                        */
/* ------------------------------------------------------------------ */
Int decNumberToInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  /* special or too many digits, or bad exponent */
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
   else { /* is a finite integer with 10 or fewer digits */
    Int d;                 /* work */
    const Unit *up;              /* .. */
    uInt hi=0, lo;               /* .. */
    up=dn->lsu;                  /* -> lsu */
    lo=*up;                /* get 1 to 9 digits */
    #if DECDPUN>1          /* split to higher */
      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    /* collect remaining Units, if any, into hi */
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
    /* now low has the lsd, hi the remainder */
    if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
      /* most-negative is a reprieve */
      if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
      /* bad -- drop through */
      }
     else { /* in-range always */
      Int i=X10(hi)+lo;
      if (dn->bits&DECNEG) return -i;
      return i;
      }
    } /* integer */
  decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
  return 0;
  } /* decNumberToInt32 */

uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif
  /* special or too many digits, or bad exponent, or negative (<0) */
  if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
    || (dn->bits&DECNEG && !ISZERO(dn)));           /* bad */
   else { /* is a finite integer with 10 or fewer digits */
    Int d;                 /* work */
    const Unit *up;              /* .. */
    uInt hi=0, lo;               /* .. */
    up=dn->lsu;                  /* -> lsu */
    lo=*up;                /* get 1 to 9 digits */
    #if DECDPUN>1          /* split to higher */
      hi=lo/10;
      lo=lo%10;
    #endif
    up++;
    /* collect remaining Units, if any, into hi */
    for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];

    /* now low has the lsd, hi the remainder */
    if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
     else return X10(hi)+lo;
    } /* integer */
  decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
  return 0;
  } /* decNumberToUInt32 */

/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string                 */
/* to-engineering-string -- conversion to numeric string          */
/*                                                    */
/*   decNumberToString(dn, string);                         */
/*   decNumberToEngString(dn, string);                            */
/*                                                    */
/*  dn is the decNumber to convert                          */
/*  string is the string where the result will be laid out        */
/*                                                    */
/*  string must be at least dn->digits+14 characters long         */
/*                                                    */
/*  No error is possible, and no status can be set.               */
/* ------------------------------------------------------------------ */
char * decNumberToString(const decNumber *dn, char *string){
  decToString(dn, string, 0);
  return string;
  } /* DecNumberToString */

char * decNumberToEngString(const decNumber *dn, char *string){
  decToString(dn, string, 1);
  return string;
  } /* DecNumberToEngString */

/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string                    */
/*                                                    */
/* decNumberFromString -- convert string to decNumber             */
/*   dn            -- the number structure to fill                      */
/*   chars[]   -- the string to convert ('\0' terminated)         */
/*   set       -- the context used for processing any error,            */
/*            determining the maximum precision available         */
/*            (set.digits), determining the maximum and minimum   */
/*            exponent (set.emax and set.emin), determining if    */
/*            extended values are allowed, and checking the       */
/*            rounding mode if overflow occurs or rounding is     */
/*            needed.                                 */
/*                                                    */
/* The length of the coefficient and the size of the exponent are     */
/* checked by this routine, so the correct error (Underflow or          */
/* Overflow) can be reported or rounding applied, as necessary.         */
/*                                                    */
/* If bad syntax is detected, the result will be a quiet NaN.           */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromString(decNumber *dn, const char chars[],
                        decContext *set) {
  Int exponent=0;          /* working exponent [assume 0] */
  uByte bits=0;                  /* working flags [assume +ve] */
  Unit      *res;                /* where result will be built */
  Unit      resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
                           /* [+9 allows for ln() constants] */
  Unit      *allocres=NULL;            /* -> allocated result, iff allocated */
  Int d=0;                 /* count of digits found in decimal part */
  const char *dotchar=NULL;      /* where dot was found */
  const char *cfirst=chars;      /* -> first character of decimal part */
  const char *last=NULL;         /* -> last digit of decimal part */
  const char *c;           /* work */
  Unit      *up;                 /* .. */
  #if DECDPUN>1
  Int cut, out;            /* .. */
  #endif
  Int residue;             /* rounding residue */
  uInt      status=0;            /* error code */

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
    return decNumberZero(dn);
  #endif

  do {                           /* status & malloc protection */
    for (c=chars;; c++) {        /* -> input character */
      if (*c>='0' && *c<='9') {        /* test for Arabic digit */
      last=c;
      d++;                 /* count of real digits */
      continue;            /* still in decimal part */
      }
      if (*c=='.' && dotchar==NULL) { /* first '.' */
      dotchar=c;           /* record offset into decimal part */
      if (c==cfirst) cfirst++;   /* first digit must follow */
      continue;}
      if (c==chars) {            /* first in string... */
      if (*c=='-') {             /* valid - sign */
        cfirst++;
        bits=DECNEG;
        continue;}
      if (*c=='+') {             /* valid + sign */
        cfirst++;
        continue;}
      }
      /* *c is not a digit, or a valid +, -, or '.' */
      break;
      } /* c */

    if (last==NULL) {            /* no digits yet */
      status=DEC_Conversion_syntax;/* assume the worst */
      if (*c=='\0') break;       /* and no more to come... */
      #if DECSUBSET
      /* if subset then infinities and NaNs are not allowed */
      if (!set->extended) break;   /* hopeless */
      #endif
      /* Infinities and NaNs are possible, here */
      if (dotchar!=NULL) break;        /* .. unless had a dot */
      decNumberZero(dn);         /* be optimistic */
      if (decBiStr(c, "infinity", "INFINITY")
       || decBiStr(c, "inf", "INF")) {
      dn->bits=bits | DECINF;
      status=0;            /* is OK */
      break; /* all done */
      }
      /* a NaN expected */
      /* 2003.09.10 NaNs are now permitted to have a sign */
      dn->bits=bits | DECNAN;    /* assume simple NaN */
      if (*c=='s' || *c=='S') {        /* looks like an sNaN */
      c++;
      dn->bits=bits | DECSNAN;
      }
      if (*c!='n' && *c!='N') break;      /* check caseless "NaN" */
      c++;
      if (*c!='a' && *c!='A') break;      /* .. */
      c++;
      if (*c!='n' && *c!='N') break;      /* .. */
      c++;
      /* now either nothing, or nnnn payload, expected */
      /* -> start of integer and skip leading 0s [including plain 0] */
      for (cfirst=c; *cfirst=='0';) cfirst++;
      if (*cfirst=='\0') {       /* "NaN" or "sNaN", maybe with all 0s */
      status=0;            /* it's good */
      break;                     /* .. */
      }
      /* something other than 0s; setup last and d as usual [no dots] */
      for (c=cfirst;; c++, d++) {
      if (*c<'0' || *c>'9') break; /* test for Arabic digit */
      last=c;
      }
      if (*c!='\0') break;       /* not all digits */
      if (d>set->digits-1) {
      /* [NB: payload in a decNumber can be full length unless */
      /* clamped, in which case can only be digits-1] */
      if (set->clamp) break;
      if (d>set->digits) break;
      } /* too many digits? */
      /* good; drop through to convert the integer to coefficient */
      status=0;                  /* syntax is OK */
      bits=dn->bits;             /* for copy-back */
      } /* last==NULL */

     else if (*c!='\0') {        /* more to process... */
      /* had some digits; exponent is only valid sequence now */
      Flag nege;           /* 1=negative exponent */
      const char *firstexp;      /* -> first significant exponent digit */
      status=DEC_Conversion_syntax;/* assume the worst */
      if (*c!='e' && *c!='E') break;
      /* Found 'e' or 'E' -- now process explicit exponent */
      /* 1998.07.11: sign no longer required */
      nege=0;
      c++;                 /* to (possible) sign */
      if (*c=='-') {nege=1; c++;}
       else if (*c=='+') c++;
      if (*c=='\0') break;

      for (; *c=='0' && *(c+1)!='\0';) c++;  /* strip insignificant zeros */
      firstexp=c;                  /* save exponent digit place */
      for (; ;c++) {
      if (*c<'0' || *c>'9') break;       /* not a digit */
      exponent=X10(exponent)+(Int)*c-(Int)'0';
      } /* c */
      /* if not now on a '\0', *c must not be a digit */
      if (*c!='\0') break;

      /* (this next test must be after the syntax checks) */
      /* if it was too long the exponent may have wrapped, so check */
      /* carefully and set it to a certain overflow if wrap possible */
      if (c>=firstexp+9+1) {
      if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
      /* [up to 1999999999 is OK, for example 1E-1000000998] */
      }
      if (nege) exponent=-exponent; /* was negative */
      status=0;                     /* is OK */
      } /* stuff after digits */

    /* Here when whole string has been inspected; syntax is good */
    /* cfirst->first digit (never dot), last->last digit (ditto) */

    /* strip leading zeros/dot [leave final 0 if all 0's] */
    if (*cfirst=='0') {             /* [cfirst has stepped over .] */
      for (c=cfirst; c<last; c++, cfirst++) {
      if (*c=='.') continue;        /* ignore dots */
      if (*c!='0') break;           /* non-zero found */
      d--;                    /* 0 stripped */
      } /* c */
      #if DECSUBSET
      /* make a rapid exit for easy zeros if !extended */
      if (*cfirst=='0' && !set->extended) {
      decNumberZero(dn);            /* clean result */
      break;                        /* [could be return] */
      }
      #endif
      } /* at least one leading 0 */

    /* Handle decimal point... */
    if (dotchar!=NULL && dotchar<last)    /* non-trailing '.' found? */
      exponent-=(last-dotchar);           /* adjust exponent */
    /* [we can now ignore the .] */

    /* OK, the digits string is good.  Assemble in the decNumber, or in */
    /* a temporary units array if rounding is needed */
    if (d<=set->digits) res=dn->lsu;      /* fits into supplied decNumber */
     else {                   /* rounding needed */
      Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
      res=resbuff;                  /* assume use local buffer */
      if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
      allocres=(Unit *)malloc(needbytes);
      if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
      res=allocres;
      }
      }
    /* res now -> number lsu, buffer, or allocated storage for Unit array */

    /* Place the coefficient into the selected Unit array */
    /* [this is often 70% of the cost of this function when DECDPUN>1] */
    #if DECDPUN>1
    out=0;                 /* accumulator */
    up=res+D2U(d)-1;             /* -> msu */
    cut=d-(up-res)*DECDPUN;      /* digits in top unit */
    for (c=cfirst;; c++) {       /* along the digits */
      if (*c=='.') continue;     /* ignore '.' [don't decrement cut] */
      out=X10(out)+(Int)*c-(Int)'0';
      if (c==last) break;        /* done [never get to trailing '.'] */
      cut--;
      if (cut>0) continue;       /* more for this unit */
      *up=(Unit)out;             /* write unit */
      up--;                /* prepare for unit below.. */
      cut=DECDPUN;               /* .. */
      out=0;                     /* .. */
      } /* c */
    *up=(Unit)out;               /* write lsu */

    #else
    /* DECDPUN==1 */
    up=res;                /* -> lsu */
    for (c=last; c>=cfirst; c--) { /* over each character, from least */
      if (*c=='.') continue;     /* ignore . [don't step up] */
      *up=(Unit)((Int)*c-(Int)'0');
      up++;
      } /* c */
    #endif

    dn->bits=bits;
    dn->exponent=exponent;
    dn->digits=d;

    /* if not in number (too long) shorten into the number */
    if (d>set->digits) {
      residue=0;
      decSetCoeff(dn, set, res, d, &residue, &status);
      /* always check for overflow or subnormal and round as needed */
      decFinalize(dn, set, &residue, &status);
      }
     else { /* no rounding, but may still have overflow or subnormal */
      /* [these tests are just for performance; finalize repeats them] */
      if ((dn->exponent-1<set->emin-dn->digits)
       || (dn->exponent-1>set->emax-set->digits)) {
      residue=0;
      decFinalize(dn, set, &residue, &status);
      }
      }
    /* decNumberShow(dn); */
    } while(0);                     /* [for break] */

  if (allocres!=NULL) free(allocres);     /* drop any storage used */
  if (status!=0) decStatus(dn, status, set);
  return dn;
  } /* decNumberFromString */

/* ================================================================== */
/* Operators                                                */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberAbs -- absolute value operator                        */
/*                                                    */
/*   This computes C = abs(A)                               */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* See also decNumberCopyAbs for a quiet bitwise version of this.     */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* This has the same effect as decNumberPlus unless A is negative,    */
/* in which case it has the same effect as decNumberMinus.        */
/* ------------------------------------------------------------------ */
decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
                   decContext *set) {
  decNumber dzero;                  /* for 0 */
  uInt status=0;              /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);            /* set 0 */
  dzero.exponent=rhs->exponent;           /* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberAbs */

/* ------------------------------------------------------------------ */
/* decNumberAdd -- add two Numbers                          */
/*                                                    */
/*   This computes C = A + B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* This just calls the routine shared with Subtract               */
decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decAddOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberAdd */

/* ------------------------------------------------------------------ */
/* decNumberAnd -- AND two Numbers, digitwise                     */
/*                                                    */
/*   This computes C = A & B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X&X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context (used for result length and error report)     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Logical function restrictions apply (see above); a NaN is            */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;              /* -> operands */
  const Unit *msua, *msub;          /* -> operand msus */
  Unit *uc,  *msuc;                 /* -> result and its msu */
  Int msudigs;                /* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }

  /* operands are valid */
  ua=lhs->lsu;                      /* bottom-up */
  ub=rhs->lsu;                      /* .. */
  uc=res->lsu;                      /* .. */
  msua=ua+D2U(lhs->digits)-1;       /* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;       /* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;       /* -> msu of result */
  msudigs=MSUDIGITS(set->digits);   /* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {    /* Unit loop */
    Unit a, b;                      /* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                    /* can now write back */
    if (a|b) {                      /* maybe 1 bits to examine */
      Int i, j;
      *uc=0;                        /* can now write back */
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
      if (a&b&1) *uc=*uc+(Unit)powers[i];  /* effect AND */
      j=a%10;
      a=a/10;
      j|=b%10;
      b=b/10;
      if (j>1) {
        decStatus(res, DEC_Invalid_operation, set);
        return res;
        }
      if (uc==msuc && i==msudigs-1) break; /* just did final digit */
      } /* each digit */
      } /* both OK */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                  /* integer */
  res->bits=0;                      /* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberAnd */

/* ------------------------------------------------------------------ */
/* decNumberCompare -- compare two Numbers                        */
/*                                                    */
/*   This computes C = A ? B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for one digit (or NaN).                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
                       const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPARE, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompare */

/* ------------------------------------------------------------------ */
/* decNumberCompareSignal -- compare, signalling on all NaNs            */
/*                                                    */
/*   This computes C = A ? B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for one digit (or NaN).                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareSignal */

/* ------------------------------------------------------------------ */
/* decNumberCompareTotal -- compare two Numbers, using total ordering */
/*                                                    */
/*   This computes C = A ? B, under total ordering                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1.                                             */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
                          const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareTotal */

/* ------------------------------------------------------------------ */
/* decNumberCompareTotalMag -- compare, total ordering of magnitudes  */
/*                                                    */
/*   This computes C = |A| ? |B|, under total ordering                  */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for one digit; the result will always be one of  */
/* -1, 0, or 1.                                             */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
                             const decNumber *rhs, decContext *set) {
  uInt status=0;           /* accumulator */
  uInt needbytes;          /* for space calculations */
  decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber bufb[D2N(DECBUFFER+1)];
  decNumber *allocbufb=NULL;     /* -> allocated bufb, iff allocated */
  decNumber *a, *b;              /* temporary pointers */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                              /* protect allocated storage */
    /* if either is negative, take a copy and absolute */
    if (decNumberIsNegative(lhs)) { /* lhs<0 */
      a=bufa;
      needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) { /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {        /* hopeless -- abandon */
        status|=DEC_Insufficient_storage;
        break;}
      a=allocbufa;                  /* use the allocated space */
      }
      decNumberCopy(a, lhs);        /* copy content */
      a->bits&=~DECNEG;             /* .. and clear the sign */
      lhs=a;                        /* use copy from here on */
      }
    if (decNumberIsNegative(rhs)) { /* rhs<0 */
      b=bufb;
      needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufb)) { /* need malloc space */
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {        /* hopeless -- abandon */
        status|=DEC_Insufficient_storage;
        break;}
      b=allocbufb;                  /* use the allocated space */
      }
      decNumberCopy(b, rhs);        /* copy content */
      b->bits&=~DECNEG;             /* .. and clear the sign */
      rhs=b;                        /* use copy from here on */
      }
    decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
    } while(0);                     /* end protected */

  if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
  if (allocbufb!=NULL) free(allocbufb); /* .. */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberCompareTotalMag */

/* ------------------------------------------------------------------ */
/* decNumberDivide -- divide one number by another                */
/*                                                    */
/*   This computes C = A / B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
                      const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberDivide */

/* ------------------------------------------------------------------ */
/* decNumberDivideInteger -- divide and return integer quotient         */
/*                                                    */
/*   This computes C = A # B, where # is the integer divide operator  */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X#X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberDivideInteger */

/* ------------------------------------------------------------------ */
/* decNumberExp -- exponentiation                           */
/*                                                    */
/*   This computes C = exp(A)                               */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                    */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).          */
/*                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decExpOp which can handle the slightly wider */
/* (double) range needed by Ln (which has to be able to calculate     */
/* exp(-a) where a can be the tiniest number (Ntiny).             */
/* ------------------------------------------------------------------ */
decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
                   decContext *set) {
  uInt status=0;              /* accumulator */
  #if DECSUBSET
  decNumber *allocrhs=NULL;      /* non-NULL if rounded rhs allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; these restrictions ensure that if h=8 (see */
  /* decExpOp) then the result will either overflow or underflow to 0. */
  /* Other math functions restrict the input range, too, for inverses. */
  /* If not violated then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    decExpOp(res, rhs, set, &status);
    } while(0);                     /* end protected */

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);    /* drop any storage used */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberExp */

/* ------------------------------------------------------------------ */
/* decNumberFMA -- fused multiply add                             */
/*                                                    */
/*   This computes D = (A * B) + C with only one rounding         */
/*                                                    */
/*   res is D, the result.  D may be A or B or C (e.g., X=FMA(X,X,X)) */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   fhs is C [far hand side]                               */
/*   set is the context                                     */
/*                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, const decNumber *fhs,
                   decContext *set) {
  uInt status=0;           /* accumulator */
  decContext dcmul;              /* context for the multiplication */
  uInt needbytes;          /* for space calculations */
  decNumber bufa[D2N(DECBUFFER*2+1)];
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *acc;          /* accumulator pointer */
  decNumber dzero;               /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
  #endif

  do {                              /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {           /* [undefined if subset] */
      status|=DEC_Invalid_operation;
      break;}
    #endif
    /* Check math restrictions [these ensure no overflow or underflow] */
    if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
     || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
     || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
    /* set up context for multiply */
    dcmul=*set;
    dcmul.digits=lhs->digits+rhs->digits; /* just enough */
    /* [The above may be an over-estimate for subset arithmetic, but that's OK] */
    dcmul.emax=DEC_MAX_EMAX;        /* effectively unbounded .. */
    dcmul.emin=DEC_MIN_EMIN;        /* [thanks to Math restrictions] */
    /* set up decNumber space to receive the result of the multiply */
    acc=bufa;                       /* may fit */
    needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {   /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {        /* hopeless -- abandon */
      status|=DEC_Insufficient_storage;
      break;}
      acc=allocbufa;                /* use the allocated space */
      }
    /* multiply with extended range and necessary precision */
    /*printf("emin=%ld\n", dcmul.emin); */
    decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
    /* Only Invalid operation (from sNaN or Inf * 0) is possible in */
    /* status; if either is seen than ignore fhs (in case it is */
    /* another sNaN) and set acc to NaN unless we had an sNaN */
    /* [decMultiplyOp leaves that to caller] */
    /* Note sNaN has to go through addOp to shorten payload if */
    /* necessary */
    if ((status&DEC_Invalid_operation)!=0) {
      if (!(status&DEC_sNaN)) {           /* but be true invalid */
      decNumberZero(res);           /* acc not yet set */
      res->bits=DECNAN;
      break;
      }
      decNumberZero(&dzero);        /* make 0 (any non-NaN would do) */
      fhs=&dzero;             /* use that */
      }
    #if DECCHECK
     else { /* multiply was OK */
      if (status!=0) printf("Status=%08lx after FMA multiply\n", status);
      }
    #endif
    /* add the third operand and result -> res, and all is done */
    decAddOp(res, acc, fhs, set, 0, &status);
    } while(0);                     /* end protected */

  if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberFMA */

/* ------------------------------------------------------------------ */
/* decNumberInvert -- invert a Number, digitwise                  */
/*                                                    */
/*   This computes C = ~A                                   */
/*                                                    */
/*   res is C, the result.  C may be A (e.g., X=~X)               */
/*   rhs is A                                               */
/*   set is the context (used for result length and error report)     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Logical function restrictions apply (see above); a NaN is            */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
                      decContext *set) {
  const Unit *ua, *msua;            /* -> operand and its msu */
  Unit      *uc, *msuc;             /* -> result and its msu */
  Int msudigs;                /* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operand is valid */
  ua=rhs->lsu;                      /* bottom-up */
  uc=res->lsu;                      /* .. */
  msua=ua+D2U(rhs->digits)-1;       /* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;       /* -> msu of result */
  msudigs=MSUDIGITS(set->digits);   /* [faster than remainder] */
  for (; uc<=msuc; ua++, uc++) {    /* Unit loop */
    Unit a;                   /* extract unit */
    Int      i, j;                        /* work */
    if (ua>msua) a=0;
     else a=*ua;
    *uc=0;                    /* can now write back */
    /* always need to examine all bits in rhs */
    /* This loop could be unrolled and/or use BIN2BCD tables */
    for (i=0; i<DECDPUN; i++) {
      if ((~a)&1) *uc=*uc+(Unit)powers[i];   /* effect INVERT */
      j=a%10;
      a=a/10;
      if (j>1) {
      decStatus(res, DEC_Invalid_operation, set);
      return res;
      }
      if (uc==msuc && i==msudigs-1) break;   /* just did final digit */
      } /* each digit */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                  /* integer */
  res->bits=0;                      /* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberInvert */

/* ------------------------------------------------------------------ */
/* decNumberLn -- natural logarithm                         */
/*                                                    */
/*   This computes C = ln(A)                                */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Notable cases:                                     */
/*   A<0 -> Invalid                                         */
/*   A=0 -> -Infinity (Exact)                               */
/*   A=+Infinity -> +Infinity (Exact)                             */
/*   A=1 exactly -> 0 (Exact)                               */
/*                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decLnOp which can handle the slightly wider  */
/* (+11) range needed by Ln, Log10, etc. (which may have to be able   */
/* to calculate at p+e+2).                                  */
/* ------------------------------------------------------------------ */
decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
                  decContext *set) {
  uInt status=0;           /* accumulator */
  #if DECSUBSET
  decNumber *allocrhs=NULL;      /* non-NULL if rounded rhs allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; this is a math function; if not violated */
  /* then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      /* special check in subset for rhs=0 */
      if (ISZERO(rhs)) {            /* +/- zeros -> error */
      status|=DEC_Invalid_operation;
      break;}
      } /* extended=0 */
    #endif
    decLnOp(res, rhs, set, &status);
    } while(0);                     /* end protected */

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);    /* drop any storage used */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberLn */

/* ------------------------------------------------------------------ */
/* decNumberLogB - get adjusted exponent, by 754r rules                 */
/*                                                    */
/*   This computes C = adjustedexponent(A)                        */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context, used only for digits and status          */
/*                                                    */
/* C must have space for 10 digits (A might have 10**9 digits and     */
/* an exponent of +999999999, or one digit and an exponent of           */
/* -1999999999).                                      */
/*                                                    */
/* This returns the adjusted exponent of A after (in theory) padding  */
/* with zeros on the right to set->digits digits while keeping the    */
/* same value.    The exponent is not limited by emin/emax.       */
/*                                                    */
/* Notable cases:                                     */
/*   A<0 -> Use |A|                                         */
/*   A=0 -> -Infinity (Division by zero)                    */
/*   A=Infinite -> +Infinity (Exact)                              */
/*   A=1 exactly -> 0 (Exact)                               */
/*   NaNs are propagated as usual                           */
/* ------------------------------------------------------------------ */
decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
                    decContext *set) {
  uInt status=0;           /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* NaNs as usual; Infinities return +Infinity; 0->oops */
  if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
   else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
   else if (decNumberIsZero(rhs)) {
    decNumberZero(res);             /* prepare for Infinity */
    res->bits=DECNEG|DECINF;        /* -Infinity */
    status|=DEC_Division_by_zero;   /* as per 754r */
    }
   else { /* finite non-zero */
    Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
    decNumberFromInt32(res, ae);    /* lay it out */
    }

  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberLogB */

/* ------------------------------------------------------------------ */
/* decNumberLog10 -- logarithm in base 10                   */
/*                                                    */
/*   This computes C = log10(A)                                   */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Notable cases:                                     */
/*   A<0 -> Invalid                                         */
/*   A=0 -> -Infinity (Exact)                               */
/*   A=+Infinity -> +Infinity (Exact)                             */
/*   A=10**n (if n is an integer) -> n (Exact)                    */
/*                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                    */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/* ------------------------------------------------------------------ */
/* This calculates ln(A)/ln(10) using appropriate precision.  For     */
/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the      */
/* requested digits and t is the number of digits in the exponent     */
/* (maximum 6).    For ln(10) it is p + 3; this is often handled by the */
/* fastpath in decLnOp.  The final division is done to the requested  */
/* precision.                                               */
/* ------------------------------------------------------------------ */
decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
                    decContext *set) {
  uInt status=0, ignore=0;       /* status accumulators */
  uInt needbytes;          /* for space calculations */
  Int p;                   /* working precision */
  Int t;                   /* digits in exponent of A */

  /* buffers for a and b working decimals */
  /* (adjustment calculator, same size) */
  decNumber bufa[D2N(DECBUFFER+2)];
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;             /* temporary a */
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbufb=NULL;     /* -> allocated bufb, iff allocated */
  decNumber *b=bufb;             /* temporary b */
  decNumber bufw[D2N(10)];       /* working 2-10 digit number */
  decNumber *w=bufw;             /* .. */
  #if DECSUBSET
  decNumber *allocrhs=NULL;      /* non-NULL if rounded rhs allocated */
  #endif

  decContext aset;               /* working context */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* Check restrictions; this is a math function; if not violated */
  /* then carry out the operation. */
  if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      /* special check in subset for rhs=0 */
      if (ISZERO(rhs)) {            /* +/- zeros -> error */
      status|=DEC_Invalid_operation;
      break;}
      } /* extended=0 */
    #endif

    decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */

    /* handle exact powers of 10; only check if +ve finite */
    if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
      Int residue=0;             /* (no residue) */
      uInt copystat=0;           /* clean status */

      /* round to a single digit... */
      aset.digits=1;
      decCopyFit(w, rhs, &aset, &residue, &copystat); /* copy & shorten */
      /* if exact and the digit is 1, rhs is a power of 10 */
      if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
      /* the exponent, conveniently, is the power of 10; making */
      /* this the result needs a little care as it might not fit, */
      /* so first convert it into the working number, and then move */
      /* to res */
      decNumberFromInt32(w, w->exponent);
      residue=0;
      decCopyFit(res, w, set, &residue, &status); /* copy & round */
      decFinish(res, set, &residue, &status);       /* cleanup/set flags */
      break;
      } /* not a power of 10 */
      } /* not a candidate for exact */

    /* simplify the information-content calculation to use 'total */
    /* number of digits in a, including exponent' as compared to the */
    /* requested digits, as increasing this will only rarely cost an */
    /* iteration in ln(a) anyway */
    t=6;                      /* it can never be >6 */

    /* allocate space when needed... */
    p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {   /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {        /* hopeless -- abandon */
      status|=DEC_Insufficient_storage;
      break;}
      a=allocbufa;                  /* use the allocated space */
      }
    aset.digits=p;                  /* as calculated */
    aset.emax=DEC_MAX_MATH;         /* usual bounds */
    aset.emin=-DEC_MAX_MATH;        /* .. */
    aset.clamp=0;             /* and no concrete format */
    decLnOp(a, rhs, &aset, &status);      /* a=ln(rhs) */

    /* skip the division if the result so far is infinite, NaN, or */
    /* zero, or there was an error; note NaN from sNaN needs copy */
    if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
    if (a->bits&DECSPECIAL || ISZERO(a)) {
      decNumberCopy(res, a);        /* [will fit] */
      break;}

    /* for ln(10) an extra 3 digits of precision are needed */
    p=set->digits+3;
    needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {   /* need malloc space */
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {        /* hopeless -- abandon */
      status|=DEC_Insufficient_storage;
      break;}
      b=allocbufb;                  /* use the allocated space */
      }
    decNumberZero(w);               /* set up 10... */
    #if DECDPUN==1
    w->lsu[1]=1; w->lsu[0]=0;       /* .. */
    #else
    w->lsu[0]=10;             /* .. */
    #endif
    w->digits=2;              /* .. */

    aset.digits=p;
    decLnOp(b, w, &aset, &ignore);  /* b=ln(10) */

    aset.digits=set->digits;        /* for final divide */
    decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
    } while(0);                     /* [for break] */

  if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
  if (allocbufb!=NULL) free(allocbufb); /* .. */
  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);    /* .. */
  #endif
  /* apply significant status */
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberLog10 */

/* ------------------------------------------------------------------ */
/* decNumberMax -- compare two Numbers and return the maximum           */
/*                                                    */
/*   This computes C = A ? B, returning the maximum by 754R rules     */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMax */

/* ------------------------------------------------------------------ */
/* decNumberMaxMag -- compare and return the maximum by magnitude     */
/*                                                    */
/*   This computes C = A ? B, returning the maximum by 754R rules     */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMaxMag */

/* ------------------------------------------------------------------ */
/* decNumberMin -- compare two Numbers and return the minimum           */
/*                                                    */
/*   This computes C = A ? B, returning the minimum by 754R rules     */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMin */

/* ------------------------------------------------------------------ */
/* decNumberMinMag -- compare and return the minimum by magnitude     */
/*                                                    */
/*   This computes C = A ? B, returning the minimum by 754R rules     */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMinMag */

/* ------------------------------------------------------------------ */
/* decNumberMinus -- prefix minus operator                        */
/*                                                    */
/*   This computes C = 0 - A                                */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* See also decNumberCopyNegate for a quiet bitwise version of this.  */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* Simply use AddOp for the subtract, which will do the necessary.    */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
                     decContext *set) {
  decNumber dzero;
  uInt status=0;              /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);            /* make 0 */
  dzero.exponent=rhs->exponent;           /* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMinus */

/* ------------------------------------------------------------------ */
/* decNumberNextMinus -- next towards -Infinity                   */
/*                                                    */
/*   This computes C = A - infinitesimal, rounded towards -Infinity   */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* This is a generalization of 754r NextDown.                     */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
                         decContext *set) {
  decNumber dtiny;                       /* constant */
  decContext workset=*set;               /* work */
  uInt status=0;                   /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* +Infinity is the special case */
  if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
    decSetMaxValue(res, set);            /* is +ve */
    /* there is no status to set */
    return res;
    }
  decNumberZero(&dtiny);                 /* start with 0 */
  dtiny.lsu[0]=1;                  /* make number that is .. */
  dtiny.exponent=DEC_MIN_EMIN-1;         /* .. smaller than tiniest */
  workset.round=DEC_ROUND_FLOOR;
  decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextMinus */

/* ------------------------------------------------------------------ */
/* decNumberNextPlus -- next towards +Infinity                    */
/*                                                    */
/*   This computes C = A + infinitesimal, rounded towards +Infinity   */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* This is a generalization of 754r NextUp.                       */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
                        decContext *set) {
  decNumber dtiny;                       /* constant */
  decContext workset=*set;               /* work */
  uInt status=0;                   /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* -Infinity is the special case */
  if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
    decSetMaxValue(res, set);
    res->bits=DECNEG;                    /* negative */
    /* there is no status to set */
    return res;
    }
  decNumberZero(&dtiny);                 /* start with 0 */
  dtiny.lsu[0]=1;                  /* make number that is .. */
  dtiny.exponent=DEC_MIN_EMIN-1;         /* .. smaller than tiniest */
  workset.round=DEC_ROUND_CEILING;
  decAddOp(res, rhs, &dtiny, &workset, 0, &status);
  status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextPlus */

/* ------------------------------------------------------------------ */
/* decNumberNextToward -- next towards rhs                        */
/*                                                    */
/*   This computes C = A +/- infinitesimal, rounded towards       */
/*   +/-Infinity in the direction of B, as per 754r nextafter rules   */
/*                                                    */
/*   res is C, the result.  C may be A or B.                      */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* This is a generalization of 754r NextAfter.                    */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs, decContext *set) {
  decNumber dtiny;                       /* constant */
  decContext workset=*set;               /* work */
  Int result;                            /* .. */
  uInt status=0;                   /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
    decNaNs(res, lhs, rhs, set, &status);
    }
   else { /* Is numeric, so no chance of sNaN Invalid, etc. */
    result=decCompare(lhs, rhs, 0); /* sign matters */
    if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
     else { /* valid compare */
      if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */
       else { /* differ: need NextPlus or NextMinus */
      uByte sub;              /* add or subtract */
      if (result<0) {               /* lhs<rhs, do nextplus */
        /* -Infinity is the special case */
        if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
          decSetMaxValue(res, set);
          res->bits=DECNEG;         /* negative */
          return res;               /* there is no status to set */
          }
        workset.round=DEC_ROUND_CEILING;
        sub=0;                /* add, please */
        } /* plus */
       else {                       /* lhs>rhs, do nextminus */
        /* +Infinity is the special case */
        if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
          decSetMaxValue(res, set);
          return res;               /* there is no status to set */
          }
        workset.round=DEC_ROUND_FLOOR;
        sub=DECNEG;                 /* subtract, please */
        } /* minus */
      decNumberZero(&dtiny);        /* start with 0 */
      dtiny.lsu[0]=1;               /* make number that is .. */
      dtiny.exponent=DEC_MIN_EMIN-1;      /* .. smaller than tiniest */
      decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
      /* turn off exceptions if the result is a normal number */
      /* (including Nmin), otherwise let all status through */
      if (decNumberIsNormal(res, set)) status=0;
      } /* unequal */
      } /* compare OK */
    } /* numeric */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberNextToward */

/* ------------------------------------------------------------------ */
/* decNumberOr -- OR two Numbers, digitwise                       */
/*                                                    */
/*   This computes C = A | B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X|X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context (used for result length and error report)     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Logical function restrictions apply (see above); a NaN is            */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
                  const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;              /* -> operands */
  const Unit *msua, *msub;          /* -> operand msus */
  Unit      *uc, *msuc;             /* -> result and its msu */
  Int msudigs;                /* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operands are valid */
  ua=lhs->lsu;                      /* bottom-up */
  ub=rhs->lsu;                      /* .. */
  uc=res->lsu;                      /* .. */
  msua=ua+D2U(lhs->digits)-1;       /* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;       /* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;       /* -> msu of result */
  msudigs=MSUDIGITS(set->digits);   /* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {    /* Unit loop */
    Unit a, b;                      /* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                    /* can now write back */
    if (a|b) {                      /* maybe 1 bits to examine */
      Int i, j;
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
      if ((a|b)&1) *uc=*uc+(Unit)powers[i];       /* effect OR */
      j=a%10;
      a=a/10;
      j|=b%10;
      b=b/10;
      if (j>1) {
        decStatus(res, DEC_Invalid_operation, set);
        return res;
        }
      if (uc==msuc && i==msudigs-1) break;        /* just did final digit */
      } /* each digit */
      } /* non-zero */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                  /* integer */
  res->bits=0;                      /* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberOr */

/* ------------------------------------------------------------------ */
/* decNumberPlus -- prefix plus operator                    */
/*                                                    */
/*   This computes C = 0 + A                                */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* See also decNumberCopy for a quiet bitwise version of this.          */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* This simply uses AddOp; Add will take fast path after preparing A. */
/* Performance is a concern here, as this routine is often used to    */
/* check operands and apply rounding and overflow/underflow testing.  */
/* ------------------------------------------------------------------ */
decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
                    decContext *set) {
  decNumber dzero;
  uInt status=0;              /* accumulator */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  decNumberZero(&dzero);            /* make 0 */
  dzero.exponent=rhs->exponent;           /* [no coefficient expansion] */
  decAddOp(res, &dzero, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberPlus */

/* ------------------------------------------------------------------ */
/* decNumberMultiply -- multiply two Numbers                      */
/*                                                    */
/*   This computes C = A x B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs, decContext *set) {
  uInt status=0;           /* accumulator */
  decMultiplyOp(res, lhs, rhs, set, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberMultiply */

/* ------------------------------------------------------------------ */
/* decNumberPower -- raise a number to a power                    */
/*                                                    */
/*   This computes C = A ** B                               */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X**X)          */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Mathematical function restrictions apply (see above); a NaN is     */
/* returned with Invalid_operation if a restriction is violated.      */
/*                                                    */
/* However, if 1999999997<=B<=999999999 and B is an integer then the  */
/* restrictions on A and the context are relaxed to the usual bounds, */
/* for compatibility with the earlier (integer power only) version    */
/* of this function.                                        */
/*                                                    */
/* When B is an integer, the result may be exact, even if rounded.    */
/*                                                    */
/* The final result is rounded according to the context; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/* ------------------------------------------------------------------ */
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
                     const decNumber *rhs, decContext *set) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;      /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;      /* .., rhs */
  #endif
  decNumber *allocdac=NULL;      /* -> allocated acc buffer, iff used */
  decNumber *allocinv=NULL;      /* -> allocated 1/x buffer, iff used */
  Int reqdigits=set->digits;     /* requested DIGITS */
  Int n;                   /* rhs in binary */
  Flag      rhsint=0;            /* 1 if rhs is an integer */
  Flag      useint=0;            /* 1 if can use integer calculation */
  Flag      isoddint=0;          /* 1 if rhs is an integer and odd */
  Int i;                   /* work */
  #if DECSUBSET
  Int dropped;             /* .. */
  #endif
  uInt      needbytes;           /* buffer size needed */
  Flag      seenbit;             /* seen a bit while powering */
  Int residue=0;           /* rounding residue */
  uInt      status=0;            /* accumulators */
  uByte bits=0;                  /* result sign if errors */
  decContext aset;               /* working context */
  decNumber dnOne;               /* work value 1... */
  /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
  decNumber dacbuff[D2N(DECBUFFER+9)];
  decNumber *dac=dacbuff;        /* -> result accumulator */
  /* same again for possible 1/lhs calculation */
  decNumber invbuff[D2N(DECBUFFER+9)];

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) { /* reduce operands and set status, as needed */
      if (lhs->digits>reqdigits) {
      alloclhs=decRoundOperand(lhs, set, &status);
      if (alloclhs==NULL) break;
      lhs=alloclhs;
      }
      if (rhs->digits>reqdigits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* handle NaNs and rhs Infinity (lhs infinity is harder) */
    if (SPECIALARGS) {
      if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
      decNaNs(res, lhs, rhs, set, &status);
      break;}
      if (decNumberIsInfinite(rhs)) {     /* rhs Infinity */
      Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */
      if (decNumberIsNegative(lhs)  /* lhs<0 */
       && !decNumberIsZero(lhs))    /* .. */
        status|=DEC_Invalid_operation;
       else {                       /* lhs >=0 */
        decNumberZero(&dnOne);      /* set up 1 */
        dnOne.lsu[0]=1;
        decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
        decNumberZero(res);         /* prepare for 0/1/Infinity */
        if (decNumberIsNegative(dac)) {    /* lhs<1 */
          if (rhsneg) res->bits|=DECINF;   /* +Infinity [else is +0] */
          }
         else if (dac->lsu[0]==0) {      /* lhs=1 */
          /* 1**Infinity is inexact, so return fully-padded 1.0000 */
          Int shift=set->digits-1;
          *res->lsu=1;             /* was 0, make int 1 */
          res->digits=decShiftToMost(res->lsu, 1, shift);
          res->exponent=-shift;          /* make 1.0000... */
          status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
          }
         else {                    /* lhs>1 */
          if (!rhsneg) res->bits|=DECINF;  /* +Infinity [else is +0] */
          }
        } /* lhs>=0 */
      break;}
      /* [lhs infinity drops through] */
      } /* specials */

    /* Original rhs may be an integer that fits and is in range */
    n=decGetInt(rhs);
    if (n!=BADINT) {                /* it is an integer */
      rhsint=1;                     /* record the fact for 1**n */
      isoddint=(Flag)n&1;           /* [works even if big] */
      if (n!=BIGEVEN && n!=BIGODD)  /* can use integer path? */
      useint=1;               /* looks good */
      }

    if (decNumberIsNegative(lhs)    /* -x .. */
      && isoddint) bits=DECNEG;           /* .. to an odd power */

    /* handle LHS infinity */
    if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
      uByte rbits=rhs->bits;        /* save */
      decNumberZero(res);           /* prepare */
      if (n==0) *res->lsu=1;        /* [-]Inf**0 => 1 */
       else {
      /* -Inf**nonint -> error */
      if (!rhsint && decNumberIsNegative(lhs)) {
        status|=DEC_Invalid_operation;     /* -Inf**nonint is error */
        break;}
      if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
      /* [otherwise will be 0 or -0] */
      res->bits=bits;
      }
      break;}

    /* similarly handle LHS zero */
    if (decNumberIsZero(lhs)) {
      if (n==0) {                  /* 0**0 => Error */
      #if DECSUBSET
      if (!set->extended) {              /* [unless subset] */
        decNumberZero(res);
        *res->lsu=1;                     /* return 1 */
        break;}
      #endif
      status|=DEC_Invalid_operation;
      }
       else {                            /* 0**x */
      uByte rbits=rhs->bits;             /* save */
      if (rbits & DECNEG) {              /* was a 0**(-n) */
        #if DECSUBSET
        if (!set->extended) {            /* [bad if subset] */
          status|=DEC_Invalid_operation;
          break;}
        #endif
        bits|=DECINF;
        }
      decNumberZero(res);                /* prepare */
      /* [otherwise will be 0 or -0] */
      res->bits=bits;
      }
      break;}

    /* here both lhs and rhs are finite; rhs==0 is handled in the */
    /* integer path.  Next handle the non-integer cases */
    if (!useint) {                  /* non-integral rhs */
      /* any -ve lhs is bad, as is either operand or context out of */
      /* bounds */
      if (decNumberIsNegative(lhs)) {
      status|=DEC_Invalid_operation;
      break;}
      if (decCheckMath(lhs, set, &status)
       || decCheckMath(rhs, set, &status)) break; /* variable status */

      decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
      aset.emax=DEC_MAX_MATH;       /* usual bounds */
      aset.emin=-DEC_MAX_MATH;            /* .. */
      aset.clamp=0;                 /* and no concrete format */

      /* calculate the result using exp(ln(lhs)*rhs), which can */
      /* all be done into the accumulator, dac.  The precision needed */
      /* is enough to contain the full information in the lhs (which */
      /* is the total digits, including exponent), or the requested */
      /* precision, if larger, + 4; 6 is used for the exponent */
      /* maximum length, and this is also used when it is shorter */
      /* than the requested digits as it greatly reduces the >0.5 ulp */
      /* cases at little cost (because Ln doubles digits each */
      /* iteration so a few extra digits rarely causes an extra */
      /* iteration) */
      aset.digits=MAXI(lhs->digits, set->digits)+6+4;
      } /* non-integer rhs */

     else { /* rhs is in-range integer */
      if (n==0) {             /* x**0 = 1 */
      /* (0**0 was handled above) */
      decNumberZero(res);           /* result=1 */
      *res->lsu=1;                  /* .. */
      break;}
      /* rhs is a non-zero integer */
      if (n<0) n=-n;                /* use abs(n) */

      aset=*set;              /* clone the context */
      aset.round=DEC_ROUND_HALF_EVEN;     /* internally use balanced */
      /* calculate the working DIGITS */
      aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
      #if DECSUBSET
      if (!set->extended) aset.digits--;     /* use classic precision */
      #endif
      /* it's an error if this is more than can be handled */
      if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
      } /* integer path */

    /* aset.digits is the count of digits for the accumulator needed */
    /* if accumulator is too long for local storage, then allocate */
    needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
    /* [needbytes also used below if 1/lhs needed] */
    if (needbytes>sizeof(dacbuff)) {
      allocdac=(decNumber *)malloc(needbytes);
      if (allocdac==NULL) {   /* hopeless -- abandon */
      status|=DEC_Insufficient_storage;
      break;}
      dac=allocdac;           /* use the allocated space */
      }
    /* here, aset is set up and accumulator is ready for use */

    if (!useint) {                       /* non-integral rhs */
      /* x ** y; special-case x=1 here as it will otherwise always */
      /* reduce to integer 1; decLnOp has a fastpath which detects */
      /* the case of x=1 */
      decLnOp(dac, lhs, &aset, &status);     /* dac=ln(lhs) */
      /* [no error possible, as lhs 0 already handled] */
      if (ISZERO(dac)) {                 /* x==1, 1.0, etc. */
      /* need to return fully-padded 1.0000 etc., but rhsint->1 */
      *dac->lsu=1;                       /* was 0, make int 1 */
      if (!rhsint) {                     /* add padding */
        Int shift=set->digits-1;
        dac->digits=decShiftToMost(dac->lsu, 1, shift);
        dac->exponent=-shift;            /* make 1.0000... */
        status|=DEC_Inexact|DEC_Rounded;   /* deemed inexact */
        }
      }
       else {
      decMultiplyOp(dac, dac, rhs, &aset, &status);  /* dac=dac*rhs */
      decExpOp(dac, dac, &aset, &status);        /* dac=exp(dac) */
      }
      /* and drop through for final rounding */
      } /* non-integer rhs */

     else {                   /* carry on with integer */
      decNumberZero(dac);           /* acc=1 */
      *dac->lsu=1;                  /* .. */

      /* if a negative power the constant 1 is needed, and if not subset */
      /* invert the lhs now rather than inverting the result later */
      if (decNumberIsNegative(rhs)) {     /* was a **-n [hence digits>0] */
      decNumber *inv=invbuff;       /* asssume use fixed buffer */
      decNumberCopy(&dnOne, dac);   /* dnOne=1;  [needed now or later] */
      #if DECSUBSET
      if (set->extended) {          /* need to calculate 1/lhs */
      #endif
        /* divide lhs into 1, putting result in dac [dac=1/dac] */
        decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
        /* now locate or allocate space for the inverted lhs */
        if (needbytes>sizeof(invbuff)) {
          allocinv=(decNumber *)malloc(needbytes);
          if (allocinv==NULL) {     /* hopeless -- abandon */
            status|=DEC_Insufficient_storage;
            break;}
          inv=allocinv;       /* use the allocated space */
          }
        /* [inv now points to big-enough buffer or allocated storage] */
        decNumberCopy(inv, dac);    /* copy the 1/lhs */
        decNumberCopy(dac, &dnOne); /* restore acc=1 */
        lhs=inv;              /* .. and go forward with new lhs */
      #if DECSUBSET
        }
      #endif
      }

      /* Raise-to-the-power loop... */
      seenbit=0;           /* set once a 1-bit is encountered */
      for (i=1;;i++){            /* for each bit [top bit ignored] */
      /* abandon if had overflow or terminal underflow */
      if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
        if (status&DEC_Overflow || ISZERO(dac)) break;
        }
      /* [the following two lines revealed an optimizer bug in a C++ */
      /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
      n=n<<1;                    /* move next bit to testable position */
      if (n<0) {           /* top bit is set */
        seenbit=1;               /* OK, significant bit seen */
        decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
        }
      if (i==31) break;    /* that was the last bit */
      if (!seenbit) continue;    /* no need to square 1 */
      decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
      } /*i*/ /* 32 bits */

      /* complete internal overflow or underflow processing */
      if (status & (DEC_Overflow|DEC_Underflow)) {
      #if DECSUBSET
      /* If subset, and power was negative, reverse the kind of -erflow */
      /* [1/x not yet done] */
      if (!set->extended && decNumberIsNegative(rhs)) {
        if (status & DEC_Overflow)
          status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
         else { /* trickier -- Underflow may or may not be set */
          status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
          status|=DEC_Overflow;
          }
        }
      #endif
      dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
      /* round subnormals [to set.digits rather than aset.digits] */
      /* or set overflow result similarly as required */
      decFinalize(dac, set, &residue, &status);
      decNumberCopy(res, dac);   /* copy to result (is now OK length) */
      break;
      }

      #if DECSUBSET
      if (!set->extended &&              /* subset math */
        decNumberIsNegative(rhs)) {      /* was a **-n [hence digits>0] */
      /* so divide result into 1 [dac=1/dac] */
      decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
      }
      #endif
      } /* rhs integer path */

    /* reduce result to the requested length and copy to result */
    decCopyFit(res, dac, set, &residue, &status);
    decFinish(res, set, &residue, &status);  /* final cleanup */
    #if DECSUBSET
    if (!set->extended) decTrim(res, set, 0, &dropped); /* trailing zeros */
    #endif
    } while(0);                     /* end protected */

  if (allocdac!=NULL) free(allocdac);     /* drop any storage used */
  if (allocinv!=NULL) free(allocinv);     /* .. */
  #if DECSUBSET
  if (alloclhs!=NULL) free(alloclhs);     /* .. */
  if (allocrhs!=NULL) free(allocrhs);     /* .. */
  #endif
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberPower */

/* ------------------------------------------------------------------ */
/* decNumberQuantize -- force exponent to requested value         */
/*                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has exponent of B.  The numerical value of C will equal A,  */
/*   except for the effects of any rounding that occurred.        */
/*                                                    */
/*   res is C, the result.  C may be A or B                       */
/*   lhs is A, the number to adjust                         */
/*   rhs is B, the number with exponent to match                  */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to that of B.          */
/* ------------------------------------------------------------------ */
decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decQuantizeOp(res, lhs, rhs, set, 1, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberQuantize */

/* ------------------------------------------------------------------ */
/* decNumberReduce -- remove trailing zeros                       */
/*                                                    */
/*   This computes C = 0 + A, and normalizes the result                 */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* Previously known as Normalize */
decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
                         decContext *set) {
  return decNumberReduce(res, rhs, set);
  } /* decNumberNormalize */

decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
                      decContext *set) {
  #if DECSUBSET
  decNumber *allocrhs=NULL;      /* non-NULL if rounded rhs allocated */
  #endif
  uInt status=0;           /* as usual */
  Int  residue=0;          /* as usual */
  Int  dropped;                  /* work */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* Infinities copy through; NaNs need usual treatment */
    if (decNumberIsNaN(rhs)) {
      decNaNs(res, rhs, NULL, set, &status);
      break;
      }

    /* reduce result to the requested length and copy to result */
    decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
    decFinish(res, set, &residue, &status);       /* cleanup/set flags */
    decTrim(res, set, 1, &dropped);         /* normalize in place */
    } while(0);                          /* end protected */

  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);         /* .. */
  #endif
  if (status!=0) decStatus(res, status, set);/* then report status */
  return res;
  } /* decNumberReduce */

/* ------------------------------------------------------------------ */
/* decNumberRescale -- force exponent to requested value          */
/*                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B.  The numerical value of C will equal A,    */
/*   except for the effects of any rounding that occurred.        */
/*                                                    */
/*   res is C, the result.  C may be A or B                       */
/*   lhs is A, the number to adjust                         */
/*   rhs is B, the requested exponent                             */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be equal to B.                  */
/* ------------------------------------------------------------------ */
decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
                       const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decQuantizeOp(res, lhs, rhs, set, 0, &status);
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberRescale */

/* ------------------------------------------------------------------ */
/* decNumberRemainder -- divide and return remainder              */
/*                                                    */
/*   This computes C = A % B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberRemainder */

/* ------------------------------------------------------------------ */
/* decNumberRemainderNear -- divide and return remainder from nearest */
/*                                                    */
/*   This computes C = A % B, where % is the IEEE remainder operator  */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X%X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
                           const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */
  decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberRemainderNear */

/* ------------------------------------------------------------------ */
/* decNumberRotate -- rotate the coefficient of a Number left/right   */
/*                                                    */
/*   This computes C = A rot B      (in base ten and rotating set->digits */
/*   digits).                                               */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=XrotX)         */
/*   lhs is A                                               */
/*   rhs is B, the number of digits to rotate (-ve to right)            */
/*   set is the context                                     */
/*                                                    */
/* The digits of the coefficient of A are rotated to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.  If lhs->digits is less than          */
/* set->digits the coefficient is padded with zeros on the left         */
/* before the rotate.  Any leading zeros in the result are removed    */
/* as usual.                                                */
/*                                                    */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.                                      */
/* C must have space for set->digits digits.                      */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.                                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
                     const decNumber *rhs, decContext *set) {
  uInt status=0;        /* accumulator */
  Int  rotate;                /* rhs as an Int */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* NaNs propagate as normal */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { /* both numeric, rhs is an integer */
    rotate=decGetInt(rhs);               /* [cannot fail] */
    if (rotate==BADINT                   /* something bad .. */
     || rotate==BIGODD || rotate==BIGEVEN    /* .. very big .. */
     || abs(rotate)>set->digits)         /* .. or out of range */
      status=DEC_Invalid_operation;
     else {                        /* rhs is OK */
      decNumberCopy(res, lhs);
      /* convert -ve rotate to equivalent positive rotation */
      if (rotate<0) rotate=set->digits+rotate;
      if (rotate!=0 && rotate!=set->digits   /* zero or full rotation */
       && !decNumberIsInfinite(res)) {         /* lhs was infinite */
      /* left-rotate to do; 0 < rotate < set->digits */
      uInt units, shift;                 /* work */
      uInt msudigits;                    /* digits in result msu */
      Unit *msu=res->lsu+D2U(res->digits)-1;      /* current msu */
      Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
      for (msu++; msu<=msumax; msu++) *msu=0;     /* ensure high units=0 */
      res->digits=set->digits;              /* now full-length */
      msudigits=MSUDIGITS(res->digits);     /* actual digits in msu */

      /* rotation here is done in-place, in three steps */
      /* 1. shift all to least up to one unit to unit-align final */
      /*    lsd [any digits shifted out are rotated to the left, */
      /*    abutted to the original msd (which may require split)] */
      /* */
      /*    [if there are no whole units left to rotate, the */
      /*    rotation is now complete] */
      /* */
      /* 2. shift to least, from below the split point only, so that */
      /*    the final msd is in the right place in its Unit [any */
      /*    digits shifted out will fit exactly in the current msu, */
      /*    left aligned, no split required] */
      /* */
      /* 3. rotate all the units by reversing left part, right */
      /*    part, and then whole */
      /* */
      /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
      /* */
      /*   start: 00a bcd efg hij klm npq */
      /* */
      /*    1a  000 0ab cde fgh|ijk lmn [pq saved] */
      /*    1b  00p qab cde fgh|ijk lmn */
      /* */
      /*    2a  00p qab cde fgh|00i jkl [mn saved] */
      /*    2b  mnp qab cde fgh|00i jkl */
      /* */
      /*    3a  fgh cde qab mnp|00i jkl */
      /*    3b  fgh cde qab mnp|jkl 00i */
      /*    3c  00i jkl mnp qab cde fgh */

      /* Step 1: amount to shift is the partial right-rotate count */
      rotate=set->digits-rotate;    /* make it right-rotate */
      units=rotate/DECDPUN;         /* whole units to rotate */
      shift=rotate%DECDPUN;         /* left-over digits count */
      if (shift>0) {                /* not an exact number of units */
        uInt save=res->lsu[0]%powers[shift];      /* save low digit(s) */
        decShiftToLeast(res->lsu, D2U(res->digits), shift);
        if (shift>msudigits) {      /* msumax-1 needs >0 digits */
          uInt rem=save%powers[shift-msudigits];/* split save */
          *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
          *(msumax-1)=*(msumax-1)
                   +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
          }
         else { /* all fits in msumax */
          *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
          }
        } /* digits shift needed */

      /* If whole units to rotate... */
      if (units>0) {                /* some to do */
        /* Step 2: the units to touch are the whole ones in rotate, */
        /*   if any, and the shift is DECDPUN-msudigits (which may be */
        /*   0, again) */
        shift=DECDPUN-msudigits;
        if (shift>0) {        /* not an exact number of units */
          uInt save=res->lsu[0]%powers[shift];  /* save low digit(s) */
          decShiftToLeast(res->lsu, units, shift);
          *msumax=*msumax+(Unit)(save*powers[msudigits]);
          } /* partial shift needed */

        /* Step 3: rotate the units array using triple reverse */
        /* (reversing is easy and fast) */
        decReverse(res->lsu+units, msumax);       /* left part */
        decReverse(res->lsu, res->lsu+units-1); /* right part */
        decReverse(res->lsu, msumax);             /* whole */
        } /* whole units to rotate */
      /* the rotation may have left an undetermined number of zeros */
      /* on the left, so true length needs to be calculated */
      res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
      } /* rotate needed */
      } /* rhs OK */
    } /* numerics */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberRotate */

/* ------------------------------------------------------------------ */
/* decNumberSameQuantum -- test for equal exponents               */
/*                                                    */
/*   res is the result number, which will contain either 0 or 1         */
/*   lhs is a number to test                                */
/*   rhs is the second (usually a pattern)                        */
/*                                                    */
/* No errors are possible and no context is needed.               */
/* ------------------------------------------------------------------ */
decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs) {
  Unit ret=0;                    /* return value */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
  #endif

  if (SPECIALARGS) {
    if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
     else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
     /* [anything else with a special gives 0] */
    }
   else if (lhs->exponent==rhs->exponent) ret=1;

  decNumberZero(res);            /* OK to overwrite an operand now */
  *res->lsu=ret;
  return res;
  } /* decNumberSameQuantum */

/* ------------------------------------------------------------------ */
/* decNumberScaleB -- multiply by a power of 10                   */
/*                                                    */
/* This computes C = A x 10**B where B is an integer (q=0) with         */
/* maximum magnitude 2*(emax+digits)                              */
/*                                                    */
/*   res is C, the result.  C may be A or B                       */
/*   lhs is A, the number to adjust                         */
/*   rhs is B, the requested power of ten to use                  */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* The result may underflow or overflow.                    */
/* ------------------------------------------------------------------ */
decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
                      const decNumber *rhs, decContext *set) {
  Int  reqexp;                /* requested exponent change [B] */
  uInt status=0;        /* accumulator */
  Int  residue;               /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* Handle special values except lhs infinite */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
    /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else {
    /* lhs is a number; rhs is a finite with q==0 */
    reqexp=decGetInt(rhs);               /* [cannot fail] */
    if (reqexp==BADINT                   /* something bad .. */
     || reqexp==BIGODD || reqexp==BIGEVEN    /* .. very big .. */
     || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
      status=DEC_Invalid_operation;
     else {                        /* rhs is OK */
      decNumberCopy(res, lhs);                 /* all done if infinite lhs */
      if (!decNumberIsInfinite(res)) {         /* prepare to scale */
      res->exponent+=reqexp;             /* adjust the exponent */
      residue=0;
      decFinalize(res, set, &residue, &status); /* .. and check */
      } /* finite LHS */
      } /* rhs OK */
    } /* rhs finite */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberScaleB */

/* ------------------------------------------------------------------ */
/* decNumberShift -- shift the coefficient of a Number left or right  */
/*                                                    */
/*   This computes C = A << B or C = A >> -B  (in base ten).            */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X<<X)          */
/*   lhs is A                                               */
/*   rhs is B, the number of digits to shift (-ve to right)       */
/*   set is the context                                     */
/*                                                    */
/* The digits of the coefficient of A are shifted to the left (if B   */
/* is positive) or to the right (if B is negative) without adjusting  */
/* the exponent or the sign of A.                           */
/*                                                    */
/* B must be an integer (q=0) and in the range -set->digits through   */
/* +set->digits.                                      */
/* C must have space for set->digits digits.                      */
/* NaNs are propagated as usual.  Infinities are unaffected (but      */
/* B must be valid).  No status is set unless B is invalid or an      */
/* operand is an sNaN.                                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
                     const decNumber *rhs, decContext *set) {
  uInt status=0;        /* accumulator */
  Int  shift;                 /* rhs as an Int */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* NaNs propagate as normal */
  if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
    decNaNs(res, lhs, rhs, set, &status);
   /* rhs must be an integer */
   else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
    status=DEC_Invalid_operation;
   else { /* both numeric, rhs is an integer */
    shift=decGetInt(rhs);                /* [cannot fail] */
    if (shift==BADINT                    /* something bad .. */
     || shift==BIGODD || shift==BIGEVEN        /* .. very big .. */
     || abs(shift)>set->digits)                /* .. or out of range */
      status=DEC_Invalid_operation;
     else {                        /* rhs is OK */
      decNumberCopy(res, lhs);
      if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
      if (shift>0) {                     /* to left */
        if (shift==set->digits) {        /* removing all */
          *res->lsu=0;             /* so place 0 */
          res->digits=1;                 /* .. */
          }
         else {                    /* */
          /* first remove leading digits if necessary */
          if (res->digits+shift>set->digits) {
            decDecap(res, res->digits+shift-set->digits);
            /* that updated res->digits; may have gone to 1 (for a */
            /* single digit or for zero */
            }
          if (res->digits>1 || *res->lsu)  /* if non-zero.. */
            res->digits=decShiftToMost(res->lsu, res->digits, shift);
          } /* partial left */
        } /* left */
       else { /* to right */
        if (-shift>=res->digits) {       /* discarding all */
          *res->lsu=0;             /* so place 0 */
          res->digits=1;                 /* .. */
          }
         else {
          decShiftToLeast(res->lsu, D2U(res->digits), -shift);
          res->digits-=(-shift);
          }
        } /* to right */
      } /* non-0 non-Inf shift */
      } /* rhs OK */
    } /* numerics */
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberShift */

/* ------------------------------------------------------------------ */
/* decNumberSquareRoot -- square root operator                    */
/*                                                    */
/*   This computes C = squareroot(A)                              */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
/* This uses the following varying-precision algorithm in:        */
/*                                                    */
/*   Properly Rounded Variable Precision Square Root, T. E. Hull and  */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
/*   pp229-237, ACM, September 1985.                              */
/*                                                    */
/* The square-root is calculated using Newton's method, after which   */
/* a check is made to ensure the result is correctly rounded.           */
/*                                                    */
/* % [Reformatted original Numerical Turing source code follows.]     */
/* function sqrt(x : real) : real                           */
/* % sqrt(x) returns the properly rounded approximation to the square */
/* % root of x, in the precision of the calling environment, or it    */
/* % fails if x < 0.                                        */
/* % t e hull and a abrham, august, 1984                    */
/* if x <= 0 then                                     */
/*   if x < 0 then                                          */
/*     assert false                                         */
/*   else                                             */
/*     result 0                                             */
/*   end if                                           */
/* end if                                             */
/* var f := setexp(x, 0)  % fraction part of x   [0.1 <= x < 1]         */
/* var e := getexp(x)     % exponent part of x                    */
/* var approx : real                                        */
/* if e mod 2 = 0  then                                     */
/*   approx := .259 + .819 * f       % approx to root of f              */
/* else                                                     */
/*   f := f/l0                 % adjustments                      */
/*   e := e + 1                %   for odd                        */
/*   approx := .0819 + 2.59 * f      %   exponent                       */
/* end if                                             */
/*                                                    */
/* var p:= 3                                                */
/* const maxp := currentprecision + 2                             */
/* loop                                                     */
/*   p := min(2*p - 2, maxp)   % p = 4,6,10, . . . , maxp         */
/*   precision p                                      */
/*   approx := .5 * (approx + f/approx)                           */
/*   exit when p = maxp                                     */
/* end loop                                           */
/*                                                    */
/* % approx is now within 1 ulp of the properly rounded square root   */
/* % of f; to ensure proper rounding, compare squares of (approx -    */
/* % l/2 ulp) and (approx + l/2 ulp) with f.                      */
/* p := currentprecision                                    */
/* begin                                              */
/*   precision p + 2                                        */
/*   const approxsubhalf := approx - setexp(.5, -p)               */
/*   if mulru(approxsubhalf, approxsubhalf) > f then              */
/*     approx := approx - setexp(.l, -p + 1)                      */
/*   else                                             */
/*     const approxaddhalf := approx + setexp(.5, -p)             */
/*     if mulrd(approxaddhalf, approxaddhalf) < f then                  */
/*     approx := approx + setexp(.l, -p + 1)                      */
/*     end if                                               */
/*   end if                                           */
/* end                                                      */
/* result setexp(approx, e div 2)  % fix exponent                 */
/* end sqrt                                           */
/* ------------------------------------------------------------------ */
decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
                        decContext *set) {
  decContext workset, approxset;   /* work contexts */
  decNumber dzero;               /* used for constant zero */
  Int  maxp;                     /* largest working precision */
  Int  workp;                    /* working precision */
  Int  residue=0;          /* rounding residue */
  uInt status=0, ignore=0;       /* status accumulators */
  uInt rstatus;                  /* .. */
  Int  exp;                /* working exponent */
  Int  ideal;                    /* ideal (preferred) exponent */
  Int  needbytes;          /* work */
  Int  dropped;                  /* .. */

  #if DECSUBSET
  decNumber *allocrhs=NULL;      /* non-NULL if rounded rhs allocated */
  #endif
  /* buffer for f [needs +1 in case DECBUFFER 0] */
  decNumber buff[D2N(DECBUFFER+1)];
  /* buffer for a [needs +2 to match likely maxp] */
  decNumber bufa[D2N(DECBUFFER+2)];
  /* buffer for temporary, b [must be same size as a] */
  decNumber bufb[D2N(DECBUFFER+2)];
  decNumber *allocbuff=NULL;     /* -> allocated buff, iff allocated */
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *allocbufb=NULL;     /* -> allocated bufb, iff allocated */
  decNumber *f=buff;             /* reduced fraction */
  decNumber *a=bufa;             /* approximation to result */
  decNumber *b=bufb;             /* intermediate result */
  /* buffer for temporary variable, up to 3 digits */
  decNumber buft[D2N(3)];
  decNumber *t=buft;             /* up-to-3-digit constant or work */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operand and set lostDigits status, as needed */
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, &status);
      if (allocrhs==NULL) break;
      /* [Note: 'f' allocation below could reuse this buffer if */
      /* used, but as this is rare they are kept separate for clarity.] */
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* handle infinities and NaNs */
    if (SPECIALARG) {
      if (decNumberIsInfinite(rhs)) {           /* an infinity */
      if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
       else decNumberCopy(res, rhs);            /* +Infinity */
      }
       else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
      break;
      }

    /* calculate the ideal (preferred) exponent [floor(exp/2)] */
    /* [We would like to write: ideal=rhs->exponent>>1, but this */
    /* generates a compiler warning.  Generated code is the same.] */
    ideal=(rhs->exponent&~1)/2;           /* target */

    /* handle zeros */
    if (ISZERO(rhs)) {
      decNumberCopy(res, rhs);            /* could be 0 or -0 */
      res->exponent=ideal;          /* use the ideal [safe] */
      /* use decFinish to clamp any out-of-range exponent, etc. */
      decFinish(res, set, &residue, &status);
      break;
      }

    /* any other -x is an oops */
    if (decNumberIsNegative(rhs)) {
      status|=DEC_Invalid_operation;
      break;
      }

    /* space is needed for three working variables */
    /*       f -- the same precision as the RHS, reduced to 0.01->0.99... */
    /*       a -- Hull's approximation -- precision, when assigned, is */
    /*            currentprecision+1 or the input argument precision, */
    /*            whichever is larger (+2 for use as temporary) */
    /*       b -- intermediate temporary result (same size as a) */
    /* if any is too long for local storage, then allocate */
    workp=MAXI(set->digits+1, rhs->digits);  /* actual rounding precision */
    maxp=workp+2;                  /* largest working precision */

    needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(buff)) {
      allocbuff=(decNumber *)malloc(needbytes);
      if (allocbuff==NULL) {  /* hopeless -- abandon */
      status|=DEC_Insufficient_storage;
      break;}
      f=allocbuff;            /* use the allocated space */
      }
    /* a and b both need to be able to hold a maxp-length number */
    needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
    if (needbytes>(Int)sizeof(bufa)) {            /* [same applies to b] */
      allocbufa=(decNumber *)malloc(needbytes);
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL || allocbufb==NULL) {   /* hopeless */
      status|=DEC_Insufficient_storage;
      break;}
      a=allocbufa;            /* use the allocated spaces */
      b=allocbufb;            /* .. */
      }

    /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
    decNumberCopy(f, rhs);
    exp=f->exponent+f->digits;                 /* adjusted to Hull rules */
    f->exponent=-(f->digits);            /* to range */

    /* set up working context */
    decContextDefault(&workset, DEC_INIT_DECIMAL64);

    /* [Until further notice, no error is possible and status bits */
    /* (Rounded, etc.) should be ignored, not accumulated.] */

    /* Calculate initial approximation, and allow for odd exponent */
    workset.digits=workp;                /* p for initial calculation */
    t->bits=0; t->digits=3;
    a->bits=0; a->digits=3;
    if ((exp & 1)==0) {                  /* even exponent */
      /* Set t=0.259, a=0.819 */
      t->exponent=-3;
      a->exponent=-3;
      #if DECDPUN>=3
      t->lsu[0]=259;
      a->lsu[0]=819;
      #elif DECDPUN==2
      t->lsu[0]=59; t->lsu[1]=2;
      a->lsu[0]=19; a->lsu[1]=8;
      #else
      t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
      a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
      #endif
      }
     else {                        /* odd exponent */
      /* Set t=0.0819, a=2.59 */
      f->exponent--;                     /* f=f/10 */
      exp++;                             /* e=e+1 */
      t->exponent=-4;
      a->exponent=-2;
      #if DECDPUN>=3
      t->lsu[0]=819;
      a->lsu[0]=259;
      #elif DECDPUN==2
      t->lsu[0]=19; t->lsu[1]=8;
      a->lsu[0]=59; a->lsu[1]=2;
      #else
      t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
      a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
      #endif
      }
    decMultiplyOp(a, a, f, &workset, &ignore);    /* a=a*f */
    decAddOp(a, a, t, &workset, 0, &ignore);      /* ..+t */
    /* [a is now the initial approximation for sqrt(f), calculated with */
    /* currentprecision, which is also a's precision.] */

    /* the main calculation loop */
    decNumberZero(&dzero);               /* make 0 */
    decNumberZero(t);                    /* set t = 0.5 */
    t->lsu[0]=5;                   /* .. */
    t->exponent=-1;                      /* .. */
    workset.digits=3;                    /* initial p */
    for (;;) {
      /* set p to min(2*p - 2, maxp)  [hence 3; or: 4, 6, 10, ... , maxp] */
      workset.digits=workset.digits*2-2;
      if (workset.digits>maxp) workset.digits=maxp;
      /* a = 0.5 * (a + f/a) */
      /* [calculated at p then rounded to currentprecision] */
      decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
      decAddOp(b, b, a, &workset, 0, &ignore);    /* b=b+a */
      decMultiplyOp(a, b, t, &workset, &ignore);  /* a=b*0.5 */
      if (a->digits==maxp) break;        /* have required digits */
      } /* loop */

    /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
    /* now reduce to length, etc.; this needs to be done with a */
    /* having the correct exponent so as to handle subnormals */
    /* correctly */
    approxset=*set;                      /* get emin, emax, etc. */
    approxset.round=DEC_ROUND_HALF_EVEN;
    a->exponent+=exp/2;                  /* set correct exponent */

    rstatus=0;                           /* clear status */
    residue=0;                           /* .. and accumulator */
    decCopyFit(a, a, &approxset, &residue, &rstatus);  /* reduce (if needed) */
    decFinish(a, &approxset, &residue, &rstatus);      /* clean and finalize */

    /* Overflow was possible if the input exponent was out-of-range, */
    /* in which case quit */
    if (rstatus&DEC_Overflow) {
      status=rstatus;                    /* use the status as-is */
      decNumberCopy(res, a);             /* copy to result */
      break;
      }

    /* Preserve status except Inexact/Rounded */
    status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));

    /* Carry out the Hull correction */
    a->exponent-=exp/2;                  /* back to 0.1->1 */

    /* a is now at final precision and within 1 ulp of the properly */
    /* rounded square root of f; to ensure proper rounding, compare */
    /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
    /* Here workset.digits=maxp and t=0.5, and a->digits determines */
    /* the ulp */
    workset.digits--;                       /* maxp-1 is OK now */
    t->exponent=-a->digits-1;               /* make 0.5 ulp */
    decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
    workset.round=DEC_ROUND_UP;
    decMultiplyOp(b, b, b, &workset, &ignore);    /* b = mulru(b, b) */
    decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
    if (decNumberIsNegative(b)) {           /* f < b [i.e., b > f] */
      /* this is the more common adjustment, though both are rare */
      t->exponent++;                        /* make 1.0 ulp */
      t->lsu[0]=1;                          /* .. */
      decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
      /* assign to approx [round to length] */
      approxset.emin-=exp/2;                /* adjust to match a */
      approxset.emax-=exp/2;
      decAddOp(a, &dzero, a, &approxset, 0, &ignore);
      }
     else {
      decAddOp(b, a, t, &workset, 0, &ignore);    /* b = a + 0.5 ulp */
      workset.round=DEC_ROUND_DOWN;
      decMultiplyOp(b, b, b, &workset, &ignore);  /* b = mulrd(b, b) */
      decCompareOp(b, b, f, &workset, COMPARE, &ignore);   /* b ? f */
      if (decNumberIsNegative(b)) {         /* b < f */
      t->exponent++;                        /* make 1.0 ulp */
      t->lsu[0]=1;                          /* .. */
      decAddOp(a, a, t, &workset, 0, &ignore);  /* a = a + 1 ulp */
      /* assign to approx [round to length] */
      approxset.emin-=exp/2;                /* adjust to match a */
      approxset.emax-=exp/2;
      decAddOp(a, &dzero, a, &approxset, 0, &ignore);
      }
      }
    /* [no errors are possible in the above, and rounding/inexact during */
    /* estimation are irrelevant, so status was not accumulated] */

    /* Here, 0.1 <= a < 1  (still), so adjust back */
    a->exponent+=exp/2;                  /* set correct exponent */

    /* count droppable zeros [after any subnormal rounding] by */
    /* trimming a copy */
    decNumberCopy(b, a);
    decTrim(b, set, 1, &dropped);        /* [drops trailing zeros] */

    /* Set Inexact and Rounded.      The answer can only be exact if */
    /* it is short enough so that squaring it could fit in workp digits, */
    /* and it cannot have trailing zeros due to clamping, so these are */
    /* the only (relatively rare) conditions a careful check is needed */
    if (b->digits*2-1 > workp && !set->clamp) { /* cannot fit */
      status|=DEC_Inexact|DEC_Rounded;
      }
     else {                        /* could be exact/unrounded */
      uInt mstatus=0;                    /* local status */
      decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
      if (mstatus&DEC_Overflow) {        /* result just won't fit */
      status|=DEC_Inexact|DEC_Rounded;
      }
       else {                            /* plausible */
      decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
      if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
       else {                            /* is Exact */
        /* here, dropped is the count of trailing zeros in 'a' */
        /* use closest exponent to ideal... */
        Int todrop=ideal-a->exponent;          /* most that can be dropped */
        if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
         else {                    /* unrounded */
          if (dropped<todrop) {          /* clamp to those available */
            todrop=dropped;
            status|=DEC_Clamped;
            }
          if (todrop>0) {                /* have some to drop */
            decShiftToLeast(a->lsu, D2U(a->digits), todrop);
            a->exponent+=todrop;         /* maintain numerical value */
            a->digits-=todrop;           /* new length */
            }
          }
        }
      }
      }

    /* double-check Underflow, as perhaps the result could not have */
    /* been subnormal (initial argument too big), or it is now Exact */
    if (status&DEC_Underflow) {
      Int ae=rhs->exponent+rhs->digits-1;    /* adjusted exponent */
      /* check if truly subnormal */
      #if DECEXTFLAG                     /* DEC_Subnormal too */
      if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
      #else
      if (ae>=set->emin*2) status&=~DEC_Underflow;
      #endif
      /* check if truly inexact */
      if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
      }

    decNumberCopy(res, a);               /* a is now the result */
    } while(0);                          /* end protected */

  if (allocbuff!=NULL) free(allocbuff);        /* drop any storage used */
  if (allocbufa!=NULL) free(allocbufa);        /* .. */
  if (allocbufb!=NULL) free(allocbufb);        /* .. */
  #if DECSUBSET
  if (allocrhs !=NULL) free(allocrhs);         /* .. */
  #endif
  if (status!=0) decStatus(res, status, set);/* then report status */
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberSquareRoot */

/* ------------------------------------------------------------------ */
/* decNumberSubtract -- subtract two Numbers                      */
/*                                                    */
/*   This computes C = A - B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X-X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* ------------------------------------------------------------------ */
decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs, decContext *set) {
  uInt status=0;              /* accumulator */

  decAddOp(res, lhs, rhs, set, DECNEG, &status);
  if (status!=0) decStatus(res, status, set);
  #if DECCHECK
  decCheckInexact(res, set);
  #endif
  return res;
  } /* decNumberSubtract */

/* ------------------------------------------------------------------ */
/* decNumberToIntegralExact -- round-to-integral-value with InExact   */
/* decNumberToIntegralValue -- round-to-integral-value                  */
/*                                                    */
/*   res is the result                                      */
/*   rhs is input number                                    */
/*   set is the context                                     */
/*                                                    */
/* res must have space for any value of rhs.                      */
/*                                                    */
/* This implements the IEEE special operators and therefore treats    */
/* special values as valid.  For finite numbers it returns        */
/* rescale(rhs, 0) if rhs->exponent is <0.                        */
/* Otherwise the result is rhs (so no error is possible, except for   */
/* sNaN).                                             */
/*                                                    */
/* The context is used for rounding mode and status after sNaN, but   */
/* the digits setting is ignored.  The Exact version will signal      */
/* Inexact if the result differs numerically from rhs; the other      */
/* never signals Inexact.                                   */
/* ------------------------------------------------------------------ */
decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
                             decContext *set) {
  decNumber dn;
  decContext workset;            /* working context */
  uInt status=0;           /* accumulator */

  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  /* handle infinities and NaNs */
  if (SPECIALARG) {
    if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */
     else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
    }
   else { /* finite */
    /* have a finite number; no error possible (res must be big enough) */
    if (rhs->exponent>=0) return decNumberCopy(res, rhs);
    /* that was easy, but if negative exponent there is work to do... */
    workset=*set;          /* clone rounding, etc. */
    workset.digits=rhs->digits;        /* no length rounding */
    workset.traps=0;             /* no traps */
    decNumberZero(&dn);          /* make a number with exponent 0 */
    decNumberQuantize(res, rhs, &dn, &workset);
    status|=workset.status;
    }
  if (status!=0) decStatus(res, status, set);
  return res;
  } /* decNumberToIntegralExact */

decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
                             decContext *set) {
  decContext workset=*set;       /* working context */
  workset.traps=0;               /* no traps */
  decNumberToIntegralExact(res, rhs, &workset);
  /* this never affects set, except for sNaNs; NaN will have been set */
  /* or propagated already, so no need to call decStatus */
  set->status|=workset.status&DEC_Invalid_operation;
  return res;
  } /* decNumberToIntegralValue */

/* ------------------------------------------------------------------ */
/* decNumberXor -- XOR two Numbers, digitwise                     */
/*                                                    */
/*   This computes C = A ^ B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X^X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context (used for result length and error report)     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Logical function restrictions apply (see above); a NaN is            */
/* returned with Invalid_operation if a restriction is violated.      */
/* ------------------------------------------------------------------ */
decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set) {
  const Unit *ua, *ub;              /* -> operands */
  const Unit *msua, *msub;          /* -> operand msus */
  Unit      *uc, *msuc;             /* -> result and its msu */
  Int msudigs;                /* digits in res msu */
  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    decStatus(res, DEC_Invalid_operation, set);
    return res;
    }
  /* operands are valid */
  ua=lhs->lsu;                      /* bottom-up */
  ub=rhs->lsu;                      /* .. */
  uc=res->lsu;                      /* .. */
  msua=ua+D2U(lhs->digits)-1;       /* -> msu of lhs */
  msub=ub+D2U(rhs->digits)-1;       /* -> msu of rhs */
  msuc=uc+D2U(set->digits)-1;       /* -> msu of result */
  msudigs=MSUDIGITS(set->digits);   /* [faster than remainder] */
  for (; uc<=msuc; ua++, ub++, uc++) {    /* Unit loop */
    Unit a, b;                      /* extract units */
    if (ua>msua) a=0;
     else a=*ua;
    if (ub>msub) b=0;
     else b=*ub;
    *uc=0;                    /* can now write back */
    if (a|b) {                      /* maybe 1 bits to examine */
      Int i, j;
      /* This loop could be unrolled and/or use BIN2BCD tables */
      for (i=0; i<DECDPUN; i++) {
      if ((a^b)&1) *uc=*uc+(Unit)powers[i];       /* effect XOR */
      j=a%10;
      a=a/10;
      j|=b%10;
      b=b/10;
      if (j>1) {
        decStatus(res, DEC_Invalid_operation, set);
        return res;
        }
      if (uc==msuc && i==msudigs-1) break;        /* just did final digit */
      } /* each digit */
      } /* non-zero */
    } /* each unit */
  /* [here uc-1 is the msu of the result] */
  res->digits=decGetDigits(res->lsu, uc-res->lsu);
  res->exponent=0;                  /* integer */
  res->bits=0;                      /* sign=0 */
  return res;  /* [no status to set] */
  } /* decNumberXor */


/* ================================================================== */
/* Utility routines                                         */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decNumberClass -- return the decClass of a decNumber                 */
/*   dn -- the decNumber to test                            */
/*   set -- the context to use for Emin                           */
/*   returns the decClass enum                                    */
/* ------------------------------------------------------------------ */
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
  if (decNumberIsSpecial(dn)) {
    if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
    if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
    /* must be an infinity */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
    return DEC_CLASS_POS_INF;
    }
  /* is finite */
  if (decNumberIsNormal(dn, set)) { /* most common */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
    return DEC_CLASS_POS_NORMAL;
    }
  /* is subnormal or zero */
  if (decNumberIsZero(dn)) {  /* most common */
    if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
    return DEC_CLASS_POS_ZERO;
    }
  if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
  return DEC_CLASS_POS_SUBNORMAL;
  } /* decNumberClass */

/* ------------------------------------------------------------------ */
/* decNumberClassToString -- convert decClass to a string         */
/*                                                    */
/*  eclass is a valid decClass                                    */
/*  returns a constant string describing the class (max 13+1 chars)   */
/* ------------------------------------------------------------------ */
const char *decNumberClassToString(enum decClass eclass) {
  if (eclass==DEC_CLASS_POS_NORMAL)    return DEC_ClassString_PN;
  if (eclass==DEC_CLASS_NEG_NORMAL)    return DEC_ClassString_NN;
  if (eclass==DEC_CLASS_POS_ZERO)      return DEC_ClassString_PZ;
  if (eclass==DEC_CLASS_NEG_ZERO)      return DEC_ClassString_NZ;
  if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
  if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
  if (eclass==DEC_CLASS_POS_INF)       return DEC_ClassString_PI;
  if (eclass==DEC_CLASS_NEG_INF)       return DEC_ClassString_NI;
  if (eclass==DEC_CLASS_QNAN)        return DEC_ClassString_QN;
  if (eclass==DEC_CLASS_SNAN)        return DEC_ClassString_SN;
  return DEC_ClassString_UN;         /* Unknown */
  } /* decNumberClassToString */

/* ------------------------------------------------------------------ */
/* decNumberCopy -- copy a number                           */
/*                                                    */
/*   dest is the target decNumber                           */
/*   src  is the source decNumber                           */
/*   returns dest                                     */
/*                                                    */
/* (dest==src is allowed and is a no-op)                    */
/* All fields are updated as required.    This is a utility operation,  */
/* so special values are unchanged and no error is possible.            */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {

  #if DECCHECK
  if (src==NULL) return decNumberZero(dest);
  #endif

  if (dest==src) return dest;            /* no copy required */

  /* Use explicit assignments here as structure assignment could copy */
  /* more than just the lsu (for small DECDPUN).  This would not affect */
  /* the value of the results, but could disturb test harness spill */
  /* checking. */
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  dest->digits=src->digits;
  dest->lsu[0]=src->lsu[0];
  if (src->digits>DECDPUN) {             /* more Units to come */
    const Unit *smsup, *s;               /* work */
    Unit  *d;                            /* .. */
    /* memcpy for the remaining Units would be safe as they cannot */
    /* overlap.    However, this explicit loop is faster in short cases. */
    d=dest->lsu+1;                       /* -> first destination */
    smsup=src->lsu+D2U(src->digits);           /* -> source msu+1 */
    for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
    }
  return dest;
  } /* decNumberCopy */

/* ------------------------------------------------------------------ */
/* decNumberCopyAbs -- quiet absolute value operator              */
/*                                                    */
/*   This sets C = abs(A)                                   */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberAbs for a checking version of this.          */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits&=~DECNEG;               /* turn off sign */
  return res;
  } /* decNumberCopyAbs */

/* ------------------------------------------------------------------ */
/* decNumberCopyNegate -- quiet negate value operator             */
/*                                                    */
/*   This sets C = negate(A)                                */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberMinus for a checking version of this.        */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  decNumberCopy(res, rhs);
  res->bits^=DECNEG;                /* invert the sign */
  return res;
  } /* decNumberCopyNegate */

/* ------------------------------------------------------------------ */
/* decNumberCopySign -- quiet copy and set sign operator          */
/*                                                    */
/*   This sets C = A with the sign of B                           */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* ------------------------------------------------------------------ */
decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
                        const decNumber *rhs) {
  uByte sign;                       /* rhs sign */
  #if DECCHECK
  if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
  #endif
  sign=rhs->bits & DECNEG;          /* save sign bit */
  decNumberCopy(res, lhs);
  res->bits&=~DECNEG;               /* clear the sign */
  res->bits|=sign;                  /* set from rhs */
  return res;
  } /* decNumberCopySign */

/* ------------------------------------------------------------------ */
/* decNumberGetBCD -- get the coefficient in BCD8                 */
/*   dn is the source decNumber                                   */
/*   bcd is the uInt array that will receive dn->digits BCD bytes,    */
/*     most-significant at offset 0                         */
/*   returns bcd                                      */
/*                                                    */
/* bcd must have at least dn->digits bytes.  No error is possible; if */
/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0.   */
/* ------------------------------------------------------------------ */
uByte * decNumberGetBCD(const decNumber *dn, uint8_t *bcd) {
  uByte *ub=bcd+dn->digits-1;    /* -> lsd */
  const Unit *up=dn->lsu;        /* Unit pointer, -> lsu */

  #if DECDPUN==1           /* trivial simple copy */
    for (; ub>=bcd; ub--, up++) *ub=*up;
  #else                          /* chopping needed */
    uInt u=*up;                  /* work */
    uInt cut=DECDPUN;            /* downcounter through unit */
    for (; ub>=bcd; ub--) {
      *ub=(uByte)(u%10);         /* [*6554 trick inhibits, here] */
      u=u/10;
      cut--;
      if (cut>0) continue;       /* more in this unit */
      up++;
      u=*up;
      cut=DECDPUN;
      }
  #endif
  return bcd;
  } /* decNumberGetBCD */

/* ------------------------------------------------------------------ */
/* decNumberSetBCD -- set (replace) the coefficient from BCD8           */
/*   dn is the target decNumber                                   */
/*   bcd is the uInt array that will source n BCD bytes, most-          */
/*     significant at offset 0                                    */
/*   n is the number of digits in the source BCD array (bcd)            */
/*   returns dn                                             */
/*                                                    */
/* dn must have space for at least n digits.  No error is possible;   */
/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1   */
/* and bcd[0] zero.                                         */
/* ------------------------------------------------------------------ */
decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
  Unit *up=dn->lsu+D2U(dn->digits)-1;     /* -> msu [target pointer] */
  const uByte *ub=bcd;              /* -> source msd */

  #if DECDPUN==1              /* trivial simple copy */
    for (; ub<bcd+n; ub++, up--) *up=*ub;
  #else                             /* some assembly needed */
    /* calculate how many digits in msu, and hence first cut */
    Int cut=MSUDIGITS(n);           /* [faster than remainder] */
    for (;up>=dn->lsu; up--) {            /* each Unit from msu */
      *up=0;                        /* will take <=DECDPUN digits */
      for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
      cut=DECDPUN;                  /* next Unit has all digits */
      }
  #endif
  dn->digits=n;                     /* set digit count */
  return dn;
  } /* decNumberSetBCD */

/* ------------------------------------------------------------------ */
/* decNumberIsNormal -- test normality of a decNumber             */
/*   dn is the decNumber to test                            */
/*   set is the context to use for Emin                           */
/*   returns 1 if |dn| is finite and >=Nmin, 0 otherwise          */
/* ------------------------------------------------------------------ */
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
  Int ae;                     /* adjusted exponent */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; /* not finite */
  if (decNumberIsZero(dn)) return 0;      /* not non-zero */

  ae=dn->exponent+dn->digits-1;           /* adjusted exponent */
  if (ae<set->emin) return 0;       /* is subnormal */
  return 1;
  } /* decNumberIsNormal */

/* ------------------------------------------------------------------ */
/* decNumberIsSubnormal -- test subnormality of a decNumber       */
/*   dn is the decNumber to test                            */
/*   set is the context to use for Emin                           */
/*   returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise    */
/* ------------------------------------------------------------------ */
Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
  Int ae;                     /* adjusted exponent */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
  #endif

  if (decNumberIsSpecial(dn)) return 0; /* not finite */
  if (decNumberIsZero(dn)) return 0;      /* not non-zero */

  ae=dn->exponent+dn->digits-1;           /* adjusted exponent */
  if (ae<set->emin) return 1;       /* is subnormal */
  return 0;
  } /* decNumberIsSubnormal */

/* ------------------------------------------------------------------ */
/* decNumberTrim -- remove insignificant zeros                    */
/*                                                    */
/*   dn is the number to trim                               */
/*   returns dn                                             */
/*                                                    */
/* All fields are updated as required.    This is a utility operation,  */
/* so special values are unchanged and no error is possible.            */
/* ------------------------------------------------------------------ */
decNumber * decNumberTrim(decNumber *dn) {
  Int  dropped;                  /* work */
  decContext set;          /* .. */
  #if DECCHECK
  if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
  #endif
  decContextDefault(&set, DEC_INIT_BASE);    /* clamp=0 */
  return decTrim(dn, &set, 0, &dropped);
  } /* decNumberTrim */

/* ------------------------------------------------------------------ */
/* decNumberVersion -- return the name and version of this module     */
/*                                                    */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
const char * decNumberVersion(void) {
  return DECVERSION;
  } /* decNumberVersion */

/* ------------------------------------------------------------------ */
/* decNumberZero -- set a number to 0                             */
/*                                                    */
/*   dn is the number to set, with space for one digit                  */
/*   returns dn                                             */
/*                                                    */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
/* Memset is not used as it is much slower in some environments. */
decNumber * decNumberZero(decNumber *dn) {

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  dn->bits=0;
  dn->exponent=0;
  dn->digits=1;
  dn->lsu[0]=0;
  return dn;
  } /* decNumberZero */

/* ================================================================== */
/* Local routines                                     */
/* ================================================================== */

/* ------------------------------------------------------------------ */
/* decToString -- lay out a number into a string                  */
/*                                                    */
/*   dn         is the number to lay out                          */
/*   string is where to lay out the number                        */
/*   eng    is 1 if Engineering, 0 if Scientific                  */
/*                                                    */
/* string must be at least dn->digits+14 characters long          */
/* No error is possible.                                    */
/*                                                    */
/* Note that this routine can generate a -0 or 0.000.  These are      */
/* never generated in subset to-number or arithmetic, but can occur   */
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234).          */
/* ------------------------------------------------------------------ */
/* If DECCHECK is enabled the string "?" is returned if a number is */
/* invalid. */
static void decToString(const decNumber *dn, char *string, Flag eng) {
  Int exp=dn->exponent;       /* local copy */
  Int e;                /* E-part value */
  Int pre;              /* digits before the '.' */
  Int cut;              /* for counting digits in a Unit */
  char *c=string;       /* work [output pointer] */
  const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
  uInt u, pow;                /* work */

  #if DECCHECK
  if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
    strcpy(string, "?");
    return;}
  #endif

  if (decNumberIsNegative(dn)) {   /* Negatives get a minus */
    *c='-';
    c++;
    }
  if (dn->bits&DECSPECIAL) {     /* Is a special value */
    if (decNumberIsInfinite(dn)) {
      strcpy(c,     "Inf");
      strcpy(c+3, "inity");
      return;}
    /* a NaN */
    if (dn->bits&DECSNAN) {      /* signalling NaN */
      *c='s';
      c++;
      }
    strcpy(c, "NaN");
    c+=3;                  /* step past */
    /* if not a clean non-zero coefficient, that's all there is in a */
    /* NaN string */
    if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
    /* [drop through to add integer] */
    }

  /* calculate how many digits in msu, and hence first cut */
  cut=MSUDIGITS(dn->digits);     /* [faster than remainder] */
  cut--;                   /* power of ten for digit */

  if (exp==0) {                  /* simple integer [common fastpath] */
    for (;up>=dn->lsu; up--) {         /* each Unit from msu */
      u=*up;                     /* contains DECDPUN digits to lay out */
      for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
      cut=DECDPUN-1;             /* next Unit has all digits */
      }
    *c='\0';                     /* terminate the string */
    return;}

  /* non-0 exponent -- assume plain form */
  pre=dn->digits+exp;            /* digits before '.' */
  e=0;                           /* no E */
  if ((exp>0) || (pre<-5)) {     /* need exponential form */
    e=exp+dn->digits-1;          /* calculate E value */
    pre=1;                 /* assume one digit before '.' */
    if (eng && (e!=0)) {         /* engineering: may need to adjust */
      Int adj;                   /* adjustment */
      /* The C remainder operator is undefined for negative numbers, so */
      /* a positive remainder calculation must be used here */
      if (e<0) {
      adj=(-e)%3;
      if (adj!=0) adj=3-adj;
      }
       else { /* e>0 */
      adj=e%3;
      }
      e=e-adj;
      /* if dealing with zero still produce an exponent which is a */
      /* multiple of three, as expected, but there will only be the */
      /* one zero before the E, still.    Otherwise note the padding. */
      if (!ISZERO(dn)) pre+=adj;
       else {  /* is zero */
      if (adj!=0) {              /* 0.00Esnn needed */
        e=e+3;
        pre=-(2-adj);
        }
      } /* zero */
      } /* eng */
    } /* need exponent */

  /* lay out the digits of the coefficient, adding 0s and . as needed */
  u=*up;
  if (pre>0) {                   /* xxx.xxx or xx00 (engineering) form */
    Int n=pre;
    for (; pre>0; pre--, c++, cut--) {
      if (cut<0) {               /* need new Unit */
      if (up==dn->lsu) break;    /* out of input digits (pre>digits) */
      up--;
      cut=DECDPUN-1;
      u=*up;
      }
      TODIGIT(u, cut, c, pow);
      }
    if (n<dn->digits) {          /* more to come, after '.' */
      *c='.'; c++;
      for (;; c++, cut--) {
      if (cut<0) {               /* need new Unit */
        if (up==dn->lsu) break;  /* out of input digits */
        up--;
        cut=DECDPUN-1;
        u=*up;
        }
      TODIGIT(u, cut, c, pow);
      }
      }
     else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
    }
   else {                  /* 0.xxx or 0.000xxx form */
    *c='0'; c++;
    *c='.'; c++;
    for (; pre<0; pre++, c++) *c='0';     /* add any 0's after '.' */
    for (; ; c++, cut--) {
      if (cut<0) {               /* need new Unit */
      if (up==dn->lsu) break;    /* out of input digits */
      up--;
      cut=DECDPUN-1;
      u=*up;
      }
      TODIGIT(u, cut, c, pow);
      }
    }

  /* Finally add the E-part, if needed.    It will never be 0, has a
     base maximum and minimum of +999999999 through -999999999, but
     could range down to -1999999998 for anormal numbers */
  if (e!=0) {
    Flag had=0;               /* 1=had non-zero */
    *c='E'; c++;
    *c='+'; c++;        /* assume positive */
    u=e;                /* .. */
    if (e<0) {
      *(c-1)='-';       /* oops, need - */
      u=-e;             /* uInt, please */
      }
    /* lay out the exponent [_itoa or equivalent is not ANSI C] */
    for (cut=9; cut>=0; cut--) {
      TODIGIT(u, cut, c, pow);
      if (*c=='0' && !had) continue;      /* skip leading zeros */
      had=1;                        /* had non-0 */
      c++;                    /* step for next */
      } /* cut */
    }
  *c='\0';      /* terminate the string (all paths) */
  return;
  } /* decToString */

/* ------------------------------------------------------------------ */
/* decAddOp -- add/subtract operation                             */
/*                                                    */
/*   This computes C = A + B                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X+X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*   negate is DECNEG if rhs should be negated, or 0 otherwise          */
/*   status accumulates status for the caller                     */
/*                                                    */
/* C must have space for set->digits digits.                      */
/* Inexact in status must be 0 for correct Exact zero sign in result  */
/* ------------------------------------------------------------------ */
/* If possible, the coefficient is calculated directly into C.          */
/* However, if:                                             */
/*   -- a digits+1 calculation is needed because the numbers are      */
/*    unaligned and span more than set->digits digits             */
/*   -- a carry to digits+1 digits looks possible                 */
/*   -- C is the same as A or B, and the result would destructively   */
/*    overlap the A or B coefficient                              */
/* then the result must be calculated into a temporary buffer.    In    */
/* this case a local (stack) buffer is used if possible, and only if  */
/* too long for that does malloc become the final resort.         */
/*                                                    */
/* Misalignment is handled as follows:                            */
/*   Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp.    */
/*   BPad: Apply the padding by a combination of shifting (whole      */
/*       units) and multiplication (part units).                  */
/*                                                    */
/* Addition, especially x=x+1, is speed-critical.                 */
/* The static buffer is larger than might be expected to allow for    */
/* calls from higher-level funtions (notable exp).                */
/* ------------------------------------------------------------------ */
static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
                      const decNumber *rhs, decContext *set,
                      uByte negate, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;      /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;      /* .., rhs */
  #endif
  Int rhsshift;            /* working shift (in Units) */
  Int maxdigits;           /* longest logical length */
  Int mult;                /* multiplier */
  Int residue;             /* rounding accumulator */
  uByte bits;                    /* result bits */
  Flag      diffsign;            /* non-0 if arguments have different sign */
  Unit      *acc;                /* accumulator for result */
  Unit      accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
                           /* allocations when called from */
                           /* other operations, notable exp] */
  Unit      *allocacc=NULL;            /* -> allocated acc buffer, iff allocated */
  Int reqdigits=set->digits;     /* local copy; requested DIGITS */
  Int padding;             /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
      alloclhs=decRoundOperand(lhs, set, status);
      if (alloclhs==NULL) break;
      lhs=alloclhs;
      }
      if (rhs->digits>reqdigits) {
      allocrhs=decRoundOperand(rhs, set, status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* note whether signs differ [used all paths] */
    diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);

    /* handle infinities and NaNs */
    if (SPECIALARGS) {              /* a special bit set */
      if (SPECIALARGS & (DECSNAN | DECNAN))  /* a NaN */
      decNaNs(res, lhs, rhs, set, status);
       else { /* one or two infinities */
      if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
        /* two infinities with different signs is invalid */
        if (decNumberIsInfinite(rhs) && diffsign) {
          *status|=DEC_Invalid_operation;
          break;
          }
        bits=lhs->bits & DECNEG;    /* get sign from LHS */
        }
       else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
      bits|=DECINF;
      decNumberZero(res);
      res->bits=bits;               /* set +/- infinity */
      } /* an infinity */
      break;
      }

    /* Quick exit for add 0s; return the non-0, modified as need be */
    if (ISZERO(lhs)) {
      Int adjust;             /* work */
      Int lexp=lhs->exponent;       /* save in case LHS==RES */
      bits=lhs->bits;               /* .. */
      residue=0;              /* clear accumulator */
      decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
      res->bits^=negate;            /* flip if rhs was negated */
      #if DECSUBSET
      if (set->extended) {          /* exponents on zeros count */
      #endif
      /* exponent will be the lower of the two */
      adjust=lexp-res->exponent;    /* adjustment needed [if -ve] */
      if (ISZERO(res)) {            /* both 0: special IEEE 854 rules */
        if (adjust<0) res->exponent=lexp;  /* set exponent */
        /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
        if (diffsign) {
          if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
           else res->bits=DECNEG;   /* preserve 0 sign */
          }
        }
       else { /* non-0 res */
        if (adjust<0) {     /* 0-padding needed */
          if ((res->digits-adjust)>set->digits) {
            adjust=res->digits-set->digits;       /* to fit exactly */
            *status|=DEC_Rounded;           /* [but exact] */
            }
          res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
          res->exponent+=adjust;            /* set the exponent. */
          }
        } /* non-0 res */
      #if DECSUBSET
      } /* extended */
      #endif
      decFinish(res, set, &residue, status);      /* clean and finalize */
      break;}

    if (ISZERO(rhs)) {              /* [lhs is non-zero] */
      Int adjust;             /* work */
      Int rexp=rhs->exponent;       /* save in case RHS==RES */
      bits=rhs->bits;               /* be clean */
      residue=0;              /* clear accumulator */
      decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
      #if DECSUBSET
      if (set->extended) {          /* exponents on zeros count */
      #endif
      /* exponent will be the lower of the two */
      /* [0-0 case handled above] */
      adjust=rexp-res->exponent;    /* adjustment needed [if -ve] */
      if (adjust<0) {       /* 0-padding needed */
        if ((res->digits-adjust)>set->digits) {
          adjust=res->digits-set->digits; /* to fit exactly */
          *status|=DEC_Rounded;           /* [but exact] */
          }
        res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
        res->exponent+=adjust;            /* set the exponent. */
        }
      #if DECSUBSET
      } /* extended */
      #endif
      decFinish(res, set, &residue, status);      /* clean and finalize */
      break;}

    /* [NB: both fastpath and mainpath code below assume these cases */
    /* (notably 0-0) have already been handled] */

    /* calculate the padding needed to align the operands */
    padding=rhs->exponent-lhs->exponent;

    /* Fastpath cases where the numbers are aligned and normal, the RHS */
    /* is all in one unit, no operand rounding is needed, and no carry, */
    /* lengthening, or borrow is needed */
    if (padding==0
      && rhs->digits<=DECDPUN
      && rhs->exponent>=set->emin   /* [some normals drop through] */
      && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
      && rhs->digits<=reqdigits
      && lhs->digits<=reqdigits) {
      Int partial=*lhs->lsu;
      if (!diffsign) {              /* adding */
      partial+=*rhs->lsu;
      if ((partial<=DECDPUNMAX)     /* result fits in unit */
       && (lhs->digits>=DECDPUN ||  /* .. and no digits-count change */
           partial<(Int)powers[lhs->digits])) { /* .. */
        if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
        *res->lsu=(Unit)partial;    /* [copy could have overwritten RHS] */
        break;
        }
      /* else drop out for careful add */
      }
       else {                       /* signs differ */
      partial-=*rhs->lsu;
      if (partial>0) { /* no borrow needed, and non-0 result */
        if (res!=lhs) decNumberCopy(res, lhs);  /* not in place */
        *res->lsu=(Unit)partial;
        /* this could have reduced digits [but result>0] */
        res->digits=decGetDigits(res->lsu, D2U(res->digits));
        break;
        }
      /* else drop out for careful subtract */
      }
      }

    /* Now align (pad) the lhs or rhs so they can be added or */
    /* subtracted, as necessary.  If one number is much larger than */
    /* the other (that is, if in plain form there is a least one */
    /* digit between the lowest digit of one and the highest of the */
    /* other) padding with up to DIGITS-1 trailing zeros may be */
    /* needed; then apply rounding (as exotic rounding modes may be */
    /* affected by the residue). */
    rhsshift=0;               /* rhs shift to left (padding) in Units */
    bits=lhs->bits;           /* assume sign is that of LHS */
    mult=1;             /* likely multiplier */

    /* [if padding==0 the operands are aligned; no padding is needed] */
    if (padding!=0) {
      /* some padding needed; always pad the RHS, as any required */
      /* padding can then be effected by a simple combination of */
      /* shifts and a multiply */
      Flag swapped=0;
      if (padding<0) {              /* LHS needs the padding */
      const decNumber *t;
      padding=-padding;       /* will be +ve */
      bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
      t=lhs; lhs=rhs; rhs=t;
      swapped=1;
      }

      /* If, after pad, rhs would be longer than lhs by digits+1 or */
      /* more then lhs cannot affect the answer, except as a residue, */
      /* so only need to pad up to a length of DIGITS+1. */
      if (rhs->digits+padding > lhs->digits+reqdigits+1) {
      /* The RHS is sufficient */
      /* for residue use the relative sign indication... */
      Int shift=reqdigits-rhs->digits;     /* left shift needed */
      residue=1;                   /* residue for rounding */
      if (diffsign) residue=-residue;          /* signs differ */
      /* copy, shortening if necessary */
      decCopyFit(res, rhs, set, &residue, status);
      /* if it was already shorter, then need to pad with zeros */
      if (shift>0) {
        res->digits=decShiftToMost(res->lsu, res->digits, shift);
        res->exponent-=shift;            /* adjust the exponent. */
        }
      /* flip the result sign if unswapped and rhs was negated */
      if (!swapped) res->bits^=negate;
      decFinish(res, set, &residue, status);      /* done */
      break;}

      /* LHS digits may affect result */
      rhsshift=D2U(padding+1)-1;    /* this much by Unit shift .. */
      mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
      } /* padding needed */

    if (diffsign) mult=-mult;       /* signs differ */

    /* determine the longer operand */
    maxdigits=rhs->digits+padding;  /* virtual length of RHS */
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;

    /* Decide on the result buffer to use; if possible place directly */
    /* into result. */
    acc=res->lsu;             /* assume add direct to result */
    /* If destructive overlap, or the number is too long, or a carry or */
    /* borrow to DIGITS+1 might be possible, a buffer must be used. */
    /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
    if ((maxdigits>=reqdigits)            /* is, or could be, too large */
     || (res==rhs && rhsshift>0)) { /* destructive overlap */
      /* buffer needed, choose it; units for maxdigits digits will be */
      /* needed, +1 Unit for carry or borrow */
      Int need=D2U(maxdigits)+1;
      acc=accbuff;                  /* assume use local buffer */
      if (need*sizeof(Unit)>sizeof(accbuff)) {
      /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
      allocacc=(Unit *)malloc(need*sizeof(Unit));
      if (allocacc==NULL) {         /* hopeless -- abandon */
        *status|=DEC_Insufficient_storage;
        break;}
      acc=allocacc;
      }
      }

    res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */
    res->exponent=lhs->exponent;    /* .. operands (even if aliased) */

    #if DECTRACE
      decDumpAr('A', lhs->lsu, D2U(lhs->digits));
      decDumpAr('B', rhs->lsu, D2U(rhs->digits));
      printf("    :h: %ld %ld\n", rhsshift, mult);
    #endif

    /* add [A+B*m] or subtract [A+B*(-m)] */
    res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
                        rhs->lsu, D2U(rhs->digits),
                        rhsshift, acc, mult)
             *DECDPUN;     /* [units -> digits] */
    if (res->digits<0) {         /* borrowed... */
      res->digits=-res->digits;
      res->bits^=DECNEG;         /* flip the sign */
      }
    #if DECTRACE
      decDumpAr('+', acc, D2U(res->digits));
    #endif

    /* If a buffer was used the result must be copied back, possibly */
    /* shortening.  (If no buffer was used then the result must have */
    /* fit, so can't need rounding and residue must be 0.) */
    residue=0;                   /* clear accumulator */
    if (acc!=res->lsu) {
      #if DECSUBSET
      if (set->extended) {       /* round from first significant digit */
      #endif
      /* remove leading zeros that were added due to rounding up to */
      /* integral Units -- before the test for rounding. */
      if (res->digits>reqdigits)
        res->digits=decGetDigits(acc, D2U(res->digits));
      decSetCoeff(res, set, acc, res->digits, &residue, status);
      #if DECSUBSET
      }
       else { /* subset arithmetic rounds from original significant digit */
      /* May have an underestimate.  This only occurs when both */
      /* numbers fit in DECDPUN digits and are padding with a */
      /* negative multiple (-10, -100...) and the top digit(s) become */
      /* 0.  (This only matters when using X3.274 rules where the */
      /* leading zero could be included in the rounding.) */
      if (res->digits<maxdigits) {
        *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
        res->digits=maxdigits;
        }
       else {
        /* remove leading zeros that added due to rounding up to */
        /* integral Units (but only those in excess of the original */
        /* maxdigits length, unless extended) before test for rounding. */
        if (res->digits>reqdigits) {
          res->digits=decGetDigits(acc, D2U(res->digits));
          if (res->digits<maxdigits) res->digits=maxdigits;
          }
        }
      decSetCoeff(res, set, acc, res->digits, &residue, status);
      /* Now apply rounding if needed before removing leading zeros. */
      /* This is safe because subnormals are not a possibility */
      if (residue!=0) {
        decApplyRound(res, set, residue, status);
        residue=0;                 /* did what needed to be done */
        }
      } /* subset */
      #endif
      } /* used buffer */

    /* strip leading zeros [these were left on in case of subset subtract] */
    res->digits=decGetDigits(res->lsu, D2U(res->digits));

    /* apply checks and rounding */
    decFinish(res, set, &residue, status);

    /* "When the sum of two operands with opposite signs is exactly */
    /* zero, the sign of that sum shall be '+' in all rounding modes */
    /* except round toward -Infinity, in which mode that sign shall be */
    /* '-'."  [Subset zeros also never have '-', set by decFinish.] */
    if (ISZERO(res) && diffsign
     #if DECSUBSET
     && set->extended
     #endif
     && (*status&DEC_Inexact)==0) {
      if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG;   /* sign - */
                          else res->bits&=~DECNEG;  /* sign + */
      }
    } while(0);                          /* end protected */

  if (allocacc!=NULL) free(allocacc);          /* drop any storage used */
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);          /* .. */
  if (alloclhs!=NULL) free(alloclhs);          /* .. */
  #endif
  return res;
  } /* decAddOp */

/* ------------------------------------------------------------------ */
/* decDivideOp -- division operation                              */
/*                                                    */
/*  This routine performs the calculations for all four division      */
/*  operators (divide, divideInteger, remainder, remainderNear).      */
/*                                                    */
/*  C=A op B                                                */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X/X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*   op      is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively.    */
/*   status is the usual accumulator                              */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* ------------------------------------------------------------------ */
/*   The underlying algorithm of this routine is the same as in the   */
/*   1981 S/370 implementation, that is, non-restoring long division  */
/*   with bi-unit (rather than bi-digit) estimation for each unit     */
/*   multiplier.  In this pseudocode overview, complications for the  */
/*   Remainder operators and division residues for exact rounding are */
/*   omitted for clarity.                                   */
/*                                                    */
/*     Prepare operands and handle special values                 */
/*     Test for x/0 and then 0/x                            */
/*     Exp =Exp1 - Exp2                                     */
/*     Exp =Exp +len(var1) -len(var2)                             */
/*     Sign=Sign1 * Sign2                                   */
/*     Pad accumulator (Var1) to double-length with 0's (pad1)          */
/*     Pad Var2 to same length as Var1                            */
/*     msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round  */
/*     have=0                                               */
/*     Do until (have=digits+1 OR residue=0)                      */
/*     if exp<0 then if integer divide/residue then leave         */
/*     this_unit=0                                          */
/*     Do forever                                     */
/*        compare numbers                                   */
/*        if <0 then leave inner_loop                             */
/*        if =0 then (* quick exit without subtract *) do         */
/*           this_unit=this_unit+1; output this_unit              */
/*           leave outer_loop; end                          */
/*        Compare lengths of numbers (mantissae):                 */
/*        If same then tops2=msu2pair -- {units 1&2 of var2}            */
/*              else tops2=msu2plus -- {0, unit 1 of var2}        */
/*        tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
/*        mult=tops1/tops2  -- Good and safe guess at divisor           */
/*        if mult=0 then mult=1                             */
/*        this_unit=this_unit+mult                          */
/*        subtract                                          */
/*        end inner_loop                                    */
/*      if have\=0 | this_unit\=0 then do                   */
/*        output this_unit                                  */
/*        have=have+1; end                                  */
/*      var2=var2/10                                        */
/*      exp=exp-1                                     */
/*      end outer_loop                                */
/*     exp=exp+1   -- set the proper exponent                     */
/*     if have=0 then generate answer=0                           */
/*     Return (Result is defined by Var1)                   */
/*                                                    */
/* ------------------------------------------------------------------ */
/* Two working buffers are needed during the division; one (digits+   */
/* 1) to accumulate the result, and the other (up to 2*digits+1) for  */
/* long subtractions.  These are acc and var1 respectively.       */
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
/* The static buffers may be larger than might be expected to allow   */
/* for calls from higher-level funtions (notable exp).                  */
/* ------------------------------------------------------------------ */
static decNumber * decDivideOp(decNumber *res,
                         const decNumber *lhs, const decNumber *rhs,
                         decContext *set, Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;      /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;      /* .., rhs */
  #endif
  Unit      accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
  Unit      *acc=accbuff;              /* -> accumulator array for result */
  Unit      *allocacc=NULL;            /* -> allocated buffer, iff allocated */
  Unit      *accnext;            /* -> where next digit will go */
  Int acclength;           /* length of acc needed [Units] */
  Int accunits;            /* count of units accumulated */
  Int accdigits;           /* count of digits accumulated */

  Unit      varbuff[SD2U(DECBUFFER*2+DECDPUN)*sizeof(Unit)]; /* buffer for var1 */
  Unit      *var1=varbuff;             /* -> var1 array for long subtraction */
  Unit      *varalloc=NULL;            /* -> allocated buffer, iff used */
  Unit      *msu1;                     /* -> msu of var1 */

  const Unit *var2;              /* -> var2 array */
  const Unit *msu2;              /* -> msu of var2 */
  Int msu2plus;            /* msu2 plus one [does not vary] */
  eInt      msu2pair;            /* msu2 pair plus one [does not vary] */

  Int var1units, var2units;      /* actual lengths */
  Int var2ulen;            /* logical length (units) */
  Int var1initpad=0;             /* var1 initial padding (digits) */
  Int maxdigits;           /* longest LHS or required acc length */
  Int mult;                /* multiplier for subtraction */
  Unit      thisunit;            /* current unit being accumulated */
  Int residue;             /* for rounding */
  Int reqdigits=set->digits;     /* requested DIGITS */
  Int exponent;            /* working exponent */
  Int maxexponent=0;             /* DIVIDE maximum exponent if unrounded */
  uByte bits;                    /* working sign */
  Unit      *target;             /* work */
  const Unit *source;            /* .. */
  uInt      const *pow;          /* .. */
  Int shift, cut;          /* .. */
  #if DECSUBSET
  Int dropped;             /* work */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
      alloclhs=decRoundOperand(lhs, set, status);
      if (alloclhs==NULL) break;
      lhs=alloclhs;
      }
      if (rhs->digits>reqdigits) {
      allocrhs=decRoundOperand(rhs, set, status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    bits=(lhs->bits^rhs->bits)&DECNEG;    /* assumed sign for divisions */

    /* handle infinities and NaNs */
    if (SPECIALARGS) {              /* a special bit set */
      if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
      decNaNs(res, lhs, rhs, set, status);
      break;
      }
      /* one or two infinities */
      if (decNumberIsInfinite(lhs)) {     /* LHS (dividend) is infinite */
      if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
          op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
        *status|=DEC_Invalid_operation;
        break;
        }
      /* [Note that infinity/0 raises no exceptions] */
      decNumberZero(res);
      res->bits=bits|DECINF;        /* set +/- infinity */
      break;
      }
       else {                       /* RHS (divisor) is infinite */
      residue=0;
      if (op&(REMAINDER|REMNEAR)) {
        /* result is [finished clone of] lhs */
        decCopyFit(res, lhs, set, &residue, status);
        }
       else {      /* a division */
        decNumberZero(res);
        res->bits=bits;       /* set +/- zero */
        /* for DIVIDEINT the exponent is always 0.  For DIVIDE, result */
        /* is a 0 with infinitely negative exponent, clamped to minimum */
        if (op&DIVIDE) {
          res->exponent=set->emin-set->digits+1;
          *status|=DEC_Clamped;
          }
        }
      decFinish(res, set, &residue, status);
      break;
      }
      }

    /* handle 0 rhs (x/0) */
    if (ISZERO(rhs)) {              /* x/0 is always exceptional */
      if (ISZERO(lhs)) {
      decNumberZero(res);           /* [after lhs test] */
      *status|=DEC_Division_undefined;/* 0/0 will become NaN */
      }
       else {
      decNumberZero(res);
      if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
       else {
        *status|=DEC_Division_by_zero; /* x/0 */
        res->bits=bits|DECINF;       /* .. is +/- Infinity */
        }
      }
      break;}

    /* handle 0 lhs (0/x) */
    if (ISZERO(lhs)) {              /* 0/x [x!=0] */
      #if DECSUBSET
      if (!set->extended) decNumberZero(res);
       else {
      #endif
      if (op&DIVIDE) {
        residue=0;
        exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
        decNumberCopy(res, lhs);    /* [zeros always fit] */
        res->bits=bits;       /* sign as computed */
        res->exponent=exponent;     /* exponent, too */
        decFinalize(res, set, &residue, status);   /* check exponent */
        }
       else if (op&DIVIDEINT) {
        decNumberZero(res);         /* integer 0 */
        res->bits=bits;       /* sign as computed */
        }
       else {                       /* a remainder */
        exponent=rhs->exponent;     /* [save in case overwrite] */
        decNumberCopy(res, lhs);    /* [zeros always fit] */
        if (exponent<res->exponent) res->exponent=exponent; /* use lower */
        }
      #if DECSUBSET
      }
      #endif
      break;}

    /* Precalculate exponent.  This starts off adjusted (and hence fits */
    /* in 31 bits) and becomes the usual unadjusted exponent as the */
    /* division proceeds.  The order of evaluation is important, here, */
    /* to avoid wrap. */
    exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);

    /* If the working exponent is -ve, then some quick exits are */
    /* possible because the quotient is known to be <1 */
    /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
    if (exponent<0 && !(op==DIVIDE)) {
      if (op&DIVIDEINT) {
      decNumberZero(res);                /* integer part is 0 */
      #if DECSUBSET
      if (set->extended)
      #endif
        res->bits=bits;            /* set +/- zero */
      break;}
      /* fastpath remainders so long as the lhs has the smaller */
      /* (or equal) exponent */
      if (lhs->exponent<=rhs->exponent) {
      if (op&REMAINDER || exponent<-1) {
        /* It is REMAINDER or safe REMNEAR; result is [finished */
        /* clone of] lhs  (r = x - 0*y) */
        residue=0;
        decCopyFit(res, lhs, set, &residue, status);
        decFinish(res, set, &residue, status);
        break;
        }
      /* [unsafe REMNEAR drops through] */
      }
      } /* fastpaths */

    /* Long (slow) division is needed; roll up the sleeves... */

    /* The accumulator will hold the quotient of the division. */
    /* If it needs to be too long for stack storage, then allocate. */
    acclength=D2U(reqdigits+DECDPUN);     /* in Units */
    if (acclength*sizeof(Unit)>sizeof(accbuff)) {
      /* printf("malloc dvacc %ld units\n", acclength); */
      allocacc=(Unit *)malloc(acclength*sizeof(Unit));
      if (allocacc==NULL) {         /* hopeless -- abandon */
      *status|=DEC_Insufficient_storage;
      break;}
      acc=allocacc;                 /* use the allocated space */
      }

    /* var1 is the padded LHS ready for subtractions. */
    /* If it needs to be too long for stack storage, then allocate. */
    /* The maximum units needed for var1 (long subtraction) is: */
    /* Enough for */
    /*         (rhs->digits+reqdigits-1) -- to allow full slide to right */
    /* or  (lhs->digits)           -- to allow for long lhs */
    /* whichever is larger */
    /*       +1            -- for rounding of slide to right */
    /*       +1            -- for leading 0s */
    /*       +1            -- for pre-adjust if a remainder or DIVIDEINT */
    /* [Note: unused units do not participate in decUnitAddSub data] */
    maxdigits=rhs->digits+reqdigits-1;
    if (lhs->digits>maxdigits) maxdigits=lhs->digits;
    var1units=D2U(maxdigits)+2;
    /* allocate a guard unit above msu1 for REMAINDERNEAR */
    if (!(op&DIVIDE)) var1units++;
    if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
      /* printf("malloc dvvar %ld units\n", var1units+1); */
      varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
      if (varalloc==NULL) {         /* hopeless -- abandon */
      *status|=DEC_Insufficient_storage;
      break;}
      var1=varalloc;                /* use the allocated space */
      }

    /* Extend the lhs and rhs to full long subtraction length.    The lhs */
    /* is truly extended into the var1 buffer, with 0 padding, so a */
    /* subtract in place is always possible.  The rhs (var2) has */
    /* virtual padding (implemented by decUnitAddSub). */
    /* One guard unit was allocated above msu1 for rem=rem+rem in */
    /* REMAINDERNEAR. */
    msu1=var1+var1units-1;          /* msu of var1 */
    source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
    for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
    for (; target>=var1; target--) *target=0;

    /* rhs (var2) is left-aligned with var1 at the start */
    var2ulen=var1units;             /* rhs logical length (units) */
    var2units=D2U(rhs->digits);           /* rhs actual length (units) */
    var2=rhs->lsu;                  /* -> rhs array */
    msu2=var2+var2units-1;          /* -> msu of var2 [never changes] */
    /* now set up the variables which will be used for estimating the */
    /* multiplication factor.  If these variables are not exact, add */
    /* 1 to make sure that the multiplier is never overestimated. */
    msu2plus=*msu2;                 /* it's value .. */
    if (var2units>1) msu2plus++;    /* .. +1 if any more */
    msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
    if (var2units>1) {              /* .. [else treat 2nd as 0] */
      msu2pair+=*(msu2-1);          /* .. */
      if (var2units>2) msu2pair++;  /* .. +1 if any more */
      }

    /* The calculation is working in units, which may have leading zeros, */
    /* but the exponent was calculated on the assumption that they are */
    /* both left-aligned.  Adjust the exponent to compensate: add the */
    /* number of leading zeros in var1 msu and subtract those in var2 msu. */
    /* [This is actually done by counting the digits and negating, as */
    /* lead1=DECDPUN-digits1, and similarly for lead2.] */
    for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
    for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;

    /* Now, if doing an integer divide or remainder, ensure that */
    /* the result will be Unit-aligned.    To do this, shift the var1 */
    /* accumulator towards least if need be.  (It's much easier to */
    /* do this now than to reassemble the residue afterwards, if */
    /* doing a remainder.)  Also ensure the exponent is not negative. */
    if (!(op&DIVIDE)) {
      Unit *u;                      /* work */
      /* save the initial 'false' padding of var1, in digits */
      var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
      /* Determine the shift to do. */
      if (exponent<0) cut=-exponent;
       else cut=DECDPUN-exponent%DECDPUN;
      decShiftToLeast(var1, var1units, cut);
      exponent+=cut;                /* maintain numerical value */
      var1initpad-=cut;             /* .. and reduce padding */
      /* clean any most-significant units which were just emptied */
      for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
      } /* align */
     else { /* is DIVIDE */
      maxexponent=lhs->exponent-rhs->exponent;    /* save */
      /* optimization: if the first iteration will just produce 0, */
      /* preadjust to skip it [valid for DIVIDE only] */
      if (*msu1<*msu2) {
      var2ulen--;             /* shift down */
      exponent-=DECDPUN;            /* update the exponent */
      }
      }

    /* ---- start the long-division loops ------------------------------ */
    accunits=0;                     /* no units accumulated yet */
    accdigits=0;              /* .. or digits */
    accnext=acc+acclength-1;        /* -> msu of acc [NB: allows digits+1] */
    for (;;) {                      /* outer forever loop */
      thisunit=0;             /* current unit assumed 0 */
      /* find the next unit */
      for (;;) {              /* inner forever loop */
      /* strip leading zero units [from either pre-adjust or from */
      /* subtract last time around].      Leave at least one unit. */
      for (; *msu1==0 && msu1>var1; msu1--) var1units--;

      if (var1units<var2ulen) break;           /* var1 too low for subtract */
      if (var1units==var2ulen) {         /* unit-by-unit compare needed */
        /* compare the two numbers, from msu */
        const Unit *pv1, *pv2;
        Unit v2;                   /* units to compare */
        pv2=msu2;                  /* -> msu */
        for (pv1=msu1; ; pv1--, pv2--) {
          /* v1=*pv1 -- always OK */
          v2=0;                    /* assume in padding */
          if (pv2>=var2) v2=*pv2;        /* in range */
          if (*pv1!=v2) break;           /* no longer the same */
          if (pv1==var1) break;          /* done; leave pv1 as is */
          }
        /* here when all inspected or a difference seen */
        if (*pv1<v2) break;              /* var1 too low to subtract */
        if (*pv1==v2) {            /* var1 == var2 */
          /* reach here if var1 and var2 are identical; subtraction */
          /* would increase digit by one, and the residue will be 0 so */
          /* the calculation is done; leave the loop with residue=0. */
          thisunit++;                    /* as though subtracted */
          *var1=0;                       /* set var1 to 0 */
          var1units=1;             /* .. */
          break;  /* from inner */
          } /* var1 == var2 */
        /* *pv1>v2.  Prepare for real subtraction; the lengths are equal */
        /* Estimate the multiplier (there's always a msu1-1)... */
        /* Bring in two units of var2 to provide a good estimate. */
        mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
        } /* lengths the same */
       else { /* var1units > var2ulen, so subtraction is safe */
        /* The var2 msu is one unit towards the lsu of the var1 msu, */
        /* so only one unit for var2 can be used. */
        mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
        }
      if (mult==0) mult=1;               /* must always be at least 1 */
      /* subtraction needed; var1 is > var2 */
      thisunit=(Unit)(thisunit+mult);          /* accumulate */
      /* subtract var1-var2, into var1; only the overlap needs */
      /* processing, as this is an in-place calculation */
      shift=var2ulen-var2units;
      #if DECTRACE
        decDumpAr('1', &var1[shift], var1units-shift);
        decDumpAr('2', var2, var2units);
        printf("m=%ld\n", -mult);
      #endif
      decUnitAddSub(&var1[shift], var1units-shift,
                  var2, var2units, 0,
                  &var1[shift], -mult);
      #if DECTRACE
        decDumpAr('#', &var1[shift], var1units-shift);
      #endif
      /* var1 now probably has leading zeros; these are removed at the */
      /* top of the inner loop. */
      } /* inner loop */

      /* The next unit has been calculated in full; unless it's a */
      /* leading zero, add to acc */
      if (accunits!=0 || thisunit!=0) {        /* is first or non-zero */
      *accnext=thisunit;                 /* store in accumulator */
      /* account exactly for the new digits */
      if (accunits==0) {
        accdigits++;                     /* at least one */
        for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
        }
       else accdigits+=DECDPUN;
      accunits++;                  /* update count */
      accnext--;                   /* ready for next */
      if (accdigits>reqdigits) break;          /* have enough digits */
      }

      /* if the residue is zero, the operation is done (unless divide */
      /* or divideInteger and still not enough digits yet) */
      if (*var1==0 && var1units==1) {          /* residue is 0 */
      if (op&(REMAINDER|REMNEAR)) break;
      if ((op&DIVIDE) && (exponent<=maxexponent)) break;
      /* [drop through if divideInteger] */
      }
      /* also done enough if calculating remainder or integer */
      /* divide and just did the last ('units') unit */
      if (exponent==0 && !(op&DIVIDE)) break;

      /* to get here, var1 is less than var2, so divide var2 by the per- */
      /* Unit power of ten and go for the next digit */
      var2ulen--;                  /* shift down */
      exponent-=DECDPUN;                 /* update the exponent */
      } /* outer loop */

    /* ---- division is complete --------------------------------------- */
    /* here: acc      has at least reqdigits+1 of good results (or fewer */
    /*                  if early stop), starting at accnext+1 (its lsu) */
    /*           var1     has any residue at the stopping point */
    /*           accunits is the number of digits collected in acc */
    if (accunits==0) {           /* acc is 0 */
      accunits=1;          /* show have a unit .. */
      accdigits=1;               /* .. */
      *accnext=0;          /* .. whose value is 0 */
      }
     else accnext++;             /* back to last placed */
    /* accnext now -> lowest unit of result */

    residue=0;                   /* assume no residue */
    if (op&DIVIDE) {
      /* record the presence of any residue, for rounding */
      if (*var1!=0 || var1units>1) residue=1;
       else { /* no residue */
      /* Had an exact division; clean up spurious trailing 0s. */
      /* There will be at most DECDPUN-1, from the final multiply, */
      /* and then only if the result is non-0 (and even) and the */
      /* exponent is 'loose'. */
      #if DECDPUN>1
      Unit lsu=*accnext;
      if (!(lsu&0x01) && (lsu!=0)) {
        /* count the trailing zeros */
        Int drop=0;
        for (;; drop++) {    /* [will terminate because lsu!=0] */
          if (exponent>=maxexponent) break;       /* don't chop real 0s */
          #if DECDPUN<=4
            if ((lsu-QUOT10(lsu, drop+1)
              *powers[drop+1])!=0) break;   /* found non-0 digit */
          #else
            if (lsu%powers[drop+1]!=0) break;     /* found non-0 digit */
          #endif
          exponent++;
          }
        if (drop>0) {
          accunits=decShiftToLeast(accnext, accunits, drop);
          accdigits=decGetDigits(accnext, accunits);
          accunits=D2U(accdigits);
          /* [exponent was adjusted in the loop] */
          }
        } /* neither odd nor 0 */
      #endif
      } /* exact divide */
      } /* divide */
     else /* op!=DIVIDE */ {
      /* check for coefficient overflow */
      if (accdigits+exponent>reqdigits) {
      *status|=DEC_Division_impossible;
      break;
      }
      if (op & (REMAINDER|REMNEAR)) {
      /* [Here, the exponent will be 0, because var1 was adjusted */
      /* appropriately.] */
      Int postshift;                     /* work */
      Flag wasodd=0;                     /* integer was odd */
      Unit *quotlsu;                     /* for save */
      Int  quotdigits;             /* .. */

      bits=lhs->bits;                    /* remainder sign is always as lhs */

      /* Fastpath when residue is truly 0 is worthwhile [and */
      /* simplifies the code below] */
      if (*var1==0 && var1units==1) {          /* residue is 0 */
        Int exp=lhs->exponent;           /* save min(exponents) */
        if (rhs->exponent<exp) exp=rhs->exponent;
        decNumberZero(res);              /* 0 coefficient */
        #if DECSUBSET
        if (set->extended)
        #endif
        res->exponent=exp;               /* .. with proper exponent */
        res->bits=(uByte)(bits&DECNEG);      /* [cleaned] */
        decFinish(res, set, &residue, status);   /* might clamp */
        break;
        }
      /* note if the quotient was odd */
      if (*accnext & 0x01) wasodd=1;           /* acc is odd */
      quotlsu=accnext;             /* save in case need to reinspect */
      quotdigits=accdigits;              /* .. */

      /* treat the residue, in var1, as the value to return, via acc */
      /* calculate the unused zero digits.  This is the smaller of: */
      /*   var1 initial padding (saved above) */
      /*   var2 residual padding, which happens to be given by: */
      postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
      /* [the 'exponent' term accounts for the shifts during divide] */
      if (var1initpad<postshift) postshift=var1initpad;

      /* shift var1 the requested amount, and adjust its digits */
      var1units=decShiftToLeast(var1, var1units, postshift);
      accnext=var1;
      accdigits=decGetDigits(var1, var1units);
      accunits=D2U(accdigits);

      exponent=lhs->exponent;       /* exponent is smaller of lhs & rhs */
      if (rhs->exponent<exponent) exponent=rhs->exponent;

      /* Now correct the result if doing remainderNear; if it */
      /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
      /* the integer was odd then the result should be rem-rhs. */
      if (op&REMNEAR) {
        Int compare, tarunits;      /* work */
        Unit *up;             /* .. */
        /* calculate remainder*2 into the var1 buffer (which has */
        /* 'headroom' of an extra unit and hence enough space) */
        /* [a dedicated 'double' loop would be faster, here] */
        tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
                         0, accnext, 1);
        /* decDumpAr('r', accnext, tarunits); */

        /* Here, accnext (var1) holds tarunits Units with twice the */
        /* remainder's coefficient, which must now be compared to the */
        /* RHS.  The remainder's exponent may be smaller than the RHS's. */
        compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
                         rhs->exponent-exponent);
        if (compare==BADINT) {           /* deep trouble */
          *status|=DEC_Insufficient_storage;
          break;}

        /* now restore the remainder by dividing by two; the lsu */
        /* is known to be even. */
        for (up=accnext; up<accnext+tarunits; up++) {
          Int half;              /* half to add to lower unit */
          half=*up & 0x01;
          *up/=2;          /* [shift] */
          if (!half) continue;
          *(up-1)+=(DECDPUNMAX+1)/2;
          }
        /* [accunits still describes the original remainder length] */

        if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
          Int exp, expunits, exprem;           /* work */
          /* This is effectively causing round-up of the quotient, */
          /* so if it was the rare case where it was full and all */
          /* nines, it would overflow and hence division-impossible */
          /* should be raised */
          Flag allnines=0;               /* 1 if quotient all nines */
          if (quotdigits==reqdigits) {     /* could be borderline */
            for (up=quotlsu; ; up++) {
            if (quotdigits>DECDPUN) {
              if (*up!=DECDPUNMAX) break;/* non-nines */
              }
             else {                      /* this is the last Unit */
              if (*up==powers[quotdigits]-1) allnines=1;
              break;
              }
            quotdigits-=DECDPUN;         /* checked those digits */
            } /* up */
            } /* borderline check */
          if (allnines) {
            *status|=DEC_Division_impossible;
            break;}

          /* rem-rhs is needed; the sign will invert.  Again, var1 */
          /* can safely be used for the working Units array. */
          exp=rhs->exponent-exponent;          /* RHS padding needed */
          /* Calculate units and remainder from exponent. */
          expunits=exp/DECDPUN;
          exprem=exp%DECDPUN;
          /* subtract [A+B*(-m)]; the result will always be negative */
          accunits=-decUnitAddSub(accnext, accunits,
                            rhs->lsu, D2U(rhs->digits),
                            expunits, accnext, -(Int)powers[exprem]);
          accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
          accunits=D2U(accdigits);  /* and recalculate the units for copy */
          /* [exponent is as for original remainder] */
          bits^=DECNEG;       /* flip the sign */
          }
        } /* REMNEAR */
      } /* REMAINDER or REMNEAR */
      } /* not DIVIDE */

    /* Set exponent and bits */
    res->exponent=exponent;
    res->bits=(uByte)(bits&DECNEG);      /* [cleaned] */

    /* Now the coefficient. */
    decSetCoeff(res, set, accnext, accdigits, &residue, status);

    decFinish(res, set, &residue, status);   /* final cleanup */

    #if DECSUBSET
    /* If a divide then strip trailing zeros if subset [after round] */
    if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, &dropped);
    #endif
    } while(0);                          /* end protected */

  if (varalloc!=NULL) free(varalloc);     /* drop any storage used */
  if (allocacc!=NULL) free(allocacc);     /* .. */
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);     /* .. */
  if (alloclhs!=NULL) free(alloclhs);     /* .. */
  #endif
  return res;
  } /* decDivideOp */

/* ------------------------------------------------------------------ */
/* decMultiplyOp -- multiplication operation                      */
/*                                                    */
/*  This routine performs the multiplication C=A x B.             */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X*X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*   status is the usual accumulator                              */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* ------------------------------------------------------------------ */
/* 'Classic' multiplication is used rather than Karatsuba, as the     */
/* latter would give only a minor improvement for the short numbers   */
/* expected to be handled most (and uses much more memory).       */
/*                                                    */
/* There are two major paths here: the general-purpose ('old code')   */
/* path which handles all DECDPUN values, and a fastpath version      */
/* which is used if 64-bit ints are available, DECDPUN<=4, and more   */
/* than two calls to decUnitAddSub would be made.                 */
/*                                                    */
/* The fastpath version lumps units together into 8-digit or 9-digit  */
/* chunks, and also uses a lazy carry strategy to minimise expensive  */
/* 64-bit divisions.  The chunks are then broken apart again into     */
/* units for continuing processing.  Despite this overhead, the         */
/* fastpath can speed up some 16-digit operations by 10x (and much    */
/* more for higher-precision calculations).                       */
/*                                                    */
/* A buffer always has to be used for the accumulator; in the           */
/* fastpath, buffers are also always needed for the chunked copies of */
/* of the operand coefficients.                                   */
/* Static buffers are larger than needed just for multiply, to allow  */
/* for calls from other operations (notably exp).                 */
/* ------------------------------------------------------------------ */
#define FASTMUL (DECUSE64 && DECDPUN<5)
static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set,
                         uInt *status) {
  Int  accunits;           /* Units of accumulator in use */
  Int  exponent;           /* work */
  Int  residue=0;          /* rounding residue */
  uByte      bits;                     /* result sign */
  Unit      *acc;                /* -> accumulator Unit array */
  Int  needbytes;          /* size calculator */
  void      *allocacc=NULL;            /* -> allocated accumulator, iff allocated */
  Unit      accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
                           /* *4 for calls from other operations) */
  const Unit *mer, *mermsup;     /* work */
  Int madlength;           /* Units in multiplicand */
  Int shift;                     /* Units to shift multiplicand by */

  #if FASTMUL
    /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
    /* (DECDPUN is 2 or 4) then work in base 10**8 */
    #if DECDPUN & 1              /* odd */
      #define FASTBASE 1000000000  /* base */
      #define FASTDIGS        9  /* digits in base */
      #define FASTLAZY         18  /* carry resolution point [1->18] */
    #else
      #define FASTBASE  100000000
      #define FASTDIGS        8
      #define FASTLAZY       1844  /* carry resolution point [1->1844] */
    #endif
    /* three buffers are used, two for chunked copies of the operands */
    /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
    /* lazy carry evaluation */
    uInt   zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
    uInt  *zlhi=zlhibuff;             /* -> lhs array */
    uInt  *alloclhi=NULL;             /* -> allocated buffer, iff allocated */
    uInt   zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
    uInt  *zrhi=zrhibuff;             /* -> rhs array */
    uInt  *allocrhi=NULL;             /* -> allocated buffer, iff allocated */
    uLong  zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
    /* [allocacc is shared for both paths, as only one will run] */
    uLong *zacc=zaccbuff;        /* -> accumulator array for exact result */
    #if DECDPUN==1
    Int        zoff;             /* accumulator offset */
    #endif
    uInt  *lip, *rip;            /* item pointers */
    uInt  *lmsi, *rmsi;          /* most significant items */
    Int        ilhs, irhs, iacc;       /* item counts in the arrays */
    Int        lazy;             /* lazy carry counter */
    uLong  lcarry;               /* uLong carry */
    uInt   carry;          /* carry (NB not uLong) */
    Int        count;            /* work */
    const  Unit *cup;            /* .. */
    Unit  *up;                   /* .. */
    uLong *lp;                   /* .. */
    Int        p;                /* .. */
  #endif

  #if DECSUBSET
    decNumber *alloclhs=NULL;    /* -> allocated buffer, iff allocated */
    decNumber *allocrhs=NULL;    /* -> allocated buffer, iff allocated */
  #endif

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  /* precalculate result sign */
  bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);

  /* handle infinities and NaNs */
  if (SPECIALARGS) {             /* a special bit set */
    if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
      decNaNs(res, lhs, rhs, set, status);
      return res;}
    /* one or two infinities; Infinity * 0 is invalid */
    if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
      ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
      *status|=DEC_Invalid_operation;
      return res;}
    decNumberZero(res);
    res->bits=bits|DECINF;       /* infinity */
    return res;}

  /* For best speed, as in DMSRCN [the original Rexx numerics */
  /* module], use the shorter number as the multiplier (rhs) and */
  /* the longer as the multiplicand (lhs) to minimise the number of */
  /* adds (partial products) */
  if (lhs->digits<rhs->digits) {   /* swap... */
    const decNumber *hold=lhs;
    lhs=rhs;
    rhs=hold;
    }

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>set->digits) {
      alloclhs=decRoundOperand(lhs, set, status);
      if (alloclhs==NULL) break;
      lhs=alloclhs;
      }
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    #if FASTMUL                  /* fastpath can be used */
    /* use the fast path if there are enough digits in the shorter */
    /* operand to make the setup and takedown worthwhile */
    #define NEEDTWO (DECDPUN*2)        /* within two decUnitAddSub calls */
    if (rhs->digits>NEEDTWO) {         /* use fastpath... */
      /* calculate the number of elements in each array */
      ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
      irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
      iacc=ilhs+irhs;

      /* allocate buffers if required, as usual */
      needbytes=ilhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zlhibuff)) {
      alloclhi=(uInt *)malloc(needbytes);
      zlhi=alloclhi;}
      needbytes=irhs*sizeof(uInt);
      if (needbytes>(Int)sizeof(zrhibuff)) {
      allocrhi=(uInt *)malloc(needbytes);
      zrhi=allocrhi;}

      /* Allocating the accumulator space needs a special case when */
      /* DECDPUN=1 because when converting the accumulator to Units */
      /* after the multiplication each 8-byte item becomes 9 1-byte */
      /* units.    Therefore iacc extra bytes are needed at the front */
      /* (rounded up to a multiple of 8 bytes), and the uLong */
      /* accumulator starts offset the appropriate number of units */
      /* to the right to avoid overwrite during the unchunking. */
      needbytes=iacc*sizeof(uLong);
      #if DECDPUN==1
      zoff=(iacc+7)/8;        /* items to offset by */
      needbytes+=zoff*8;
      #endif
      if (needbytes>(Int)sizeof(zaccbuff)) {
      allocacc=(uLong *)malloc(needbytes);
      zacc=(uLong *)allocacc;}
      if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
      *status|=DEC_Insufficient_storage;
      break;}

      acc=(Unit *)zacc;       /* -> target Unit array */
      #if DECDPUN==1
      zacc+=zoff;       /* start uLong accumulator to right */
      #endif

      /* assemble the chunked copies of the left and right sides */
      for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
      for (p=0, *lip=0; p<FASTDIGS && count>0;
           p+=DECDPUN, cup++, count-=DECDPUN)
        *lip+=*cup*powers[p];
      lmsi=lip-1;     /* save -> msi */
      for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
      for (p=0, *rip=0; p<FASTDIGS && count>0;
           p+=DECDPUN, cup++, count-=DECDPUN)
        *rip+=*cup*powers[p];
      rmsi=rip-1;     /* save -> msi */

      /* zero the accumulator */
      for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;

      /* Start the multiplication */
      /* Resolving carries can dominate the cost of accumulating the */
      /* partial products, so this is only done when necessary. */
      /* Each uLong item in the accumulator can hold values up to */
      /* 2**64-1, and each partial product can be as large as */
      /* (10**FASTDIGS-1)**2.  When FASTDIGS=9, this can be added to */
      /* itself 18.4 times in a uLong without overflowing, so during */
      /* the main calculation resolution is carried out every 18th */
      /* add -- every 162 digits.  Similarly, when FASTDIGS=8, the */
      /* partial products can be added to themselves 1844.6 times in */
      /* a uLong without overflowing, so intermediate carry */
      /* resolution occurs only every 14752 digits.  Hence for common */
      /* short numbers usually only the one final carry resolution */
      /* occurs. */
      /* (The count is set via FASTLAZY to simplify experiments to */
      /* measure the value of this approach: a 35% improvement on a */
      /* [34x34] multiply.) */
      lazy=FASTLAZY;                     /* carry delay count */
      for (rip=zrhi; rip<=rmsi; rip++) {     /* over each item in rhs */
      lp=zacc+(rip-zrhi);                /* where to add the lhs */
      for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
        *lp+=(uLong)(*lip)*(*rip);       /* [this should in-line] */
        } /* lip loop */
      lazy--;
      if (lazy>0 && rip!=rmsi) continue;
      lazy=FASTLAZY;                     /* reset delay count */
      /* spin up the accumulator resolving overflows */
      for (lp=zacc; lp<zacc+iacc; lp++) {
        if (*lp<FASTBASE) continue;      /* it fits */
        lcarry=*lp/FASTBASE;             /* top part [slow divide] */
        /* lcarry can exceed 2**32-1, so check again; this check */
        /* and occasional extra divide (slow) is well worth it, as */
        /* it allows FASTLAZY to be increased to 18 rather than 4 */
        /* in the FASTDIGS=9 case */
        if (lcarry<FASTBASE) carry=(uInt)lcarry;  /* [usual] */
         else { /* two-place carry [fairly rare] */
          uInt carry2=(uInt)(lcarry/FASTBASE);    /* top top part */
          *(lp+2)+=carry2;                    /* add to item+2 */
          *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
          carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
          }
        *(lp+1)+=carry;            /* add to item above [inline] */
        *lp-=((uLong)FASTBASE*carry);          /* [inline] */
        } /* carry resolution */
      } /* rip loop */

      /* The multiplication is complete; time to convert back into */
      /* units.    This can be done in-place in the accumulator and in */
      /* 32-bit operations, because carries were resolved after the */
      /* final add.  This needs N-1 divides and multiplies for */
      /* each item in the accumulator (which will become up to N */
      /* units, where 2<=N<=9). */
      for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
      uInt item=(uInt)*lp;               /* decapitate to uInt */
      for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
        uInt part=item/(DECDPUNMAX+1);
        *up=(Unit)(item-(part*(DECDPUNMAX+1)));
        item=part;
        } /* p */
      *up=(Unit)item; up++;              /* [final needs no division] */
      } /* lp */
      accunits=up-acc;                   /* count of units */
      }
     else { /* here to use units directly, without chunking ['old code'] */
    #endif

      /* if accumulator will be too long for local storage, then allocate */
      acc=accbuff;               /* -> assume buffer for accumulator */
      needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
      if (needbytes>(Int)sizeof(accbuff)) {
      allocacc=(Unit *)malloc(needbytes);
      if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
      acc=(Unit *)allocacc;              /* use the allocated space */
      }

      /* Now the main long multiplication loop */
      /* Unlike the equivalent in the IBM Java implementation, there */
      /* is no advantage in calculating from msu to lsu.  So, do it */
      /* by the book, as it were. */
      /* Each iteration calculates ACC=ACC+MULTAND*MULT */
      accunits=1;          /* accumulator starts at '0' */
      *acc=0;                    /* .. (lsu=0) */
      shift=0;                   /* no multiplicand shift at first */
      madlength=D2U(lhs->digits);  /* this won't change */
      mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */

      for (mer=rhs->lsu; mer<mermsup; mer++) {
      /* Here, *mer is the next Unit in the multiplier to use */
      /* If non-zero [optimization] add it... */
      if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
                                  lhs->lsu, madlength, 0,
                                  &acc[shift], *mer)
                                  + shift;
       else { /* extend acc with a 0; it will be used shortly */
        *(acc+accunits)=0;       /* [this avoids length of <=0 later] */
        accunits++;
        }
      /* multiply multiplicand by 10**DECDPUN for next Unit to left */
      shift++;             /* add this for 'logical length' */
      } /* n */
    #if FASTMUL
      } /* unchunked units */
    #endif
    /* common end-path */
    #if DECTRACE
      decDumpAr('*', acc, accunits);           /* Show exact result */
    #endif

    /* acc now contains the exact result of the multiplication, */
    /* possibly with a leading zero unit; build the decNumber from */
    /* it, noting if any residue */
    res->bits=bits;                      /* set sign */
    res->digits=decGetDigits(acc, accunits); /* count digits exactly */

    /* There can be a 31-bit wrap in calculating the exponent. */
    /* This can only happen if both input exponents are negative and */
    /* both their magnitudes are large.    If there was a wrap, set a */
    /* safe very negative exponent, from which decFinalize() will */
    /* raise a hard underflow shortly. */
    exponent=lhs->exponent+rhs->exponent;    /* calculate exponent */
    if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
      exponent=-2*DECNUMMAXE;            /* force underflow */
    res->exponent=exponent;              /* OK to overwrite now */


    /* Set the coefficient.  If any rounding, residue records */
    decSetCoeff(res, set, acc, res->digits, &residue, status);
    decFinish(res, set, &residue, status);   /* final cleanup */
    } while(0);                     /* end protected */

  if (allocacc!=NULL) free(allocacc);     /* drop any storage used */
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);     /* .. */
  if (alloclhs!=NULL) free(alloclhs);     /* .. */
  #endif
  #if FASTMUL
  if (allocrhi!=NULL) free(allocrhi);     /* .. */
  if (alloclhi!=NULL) free(alloclhi);     /* .. */
  #endif
  return res;
  } /* decMultiplyOp */

/* ------------------------------------------------------------------ */
/* decExpOp -- effect exponentiation                              */
/*                                                    */
/*   This computes C = exp(A)                               */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits. status is updated but    */
/* not set.                                           */
/*                                                    */
/* Restrictions:                                      */
/*                                                    */
/*   digits, emax, and -emin in the context must be less than           */
/*   2*DEC_MAX_MATH (1999998), and the rhs must be within these         */
/*   bounds or a zero.  This is an internal routine, so these           */
/*   restrictions are contractual and not enforced.               */
/*                                                    */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/*                                                    */
/* Finite results will always be full precision and Inexact, except   */
/* when A is a zero or -Infinity (giving 1 or 0 respectively).          */
/* ------------------------------------------------------------------ */
/* This approach used here is similar to the algorithm described in   */
/*                                                    */
/*   Variable Precision Exponential Function, T. E. Hull and            */
/*   A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
/*   pp79-91, ACM, June 1986.                               */
/*                                                    */
/* with the main difference being that the iterations in the series   */
/* evaluation are terminated dynamically (which does not require the  */
/* extra variable-precision variables which are expensive in this     */
/* context).                                                */
/*                                                    */
/* The error analysis in Hull & Abrham's paper applies except for the */
/* round-off error accumulation during the series evaluation.  This   */
/* code does not precalculate the number of iterations and so cannot  */
/* use Horner's scheme.  Instead, the accumulation is done at double- */
/* precision, which ensures that the additions of the terms are exact */
/* and do not accumulate round-off (and any round-off errors in the   */
/* terms themselves move 'to the right' faster than they can            */
/* accumulate).    This code also extends the calculation by allowing,  */
/* in the spirit of other decNumber operators, the input to be more   */
/* precise than the result (the precision used is based on the more   */
/* precise of the input or requested result).                     */
/*                                                    */
/* Implementation notes:                                    */
/*                                                    */
/* 1. This is separated out as decExpOp so it can be called from      */
/*    other Mathematical functions (notably Ln) with a wider range    */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (double) range needed by Ln (which has to be able to calculate  */
/*    exp(-x) where x can be the tiniest number (Ntiny).          */
/*                                                    */
/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop           */
/*    iterations by appoximately a third with additional (although    */
/*    diminishing) returns as the range is reduced to even smaller    */
/*    fractions.  However, h (the power of 10 used to correct the     */
/*    result at the end, see below) must be kept <=8 as otherwise     */
/*    the final result cannot be computed.  Hence the leverage is a   */
/*    sliding value (8-h), where potentially the range is reduced     */
/*    more for smaller values.                                    */
/*                                                    */
/*    The leverage that can be applied in this way is severely          */
/*    limited by the cost of the raise-to-the power at the end,         */
/*    which dominates when the number of iterations is small (less    */
/*    than ten) or when rhs is short.  As an example, the adjustment  */
/*    x**10,000,000 needs 31 multiplications, all but one full-width. */
/*                                                    */
/* 3. The restrictions (especially precision) could be raised with    */
/*    care, but the full decNumber range seems very hard within the   */
/*    32-bit limits.                                        */
/*                                                    */
/* 4. The working precisions for the static buffers are twice the     */
/*    obvious size to allow for calls from decNumberPower.        */
/* ------------------------------------------------------------------ */
decNumber * decExpOp(decNumber *res, const decNumber *rhs,
                   decContext *set, uInt *status) {
  uInt ignore=0;           /* working status */
  Int h;                   /* adjusted exponent for 0.xxxx */
  Int p;                   /* working precision */
  Int residue;                   /* rounding residue */
  uInt needbytes;          /* for space calculations */
  const decNumber *x=rhs;        /* (may point to safe copy later) */
  decContext aset, tset, dset;         /* working contexts */
  Int comp;                /* work */

  /* the argument is often copied to normalize it, so (unusually) it */
  /* is treated like other buffers, using DECBUFFER, +1 in case */
  /* DECBUFFER is 0 */
  decNumber bufr[D2N(DECBUFFER*2+1)];
  decNumber *allocrhs=NULL;      /* non-NULL if rhs buffer allocated */

  /* the working precision will be no more than set->digits+8+1 */
  /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
  /* is 0 (and twice that for the accumulator) */

  /* buffer for t, term (working precision plus) */
  decNumber buft[D2N(DECBUFFER*2+9+1)];
  decNumber *allocbuft=NULL;     /* -> allocated buft, iff allocated */
  decNumber *t=buft;             /* term */
  /* buffer for a, accumulator (working precision * 2), at least 9 */
  decNumber bufa[D2N(DECBUFFER*4+18+1)];
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;             /* accumulator */
  /* decNumber for the divisor term; this needs at most 9 digits */
  /* and so can be fixed size [16 so can use standard context] */
  decNumber bufd[D2N(16)];
  decNumber *d=bufd;             /* divisor */
  decNumber numone;              /* constant 1 */

  #if DECCHECK
  Int iterations=0;              /* for later sanity check */
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                              /* protect allocated storage */
    if (SPECIALARG) {               /* handle infinities and NaNs */
      if (decNumberIsInfinite(rhs)) {     /* an infinity */
      if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */
        decNumberZero(res);
       else decNumberCopy(res, rhs);      /* +Infinity -> self */
      }
       else decNaNs(res, rhs, NULL, set, status); /* a NaN */
      break;}

    if (ISZERO(rhs)) {              /* zeros -> exact 1 */
      decNumberZero(res);           /* make clean 1 */
      *res->lsu=1;                  /* .. */
      break;}                       /* [no status to set] */

    /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
    /* positive and negative tiny cases which will result in inexact */
    /* 1.  This also allows the later add-accumulate to always be */
    /* exact (because its length will never be more than twice the */
    /* working precision). */
    /* The comparator (tiny) needs just one digit, so use the */
    /* decNumber d for it (reused as the divisor, etc., below); its */
    /* exponent is such that if x is positive it will have */
    /* set->digits-1 zeros between the decimal point and the digit, */
    /* which is 4, and if x is negative one more zero there as the */
    /* more precise result will be of the form 0.9999999 rather than */
    /* 1.0000001.  Hence, tiny will be 0.0000004  if digits=7 and x>0 */
    /* or 0.00000004 if digits=7 and x<0.  If RHS not larger than */
    /* this then the result will be 1.000000 */
    decNumberZero(d);               /* clean */
    *d->lsu=4;                      /* set 4 .. */
    d->exponent=-set->digits;       /* * 10**(-d) */
    if (decNumberIsNegative(rhs)) d->exponent--;  /* negative case */
    comp=decCompare(d, rhs, 1);           /* signless compare */
    if (comp==BADINT) {
      *status|=DEC_Insufficient_storage;
      break;}
    if (comp>=0) {                  /* rhs < d */
      Int shift=set->digits-1;
      decNumberZero(res);           /* set 1 */
      *res->lsu=1;                  /* .. */
      res->digits=decShiftToMost(res->lsu, 1, shift);
      res->exponent=-shift;              /* make 1.0000... */
      *status|=DEC_Inexact | DEC_Rounded;    /* .. inexactly */
      break;} /* tiny */

    /* set up the context to be used for calculating a, as this is */
    /* used on both paths below */
    decContextDefault(&aset, DEC_INIT_DECIMAL64);
    /* accumulator bounds are as requested (could underflow) */
    aset.emax=set->emax;            /* usual bounds */
    aset.emin=set->emin;            /* .. */
    aset.clamp=0;             /* and no concrete format */

    /* calculate the adjusted (Hull & Abrham) exponent (where the */
    /* decimal point is just to the left of the coefficient msd) */
    h=rhs->exponent+rhs->digits;
    /* if h>8 then 10**h cannot be calculated safely; however, when */
    /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
    /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
    /* overflow (or underflow to 0) is guaranteed -- so this case can */
    /* be handled by simply forcing the appropriate excess */
    if (h>8) {                      /* overflow/underflow */
      /* set up here so Power call below will over or underflow to */
      /* zero; set accumulator to either 2 or 0.02 */
      /* [stack buffer for a is always big enough for this] */
      decNumberZero(a);
      *a->lsu=2;              /* not 1 but < exp(1) */
      if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
      h=8;                    /* clamp so 10**h computable */
      p=9;                    /* set a working precision */
      }
     else {                   /* h<=8 */
      Int maxlever=(rhs->digits>8?1:0);
      /* [could/should increase this for precisions >40 or so, too] */

      /* if h is 8, cannot normalize to a lower upper limit because */
      /* the final result will not be computable (see notes above), */
      /* but leverage can be applied whenever h is less than 8. */
      /* Apply as much as possible, up to a MAXLEVER digits, which */
      /* sets the tradeoff against the cost of the later a**(10**h). */
      /* As h is increased, the working precision below also */
      /* increases to compensate for the "constant digits at the */
      /* front" effect. */
      Int lever=MINI(8-h, maxlever);      /* leverage attainable */
      Int use=-rhs->digits-lever;   /* exponent to use for RHS */
      h+=lever;                     /* apply leverage selected */
      if (h<0) {              /* clamp */
      use+=h;                       /* [may end up subnormal] */
      h=0;
      }
      /* Take a copy of RHS if it needs normalization (true whenever x>=1) */
      if (rhs->exponent!=use) {
      decNumber *newrhs=bufr;       /* assume will fit on stack */
      needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufr)) { /* need malloc space */
        allocrhs=(decNumber *)malloc(needbytes);
        if (allocrhs==NULL) {       /* hopeless -- abandon */
          *status|=DEC_Insufficient_storage;
          break;}
        newrhs=allocrhs;            /* use the allocated space */
        }
      decNumberCopy(newrhs, rhs);   /* copy to safe space */
      newrhs->exponent=use;         /* normalize; now <1 */
      x=newrhs;               /* ready for use */
      /* decNumberShow(x); */
      }

      /* Now use the usual power series to evaluate exp(x).  The */
      /* series starts as 1 + x + x^2/2 ... so prime ready for the */
      /* third term by setting the term variable t=x, the accumulator */
      /* a=1, and the divisor d=2. */

      /* First determine the working precision.  From Hull & Abrham */
      /* this is set->digits+h+2.  However, if x is 'over-precise' we */
      /* need to allow for all its digits to potentially participate */
      /* (consider an x where all the excess digits are 9s) so in */
      /* this case use x->digits+h+2 */
      p=MAXI(x->digits, set->digits)+h+2;    /* [h<=8] */

      /* a and t are variable precision, and depend on p, so space */
      /* must be allocated for them if necessary */

      /* the accumulator needs to be able to hold 2p digits so that */
      /* the additions on the second and subsequent iterations are */
      /* sufficiently exact. */
      needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
      if (needbytes>sizeof(bufa)) { /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {        /* hopeless -- abandon */
        *status|=DEC_Insufficient_storage;
        break;}
      a=allocbufa;                  /* use the allocated space */
      }
      /* the term needs to be able to hold p digits (which is */
      /* guaranteed to be larger than x->digits, so the initial copy */
      /* is safe); it may also be used for the raise-to-power */
      /* calculation below, which needs an extra two digits */
      needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
      if (needbytes>sizeof(buft)) { /* need malloc space */
      allocbuft=(decNumber *)malloc(needbytes);
      if (allocbuft==NULL) {        /* hopeless -- abandon */
        *status|=DEC_Insufficient_storage;
        break;}
      t=allocbuft;                  /* use the allocated space */
      }

      decNumberCopy(t, x);          /* term=x */
      decNumberZero(a); *a->lsu=1;  /* accumulator=1 */
      decNumberZero(d); *d->lsu=2;  /* divisor=2 */
      decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */

      /* set up the contexts for calculating a, t, and d */
      decContextDefault(&tset, DEC_INIT_DECIMAL64);
      dset=tset;
      /* accumulator bounds are set above, set precision now */
      aset.digits=p*2;              /* double */
      /* term bounds avoid any underflow or overflow */
      tset.digits=p;
      tset.emin=DEC_MIN_EMIN;       /* [emax is plenty] */
      /* [dset.digits=16, etc., are sufficient] */

      /* finally ready to roll */
      for (;;) {
      #if DECCHECK
      iterations++;
      #endif
      /* only the status from the accumulation is interesting */
      /* [but it should remain unchanged after first add] */
      decAddOp(a, a, t, &aset, 0, status);             /* a=a+t */
      decMultiplyOp(t, t, x, &tset, &ignore);          /* t=t*x */
      decDivideOp(t, t, d, &tset, DIVIDE, &ignore);  /* t=t/d */
      /* the iteration ends when the term cannot affect the result, */
      /* if rounded to p digits, which is when its value is smaller */
      /* than the accumulator by p+1 digits.    There must also be */
      /* full precision in a. */
      if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
          && (a->digits>=p)) break;
      decAddOp(d, d, &numone, &dset, 0, &ignore);    /* d=d+1 */
      } /* iterate */

      #if DECCHECK
      /* just a sanity check; comment out test to show always */
      if (iterations>p+3)
      printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
             iterations, *status, p, x->digits);
      #endif
      } /* h<=8 */

    /* apply postconditioning: a=a**(10**h) -- this is calculated */
    /* at a slightly higher precision than Hull & Abrham suggest */
    if (h>0) {
      Int seenbit=0;             /* set once a 1-bit is seen */
      Int i;                     /* counter */
      Int n=powers[h];           /* always positive */
      aset.digits=p+2;           /* sufficient precision */
      /* avoid the overhead and many extra digits of decNumberPower */
      /* as all that is needed is the short 'multipliers' loop; here */
      /* accumulate the answer into t */
      decNumberZero(t); *t->lsu=1; /* acc=1 */
      for (i=1;;i++){            /* for each bit [top bit ignored] */
      /* abandon if have had overflow or terminal underflow */
      if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
        if (*status&DEC_Overflow || ISZERO(t)) break;}
      n=n<<1;                    /* move next bit to testable position */
      if (n<0) {           /* top bit is set */
        seenbit=1;               /* OK, have a significant bit */
        decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
        }
      if (i==31) break;    /* that was the last bit */
      if (!seenbit) continue;    /* no need to square 1 */
      decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
      } /*i*/ /* 32 bits */
      /* decNumberShow(t); */
      a=t;                 /* and carry on using t instead of a */
      }

    /* Copy and round the result to res */
    residue=1;                      /* indicate dirt to right .. */
    if (ISZERO(a)) residue=0;       /* .. unless underflowed to 0 */
    aset.digits=set->digits;        /* [use default rounding] */
    decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
    decFinish(res, set, &residue, status);       /* cleanup/set flags */
    } while(0);                     /* end protected */

  if (allocrhs !=NULL) free(allocrhs);    /* drop any storage used */
  if (allocbufa!=NULL) free(allocbufa); /* .. */
  if (allocbuft!=NULL) free(allocbuft); /* .. */
  /* [status is handled by caller] */
  return res;
  } /* decExpOp */

/* ------------------------------------------------------------------ */
/* Initial-estimate natural logarithm table                       */
/*                                                    */
/*   LNnn -- 90-entry 16-bit table for values from .10 through .99.   */
/*         The result is a 4-digit encode of the coefficient (c=the */
/*         top 14 bits encoding 0-9999) and a 2-digit encode of the */
/*         exponent (e=the bottom 2 bits encoding 0-3)            */
/*                                                    */
/*         The resulting value is given by:                       */
/*                                                    */
/*           v = -c * 10**(-e-3)                            */
/*                                                    */
/*         where e and c are extracted from entry k = LNnn[x-10]    */
/*         where x is truncated (NB) into the range 10 through 99,  */
/*         and then c = k>>2 and e = k&3.                   */
/* ------------------------------------------------------------------ */
const uShort LNnn[90]={9016,  8652,  8316,  8008,  7724,  7456,    7208,
  6972,      6748,      6540,  6340,  6148,  5968,  5792,  5628,  5464,  5312,
  5164,      5020,      4884,  4748,  4620,  4496,  4376,  4256,  4144,  4032,
 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
 10197,      9685,      9177,  8677,  8185,  7697,  7213,  6737,  6269,  5801,
  5341,      4889,      4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
 10130,      6046, 20055};

/* ------------------------------------------------------------------ */
/* decLnOp -- effect natural logarithm                            */
/*                                                    */
/*   This computes C = ln(A)                                */
/*                                                    */
/*   res is C, the result.  C may be A                            */
/*   rhs is A                                               */
/*   set is the context; note that rounding mode has no effect          */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Notable cases:                                     */
/*   A<0 -> Invalid                                         */
/*   A=0 -> -Infinity (Exact)                               */
/*   A=+Infinity -> +Infinity (Exact)                             */
/*   A=1 exactly -> 0 (Exact)                               */
/*                                                    */
/* Restrictions (as for Exp):                               */
/*                                                    */
/*   digits, emax, and -emin in the context must be less than           */
/*   DEC_MAX_MATH+11 (1000010), and the rhs must be within these      */
/*   bounds or a zero.  This is an internal routine, so these           */
/*   restrictions are contractual and not enforced.               */
/*                                                    */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
/* almost always be correctly rounded, but may be up to 1 ulp in      */
/* error in rare cases.                                     */
/* ------------------------------------------------------------------ */
/* The result is calculated using Newton's method, with each            */
/* iteration calculating a' = a + x * exp(-a) - 1.  See, for example, */
/* Epperson 1989.                                     */
/*                                                    */
/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
/* This has to be calculated at the sum of the precision of x and the */
/* working precision.                                       */
/*                                                    */
/* Implementation notes:                                    */
/*                                                    */
/* 1. This is separated out as decLnOp so it can be called from         */
/*    other Mathematical functions (e.g., Log 10) with a wider range  */
/*    than normal.  In particular, it can handle the slightly wider   */
/*    (+9+2) range needed by a power function.                    */
/*                                                    */
/* 2. The speed of this function is about 10x slower than exp, as     */
/*    it typically needs 4-6 iterations for short numbers, and the    */
/*    extra precision needed adds a squaring effect, twice.       */
/*                                                    */
/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40,   */
/*    as these are common requests.  ln(10) is used by log10(x).      */
/*                                                    */
/* 4. An iteration might be saved by widening the LNnn table, and     */
/*    would certainly save at least one if it were made ten times     */
/*    bigger, too (for truncated fractions 0.100 through 0.999).      */
/*    However, for most practical evaluations, at least four or five  */
/*    iterations will be neede -- so this would only speed up by      */
/*    20-25% and that probably does not justify increasing the table  */
/*    size.                                           */
/*                                                    */
/* 5. The static buffers are larger than might be expected to allow   */
/*    for calls from decNumberPower.                              */
/* ------------------------------------------------------------------ */
decNumber * decLnOp(decNumber *res, const decNumber *rhs,
                decContext *set, uInt *status) {
  uInt ignore=0;           /* working status accumulator */
  uInt needbytes;          /* for space calculations */
  Int residue;                   /* rounding residue */
  Int r;                   /* rhs=f*10**r [see below] */
  Int p;                   /* working precision */
  Int pp;                  /* precision for iteration */
  Int t;                   /* work */

  /* buffers for a (accumulator, typically precision+2) and b */
  /* (adjustment calculator, same size) */
  decNumber bufa[D2N(DECBUFFER+12)];
  decNumber *allocbufa=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *a=bufa;             /* accumulator/work */
  decNumber bufb[D2N(DECBUFFER*2+2)];
  decNumber *allocbufb=NULL;     /* -> allocated bufa, iff allocated */
  decNumber *b=bufb;             /* adjustment/work */

  decNumber  numone;             /* constant 1 */
  decNumber  cmp;          /* work */
  decContext aset, bset;         /* working contexts */

  #if DECCHECK
  Int iterations=0;              /* for later sanity check */
  if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
  #endif

  do {                              /* protect allocated storage */
    if (SPECIALARG) {               /* handle infinities and NaNs */
      if (decNumberIsInfinite(rhs)) {     /* an infinity */
      if (decNumberIsNegative(rhs)) /* -Infinity -> error */
        *status|=DEC_Invalid_operation;
       else decNumberCopy(res, rhs);      /* +Infinity -> self */
      }
       else decNaNs(res, rhs, NULL, set, status); /* a NaN */
      break;}

    if (ISZERO(rhs)) {              /* +/- zeros -> -Infinity */
      decNumberZero(res);           /* make clean */
      res->bits=DECINF|DECNEG;            /* set - infinity */
      break;}                       /* [no status to set] */

    /* Non-zero negatives are bad... */
    if (decNumberIsNegative(rhs)) { /* -x -> error */
      *status|=DEC_Invalid_operation;
      break;}

    /* Here, rhs is positive, finite, and in range */

    /* lookaside fastpath code for ln(2) and ln(10) at common lengths */
    if (rhs->exponent==0 && set->digits<=40) {
      #if DECDPUN==1
      if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
      #else
      if (rhs->lsu[0]==10 && rhs->digits==2) {              /* ln(10) */
      #endif
      aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
      #define LN10 "2.302585092994045684017991454684364207601"
      decNumberFromString(res, LN10, &aset);
      *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
      break;}
      if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
      aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
      #define LN2 "0.6931471805599453094172321214581765680755"
      decNumberFromString(res, LN2, &aset);
      *status|=(DEC_Inexact | DEC_Rounded);
      break;}
      } /* integer and short */

    /* Determine the working precision.    This is normally the */
    /* requested precision + 2, with a minimum of 9.  However, if */
    /* the rhs is 'over-precise' then allow for all its digits to */
    /* potentially participate (consider an rhs where all the excess */
    /* digits are 9s) so in this case use rhs->digits+2. */
    p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;

    /* Allocate space for the accumulator and the high-precision */
    /* adjustment calculator, if necessary.  The accumulator must */
    /* be able to hold p digits, and the adjustment up to */
    /* rhs->digits+p digits.  They are also made big enough for 16 */
    /* digits so that they can be used for calculating the initial */
    /* estimate. */
    needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufa)) {     /* need malloc space */
      allocbufa=(decNumber *)malloc(needbytes);
      if (allocbufa==NULL) {        /* hopeless -- abandon */
      *status|=DEC_Insufficient_storage;
      break;}
      a=allocbufa;                  /* use the allocated space */
      }
    pp=p+rhs->digits;
    needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
    if (needbytes>sizeof(bufb)) {     /* need malloc space */
      allocbufb=(decNumber *)malloc(needbytes);
      if (allocbufb==NULL) {        /* hopeless -- abandon */
      *status|=DEC_Insufficient_storage;
      break;}
      b=allocbufb;                  /* use the allocated space */
      }

    /* Prepare an initial estimate in acc. Calculate this by */
    /* considering the coefficient of x to be a normalized fraction, */
    /* f, with the decimal point at far left and multiplied by */
    /* 10**r.  Then, rhs=f*10**r and 0.1<=f<1, and */
    /*       ln(x) = ln(f) + ln(10)*r */
    /* Get the initial estimate for ln(f) from a small lookup */
    /* table (see above) indexed by the first two digits of f, */
    /* truncated. */

    decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
    r=rhs->exponent+rhs->digits;    /* 'normalised' exponent */
    decNumberFromInt32(a, r);       /* a=r */
    decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */
    b->exponent=-6;                 /*  .. */
    decMultiplyOp(a, a, b, &aset, &ignore);  /* a=a*b */
    /* now get top two digits of rhs into b by simple truncate and */
    /* force to integer */
    residue=0;                      /* (no residue) */
    aset.digits=2; aset.round=DEC_ROUND_DOWN;
    decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
    b->exponent=0;                  /* make integer */
    t=decGetInt(b);                 /* [cannot fail] */
    if (t<10) t=X10(t);             /* adjust single-digit b */
    t=LNnn[t-10];             /* look up ln(b) */
    decNumberFromInt32(b, t>>2);    /* b=ln(b) coefficient */
    b->exponent=-(t&3)-3;           /* set exponent */
    b->bits=DECNEG;                 /* ln(0.10)->ln(0.99) always -ve */
    aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
    decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
    /* the initial estimate is now in a, with up to 4 digits correct. */
    /* When rhs is at or near Nmax the estimate will be low, so we */
    /* will approach it from below, avoiding overflow when calling exp. */

    decNumberZero(&numone); *numone.lsu=1;   /* constant 1 for adjustment */

    /* accumulator bounds are as requested (could underflow, but */
    /* cannot overflow) */
    aset.emax=set->emax;
    aset.emin=set->emin;
    aset.clamp=0;             /* no concrete format */
    /* set up a context to be used for the multiply and subtract */
    bset=aset;
    bset.emax=DEC_MAX_MATH*2;       /* use double bounds for the */
    bset.emin=-DEC_MAX_MATH*2;            /* adjustment calculation */
                              /* [see decExpOp call below] */
    /* for each iteration double the number of digits to calculate, */
    /* up to a maximum of p */
    pp=9;                     /* initial precision */
    /* [initially 9 as then the sequence starts 7+2, 16+2, and */
    /* 34+2, which is ideal for standard-sized numbers] */
    aset.digits=pp;                 /* working context */
    bset.digits=pp+rhs->digits;           /* wider context */
    for (;;) {                      /* iterate */
      #if DECCHECK
      iterations++;
      if (iterations>24) break;           /* consider 9 * 2**24 */
      #endif
      /* calculate the adjustment (exp(-a)*x-1) into b.      This is a */
      /* catastrophic subtraction but it really is the difference */
      /* from 1 that is of interest. */
      /* Use the internal entry point to Exp as it allows the double */
      /* range for calculating exp(-a) when a is the tiniest subnormal. */
      a->bits^=DECNEG;              /* make -a */
      decExpOp(b, a, &bset, &ignore);     /* b=exp(-a) */
      a->bits^=DECNEG;              /* restore sign of a */
      /* now multiply by rhs and subtract 1, at the wider precision */
      decMultiplyOp(b, b, rhs, &bset, &ignore);        /* b=b*rhs */
      decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */

      /* the iteration ends when the adjustment cannot affect the */
      /* result by >=0.5 ulp (at the requested digits), which */
      /* is when its value is smaller than the accumulator by */
      /* set->digits+1 digits (or it is zero) -- this is a looser */
      /* requirement than for Exp because all that happens to the */
      /* accumulator after this is the final rounding (but note that */
      /* there must also be full precision in a, or a=0). */

      if (decNumberIsZero(b) ||
        (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
      if (a->digits==p) break;
      if (decNumberIsZero(a)) {
        decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
        if (cmp.lsu[0]==0) a->exponent=0;        /* yes, exact 0 */
         else *status|=(DEC_Inexact | DEC_Rounded);  /* no, inexact */
        break;
        }
      /* force padding if adjustment has gone to 0 before full length */
      if (decNumberIsZero(b)) b->exponent=a->exponent-p;
      }

      /* not done yet ... */
      decAddOp(a, a, b, &aset, 0, &ignore);  /* a=a+b for next estimate */
      if (pp==p) continue;               /* precision is at maximum */
      /* lengthen the next calculation */
      pp=pp*2;                           /* double precision */
      if (pp>p) pp=p;                    /* clamp to maximum */
      aset.digits=pp;                    /* working context */
      bset.digits=pp+rhs->digits;        /* wider context */
      } /* Newton's iteration */

    #if DECCHECK
    /* just a sanity check; remove the test to show always */
    if (iterations>24)
      printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
          iterations, *status, p, rhs->digits);
    #endif

    /* Copy and round the result to res */
    residue=1;                      /* indicate dirt to right */
    if (ISZERO(a)) residue=0;       /* .. unless underflowed to 0 */
    aset.digits=set->digits;        /* [use default rounding] */
    decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
    decFinish(res, set, &residue, status);       /* cleanup/set flags */
    } while(0);                     /* end protected */

  if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
  if (allocbufb!=NULL) free(allocbufb); /* .. */
  /* [status is handled by caller] */
  return res;
  } /* decLnOp */

/* ------------------------------------------------------------------ */
/* decQuantizeOp  -- force exponent to requested value                  */
/*                                                    */
/*   This computes C = op(A, B), where op adjusts the coefficient     */
/*   of C (by rounding or shifting) such that the exponent (-scale)   */
/*   of C has the value B or matches the exponent of B.                 */
/*   The numerical value of C will equal A, except for the effects of */
/*   any rounding that occurred.                            */
/*                                                    */
/*   res is C, the result.  C may be A or B                       */
/*   lhs is A, the number to adjust                         */
/*   rhs is B, the requested exponent                             */
/*   set is the context                                     */
/*   quant is 1 for quantize or 0 for rescale                     */
/*   status is the status accumulator (this can be called without     */
/*        risk of control loss)                             */
/*                                                    */
/* C must have space for set->digits digits.                      */
/*                                                    */
/* Unless there is an error or the result is infinite, the exponent   */
/* after the operation is guaranteed to be that requested.        */
/* ------------------------------------------------------------------ */
static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
                         const decNumber *rhs, decContext *set,
                         Flag quant, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;      /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;      /* .., rhs */
  #endif
  const decNumber *inrhs=rhs;    /* save original rhs */
  Int reqdigits=set->digits;     /* requested DIGITS */
  Int reqexp;                    /* requested exponent [-scale] */
  Int residue=0;           /* rounding residue */
  Int etiny=set->emin-(reqdigits-1);

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>reqdigits) {
      alloclhs=decRoundOperand(lhs, set, status);
      if (alloclhs==NULL) break;
      lhs=alloclhs;
      }
      if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
      allocrhs=decRoundOperand(rhs, set, status);
      if (allocrhs==NULL) break;
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* Handle special values */
    if (SPECIALARGS) {
      /* NaNs get usual processing */
      if (SPECIALARGS & (DECSNAN | DECNAN))
      decNaNs(res, lhs, rhs, set, status);
      /* one infinity but not both is bad */
      else if ((lhs->bits ^ rhs->bits) & DECINF)
      *status|=DEC_Invalid_operation;
      /* both infinity: return lhs */
      else decNumberCopy(res, lhs);      /* [nop if in place] */
      break;
      }

    /* set requested exponent */
    if (quant) reqexp=inrhs->exponent;    /* quantize -- match exponents */
     else {                   /* rescale -- use value of rhs */
      /* Original rhs must be an integer that fits and is in range, */
      /* which could be from -1999999997 to +999999999, thanks to */
      /* subnormals */
      reqexp=decGetInt(inrhs);                 /* [cannot fail] */
      }

    #if DECSUBSET
    if (!set->extended) etiny=set->emin;     /* no subnormals */
    #endif

    if (reqexp==BADINT                   /* bad (rescale only) or .. */
     || reqexp==BIGODD || reqexp==BIGEVEN    /* very big (ditto) or .. */
     || (reqexp<etiny)                   /* < lowest */
     || (reqexp>set->emax)) {            /* > emax */
      *status|=DEC_Invalid_operation;
      break;}

    /* the RHS has been processed, so it can be overwritten now if necessary */
    if (ISZERO(lhs)) {                   /* zero coefficient unchanged */
      decNumberCopy(res, lhs);                 /* [nop if in place] */
      res->exponent=reqexp;              /* .. just set exponent */
      #if DECSUBSET
      if (!set->extended) res->bits=0;         /* subset specification; no -0 */
      #endif
      }
     else {                        /* non-zero lhs */
      Int adjust=reqexp-lhs->exponent;         /* digit adjustment needed */
      /* if adjusted coefficient will definitely not fit, give up now */
      if ((lhs->digits-adjust)>reqdigits) {
      *status|=DEC_Invalid_operation;
      break;
      }

      if (adjust>0) {                    /* increasing exponent */
      /* this will decrease the length of the coefficient by adjust */
      /* digits, and must round as it does so */
      decContext workset;                /* work */
      workset=*set;                      /* clone rounding, etc. */
      workset.digits=lhs->digits-adjust;   /* set requested length */
      /* [note that the latter can be <1, here] */
      decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
      decApplyRound(res, &workset, residue, status);    /* .. and round */
      residue=0;                            /* [used] */
      /* If just rounded a 999s case, exponent will be off by one; */
      /* adjust back (after checking space), if so. */
      if (res->exponent>reqexp) {
        /* re-check needed, e.g., for quantize(0.9999, 0.001) under */
        /* set->digits==3 */
        if (res->digits==reqdigits) {          /* cannot shift by 1 */
          *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
          *status|=DEC_Invalid_operation;
          break;
          }
        res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
        res->exponent--;                 /* (re)adjust the exponent. */
        }
      #if DECSUBSET
      if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
      #endif
      } /* increase */
       else /* adjust<=0 */ {            /* decreasing or = exponent */
      /* this will increase the length of the coefficient by -adjust */
      /* digits, by adding zero or more trailing zeros; this is */
      /* already checked for fit, above */
      decNumberCopy(res, lhs);           /* [it will fit] */
      /* if padding needed (adjust<0), add it now... */
      if (adjust<0) {
        res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
        res->exponent+=adjust;           /* adjust the exponent */
        }
      } /* decrease */
      } /* non-zero */

    /* Check for overflow [do not use Finalize in this case, as an */
    /* overflow here is a "don't fit" situation] */
    if (res->exponent>set->emax-res->digits+1) {  /* too big */
      *status|=DEC_Invalid_operation;
      break;
      }
     else {
      decFinalize(res, set, &residue, status);    /* set subnormal flags */
      *status&=~DEC_Underflow;            /* suppress Underflow [754r] */
      }
    } while(0);                     /* end protected */

  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);     /* drop any storage used */
  if (alloclhs!=NULL) free(alloclhs);     /* .. */
  #endif
  return res;
  } /* decQuantizeOp */

/* ------------------------------------------------------------------ */
/* decCompareOp -- compare, min, or max two Numbers               */
/*                                                    */
/*   This computes C = A ? B and carries out one of four operations:  */
/*     COMPARE      -- returns the signum (as a number) giving the      */
/*               result of a comparison unless one or both        */
/*               operands is a NaN (in which case a NaN results)  */
/*     COMPSIG      -- as COMPARE except that a quiet NaN raises        */
/*               Invalid operation.                         */
/*     COMPMAX      -- returns the larger of the operands, using the    */
/*               754r maxnum operation                      */
/*     COMPMAXMAG -- ditto, comparing absolute values             */
/*     COMPMIN      -- the 754r minnum operation                        */
/*     COMPMINMAG -- ditto, comparing absolute values             */
/*     COMTOTAL     -- returns the signum (as a number) giving the      */
/*               result of a comparison using 754r total ordering */
/*                                                    */
/*   res is C, the result.  C may be A and/or B (e.g., X=X?X)           */
/*   lhs is A                                               */
/*   rhs is B                                               */
/*   set is the context                                     */
/*   op      is the operation flag                                */
/*   status is the usual accumulator                              */
/*                                                    */
/* C must have space for one digit for COMPARE or set->digits for     */
/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG.                   */
/* ------------------------------------------------------------------ */
/* The emphasis here is on speed for common cases, and avoiding         */
/* coefficient comparison if possible.                            */
/* ------------------------------------------------------------------ */
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
                   const decNumber *rhs, decContext *set,
                   Flag op, uInt *status) {
  #if DECSUBSET
  decNumber *alloclhs=NULL;      /* non-NULL if rounded lhs allocated */
  decNumber *allocrhs=NULL;      /* .., rhs */
  #endif
  Int result=0;            /* default result value */
  uByte merged;                  /* work */

  #if DECCHECK
  if (decCheckOperands(res, lhs, rhs, set)) return res;
  #endif

  do {                           /* protect allocated storage */
    #if DECSUBSET
    if (!set->extended) {
      /* reduce operands and set lostDigits status, as needed */
      if (lhs->digits>set->digits) {
      alloclhs=decRoundOperand(lhs, set, status);
      if (alloclhs==NULL) {result=BADINT; break;}
      lhs=alloclhs;
      }
      if (rhs->digits>set->digits) {
      allocrhs=decRoundOperand(rhs, set, status);
      if (allocrhs==NULL) {result=BADINT; break;}
      rhs=allocrhs;
      }
      }
    #endif
    /* [following code does not require input rounding] */

    /* If total ordering then handle differing signs 'up front' */
    if (op==COMPTOTAL) {            /* total ordering */
      if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
      result=-1;
      break;
      }
      if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
      result=+1;
      break;
      }
      }

    /* handle NaNs specially; let infinities drop through */
    /* This assumes sNaN (even just one) leads to NaN. */
    merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
    if (merged) {             /* a NaN bit set */
      if (op==COMPARE);             /* result will be NaN */
       else if (op==COMPSIG)        /* treat qNaN as sNaN */
      *status|=DEC_Invalid_operation | DEC_sNaN;
       else if (op==COMPTOTAL) {    /* total ordering, always finite */
      /* signs are known to be the same; compute the ordering here */
      /* as if the signs are both positive, then invert for negatives */
      if (!decNumberIsNaN(lhs)) result=-1;
       else if (!decNumberIsNaN(rhs)) result=+1;
       /* here if both NaNs */
       else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
       else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
       else { /* both NaN or both sNaN */
        /* now it just depends on the payload */
        result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
                        rhs->lsu, D2U(rhs->digits), 0);
        /* [Error not possible, as these are 'aligned'] */
        } /* both same NaNs */
      if (decNumberIsNegative(lhs)) result=-result;
      break;
      } /* total order */

       else if (merged & DECSNAN);       /* sNaN -> qNaN */
       else { /* here if MIN or MAX and one or two quiet NaNs */
      /* min or max -- 754r rules ignore single NaN */
      if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
        /* just one NaN; force choice to be the non-NaN operand */
        op=COMPMAX;
        if (lhs->bits & DECNAN) result=-1; /* pick rhs */
                       else result=+1; /* pick lhs */
        break;
        }
      } /* max or min */
      op=COMPNAN;                  /* use special path */
      decNaNs(res, lhs, rhs, set, status);   /* propagate NaN */
      break;
      }
    /* have numbers */
    if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
     else result=decCompare(lhs, rhs, 0);    /* sign matters */
    } while(0);                          /* end protected */

  if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
   else {
    if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
      if (op==COMPTOTAL && result==0) {
      /* operands are numerically equal or same NaN (and same sign, */
      /* tested first); if identical, leave result 0 */
      if (lhs->exponent!=rhs->exponent) {
        if (lhs->exponent<rhs->exponent) result=-1;
         else result=+1;
        if (decNumberIsNegative(lhs)) result=-result;
        } /* lexp!=rexp */
      } /* total-order by exponent */
      decNumberZero(res);           /* [always a valid result] */
      if (result!=0) {              /* must be -1 or +1 */
      *res->lsu=1;
      if (result<0) res->bits=DECNEG;
      }
      }
     else if (op==COMPNAN);         /* special, drop through */
     else {                   /* MAX or MIN, non-NaN result */
      Int residue=0;                /* rounding accumulator */
      /* choose the operand for the result */
      const decNumber *choice;
      if (result==0) { /* operands are numerically equal */
      /* choose according to sign then exponent (see 754r) */
      uByte slhs=(lhs->bits & DECNEG);
      uByte srhs=(rhs->bits & DECNEG);
      #if DECSUBSET
      if (!set->extended) {         /* subset: force left-hand */
        op=COMPMAX;
        result=+1;
        }
      else
      #endif
      if (slhs!=srhs) {    /* signs differ */
        if (slhs) result=-1;     /* rhs is max */
             else result=+1;     /* lhs is max */
        }
       else if (slhs && srhs) {  /* both negative */
        if (lhs->exponent<rhs->exponent) result=+1;
                              else result=-1;
        /* [if equal, use lhs, technically identical] */
        }
       else {                    /* both positive */
        if (lhs->exponent>rhs->exponent) result=+1;
                              else result=-1;
        /* [ditto] */
        }
      } /* numerically equal */
      /* here result will be non-0; reverse if looking for MIN */
      if (op==COMPMIN || op==COMPMINMAG) result=-result;
      choice=(result>0 ? lhs : rhs);      /* choose */
      /* copy chosen to result, rounding if need be */
      decCopyFit(res, choice, set, &residue, status);
      decFinish(res, set, &residue, status);
      }
    }
  #if DECSUBSET
  if (allocrhs!=NULL) free(allocrhs);     /* free any storage used */
  if (alloclhs!=NULL) free(alloclhs);     /* .. */
  #endif
  return res;
  } /* decCompareOp */

/* ------------------------------------------------------------------ */
/* decCompare -- compare two decNumbers by numerical value        */
/*                                                    */
/*  This routine compares A ? B without altering them.                  */
/*                                                    */
/*  Arg1 is A, a decNumber which is not a NaN                     */
/*  Arg2 is B, a decNumber which is not a NaN                     */
/*  Arg3 is 1 for a sign-independent compare, 0 otherwise         */
/*                                                    */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error)                  */
/* ------------------------------------------------------------------ */
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
                  Flag abs) {
  Int result;                    /* result value */
  Int sigr;                /* rhs signum */
  Int compare;             /* work */

  result=1;                        /* assume signum(lhs) */
  if (ISZERO(lhs)) result=0;
  if (abs) {
    if (ISZERO(rhs)) return result;      /* LHS wins or both 0 */
    /* RHS is non-zero */
    if (result==0) return -1;            /* LHS is 0; RHS wins */
    /* [here, both non-zero, result=1] */
    }
   else {                          /* signs matter */
    if (result && decNumberIsNegative(lhs)) result=-1;
    sigr=1;                        /* compute signum(rhs) */
    if (ISZERO(rhs)) sigr=0;
     else if (decNumberIsNegative(rhs)) sigr=-1;
    if (result > sigr) return +1;        /* L > R, return 1 */
    if (result < sigr) return -1;        /* L < R, return -1 */
    if (result==0) return 0;               /* both 0 */
    }

  /* signums are the same; both are non-zero */
  if ((lhs->bits | rhs->bits) & DECINF) {    /* one or more infinities */
    if (decNumberIsInfinite(rhs)) {
      if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
       else result=-result;              /* only rhs infinite */
      }
    return result;
    }
  /* must compare the coefficients, allowing for exponents */
  if (lhs->exponent>rhs->exponent) {           /* LHS exponent larger */
    /* swap sides, and sign */
    const decNumber *temp=lhs;
    lhs=rhs;
    rhs=temp;
    result=-result;
    }
  compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
                   rhs->lsu, D2U(rhs->digits),
                   rhs->exponent-lhs->exponent);
  if (compare!=BADINT) compare*=result;        /* comparison succeeded */
  return compare;
  } /* decCompare */

/* ------------------------------------------------------------------ */
/* decUnitCompare -- compare two >=0 integers in Unit arrays            */
/*                                                    */
/*  This routine compares A ? B*10**E where A and B are unit arrays   */
/*  A is a plain integer                                    */
/*  B has an exponent of E (which must be non-negative)                 */
/*                                                    */
/*  Arg1 is A first Unit (lsu)                                    */
/*  Arg2 is A length in Units                               */
/*  Arg3 is B first Unit (lsu)                                    */
/*  Arg4 is B length in Units                               */
/*  Arg5 is E (0 if the units are aligned)                        */
/*                                                    */
/*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
/*  (the only possible failure is an allocation error, which can      */
/*  only occur if E!=0)                                     */
/* ------------------------------------------------------------------ */
static Int decUnitCompare(const Unit *a, Int alength,
                    const Unit *b, Int blength, Int exp) {
  Unit      *acc;                /* accumulator for result */
  Unit      accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
  Unit      *allocacc=NULL;            /* -> allocated acc buffer, iff allocated */
  Int accunits, need;            /* units in use or needed for acc */
  const Unit *l, *r, *u;         /* work */
  Int expunits, exprem, result;  /* .. */

  if (exp==0) {                  /* aligned; fastpath */
    if (alength>blength) return 1;
    if (alength<blength) return -1;
    /* same number of units in both -- need unit-by-unit compare */
    l=a+alength-1;
    r=b+alength-1;
    for (;l>=a; l--, r--) {
      if (*l>*r) return 1;
      if (*l<*r) return -1;
      }
    return 0;                    /* all units match */
    } /* aligned */

  /* Unaligned.    If one is >1 unit longer than the other, padded */
  /* approximately, then can return easily */
  if (alength>blength+(Int)D2U(exp)) return 1;
  if (alength+1<blength+(Int)D2U(exp)) return -1;

  /* Need to do a real subtract.  For this, a result buffer is needed */
  /* even though only the sign is of interest.  Its length needs */
  /* to be the larger of alength and padded blength, +2 */
  need=blength+D2U(exp);            /* maximum real length of B */
  if (need<alength) need=alength;
  need+=2;
  acc=accbuff;                      /* assume use local buffer */
  if (need*sizeof(Unit)>sizeof(accbuff)) {
    allocacc=(Unit *)malloc(need*sizeof(Unit));
    if (allocacc==NULL) return BADINT;    /* hopeless -- abandon */
    acc=allocacc;
    }
  /* Calculate units and remainder from exponent. */
  expunits=exp/DECDPUN;
  exprem=exp%DECDPUN;
  /* subtract [A+B*(-m)] */
  accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
                   -(Int)powers[exprem]);
  /* [UnitAddSub result may have leading zeros, even on zero] */
  if (accunits<0) result=-1;        /* negative result */
   else {                     /* non-negative result */
    /* check units of the result before freeing any storage */
    for (u=acc; u<acc+accunits-1 && *u==0;) u++;
    result=(*u==0 ? 0 : +1);
    }
  /* clean up and return the result */
  if (allocacc!=NULL) free(allocacc);     /* drop any storage used */
  return result;
  } /* decUnitCompare */

/* ------------------------------------------------------------------ */
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays   */
/*                                                    */
/*  This routine performs the calculation:                        */
/*                                                    */
/*  C=A+(B*M)                                               */
/*                                                    */
/*  Where M is in the range -DECDPUNMAX through +DECDPUNMAX.            */
/*                                                    */
/*  A may be shorter or longer than B.                            */
/*                                                    */
/*  Leading zeros are not removed after a calculation.      The result is */
/*  either the same length as the longer of A and B (adding any         */
/*  shift), or one Unit longer than that (if a Unit carry occurred).  */
/*                                                    */
/*  A and B content are not altered unless C is also A or B.            */
/*  C may be the same array as A or B, but only if no zero padding is */
/*  requested (that is, C may be B only if bshift==0).                  */
/*  C is filled from the lsu; only those units necessary to complete  */
/*  the calculation are referenced.                         */
/*                                                    */
/*  Arg1 is A first Unit (lsu)                                    */
/*  Arg2 is A length in Units                               */
/*  Arg3 is B first Unit (lsu)                                    */
/*  Arg4 is B length in Units                               */
/*  Arg5 is B shift in Units  (>=0; pads with 0 units if positive)    */
/*  Arg6 is C first Unit (lsu)                                    */
/*  Arg7 is M, the multiplier                               */
/*                                                    */
/*  returns the count of Units written to C, which will be non-zero   */
/*  and negated if the result is negative.  That is, the sign of the  */
/*  returned Int is the sign of the result (positive for zero) and    */
/*  the absolute value of the Int is the count of Units.          */
/*                                                    */
/*  It is the caller's responsibility to make sure that C size is     */
/*  safe, allowing space if necessary for a one-Unit carry.       */
/*                                                    */
/*  This routine is severely performance-critical; *any* change here  */
/*  must be measured (timed) to assure no performance degradation.    */
/*  In particular, trickery here tends to be counter-productive, as   */
/*  increased complexity of code hurts register optimizations on      */
/*  register-poor architectures.  Avoiding divisions is nearly          */
/*  always a Good Idea, however.                            */
/*                                                    */
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark  */
/* (IBM Warwick, UK) for some of the ideas used in this routine.      */
/* ------------------------------------------------------------------ */
static Int decUnitAddSub(const Unit *a, Int alength,
                   const Unit *b, Int blength, Int bshift,
                   Unit *c, Int m) {
  const Unit *alsu=a;            /* A lsu [need to remember it] */
  Unit *clsu=c;                  /* C ditto */
  Unit *minC;                    /* low water mark for C */
  Unit *maxC;                    /* high water mark for C */
  eInt carry=0;                  /* carry integer (could be Long) */
  Int  add;                /* work */
  #if DECDPUN<=4           /* myriadal, millenary, etc. */
  Int  est;                /* estimated quotient */
  #endif

  #if DECTRACE
  if (alength<1 || blength<1)
    printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
  #endif

  maxC=c+alength;          /* A is usually the longer */
  minC=c+blength;          /* .. and B the shorter */
  if (bshift!=0) {               /* B is shifted; low As copy across */
    minC+=bshift;
    /* if in place [common], skip copy unless there's a gap [rare] */
    if (a==c && bshift<=alength) {
      c+=bshift;
      a+=bshift;
      }
     else for (; c<clsu+bshift; a++, c++) {  /* copy needed */
      if (a<alsu+alength) *c=*a;
       else *c=0;
      }
    }
  if (minC>maxC) { /* swap */
    Unit *hold=minC;
    minC=maxC;
    maxC=hold;
    }

  /* For speed, do the addition as two loops; the first where both A */
  /* and B contribute, and the second (if necessary) where only one or */
  /* other of the numbers contribute. */
  /* Carry handling is the same (i.e., duplicated) in each case. */
  for (; c<minC; c++) {
    carry+=*a;
    a++;
    carry+=((eInt)*b)*m;            /* [special-casing m=1/-1 */
    b++;                      /* here is not a win] */
    /* here carry is new Unit of digits; it could be +ve or -ve */
    if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    #if DECDPUN==4                       /* use divide-by-multiply */
      if (carry>=0) {
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* likely quotient [89%] */
      if (*c<DECDPUNMAX+1) continue;           /* estimate was correct */
      carry++;
      *c-=DECDPUNMAX+1;
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;           /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* likely quotient [99%] */
      if (*c<DECDPUNMAX+1) continue;           /* estimate was correct */
      carry++;
      *c-=DECDPUNMAX+1;
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;           /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      /* Can use QUOT10 as carry <= 4 digits */
      if (carry>=0) {
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* quotient */
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
    #else
      /* remainder operator is undefined if negative, so must test */
      if ((ueInt)carry<(DECDPUNMAX+1)*2) {   /* fastpath carry +1 */
      *c=(Unit)(carry-(DECDPUNMAX+1));     /* [helps additions] */
      carry=1;
      continue;
      }
      if (carry>=0) {
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1);
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } /* c */

  /* now may have one or other to complete */
  /* [pretest to avoid loop setup/shutdown] */
  if (c<maxC) for (; c<maxC; c++) {
    if (a<alsu+alength) {           /* still in A */
      carry+=*a;
      a++;
      }
     else {                   /* inside B */
      carry+=((eInt)*b)*m;
      b++;
      }
    /* here carry is new Unit of digits; it could be +ve or -ve and */
    /* magnitude up to DECDPUNMAX squared */
    if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
      *c=(Unit)carry;
      carry=0;
      continue;
      }
    /* result for this unit is negative or >DECDPUNMAX */
    #if DECDPUN==4                       /* use divide-by-multiply */
      if (carry>=0) {
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* likely quotient [79.7%] */
      if (*c<DECDPUNMAX+1) continue;           /* estimate was correct */
      carry++;
      *c-=DECDPUNMAX+1;
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>11)*53687)>>18;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;           /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN==3
      if (carry>=0) {
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* likely quotient [99%] */
      if (*c<DECDPUNMAX+1) continue;           /* estimate was correct */
      carry++;
      *c-=DECDPUNMAX+1;
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=(((ueInt)carry>>3)*16777)>>21;
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
      if (*c<DECDPUNMAX+1) continue;           /* was OK */
      carry++;
      *c-=DECDPUNMAX+1;
    #elif DECDPUN<=2
      if (carry>=0) {
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
      carry=est;                   /* quotient */
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      est=QUOT10(carry, DECDPUN);
      *c=(Unit)(carry-est*(DECDPUNMAX+1));
      carry=est-(DECDPUNMAX+1);                /* correctly negative */
    #else
      if ((ueInt)carry<(DECDPUNMAX+1)*2){    /* fastpath carry 1 */
      *c=(Unit)(carry-(DECDPUNMAX+1));
      carry=1;
      continue;
      }
      /* remainder operator is undefined if negative, so must test */
      if (carry>=0) {
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1);
      continue;
      }
      /* negative case */
      carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
      *c=(Unit)(carry%(DECDPUNMAX+1));
      carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
    #endif
    } /* c */

  /* OK, all A and B processed; might still have carry or borrow */
  /* return number of Units in the result, negated if a borrow */
  if (carry==0) return c-clsu;         /* no carry, so no more to do */
  if (carry>0) {           /* positive carry */
    *c=(Unit)carry;              /* place as new unit */
    c++;                   /* .. */
    return c-clsu;
    }
  /* -ve carry: it's a borrow; complement needed */
  add=1;                   /* temporary carry... */
  for (c=clsu; c<maxC; c++) {
    add=DECDPUNMAX+add-*c;
    if (add<=DECDPUNMAX) {
      *c=(Unit)add;
      add=0;
      }
     else {
      *c=0;
      add=1;
      }
    }
  /* add an extra unit iff it would be non-zero */
  #if DECTRACE
    printf("UAS borrow: add %ld, carry %ld\n", add, carry);
  #endif
  if ((add-carry-1)!=0) {
    *c=(Unit)(add-carry-1);
    c++;                /* interesting, include it */
    }
  return clsu-c;        /* -ve result indicates borrowed */
  } /* decUnitAddSub */

/* ------------------------------------------------------------------ */
/* decTrim -- trim trailing zeros or normalize                    */
/*                                                    */
/*   dn is the number to trim or normalize                        */
/*   set is the context to use to check for clamp                 */
/*   all is 1 to remove all trailing zeros, 0 for just fraction ones  */
/*   dropped returns the number of discarded trailing zeros       */
/*   returns dn                                             */
/*                                                    */
/* If clamp is set in the context then the number of zeros trimmed    */
/* may be limited if the exponent is high.                        */
/* All fields are updated as required.    This is a utility operation,  */
/* so special values are unchanged and no error is possible.            */
/* ------------------------------------------------------------------ */
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
                     Int *dropped) {
  Int d, exp;                    /* work */
  uInt      cut;                 /* .. */
  Unit      *up;                 /* -> current Unit */

  #if DECCHECK
  if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
  #endif

  *dropped=0;                       /* assume no zeros dropped */
  if ((dn->bits & DECSPECIAL)       /* fast exit if special .. */
    || (*dn->lsu & 0x01)) return dn;      /* .. or odd */
  if (ISZERO(dn)) {                 /* .. or 0 */
    dn->exponent=0;                 /* (sign is preserved) */
    return dn;
    }

  /* have a finite number which is even */
  exp=dn->exponent;
  cut=1;                   /* digit (1-DECDPUN) in Unit */
  up=dn->lsu;                    /* -> current Unit */
  for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
    /* slice by powers */
    #if DECDPUN<=4
      uInt quot=QUOT10(*up, cut);
      if ((*up-quot*powers[cut])!=0) break;  /* found non-0 digit */
    #else
      if (*up%powers[cut]!=0) break;           /* found non-0 digit */
    #endif
    /* have a trailing 0 */
    if (!all) {                  /* trimming */
      /* [if exp>0 then all trailing 0s are significant for trim] */
      if (exp<=0) {              /* if digit might be significant */
      if (exp==0) break;         /* then quit */
      exp++;                     /* next digit might be significant */
      }
      }
    cut++;                 /* next power */
    if (cut>DECDPUN) {           /* need new Unit */
      up++;
      cut=1;
      }
    } /* d */
  if (d==0) return dn;           /* none to drop */

  /* may need to limit drop if clamping */
  if (set->clamp) {
    Int maxd=set->emax-set->digits+1-dn->exponent;
    if (maxd<=0) return dn;      /* nothing possible */
    if (d>maxd) d=maxd;
    }

  /* effect the drop */
  decShiftToLeast(dn->lsu, D2U(dn->digits), d);
  dn->exponent+=d;               /* maintain numerical value */
  dn->digits-=d;           /* new length */
  *dropped=d;                    /* report the count */
  return dn;
  } /* decTrim */

/* ------------------------------------------------------------------ */
/* decReverse -- reverse a Unit array in place                    */
/*                                                    */
/*   ulo    is the start of the array                             */
/*   uhi    is the end of the array (highest Unit to include)           */
/*                                                    */
/* The units ulo through uhi are reversed in place (if the number     */
/* of units is odd, the middle one is untouched).  Note that the      */
/* digit(s) in each unit are unaffected.                    */
/* ------------------------------------------------------------------ */
static void decReverse(Unit *ulo, Unit *uhi) {
  Unit temp;
  for (; ulo<uhi; ulo++, uhi--) {
    temp=*ulo;
    *ulo=*uhi;
    *uhi=temp;
    }
  return;
  } /* decReverse */

/* ------------------------------------------------------------------ */
/* decShiftToMost -- shift digits in array towards most significant   */
/*                                                    */
/*   uar    is the array                                    */
/*   digits is the count of digits in use in the array                  */
/*   shift  is the number of zeros to pad with (least significant);   */
/*     it must be zero or positive                          */
/*                                                    */
/*   returns the new length of the integer in the array, in digits    */
/*                                                    */
/* No overflow is permitted (that is, the uar array must be known to  */
/* be large enough to hold the result, after shifting).                 */
/* ------------------------------------------------------------------ */
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
  Unit      *target, *source, *first;  /* work */
  Int cut;                 /* odd 0's to add */
  uInt      next;                /* work */

  if (shift==0) return digits;         /* [fastpath] nothing to do */
  if ((digits+shift)<=DECDPUN) {   /* [fastpath] single-unit case */
    *uar=(Unit)(*uar*powers[shift]);
    return digits+shift;
    }

  next=0;                  /* all paths */
  source=uar+D2U(digits)-1;      /* where msu comes from */
  target=source+D2U(shift);      /* where upper part of first cut goes */
  cut=DECDPUN-MSUDIGITS(shift);        /* where to slice */
  if (cut==0) {                  /* unit-boundary case */
    for (; source>=uar; source--, target--) *target=*source;
    }
   else {
    first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
    for (; source>=uar; source--, target--) {
      /* split the source Unit and accumulate remainder for next */
      #if DECDPUN<=4
      uInt quot=QUOT10(*source, cut);
      uInt rem=*source-quot*powers[cut];
      next+=quot;
      #else
      uInt rem=*source%powers[cut];
      next+=*source/powers[cut];
      #endif
      if (target<=first) *target=(Unit)next;   /* write to target iff valid */
      next=rem*powers[DECDPUN-cut];        /* save remainder for next Unit */
      }
    } /* shift-move */

  /* propagate any partial unit to one below and clear the rest */
  for (; target>=uar; target--) {
    *target=(Unit)next;
    next=0;
    }
  return digits+shift;
  } /* decShiftToMost */

/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
/*                                                    */
/*   uar   is the array                                     */
/*   units is length of the array, in units                       */
/*   shift is the number of digits to remove from the lsu end; it     */
/*     must be zero or positive and <= than units*DECDPUN.        */
/*                                                    */
/*   returns the new length of the integer in the array, in units     */
/*                                                    */
/* Removed digits are discarded (lost).    Units not required to hold   */
/* the final result are unchanged.                          */
/* ------------------------------------------------------------------ */
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
  Unit      *target, *up;              /* work */
  Int cut, count;          /* work */
  Int quot, rem;           /* for division */

  if (shift==0) return units;    /* [fastpath] nothing to do */
  if (shift==units*DECDPUN) {    /* [fastpath] little to do */
    *uar=0;                /* all digits cleared gives zero */
    return 1;                    /* leaves just the one */
    }

  target=uar;                    /* both paths */
  cut=MSUDIGITS(shift);
  if (cut==DECDPUN) {            /* unit-boundary case; easy */
    up=uar+D2U(shift);
    for (; up<uar+units; target++, up++) *target=*up;
    return target-uar;
    }

  /* messier */
  up=uar+D2U(shift-cut);         /* source; correct to whole Units */
  count=units*DECDPUN-shift;     /* the maximum new length */
  #if DECDPUN<=4
    quot=QUOT10(*up, cut);
  #else
    quot=*up/powers[cut];
  #endif
  for (; ; target++) {
    *target=(Unit)quot;
    count-=(DECDPUN-cut);
    if (count<=0) break;
    up++;
    quot=*up;
    #if DECDPUN<=4
      quot=QUOT10(quot, cut);
      rem=*up-quot*powers[cut];
    #else
      rem=quot%powers[cut];
      quot=quot/powers[cut];
    #endif
    *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
    count-=cut;
    if (count<=0) break;
    }
  return target-uar+1;
  } /* decShiftToLeast */

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decRoundOperand -- round an operand    [used for subset only]        */
/*                                                    */
/*   dn is the number to round (dn->digits is > set->digits)            */
/*   set is the relevant context                            */
/*   status is the status accumulator                             */
/*                                                    */
/*   returns an allocated decNumber with the rounded result.            */
/*                                                    */
/* lostDigits and other status may be set by this.                */
/*                                                    */
/* Since the input is an operand, it must not be modified.        */
/* Instead, return an allocated decNumber, rounded as required.         */
/* It is the caller's responsibility to free the allocated storage.   */
/*                                                    */
/* If no storage is available then the result cannot be used, so NULL */
/* is returned.                                             */
/* ------------------------------------------------------------------ */
static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
                          uInt *status) {
  decNumber *res;             /* result structure */
  uInt newstatus=0;                 /* status from round */
  Int  residue=0;             /* rounding accumulator */

  /* Allocate storage for the returned decNumber, big enough for the */
  /* length specified by the context */
  res=(decNumber *)malloc(sizeof(decNumber)
                    +(D2U(set->digits)-1)*sizeof(Unit));
  if (res==NULL) {
    *status|=DEC_Insufficient_storage;
    return NULL;
    }
  decCopyFit(res, dn, set, &residue, &newstatus);
  decApplyRound(res, set, residue, &newstatus);

  /* If that set Inexact then "lost digits" is raised... */
  if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
  *status|=newstatus;
  return res;
  } /* decRoundOperand */
#endif

/* ------------------------------------------------------------------ */
/* decCopyFit -- copy a number, truncating the coefficient if needed  */
/*                                                    */
/*   dest is the target decNumber                           */
/*   src  is the source decNumber                           */
/*   set is the context [used for length (digits) and rounding mode]  */
/*   residue is the residue accumulator                           */
/*   status contains the current status to be updated             */
/*                                                    */
/* (dest==src is allowed and will be a no-op if fits)             */
/* All fields are updated as required.                            */
/* ------------------------------------------------------------------ */
static void decCopyFit(decNumber *dest, const decNumber *src,
                   decContext *set, Int *residue, uInt *status) {
  dest->bits=src->bits;
  dest->exponent=src->exponent;
  decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
  } /* decCopyFit */

/* ------------------------------------------------------------------ */
/* decSetCoeff -- set the coefficient of a number                 */
/*                                                    */
/*   dn        is the number whose coefficient array is to be set.            */
/*       It must have space for set->digits digits                */
/*   set   is the context [for size]                              */
/*   lsu   -> lsu of the source coefficient [may be dn->lsu]            */
/*   len   is digits in the source coefficient [may be dn->digits]    */
/*   residue is the residue accumulator.  This has values as in         */
/*       decApplyRound, and will be unchanged unless the          */
/*       target size is less than len.  In this case, the         */
/*       coefficient is truncated and the residue is updated to     */
/*       reflect the previous residue and the dropped digits.           */
/*   status is the status accumulator, as usual                   */
/*                                                    */
/* The coefficient may already be in the number, or it can be an      */
/* external intermediate array.      If it is in the number, lsu must ==  */
/* dn->lsu and len must == dn->digits.                            */
/*                                                    */
/* Note that the coefficient length (len) may be < set->digits, and   */
/* in this case this merely copies the coefficient (or is a no-op     */
/* if dn->lsu==lsu).                                        */
/*                                                    */
/* Note also that (only internally, from decQuantizeOp and        */
/* decSetSubnormal) the value of set->digits may be less than one,    */
/* indicating a round to left.      This routine handles that case            */
/* correctly; caller ensures space.                         */
/*                                                    */
/* dn->digits, dn->lsu (and as required), and dn->exponent are          */
/* updated as necessary.   dn->bits (sign) is unchanged.          */
/*                                                    */
/* DEC_Rounded status is set if any digits are discarded.         */
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
/*                 incoming residue was non-0 (implies rounded) */
/* ------------------------------------------------------------------ */
/* mapping array: maps 0-9 to canonical residues, so that a residue */
/* can be adjusted in the range [-1, +1] and achieve correct rounding */
/*                       0  1  2    3  4  5      6  7  8  9 */
static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
                  Int len, Int *residue, uInt *status) {
  Int discard;          /* number of digits to discard */
  uInt      cut;              /* cut point in Unit */
  const Unit *up;       /* work */
  Unit      *target;          /* .. */
  Int count;                  /* .. */
  #if DECDPUN<=4
  uInt      temp;             /* .. */
  #endif

  discard=len-set->digits;    /* digits to discard */
  if (discard<=0) {           /* no digits are being discarded */
    if (dn->lsu!=lsu) {       /* copy needed */
      /* copy the coefficient array to the result number; no shift needed */
      count=len;        /* avoids D2U */
      up=lsu;
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
      *target=*up;
      dn->digits=len;         /* set the new length */
      }
    /* dn->exponent and residue are unchanged, record any inexactitude */
    if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
    return;
    }

  /* some digits must be discarded ... */
  dn->exponent+=discard;      /* maintain numerical value */
  *status|=DEC_Rounded;       /* accumulate Rounded status */
  if (*residue>1) *residue=1; /* previous residue now to right, so reduce */

  if (discard>len) {          /* everything, +1, is being discarded */
    /* guard digit is 0 */
    /* residue is all the number [NB could be all 0s] */
    if (*residue<=0) {        /* not already positive */
      count=len;        /* avoids D2U */
      for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
      *residue=1;
      break;                  /* no need to check any others */
      }
      }
    if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
    *dn->lsu=0;               /* coefficient will now be 0 */
    dn->digits=1;       /* .. */
    return;
    } /* total discard */

  /* partial discard [most common case] */
  /* here, at least the first (most significant) discarded digit exists */

  /* spin up the number, noting residue during the spin, until get to */
  /* the Unit with the first discarded digit.  When reach it, extract */
  /* it and remember its position */
  count=0;
  for (up=lsu;; up++) {
    count+=DECDPUN;
    if (count>=discard) break; /* full ones all checked */
    if (*up!=0) *residue=1;
    } /* up */

  /* here up -> Unit with first discarded digit */
  cut=discard-(count-DECDPUN)-1;
  if (cut==DECDPUN-1) {       /* unit-boundary case (fast) */
    Unit half=(Unit)powers[DECDPUN]>>1;
    /* set residue directly */
    if (*up>=half) {
      if (*up>half) *residue=7;
      else *residue+=5;       /* add sticky bit */
      }
     else { /* <half */
      if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
      }
    if (set->digits<=0) {     /* special for Quantize/Subnormal :-( */
      *dn->lsu=0;       /* .. result is 0 */
      dn->digits=1;           /* .. */
      }
     else {             /* shift to least */
      count=set->digits;      /* now digits to end up with */
      dn->digits=count;       /* set the new length */
      up++;             /* move to next */
      /* on unit boundary, so shift-down copy loop is simple */
      for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
      *target=*up;
      }
    } /* unit-boundary case */

   else { /* discard digit is in low digit(s), and not top digit */
    uInt  discard1;              /* first discarded digit */
    uInt  quot, rem;             /* for divisions */
    if (cut==0) quot=*up;        /* is at bottom of unit */
     else /* cut>0 */ {          /* it's not at bottom of unit */
      #if DECDPUN<=4
      quot=QUOT10(*up, cut);
      rem=*up-quot*powers[cut];
      #else
      rem=*up%powers[cut];
      quot=*up/powers[cut];
      #endif
      if (rem!=0) *residue=1;
      }
    /* discard digit is now at bottom of quot */
    #if DECDPUN<=4
      temp=(quot*6554)>>16;      /* fast /10 */
      /* Vowels algorithm here not a win (9 instructions) */
      discard1=quot-X10(temp);
      quot=temp;
    #else
      discard1=quot%10;
      quot=quot/10;
    #endif
    /* here, discard1 is the guard digit, and residue is everything */
    /* else [use mapping array to accumulate residue safely] */
    *residue+=resmap[discard1];
    cut++;                 /* update cut */
    /* here: up -> Unit of the array with bottom digit */
    /*           cut is the division point for each Unit */
    /*           quot holds the uncut high-order digits for the current unit */
    if (set->digits<=0) {        /* special for Quantize/Subnormal :-( */
      *dn->lsu=0;          /* .. result is 0 */
      dn->digits=1;              /* .. */
      }
     else {                /* shift to least needed */
      count=set->digits;         /* now digits to end up with */
      dn->digits=count;          /* set the new length */
      /* shift-copy the coefficient array to the result number */
      for (target=dn->lsu; ; target++) {
      *target=(Unit)quot;
      count-=(DECDPUN-cut);
      if (count<=0) break;
      up++;
      quot=*up;
      #if DECDPUN<=4
        quot=QUOT10(quot, cut);
        rem=*up-quot*powers[cut];
      #else
        rem=quot%powers[cut];
        quot=quot/powers[cut];
      #endif
      *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
      count-=cut;
      if (count<=0) break;
      } /* shift-copy loop */
      } /* shift to least */
    } /* not unit boundary */

  if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
  return;
  } /* decSetCoeff */

/* ------------------------------------------------------------------ */
/* decApplyRound -- apply pending rounding to a number                  */
/*                                                    */
/*   dn        is the number, with space for set->digits digits         */
/*   set   is the context [for size and rounding mode]                  */
/*   residue indicates pending rounding, being any accumulated          */
/*       guard and sticky information.  It may be:                */
/*       6-9: rounding digit is >5                          */
/*       5: rounding digit is exactly half-way              */
/*       1-4: rounding digit is <5 and >0                   */
/*       0: the coefficient is exact                        */
/*      -1: as 1, but the hidden digits are subtractive, that     */
/*          is, of the opposite sign to dn.      In this case the     */
/*          coefficient must be non-0.  This case occurs when     */
/*          subtracting a small number (which can be reduced to   */
/*          a sticky bit); see decAddOp.                    */
/*   status is the status accumulator, as usual                   */
/*                                                    */
/* This routine applies rounding while keeping the length of the      */
/* coefficient constant.  The exponent and status are unchanged         */
/* except if:                                               */
/*                                                    */
/*   -- the coefficient was increased and is all nines (in which      */
/*    case Overflow could occur, and is handled directly here so    */
/*    the caller does not need to re-test for overflow)           */
/*                                                    */
/*   -- the coefficient was decreased and becomes all nines (in which */
/*    case Underflow could occur, and is also handled directly).    */
/*                                                    */
/* All fields in dn are updated as required.                      */
/*                                                    */
/* ------------------------------------------------------------------ */
static void decApplyRound(decNumber *dn, decContext *set, Int residue,
                    uInt *status) {
  Int  bump;                  /* 1 if coefficient needs to be incremented */
                        /* -1 if coefficient needs to be decremented */

  if (residue==0) return;     /* nothing to apply */

  bump=0;               /* assume a smooth ride */

  /* now decide whether, and how, to round, depending on mode */
  switch (set->round) {
    case DEC_ROUND_05UP: {    /* round zero or five up (for reround) */
      /* This is the same as DEC_ROUND_DOWN unless there is a */
      /* positive residue and the lsd of dn is 0 or 5, in which case */
      /* it is bumped; when residue is <0, the number is therefore */
      /* bumped down unless the final digit was 1 or 6 (in which */
      /* case it is bumped down and then up -- a no-op) */
      Int lsd5=*dn->lsu%5;     /* get lsd and quintate */
      if (residue<0 && lsd5!=1) bump=-1;
       else if (residue>0 && lsd5==0) bump=1;
      /* [bump==1 could be applied directly; use common path for clarity] */
      break;} /* r-05 */

    case DEC_ROUND_DOWN: {
      /* no change, except if negative residue */
      if (residue<0) bump=-1;
      break;} /* r-d */

    case DEC_ROUND_HALF_DOWN: {
      if (residue>5) bump=1;
      break;} /* r-h-d */

    case DEC_ROUND_HALF_EVEN: {
      if (residue>5) bump=1;        /* >0.5 goes up */
       else if (residue==5) {       /* exactly 0.5000... */
      /* 0.5 goes up iff [new] lsd is odd */
      if (*dn->lsu & 0x01) bump=1;
      }
      break;} /* r-h-e */

    case DEC_ROUND_HALF_UP: {
      if (residue>=5) bump=1;
      break;} /* r-h-u */

    case DEC_ROUND_UP: {
      if (residue>0) bump=1;
      break;} /* r-u */

    case DEC_ROUND_CEILING: {
      /* same as _UP for positive numbers, and as _DOWN for negatives */
      /* [negative residue cannot occur on 0] */
      if (decNumberIsNegative(dn)) {
      if (residue<0) bump=-1;
      }
       else {
      if (residue>0) bump=1;
      }
      break;} /* r-c */

    case DEC_ROUND_FLOOR: {
      /* same as _UP for negative numbers, and as _DOWN for positive */
      /* [negative residue cannot occur on 0] */
      if (!decNumberIsNegative(dn)) {
      if (residue<0) bump=-1;
      }
       else {
      if (residue>0) bump=1;
      }
      break;} /* r-f */

    default: {        /* e.g., DEC_ROUND_MAX */
      *status|=DEC_Invalid_context;
      #if DECTRACE || (DECCHECK && DECVERB)
      printf("Unknown rounding mode: %d\n", set->round);
      #endif
      break;}
    } /* switch */

  /* now bump the number, up or down, if need be */
  if (bump==0) return;                   /* no action required */

  /* Simply use decUnitAddSub unless bumping up and the number is */
  /* all nines.    In this special case set to 100... explicitly */
  /* and adjust the exponent by one (as otherwise could overflow */
  /* the array) */
  /* Similarly handle all-nines result if bumping down. */
  if (bump>0) {
    Unit *up;                            /* work */
    uInt count=dn->digits;               /* digits to be checked */
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
      /* this is the last Unit (the msu) */
      if (*up!=powers[count]-1) break;     /* not still 9s */
      /* here if it, too, is all nines */
      *up=(Unit)powers[count-1];         /* here 999 -> 100 etc. */
      for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
      dn->exponent++;                    /* and bump exponent */
      /* [which, very rarely, could cause Overflow...] */
      if ((dn->exponent+dn->digits)>set->emax+1) {
        decSetOverflow(dn, set, status);
        }
      return;                            /* done */
      }
      /* a full unit to check, with more to come */
      if (*up!=DECDPUNMAX) break;        /* not still 9s */
      count-=DECDPUN;
      } /* up */
    } /* bump>0 */
   else {                          /* -1 */
    /* here checking for a pre-bump of 1000... (leading 1, all */
    /* other digits zero) */
    Unit *up, *sup;                      /* work */
    uInt count=dn->digits;               /* digits to be checked */
    for (up=dn->lsu; ; up++) {
      if (count<=DECDPUN) {
      /* this is the last Unit (the msu) */
      if (*up!=powers[count-1]) break;     /* not 100.. */
      /* here if have the 1000... case */
      sup=up;                            /* save msu pointer */
      *up=(Unit)powers[count]-1;         /* here 100 in msu -> 999 */
      /* others all to all-nines, too */
      for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
      dn->exponent--;                    /* and bump exponent */

      /* iff the number was at the subnormal boundary (exponent=etiny) */
      /* then the exponent is now out of range, so it will in fact get */
      /* clamped to etiny and the final 9 dropped. */
      /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
      /*      dn->exponent, set->digits); */
      if (dn->exponent+1==set->emin-set->digits+1) {
        if (count==1 && dn->digits==1) *sup=0;  /* here 9 -> 0[.9] */
         else {
          *sup=(Unit)powers[count-1]-1;    /* here 999.. in msu -> 99.. */
          dn->digits--;
          }
        dn->exponent++;
        *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
        }
      return;                            /* done */
      }

      /* a full unit to check, with more to come */
      if (*up!=0) break;                 /* not still 0s */
      count-=DECDPUN;
      } /* up */

    } /* bump<0 */

  /* Actual bump needed.  Do it. */
  decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
  } /* decApplyRound */

#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decFinish -- finish processing a number                        */
/*                                                    */
/*   dn is the number                                       */
/*   set is the context                                     */
/*   residue is the rounding accumulator (as in decApplyRound)          */
/*   status is the accumulator                                    */
/*                                                    */
/* This finishes off the current number by:                       */
/*    1. If not extended:                                   */
/*     a. Converting a zero result to clean '0'             */
/*     b. Reducing positive exponents to 0, if would fit in digits  */
/*    2. Checking for overflow and subnormals (always)                  */
/* Note this is just Finalize when no subset arithmetic.          */
/* All fields are updated as required.                            */
/* ------------------------------------------------------------------ */
static void decFinish(decNumber *dn, decContext *set, Int *residue,
                  uInt *status) {
  if (!set->extended) {
    if ISZERO(dn) {              /* value is zero */
      dn->exponent=0;            /* clean exponent .. */
      dn->bits=0;          /* .. and sign */
      return;                    /* no error possible */
      }
    if (dn->exponent>=0) {       /* non-negative exponent */
      /* >0; reduce to integer if possible */
      if (set->digits >= (dn->exponent+dn->digits)) {
      dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
      dn->exponent=0;
      }
      }
    } /* !extended */

  decFinalize(dn, set, residue, status);
  } /* decFinish */
#endif

/* ------------------------------------------------------------------ */
/* decFinalize -- final check, clamp, and round of a number       */
/*                                                    */
/*   dn is the number                                       */
/*   set is the context                                     */
/*   residue is the rounding accumulator (as in decApplyRound)          */
/*   status is the status accumulator                             */
/*                                                    */
/* This finishes off the current number by checking for subnormal     */
/* results, applying any pending rounding, checking for overflow,     */
/* and applying any clamping.                               */
/* Underflow and overflow conditions are raised as appropriate.         */
/* All fields are updated as required.                            */
/* ------------------------------------------------------------------ */
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
                  uInt *status) {
  Int shift;                        /* shift needed if clamping */
  Int tinyexp=set->emin-dn->digits+1;     /* precalculate subnormal boundary */

  /* Must be careful, here, when checking the exponent as the */
  /* adjusted exponent could overflow 31 bits [because it may already */
  /* be up to twice the expected]. */

  /* First test for subnormal.      This must be done before any final */
  /* round as the result could be rounded to Nmin or 0. */
  if (dn->exponent<=tinyexp) {            /* prefilter */
    Int comp;
    decNumber nmin;
    /* A very nasty case here is dn == Nmin and residue<0 */
    if (dn->exponent<tinyexp) {
      /* Go handle subnormals; this will apply round if needed. */
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    /* Equals case: only subnormal if dn=Nmin and negative residue */
    decNumberZero(&nmin);
    nmin.lsu[0]=1;
    nmin.exponent=set->emin;
    comp=decCompare(dn, &nmin, 1);          /* (signless compare) */
    if (comp==BADINT) {                     /* oops */
      *status|=DEC_Insufficient_storage;    /* abandon... */
      return;
      }
    if (*residue<0 && comp==0) {            /* neg residue and dn==Nmin */
      decApplyRound(dn, set, *residue, status);   /* might force down */
      decSetSubnormal(dn, set, residue, status);
      return;
      }
    }

  /* now apply any pending round (this could raise overflow). */
  if (*residue!=0) decApplyRound(dn, set, *residue, status);

  /* Check for overflow [redundant in the 'rare' case] or clamp */
  if (dn->exponent<=set->emax-set->digits+1) return;   /* neither needed */


  /* here when might have an overflow or clamp to do */
  if (dn->exponent>set->emax-dn->digits+1) {           /* too big */
    decSetOverflow(dn, set, status);
    return;
    }
  /* here when the result is normal but in clamp range */
  if (!set->clamp) return;

  /* here when need to apply the IEEE exponent clamp (fold-down) */
  shift=dn->exponent-(set->emax-set->digits+1);

  /* shift coefficient (if non-zero) */
  if (!ISZERO(dn)) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
    }
  dn->exponent-=shift;   /* adjust the exponent to match */
  *status|=DEC_Clamped;  /* and record the dirty deed */
  return;
  } /* decFinalize */

/* ------------------------------------------------------------------ */
/* decSetOverflow -- set number to proper overflow value          */
/*                                                    */
/*   dn is the number (used for sign [only] and result)                 */
/*   set is the context [used for the rounding mode, etc.]        */
/*   status contains the current status to be updated             */
/*                                                    */
/* This sets the sign of a number and sets its value to either          */
/* Infinity or the maximum finite value, depending on the sign of     */
/* dn and the rounding mode, following IEEE 854 rules.                  */
/* ------------------------------------------------------------------ */
static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
  Flag needmax=0;          /* result is maximum finite value */
  uByte sign=dn->bits&DECNEG;    /* clean and save sign bit */

  if (ISZERO(dn)) {              /* zero does not overflow magnitude */
    Int emax=set->emax;                  /* limit value */
    if (set->clamp) emax-=set->digits-1;     /* lower if clamping */
    if (dn->exponent>emax) {             /* clamp required */
      dn->exponent=emax;
      *status|=DEC_Clamped;
      }
    return;
    }

  decNumberZero(dn);
  switch (set->round) {
    case DEC_ROUND_DOWN: {
      needmax=1;           /* never Infinity */
      break;} /* r-d */
    case DEC_ROUND_05UP: {
      needmax=1;           /* never Infinity */
      break;} /* r-05 */
    case DEC_ROUND_CEILING: {
      if (sign) needmax=1;       /* Infinity if non-negative */
      break;} /* r-c */
    case DEC_ROUND_FLOOR: {
      if (!sign) needmax=1;      /* Infinity if negative */
      break;} /* r-f */
    default: break;              /* Infinity in all other cases */
    }
  if (needmax) {
    decSetMaxValue(dn, set);
    dn->bits=sign;               /* set sign */
    }
   else dn->bits=sign|DECINF;    /* Value is +/-Infinity */
  *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
  } /* decSetOverflow */

/* ------------------------------------------------------------------ */
/* decSetMaxValue -- set number to +Nmax (maximum normal value)         */
/*                                                    */
/*   dn is the number to set                                */
/*   set is the context [used for digits and emax]                */
/*                                                    */
/* This sets the number to the maximum positive value.                  */
/* ------------------------------------------------------------------ */
static void decSetMaxValue(decNumber *dn, decContext *set) {
  Unit *up;                /* work */
  Int count=set->digits;         /* nines to add */
  dn->digits=count;
  /* fill in all nines to set maximum value */
  for (up=dn->lsu; ; up++) {
    if (count>DECDPUN) *up=DECDPUNMAX;    /* unit full o'nines */
     else {                   /* this is the msu */
      *up=(Unit)(powers[count]-1);
      break;
      }
    count-=DECDPUN;              /* filled those digits */
    } /* up */
  dn->bits=0;                    /* + sign */
  dn->exponent=set->emax-set->digits+1;
  } /* decSetMaxValue */

/* ------------------------------------------------------------------ */
/* decSetSubnormal -- process value whose exponent is <Emin       */
/*                                                    */
/*   dn is the number (used as input as well as output; it may have   */
/*       an allowed subnormal value, which may need to be rounded)  */
/*   set is the context [used for the rounding mode]              */
/*   residue is any pending residue                         */
/*   status contains the current status to be updated             */
/*                                                    */
/* If subset mode, set result to zero and set Underflow flags.          */
/*                                                    */
/* Value may be zero with a low exponent; this does not set Subnormal */
/* but the exponent will be clamped to Etiny.                     */
/*                                                    */
/* Otherwise ensure exponent is not out of range, and round as          */
/* necessary.  Underflow is set if the result is Inexact.         */
/* ------------------------------------------------------------------ */
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
                      uInt *status) {
  Int      dnexp;       /* saves original exponent */
  decContext workset;         /* work */
  Int      etiny, adjust;   /* .. */

  #if DECSUBSET
  /* simple set to zero and 'hard underflow' for subset */
  if (!set->extended) {
    decNumberZero(dn);
    /* always full overflow */
    *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
    return;
    }
  #endif

  /* Full arithmetic -- allow subnormals, rounded to minimum exponent */
  /* (Etiny) if needed */
  etiny=set->emin-(set->digits-1);  /* smallest allowed exponent */

  if ISZERO(dn) {             /* value is zero */
    /* residue can never be non-zero here */
    #if DECCHECK
      if (*residue!=0) {
      printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
      *status|=DEC_Invalid_operation;
      }
    #endif
    if (dn->exponent<etiny) {       /* clamp required */
      dn->exponent=etiny;
      *status|=DEC_Clamped;
      }
    return;
    }

  *status|=DEC_Subnormal;           /* have a non-zero subnormal */
  adjust=etiny-dn->exponent;        /* calculate digits to remove */
  if (adjust<=0) {                  /* not out of range; unrounded */
    /* residue can never be non-zero here, except in the Nmin-residue */
    /* case (which is a subnormal result), so can take fast-path here */
    /* it may already be inexact (from setting the coefficient) */
    if (*status&DEC_Inexact) *status|=DEC_Underflow;
    return;
    }

  /* adjust>0, so need to rescale the result so exponent becomes Etiny */
  /* [this code is similar to that in rescale] */
  dnexp=dn->exponent;               /* save exponent */
  workset=*set;                     /* clone rounding, etc. */
  workset.digits=dn->digits-adjust; /* set requested length */
  workset.emin-=adjust;             /* and adjust emin to match */
  /* [note that the latter can be <1, here, similar to Rescale case] */
  decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
  decApplyRound(dn, &workset, *residue, status);

  /* Use 754R/854 default rule: Underflow is set iff Inexact */
  /* [independent of whether trapped] */
  if (*status&DEC_Inexact) *status|=DEC_Underflow;

  /* if rounded up a 999s case, exponent will be off by one; adjust */
  /* back if so [it will fit, because it was shortened earlier] */
  if (dn->exponent>etiny) {
    dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
    dn->exponent--;                 /* (re)adjust the exponent. */
    }

  /* if rounded to zero, it is by definition clamped... */
  if (ISZERO(dn)) *status|=DEC_Clamped;
  } /* decSetSubnormal */

/* ------------------------------------------------------------------ */
/* decCheckMath - check entry conditions for a math function            */
/*                                                    */
/*   This checks the context and the operand                      */
/*                                                    */
/*   rhs is the operand to check                            */
/*   set is the context to check                            */
/*   status is unchanged if both are good                   */
/*                                                    */
/* returns non-zero if status is changed, 0 otherwise             */
/*                                                    */
/* Restrictions enforced:                                   */
/*                                                    */
/*   digits, emax, and -emin in the context must be less than           */
/*   DEC_MAX_MATH (999999), and A must be within these bounds if      */
/*   non-zero.    Invalid_operation is set in the status if a           */
/*   restriction is violated.                               */
/* ------------------------------------------------------------------ */
static uInt decCheckMath(const decNumber *rhs, decContext *set,
                   uInt *status) {
  uInt save=*status;                     /* record */
  if (set->digits>DEC_MAX_MATH
   || set->emax>DEC_MAX_MATH
   || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
   else if ((rhs->digits>DEC_MAX_MATH
     || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
     || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
     && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
  return (*status!=save);
  } /* decCheckMath */

/* ------------------------------------------------------------------ */
/* decGetInt -- get integer from a number                   */
/*                                                    */
/*   dn is the number [which will not be altered]                 */
/*                                                    */
/*   returns one of:                                        */
/*     BADINT if there is a non-zero fraction                     */
/*     the converted integer                                */
/*     BIGEVEN if the integer is even and magnitude > 2*10**9           */
/*     BIGODD  if the integer is odd  and magnitude > 2*10**9           */
/*                                                    */
/* This checks and gets a whole number from the input decNumber.      */
/* The sign can be determined from dn by the caller when BIGEVEN or   */
/* BIGODD is returned.                                      */
/* ------------------------------------------------------------------ */
static Int decGetInt(const decNumber *dn) {
  Int  theInt;                      /* result accumulator */
  const Unit *up;             /* work */
  Int  got;                   /* digits (real or not) processed */
  Int  ilength=dn->digits+dn->exponent; /* integral length */
  Flag neg=decNumberIsNegative(dn); /* 1 if -ve */

  /* The number must be an integer that fits in 10 digits */
  /* Assert, here, that 10 is enough for any rescale Etiny */
  #if DEC_MAX_EMAX > 999999999
    #error GetInt may need updating [for Emax]
  #endif
  #if DEC_MIN_EMIN < -999999999
    #error GetInt may need updating [for Emin]
  #endif
  if (ISZERO(dn)) return 0;         /* zeros are OK, with any exponent */

  up=dn->lsu;                       /* ready for lsu */
  theInt=0;                   /* ready to accumulate */
  if (dn->exponent>=0) {            /* relatively easy */
    /* no fractional part [usual]; allow for positive exponent */
    got=dn->exponent;
    }
   else { /* -ve exponent; some fractional part to check and discard */
    Int count=-dn->exponent;        /* digits to discard */
    /* spin up whole units until reach the Unit with the unit digit */
    for (; count>=DECDPUN; up++) {
      if (*up!=0) return BADINT;    /* non-zero Unit to discard */
      count-=DECDPUN;
      }
    if (count==0) got=0;            /* [a multiple of DECDPUN] */
     else {                   /* [not multiple of DECDPUN] */
      Int rem;                      /* work */
      /* slice off fraction digits and check for non-zero */
      #if DECDPUN<=4
      theInt=QUOT10(*up, count);
      rem=*up-theInt*powers[count];
      #else
      rem=*up%powers[count];        /* slice off discards */
      theInt=*up/powers[count];
      #endif
      if (rem!=0) return BADINT;    /* non-zero fraction */
      /* it looks good */
      got=DECDPUN-count;            /* number of digits so far */
      up++;                   /* ready for next */
      }
    }
  /* now it's known there's no fractional part */

  /* tricky code now, to accumulate up to 9.3 digits */
  if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */

  if (ilength<11) {
    Int save=theInt;
    /* collect any remaining unit(s) */
    for (; got<ilength; up++) {
      theInt+=*up*powers[got];
      got+=DECDPUN;
      }
    if (ilength==10) {              /* need to check for wrap */
      if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
       /* [that test also disallows the BADINT result case] */
       else if (neg && theInt>1999999997) ilength=11;
       else if (!neg && theInt>999999999) ilength=11;
      if (ilength==11) theInt=save; /* restore correct low bit */
      }
    }

  if (ilength>10) {                 /* too big */
    if (theInt&1) return BIGODD;    /* bottom bit 1 */
    return BIGEVEN;                 /* bottom bit 0 */
    }

  if (neg) theInt=-theInt;          /* apply sign */
  return theInt;
  } /* decGetInt */

/* ------------------------------------------------------------------ */
/* decDecap -- decapitate the coefficient of a number             */
/*                                                    */
/*   dn       is the number to be decapitated                     */
/*   drop is the number of digits to be removed from the left of dn;  */
/*     this must be <= dn->digits (if equal, the coefficient is         */
/*     set to 0)                                      */
/*                                                    */
/* Returns dn; dn->digits will be <= the initial digits less drop     */
/* (after removing drop digits there may be leading zero digits         */
/* which will also be removed).      Only dn->lsu and dn->digits change.  */
/* ------------------------------------------------------------------ */
static decNumber *decDecap(decNumber *dn, Int drop) {
  Unit *msu;                        /* -> target cut point */
  Int cut;                    /* work */
  if (drop>=dn->digits) {           /* losing the whole thing */
    #if DECCHECK
    if (drop>dn->digits)
      printf("decDecap called with drop>digits [%ld>%ld]\n",
           (LI)drop, (LI)dn->digits);
    #endif
    dn->lsu[0]=0;
    dn->digits=1;
    return dn;
    }
  msu=dn->lsu+D2U(dn->digits-drop)-1;     /* -> likely msu */
  cut=MSUDIGITS(dn->digits-drop);   /* digits to be in use in msu */
  if (cut!=DECDPUN) *msu%=powers[cut];    /* clear left digits */
  /* that may have left leading zero digits, so do a proper count... */
  dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
  return dn;
  } /* decDecap */

/* ------------------------------------------------------------------ */
/* decBiStr -- compare string with pairwise options               */
/*                                                    */
/*   targ is the string to compare                          */
/*   str1 is one of the strings to compare against (length may be 0)  */
/*   str2 is the other; it must be the same length as str1        */
/*                                                    */
/*   returns 1 if strings compare equal, (that is, it is the same     */
/*   length as str1 and str2, and each character of targ is in either */
/*   str1 or str2 in the corresponding position), or 0 otherwise      */
/*                                                    */
/* This is used for generic caseless compare, including the awkward   */
/* case of the Turkish dotted and dotless Is.  Use as (for example):  */
/*   if (decBiStr(test, "mike", "MIKE")) ...                      */
/* ------------------------------------------------------------------ */
static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
  for (;;targ++, str1++, str2++) {
    if (*targ!=*str1 && *targ!=*str2) return 0;
    /* *targ has a match in one (or both, if terminator) */
    if (*targ=='\0') break;
    } /* forever */
  return 1;
  } /* decBiStr */

/* ------------------------------------------------------------------ */
/* decNaNs -- handle NaN operand or operands                      */
/*                                                    */
/*   res     is the result number                           */
/*   lhs     is the first operand                           */
/*   rhs     is the second operand, or NULL if none               */
/*   context is used to limit payload length                      */
/*   status  contains the current status                    */
/*   returns res in case convenient                         */
/*                                                    */
/* Called when one or both operands is a NaN, and propagates the      */
/* appropriate result to res.  When an sNaN is found, it is changed   */
/* to a qNaN and Invalid operation is set.                        */
/* ------------------------------------------------------------------ */
static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
                     const decNumber *rhs, decContext *set,
                     uInt *status) {
  /* This decision tree ends up with LHS being the source pointer, */
  /* and status updated if need be */
  if (lhs->bits & DECSNAN)
    *status|=DEC_Invalid_operation | DEC_sNaN;
   else if (rhs==NULL);
   else if (rhs->bits & DECSNAN) {
    lhs=rhs;
    *status|=DEC_Invalid_operation | DEC_sNaN;
    }
   else if (lhs->bits & DECNAN);
   else lhs=rhs;

  /* propagate the payload */
  if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */
   else { /* too long */
    const Unit *ul;
    Unit *ur, *uresp1;
    /* copy safe number of units, then decapitate */
    res->bits=lhs->bits;            /* need sign etc. */
    uresp1=res->lsu+D2U(set->digits);
    for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
    res->digits=D2U(set->digits)*DECDPUN;
    /* maybe still too long */
    if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
    }

  res->bits&=~DECSNAN;        /* convert any sNaN to NaN, while */
  res->bits|=DECNAN;          /* .. preserving sign */
  res->exponent=0;            /* clean exponent */
                        /* [coefficient was copied/decapitated] */
  return res;
  } /* decNaNs */

/* ------------------------------------------------------------------ */
/* decStatus -- apply non-zero status                             */
/*                                                    */
/*   dn         is the number to set if error                     */
/*   status contains the current status (not yet in context)            */
/*   set    is the context                                  */
/*                                                    */
/* If the status is an error status, the number is set to a NaN,      */
/* unless the error was an overflow, divide-by-zero, or underflow,    */
/* in which case the number will have already been set.                 */
/*                                                    */
/* The context status is then updated with the new status.  Note that */
/* this may raise a signal, so control may never return from this     */
/* routine (hence resources must be recovered before it is called).   */
/* ------------------------------------------------------------------ */
static void decStatus(decNumber *dn, uInt status, decContext *set) {
  if (status & DEC_NaNs) {          /* error status -> NaN */
    /* if cause was an sNaN, clear and propagate [NaN is already set up] */
    if (status & DEC_sNaN) status&=~DEC_sNaN;
     else {
      decNumberZero(dn);            /* other error: clean throughout */
      dn->bits=DECNAN;              /* and make a quiet NaN */
      }
    }
  decContextSetStatus(set, status); /* [may not return] */
  return;
  } /* decStatus */

/* ------------------------------------------------------------------ */
/* decGetDigits -- count digits in a Units array                  */
/*                                                    */
/*   uar is the Unit array holding the number (this is often an         */
/*        accumulator of some sort)                         */
/*   len is the length of the array in units [>=1]                */
/*                                                    */
/*   returns the number of (significant) digits in the array            */
/*                                                    */
/* All leading zeros are excluded, except the last if the array has   */
/* only zero Units.                                         */
/* ------------------------------------------------------------------ */
/* This may be called twice during some operations. */
static Int decGetDigits(Unit *uar, Int len) {
  Unit *up=uar+(len-1);          /* -> msu */
  Int  digits=(len-1)*DECDPUN+1;   /* possible digits excluding msu */
  #if DECDPUN>4
  uInt const *pow;               /* work */
  #endif
                           /* (at least 1 in final msu) */
  #if DECCHECK
  if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
  #endif

  for (; up>=uar; up--) {
    if (*up==0) {          /* unit is all 0s */
      if (digits==1) break;      /* a zero has one digit */
      digits-=DECDPUN;           /* adjust for 0 unit */
      continue;}
    /* found the first (most significant) non-zero Unit */
    #if DECDPUN>1          /* not done yet */
    if (*up<10) break;           /* is 1-9 */
    digits++;
    #if DECDPUN>2          /* not done yet */
    if (*up<100) break;          /* is 10-99 */
    digits++;
    #if DECDPUN>3          /* not done yet */
    if (*up<1000) break;         /* is 100-999 */
    digits++;
    #if DECDPUN>4          /* count the rest ... */
    for (pow=&powers[4]; *up>=*pow; pow++) digits++;
    #endif
    #endif
    #endif
    #endif
    break;
    } /* up */
  return digits;
  } /* decGetDigits */

#if DECTRACE | DECCHECK
/* ------------------------------------------------------------------ */
/* decNumberShow -- display a number [debug aid]                  */
/*   dn is the number to show                               */
/*                                                    */
/* Shows: sign, exponent, coefficient (msu first), digits         */
/*    or: sign, special-value                               */
/* ------------------------------------------------------------------ */
/* this is public so other modules can use it */
void decNumberShow(const decNumber *dn) {
  const Unit *up;          /* work */
  uInt u, d;                     /* .. */
  Int cut;                 /* .. */
  char isign='+';          /* main sign */
  if (dn==NULL) {
    printf("NULL\n");
    return;}
  if (decNumberIsNegative(dn)) isign='-';
  printf(" >> %c ", isign);
  if (dn->bits&DECSPECIAL) {     /* Is a special value */
    if (decNumberIsInfinite(dn)) printf("Infinity");
     else {                        /* a NaN */
      if (dn->bits&DECSNAN) printf("sNaN");  /* signalling NaN */
       else printf("NaN");
      }
    /* if coefficient and exponent are 0, no more to do */
    if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
      printf("\n");
      return;}
    /* drop through to report other information */
    printf(" ");
    }

  /* now carefully display the coefficient */
  up=dn->lsu+D2U(dn->digits)-1;           /* msu */
  printf("%ld", (LI)*up);
  for (up=up-1; up>=dn->lsu; up--) {
    u=*up;
    printf(":");
    for (cut=DECDPUN-1; cut>=0; cut--) {
      d=u/powers[cut];
      u-=d*powers[cut];
      printf("%ld", (LI)d);
      } /* cut */
    } /* up */
  if (dn->exponent!=0) {
    char esign='+';
    if (dn->exponent<0) esign='-';
    printf(" E%c%ld", esign, (LI)abs(dn->exponent));
    }
  printf(" [%ld]\n", (LI)dn->digits);
  } /* decNumberShow */
#endif

#if DECTRACE || DECCHECK
/* ------------------------------------------------------------------ */
/* decDumpAr -- display a unit array [debug/check aid]                  */
/*   name is a single-character tag name                    */
/*   ar       is the array to display                             */
/*   len  is the length of the array in Units                     */
/* ------------------------------------------------------------------ */
static void decDumpAr(char name, const Unit *ar, Int len) {
  Int i;
  const char *spec;
  #if DECDPUN==9
    spec="%09d ";
  #elif DECDPUN==8
    spec="%08d ";
  #elif DECDPUN==7
    spec="%07d ";
  #elif DECDPUN==6
    spec="%06d ";
  #elif DECDPUN==5
    spec="%05d ";
  #elif DECDPUN==4
    spec="%04d ";
  #elif DECDPUN==3
    spec="%03d ";
  #elif DECDPUN==2
    spec="%02d ";
  #else
    spec="%d ";
  #endif
  printf("  :%c: ", name);
  for (i=len-1; i>=0; i--) {
    if (i==len-1) printf("%ld ", (LI)ar[i]);
     else printf(spec, ar[i]);
    }
  printf("\n");
  return;}
#endif

#if DECCHECK
/* ------------------------------------------------------------------ */
/* decCheckOperands -- check operand(s) to a routine              */
/*   res is the result structure (not checked; it will be set to      */
/*        quiet NaN if error found (and it is not NULL))          */
/*   lhs is the first operand (may be DECUNRESU)                  */
/*   rhs is the second (may be DECUNUSED)                   */
/*   set is the context (may be DECUNCONT)                        */
/*   returns 0 if both operands, and the context are clean, or 1      */
/*     otherwise (in which case the context will show an error,         */
/*     unless NULL).  Note that res is not cleaned; caller should     */
/*     handle this so res=NULL case is safe.                      */
/* The caller is expected to abandon immediately if 1 is returned.    */
/* ------------------------------------------------------------------ */
static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
                       const decNumber *rhs, decContext *set) {
  Flag bad=0;
  if (set==NULL) {               /* oops; hopeless */
    #if DECTRACE || DECVERB
    printf("Reference to context is NULL.\n");
    #endif
    bad=1;
    return 1;}
   else if (set!=DECUNCONT
     && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
    bad=1;
    #if DECTRACE || DECVERB
    printf("Bad context [digits=%ld round=%ld].\n",
         (LI)set->digits, (LI)set->round);
    #endif
    }
   else {
    if (res==NULL) {
      bad=1;
      #if DECTRACE
      /* this one not DECVERB as standard tests include NULL */
      printf("Reference to result is NULL.\n");
      #endif
      }
    if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
    if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
    }
  if (bad) {
    if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
    if (res!=DECUNRESU && res!=NULL) {
      decNumberZero(res);
      res->bits=DECNAN;       /* qNaN */
      }
    }
  return bad;
  } /* decCheckOperands */

/* ------------------------------------------------------------------ */
/* decCheckNumber -- check a number                         */
/*   dn is the number to check                                    */
/*   returns 0 if the number is clean, or 1 otherwise             */
/*                                                    */
/* The number is considered valid if it could be a result from some   */
/* operation in some valid context.                         */
/* ------------------------------------------------------------------ */
static Flag decCheckNumber(const decNumber *dn) {
  const Unit *up;       /* work */
  uInt maxuint;               /* .. */
  Int ae, d, digits;          /* .. */
  Int emin, emax;       /* .. */

  if (dn==NULL) {       /* hopeless */
    #if DECTRACE
    /* this one not DECVERB as standard tests include NULL */
    printf("Reference to decNumber is NULL.\n");
    #endif
    return 1;}

  /* check special values */
  if (dn->bits & DECSPECIAL) {
    if (dn->exponent!=0) {
      #if DECTRACE || DECVERB
      printf("Exponent %ld (not 0) for a special value [%02x].\n",
           (LI)dn->exponent, dn->bits);
      #endif
      return 1;}

    /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
    if (decNumberIsInfinite(dn)) {
      if (dn->digits!=1) {
      #if DECTRACE || DECVERB
      printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
      #endif
      return 1;}
      if (*dn->lsu!=0) {
      #if DECTRACE || DECVERB
      printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
      #endif
      decDumpAr('I', dn->lsu, D2U(dn->digits));
      return 1;}
      } /* Inf */
    /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
    /*               concrete formats (decimal64, etc.). */
    return 0;
    }

  /* check the coefficient */
  if (dn->digits<1 || dn->digits>DECNUMMAXP) {
    #if DECTRACE || DECVERB
    printf("Digits %ld in number.\n", (LI)dn->digits);
    #endif
    return 1;}

  d=dn->digits;

  for (up=dn->lsu; d>0; up++) {
    if (d>DECDPUN) maxuint=DECDPUNMAX;
     else {             /* reached the msu */
      maxuint=powers[d]-1;
      if (dn->digits>1 && *up<powers[d-1]) {
      #if DECTRACE || DECVERB
      printf("Leading 0 in number.\n");
      decNumberShow(dn);
      #endif
      return 1;}
      }
    if (*up>maxuint) {
      #if DECTRACE || DECVERB
      printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
            (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
      #endif
      return 1;}
    d-=DECDPUN;
    }

  /* check the exponent.  Note that input operands can have exponents */
  /* which are out of the set->emin/set->emax and set->digits range */
  /* (just as they can have more digits than set->digits). */
  ae=dn->exponent+dn->digits-1;        /* adjusted exponent */
  emax=DECNUMMAXE;
  emin=DECNUMMINE;
  digits=DECNUMMAXP;
  if (ae<emin-(digits-1)) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}
  if (ae>+emax) {
    #if DECTRACE || DECVERB
    printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
    decNumberShow(dn);
    #endif
    return 1;}

  return 0;        /* it's OK */
  } /* decCheckNumber */

/* ------------------------------------------------------------------ */
/* decCheckInexact -- check a normal finite inexact result has digits */
/*   dn is the number to check                                    */
/*   set is the context (for status and precision)                */
/*   sets Invalid operation, etc., if some digits are missing           */
/* [this check is not made for DECSUBSET compilation or when            */
/* subnormal is not set]                                    */
/* ------------------------------------------------------------------ */
static void decCheckInexact(const decNumber *dn, decContext *set) {
  #if !DECSUBSET && DECEXTFLAG
    if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
     && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
      #if DECTRACE || DECVERB
      printf("Insufficient digits [%ld] on normal Inexact result.\n",
           (LI)dn->digits);
      decNumberShow(dn);
      #endif
      decContextSetStatus(set, DEC_Invalid_operation);
      }
  #else
    /* next is a noop for quiet compiler */
    if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
  #endif
  return;
  } /* decCheckInexact */
#endif

#if DECALLOC
#undef malloc
#undef free
/* ------------------------------------------------------------------ */
/* decMalloc -- accountable allocation routine                    */
/*   n is the number of bytes to allocate                   */
/*                                                    */
/* Semantics is the same as the stdlib malloc routine, but bytes      */
/* allocated are accounted for globally, and corruption fences are    */
/* added before and after the 'actual' storage.                   */
/* ------------------------------------------------------------------ */
/* This routine allocates storage with an extra twelve bytes; 8 are   */
/* at the start and hold:                                   */
/*   0-3 the original length requested                            */
/*   4-7 buffer corruption detection fence (DECFENCE, x4)         */
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
/* ------------------------------------------------------------------ */
static void *decMalloc(size_t n) {
  uInt      size=n+12;           /* true size */
  void      *alloc;                    /* -> allocated storage */
  uInt      *j;                  /* work */
  uByte *b, *b0;           /* .. */

  alloc=malloc(size);            /* -> allocated storage */
  if (alloc==NULL) return NULL;        /* out of strorage */
  b0=(uByte *)alloc;             /* as bytes */
  decAllocBytes+=n;              /* account for storage */
  j=(uInt *)alloc;               /* -> first four bytes */
  *j=n;                          /* save n */
  /* printf(" alloc ++ dAB: %ld (%d)\n", decAllocBytes, n); */
  for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
  for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
  return b0+8;                   /* -> play area */
  } /* decMalloc */

/* ------------------------------------------------------------------ */
/* decFree -- accountable free routine                            */
/*   alloc is the storage to free                           */
/*                                                    */
/* Semantics is the same as the stdlib malloc routine, except that    */
/* the global storage accounting is updated and the fences are          */
/* checked to ensure that no routine has written 'out of bounds'.     */
/* ------------------------------------------------------------------ */
/* This routine first checks that the fences have not been corrupted. */
/* It then frees the storage using the 'truw' storage address (that   */
/* is, offset by 8).                                        */
/* ------------------------------------------------------------------ */
static void decFree(void *alloc) {
  uInt      *j, n;                     /* pointer, original length */
  uByte *b, *b0;           /* work */

  if (alloc==NULL) return;       /* allowed; it's a nop */
  b0=(uByte *)alloc;             /* as bytes */
  b0-=8;                   /* -> true start of storage */
  j=(uInt *)b0;                  /* -> first four bytes */
  n=*j;                          /* lift */
  for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
         b-b0-8, (Int)b0);
  for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
    printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
         b-b0-8, (Int)b0, n);
  free(b0);                /* drop the storage */
  decAllocBytes-=n;              /* account for storage */
  /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
  } /* decFree */
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#endif

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