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decimal128.c

/* Decimal 128-bit format 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 128-bit format module                            */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for decimal128 format numbers.  */
/* Conversions are supplied to and from decNumber and String.           */
/*                                                    */
/* This is used when decNumber provides operations, either for all    */
/* operations or as a proxy between decNumber and decSingle.            */
/*                                                    */
/* Error handling is the same as decNumber (qv.).                 */
/* ------------------------------------------------------------------ */
#include <string.h>           /* [for memset/memcpy] */
#include <stdio.h>            /* [for printf] */

#include "dconfig.h"          /* GCC definitions */
#define      DECNUMDIGITS 34      /* make decNumbers with space for 34 */
#include "decNumber.h"        /* base number library */
#include "decNumberLocal.h"   /* decNumber local types, etc. */
#include "decimal128.h"       /* our primary include */

/* Utility routines and tables [in decimal64.c] */
extern const uInt   COMBEXP[32], COMBMSD[32];
extern const uShort DPD2BIN[1024];
extern const uShort BIN2DPD[1000];  /* [not used] */
extern const uByte  BIN2CHAR[4001];

extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
extern void decDigitsToDPD(const decNumber *, uInt *, Int);

#if DECTRACE || DECCHECK
void decimal128Show(const decimal128 *);    /* for debug */
extern void decNumberShow(const decNumber *);     /* .. */
#endif

/* Useful macro */
/* Clear a structure (e.g., a decNumber) */
#define DEC_clear(d) memset(d, 0, sizeof(*d))

/* ------------------------------------------------------------------ */
/* decimal128FromNumber -- convert decNumber to decimal128        */
/*                                                    */
/*   ds is the target decimal128                            */
/*   dn is the source number (assumed valid)                      */
/*   set is the context, used only for reporting errors                 */
/*                                                    */
/* The set argument is used only for status reporting and for the     */
/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
/* digits or an overflow is detected).    If the exponent is out of the */
/* valid range then Overflow or Underflow will be raised.         */
/* After Underflow a subnormal result is possible.                */
/*                                                    */
/* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
/* by reducing its exponent and multiplying the coefficient by a      */
/* power of ten, or if the exponent on a zero had to be clamped.      */
/* ------------------------------------------------------------------ */
decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,
                          decContext *set) {
  uInt status=0;           /* status accumulator */
  Int ae;                  /* adjusted exponent */
  decNumber  dw;           /* work */
  decContext dc;           /* .. */
  uInt *pu;                /* .. */
  uInt comb, exp;          /* .. */
  uInt targar[4]={0,0,0,0};      /* target 128-bit */
  #define targhi targar[3]       /* name the word with the sign */
  #define targmh targar[2]       /* name the words */
  #define targml targar[1]       /* .. */
  #define targlo targar[0]       /* .. */

  /* If the number has too many digits, or the exponent could be */
  /* out of range then reduce the number under the appropriate */
  /* constraints.  This could push the number to Infinity or zero, */
  /* so this check and rounding must be done before generating the */
  /* decimal128] */
  ae=dn->exponent+dn->digits-1;                /* [0 if special] */
  if (dn->digits>DECIMAL128_Pmax         /* too many digits */
   || ae>DECIMAL128_Emax                 /* likely overflow */
   || ae<DECIMAL128_Emin) {              /* likely underflow */
    decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
    dc.round=set->round;                 /* use supplied rounding */
    decNumberPlus(&dw, dn, &dc);         /* (round and check) */
    /* [this changes -0 to 0, so enforce the sign...] */
    dw.bits|=dn->bits&DECNEG;
    status=dc.status;                    /* save status */
    dn=&dw;                        /* use the work number */
    } /* maybe out of range */

  if (dn->bits&DECSPECIAL) {                /* a special value */
    if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
     else {                           /* sNaN or qNaN */
      if ((*dn->lsu!=0 || dn->digits>1)           /* non-zero coefficient */
       && (dn->digits<DECIMAL128_Pmax)) {   /* coefficient fits */
      decDigitsToDPD(dn, targar, 0);
      }
      if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
       else targhi|=DECIMAL_sNaN<<24;
      } /* a NaN */
    } /* special */

   else { /* is finite */
    if (decNumberIsZero(dn)) {                 /* is a zero */
      /* set and clamp exponent */
      if (dn->exponent<-DECIMAL128_Bias) {
      exp=0;                             /* low clamp */
      status|=DEC_Clamped;
      }
       else {
      exp=dn->exponent+DECIMAL128_Bias;    /* bias exponent */
      if (exp>DECIMAL128_Ehigh) {        /* top clamp */
        exp=DECIMAL128_Ehigh;
        status|=DEC_Clamped;
        }
      }
      comb=(exp>>9) & 0x18;         /* msd=0, exp top 2 bits .. */
      }
     else {                   /* non-zero finite number */
      uInt msd;                     /* work */
      Int pad=0;              /* coefficient pad digits */

      /* the dn is known to fit, but it may need to be padded */
      exp=(uInt)(dn->exponent+DECIMAL128_Bias);    /* bias exponent */
      if (exp>DECIMAL128_Ehigh) {            /* fold-down case */
      pad=exp-DECIMAL128_Ehigh;
      exp=DECIMAL128_Ehigh;                  /* [to maximum] */
      status|=DEC_Clamped;
      }

      /* [fastpath for common case is not a win, here] */
      decDigitsToDPD(dn, targar, pad);
      /* save and clear the top digit */
      msd=targhi>>14;
      targhi&=0x00003fff;

      /* create the combination field */
      if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
           else comb=((exp>>9) & 0x18) | msd;
      }
    targhi|=comb<<26;            /* add combination field .. */
    targhi|=(exp&0xfff)<<14;     /* .. and exponent continuation */
    } /* finite */

  if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */

  /* now write to storage; this is endian */
  pu=(uInt *)d128->bytes;        /* overlay */
  if (DECLITEND) {
    pu[0]=targlo;          /* directly store the low int */
    pu[1]=targml;          /* then the mid-low */
    pu[2]=targmh;          /* then the mid-high */
    pu[3]=targhi;          /* then the high int */
    }
   else {
    pu[0]=targhi;          /* directly store the high int */
    pu[1]=targmh;          /* then the mid-high */
    pu[2]=targml;          /* then the mid-low */
    pu[3]=targlo;          /* then the low int */
    }

  if (status!=0) decContextSetStatus(set, status); /* pass on status */
  /* decimal128Show(d128); */
  return d128;
  } /* decimal128FromNumber */

/* ------------------------------------------------------------------ */
/* decimal128ToNumber -- convert decimal128 to decNumber          */
/*   d128 is the source decimal128                          */
/*   dn is the target number, with appropriate space              */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {
  uInt msd;                /* coefficient MSD */
  uInt exp;                /* exponent top two bits */
  uInt comb;                     /* combination field */
  const uInt *pu;          /* work */
  Int  need;                     /* .. */
  uInt sourar[4];          /* source 128-bit */
  #define sourhi sourar[3]       /* name the word with the sign */
  #define sourmh sourar[2]       /* and the mid-high word */
  #define sourml sourar[1]       /* and the mod-low word */
  #define sourlo sourar[0]       /* and the lowest word */

  /* load source from storage; this is endian */
  pu=(const uInt *)d128->bytes;        /* overlay */
  if (DECLITEND) {
    sourlo=pu[0];          /* directly load the low int */
    sourml=pu[1];          /* then the mid-low */
    sourmh=pu[2];          /* then the mid-high */
    sourhi=pu[3];          /* then the high int */
    }
   else {
    sourhi=pu[0];          /* directly load the high int */
    sourmh=pu[1];          /* then the mid-high */
    sourml=pu[2];          /* then the mid-low */
    sourlo=pu[3];          /* then the low int */
    }

  comb=(sourhi>>26)&0x1f;        /* combination field */

  decNumberZero(dn);             /* clean number */
  if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */

  msd=COMBMSD[comb];             /* decode the combination field */
  exp=COMBEXP[comb];             /* .. */

  if (exp==3) {                  /* is a special */
    if (msd==0) {
      dn->bits|=DECINF;
      return dn;           /* no coefficient needed */
      }
    else if (sourhi&0x02000000) dn->bits|=DECSNAN;
    else dn->bits|=DECNAN;
    msd=0;                 /* no top digit */
    }
   else {                  /* is a finite number */
    dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
    }

  /* get the coefficient */
  sourhi&=0x00003fff;            /* clean coefficient continuation */
  if (msd) {                     /* non-zero msd */
    sourhi|=msd<<14;             /* prefix to coefficient */
    need=12;                     /* process 12 declets */
    }
   else { /* msd=0 */
    if (sourhi) need=11;         /* declets to process */
     else if (sourmh) need=10;
     else if (sourml) need=7;
     else if (sourlo) need=4;
     else return dn;             /* easy: coefficient is 0 */
    } /*msd=0 */

  decDigitsFromDPD(dn, sourar, need);     /* process declets */
  /* decNumberShow(dn); */
  return dn;
  } /* decimal128ToNumber */

/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string                 */
/* to-engineering-string -- conversion to numeric string          */
/*                                                    */
/*   decimal128ToString(d128, string);                            */
/*   decimal128ToEngString(d128, string);                   */
/*                                                    */
/*  d128 is the decimal128 format number to convert               */
/*  string is the string where the result will be laid out        */
/*                                                    */
/*  string must be at least 24 characters                   */
/*                                                    */
/*  No error is possible, and no status can be set.               */
/* ------------------------------------------------------------------ */
char * decimal128ToEngString(const decimal128 *d128, char *string){
  decNumber dn;                     /* work */
  decimal128ToNumber(d128, &dn);
  decNumberToEngString(&dn, string);
  return string;
  } /* decimal128ToEngString */

char * decimal128ToString(const decimal128 *d128, char *string){
  uInt msd;                /* coefficient MSD */
  Int  exp;                /* exponent top two bits or full */
  uInt comb;                     /* combination field */
  char *cstart;                  /* coefficient start */
  char *c;                 /* output pointer in string */
  const uInt *pu;          /* work */
  char *s, *t;                   /* .. (source, target) */
  Int  dpd;                /* .. */
  Int  pre, e;                   /* .. */
  const uByte *u;          /* .. */

  uInt sourar[4];          /* source 128-bit */
  #define sourhi sourar[3]       /* name the word with the sign */
  #define sourmh sourar[2]       /* and the mid-high word */
  #define sourml sourar[1]       /* and the mod-low word */
  #define sourlo sourar[0]       /* and the lowest word */

  /* load source from storage; this is endian */
  pu=(const uInt *)d128->bytes;        /* overlay */
  if (DECLITEND) {
    sourlo=pu[0];          /* directly load the low int */
    sourml=pu[1];          /* then the mid-low */
    sourmh=pu[2];          /* then the mid-high */
    sourhi=pu[3];          /* then the high int */
    }
   else {
    sourhi=pu[0];          /* directly load the high int */
    sourmh=pu[1];          /* then the mid-high */
    sourml=pu[2];          /* then the mid-low */
    sourlo=pu[3];          /* then the low int */
    }

  c=string;                /* where result will go */
  if (((Int)sourhi)<0) *c++='-';   /* handle sign */

  comb=(sourhi>>26)&0x1f;        /* combination field */
  msd=COMBMSD[comb];             /* decode the combination field */
  exp=COMBEXP[comb];             /* .. */

  if (exp==3) {
    if (msd==0) {          /* infinity */
      strcpy(c,     "Inf");
      strcpy(c+3, "inity");
      return string;             /* easy */
      }
    if (sourhi&0x02000000) *c++='s'; /* sNaN */
    strcpy(c, "NaN");            /* complete word */
    c+=3;                  /* step past */
    if (sourlo==0 && sourml==0 && sourmh==0
     && (sourhi&0x0003ffff)==0) return string; /* zero payload */
    /* otherwise drop through to add integer; set correct exp */
    exp=0; msd=0;          /* setup for following code */
    }
   else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */

  /* convert 34 digits of significand to characters */
  cstart=c;                /* save start of coefficient */
  if (msd) *c++='0'+(char)msd;         /* non-zero most significant digit */

  /* Now decode the declets.  After extracting each one, it is */
  /* decoded to binary and then to a 4-char sequence by table lookup; */
  /* the 4-chars are a 1-char length (significant digits, except 000 */
  /* has length 0).  This allows us to left-align the first declet */
  /* with non-zero content, then remaining ones are full 3-char */
  /* length.  We use fixed-length memcpys because variable-length */
  /* causes a subroutine call in GCC.  (These are length 4 for speed */
  /* and are safe because the array has an extra terminator byte.) */
  #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4];               \
               if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}      \
                else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}
  dpd=(sourhi>>4)&0x3ff;                 /* declet 1 */
  dpd2char;
  dpd=((sourhi&0xf)<<6) | (sourmh>>26);        /* declet 2 */
  dpd2char;
  dpd=(sourmh>>16)&0x3ff;                /* declet 3 */
  dpd2char;
  dpd=(sourmh>>6)&0x3ff;                 /* declet 4 */
  dpd2char;
  dpd=((sourmh&0x3f)<<4) | (sourml>>28);     /* declet 5 */
  dpd2char;
  dpd=(sourml>>18)&0x3ff;                /* declet 6 */
  dpd2char;
  dpd=(sourml>>8)&0x3ff;                 /* declet 7 */
  dpd2char;
  dpd=((sourml&0xff)<<2) | (sourlo>>30);     /* declet 8 */
  dpd2char;
  dpd=(sourlo>>20)&0x3ff;                /* declet 9 */
  dpd2char;
  dpd=(sourlo>>10)&0x3ff;                /* declet 10 */
  dpd2char;
  dpd=(sourlo)&0x3ff;                    /* declet 11 */
  dpd2char;

  if (c==cstart) *c++='0';       /* all zeros -- make 0 */

  if (exp==0) {                  /* integer or NaN case -- easy */
    *c='\0';                     /* terminate */
    return string;
    }

  /* non-0 exponent */
  e=0;                           /* assume no E */
  pre=c-cstart+exp;
  /* [here, pre-exp is the digits count (==1 for zero)] */
  if (exp>0 || pre<-5) {         /* need exponential form */
    e=pre-1;                     /* calculate E value */
    pre=1;                 /* assume one digit before '.' */
    } /* exponential form */

  /* modify the coefficient, adding 0s, '.', and E+nn as needed */
  s=c-1;                   /* source (LSD) */
  if (pre>0) {                   /* ddd.ddd (plain), perhaps with E */
    char *dotat=cstart+pre;
    if (dotat<c) {               /* if embedded dot needed... */
      t=c;                    /* target */
      for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
      *t='.';                       /* insert the dot */
      c++;                    /* length increased by one */
      }

    /* finally add the E-part, if needed; it will never be 0, and has */
    /* a maximum length of 4 digits */
    if (e!=0) {
      *c++='E';                  /* starts with E */
      *c++='+';                  /* assume positive */
      if (e<0) {
      *(c-1)='-';          /* oops, need '-' */
      e=-e;                /* uInt, please */
      }
      if (e<1000) {              /* 3 (or fewer) digits case */
      u=&BIN2CHAR[e*4];    /* -> length byte */
      memcpy(c, u+4-*u, 4);      /* copy fixed 4 characters [is safe] */
      c+=*u;                     /* bump pointer appropriately */
      }
       else {                    /* 4-digits */
      Int thou=((e>>3)*1049)>>17; /* e/1000 */
      Int rem=e-(1000*thou);      /* e%1000 */
      *c++='0'+(char)thou;
      u=&BIN2CHAR[rem*4];        /* -> length byte */
      memcpy(c, u+1, 4);         /* copy fixed 3+1 characters [is safe] */
      c+=3;                /* bump pointer, always 3 digits */
      }
      }
    *c='\0';                     /* add terminator */
    /*printf("res %s\n", string); */
    return string;
    } /* pre>0 */

  /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
  t=c+1-pre;
  *(t+1)='\0';                      /* can add terminator now */
  for (; s>=cstart; s--, t--) *t=*s;      /* shift whole coefficient right */
  c=cstart;
  *c++='0';                   /* always starts with 0. */
  *c++='.';
  for (; pre<0; pre++) *c++='0';    /* add any 0's after '.' */
  /*printf("res %s\n", string); */
  return string;
  } /* decimal128ToString */

/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string                    */
/*                                                    */
/*   decimal128FromString(result, string, set);                   */
/*                                                    */
/*  result  is the decimal128 format number which gets the result of  */
/*        the conversion                                    */
/*  *string is the character string which should contain a valid      */
/*        number (which may be a special value)             */
/*  set         is the context                                    */
/*                                                    */
/* The context is supplied to this routine is used for error handling */
/* (setting of status and traps) and for the rounding mode, only.     */
/* If an error occurs, the result will be a valid decimal128 NaN.     */
/* ------------------------------------------------------------------ */
decimal128 * decimal128FromString(decimal128 *result, const char *string,
                          decContext *set) {
  decContext dc;                   /* work */
  decNumber dn;                          /* .. */

  decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */
  dc.round=set->round;                     /* use supplied rounding */

  decNumberFromString(&dn, string, &dc);     /* will round if needed */
  decimal128FromNumber(result, &dn, &dc);
  if (dc.status!=0) {                    /* something happened */
    decContextSetStatus(set, dc.status);     /* .. pass it on */
    }
  return result;
  } /* decimal128FromString */

/* ------------------------------------------------------------------ */
/* decimal128IsCanonical -- test whether encoding is canonical          */
/*   d128 is the source decimal128                          */
/*   returns 1 if the encoding of d128 is canonical, 0 otherwise      */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
uint32_t decimal128IsCanonical(const decimal128 *d128) {
  decNumber dn;                     /* work */
  decimal128 canon;                  /* .. */
  decContext dc;              /* .. */
  decContextDefault(&dc, DEC_INIT_DECIMAL128);
  decimal128ToNumber(d128, &dn);
  decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
  return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
  } /* decimal128IsCanonical */

/* ------------------------------------------------------------------ */
/* decimal128Canonical -- copy an encoding, ensuring it is canonical  */
/*   d128 is the source decimal128                          */
/*   result is the target (may be the same decimal128)                  */
/*   returns result                                         */
/* No error is possible.                                    */
/* ------------------------------------------------------------------ */
decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {
  decNumber dn;                     /* work */
  decContext dc;              /* .. */
  decContextDefault(&dc, DEC_INIT_DECIMAL128);
  decimal128ToNumber(d128, &dn);
  decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */
  return result;
  } /* decimal128Canonical */

#if DECTRACE || DECCHECK
/* Macros for accessing decimal128 fields.  These assume the argument
   is a reference (pointer) to the decimal128 structure, and the
   decimal128 is in network byte order (big-endian) */
/* Get sign */
#define decimal128Sign(d)     ((unsigned)(d)->bytes[0]>>7)

/* Get combination field */
#define decimal128Comb(d)     (((d)->bytes[0] & 0x7c)>>2)

/* Get exponent continuation [does not remove bias] */
#define decimal128ExpCon(d)   ((((d)->bytes[0] & 0x03)<<10)       \
                        | ((unsigned)(d)->bytes[1]<<2)            \
                        | ((unsigned)(d)->bytes[2]>>6))

/* Set sign [this assumes sign previously 0] */
#define decimal128SetSign(d, b) {                           \
  (d)->bytes[0]|=((unsigned)(b)<<7);}

/* Set exponent continuation [does not apply bias] */
/* This assumes range has been checked and exponent previously 0; */
/* type of exponent must be unsigned */
#define decimal128SetExpCon(d, e) {                         \
  (d)->bytes[0]|=(uint8_t)((e)>>10);                              \
  (d)->bytes[1] =(uint8_t)(((e)&0x3fc)>>2);                       \
  (d)->bytes[2]|=(uint8_t)(((e)&0x03)<<6);}

/* ------------------------------------------------------------------ */
/* decimal128Show -- display a decimal128 in hexadecimal [debug aid]  */
/*   d128 -- the number to show                                   */
/* ------------------------------------------------------------------ */
/* Also shows sign/cob/expconfields extracted */
void decimal128Show(const decimal128 *d128) {
  char buf[DECIMAL128_Bytes*2+1];
  Int i, j=0;

  if (DECLITEND) {
    for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
      sprintf(&buf[j], "%02x", d128->bytes[15-i]);
      }
    printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
         d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
         ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|
         (d128->bytes[13]>>6));
    }
   else {
    for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
      sprintf(&buf[j], "%02x", d128->bytes[i]);
      }
    printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
         decimal128Sign(d128), decimal128Comb(d128),
         decimal128ExpCon(d128));
    }
  } /* decimal128Show */
#endif

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