libdecnumber/dpd/decimal64.c

   1 /* Decimal 64-bit format module for the decNumber C Library.
   2    Copyright (C) 2005, 2007 Free Software Foundation, Inc.
   3    Contributed by IBM Corporation.  Author Mike Cowlishaw.
   4
   5    This file is part of GCC.
   6
   7    GCC is free software; you can redistribute it and/or modify it under
   8    the terms of the GNU General Public License as published by the Free
   9    Software Foundation; either version 2, or (at your option) any later
  10    version.
  11
  12    In addition to the permissions in the GNU General Public License,
  13    the Free Software Foundation gives you unlimited permission to link
  14    the compiled version of this file into combinations with other
  15    programs, and to distribute those combinations without any
  16    restriction coming from the use of this file.  (The General Public
  17    License restrictions do apply in other respects; for example, they
  18    cover modification of the file, and distribution when not linked
  19    into a combine executable.)
  20
  21    GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  22    WARRANTY; without even the implied warranty of MERCHANTABILITY or
  23    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  24    for more details.
  25
  26    You should have received a copy of the GNU General Public License
  27    along with GCC; see the file COPYING.  If not, write to the Free
  28    Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  29    02110-1301, USA.  */
  30
  31 /* ------------------------------------------------------------------ */
  32 /* Decimal 64-bit format module                                       */
  33 /* ------------------------------------------------------------------ */
  34 /* This module comprises the routines for decimal64 format numbers.   */
  35 /* Conversions are supplied to and from decNumber and String.         */
  36 /*                                                                    */
  37 /* This is used when decNumber provides operations, either for all    */
  38 /* operations or as a proxy between decNumber and decSingle.          */
  39 /*                                                                    */
  40 /* Error handling is the same as decNumber (qv.).                     */
  41 /* ------------------------------------------------------------------ */
  42 #include "qemu/osdep.h"
  43
  44 #include "libdecnumber/dconfig.h"
  45 #define  DECNUMDIGITS 16      /* make decNumbers with space for 16 */
  46 #include "libdecnumber/decNumber.h"
  47 #include "libdecnumber/decNumberLocal.h"
  48 #include "libdecnumber/dpd/decimal64.h"
  49
  50 /* Utility routines and tables [in decimal64.c]; externs for C++ */
  51 extern const uInt COMBEXP[32], COMBMSD[32];
  52 extern const uByte  BIN2CHAR[4001];
  53
  54 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
  55 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
  56
  57 #if DECTRACE || DECCHECK
  58 void decimal64Show(const decimal64 *);            /* for debug */
  59 extern void decNumberShow(const decNumber *);     /* .. */
  60 #endif
  61
  62 /* Useful macro */
  63 /* Clear a structure (e.g., a decNumber) */
  64 #define DEC_clear(d) memset(d, 0, sizeof(*d))
  65
  66 /* define and include the tables to use for conversions */
  67 #define DEC_BIN2CHAR 1
  68 #define DEC_DPD2BIN  1
  69 #define DEC_BIN2DPD  1             /* used for all sizes */
  70 #include "libdecnumber/decDPD.h"
  71
  72 /* ------------------------------------------------------------------ */
  73 /* decimal64FromNumber -- convert decNumber to decimal64              */
  74 /*                                                                    */
  75 /*   ds is the target decimal64                                       */
  76 /*   dn is the source number (assumed valid)                          */
  77 /*   set is the context, used only for reporting errors               */
  78 /*                                                                    */
  79 /* The set argument is used only for status reporting and for the     */
  80 /* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */
  81 /* digits or an overflow is detected).  If the exponent is out of the */
  82 /* valid range then Overflow or Underflow will be raised.             */
  83 /* After Underflow a subnormal result is possible.                    */
  84 /*                                                                    */
  85 /* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
  86 /* by reducing its exponent and multiplying the coefficient by a      */
  87 /* power of ten, or if the exponent on a zero had to be clamped.      */
  88 /* ------------------------------------------------------------------ */
  89 decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,
  90                                 decContext *set) {
  91   uInt status=0;                   /* status accumulator */
  92   Int ae;                          /* adjusted exponent */
  93   decNumber  dw;                   /* work */
  94   decContext dc;                   /* .. */
  95   uInt *pu;                        /* .. */
  96   uInt comb, exp;                  /* .. */
  97   uInt targar[2]={0, 0};           /* target 64-bit */
  98   #define targhi targar[1]         /* name the word with the sign */
  99   #define targlo targar[0]         /* and the other */
 100
 101   /* If the number has too many digits, or the exponent could be */
 102   /* out of range then reduce the number under the appropriate */
 103   /* constraints.  This could push the number to Infinity or zero, */
 104   /* so this check and rounding must be done before generating the */
 105   /* decimal64] */
 106   ae=dn->exponent+dn->digits-1;              /* [0 if special] */
 107   if (dn->digits>DECIMAL64_Pmax              /* too many digits */
 108    || ae>DECIMAL64_Emax                      /* likely overflow */
 109    || ae<DECIMAL64_Emin) {                   /* likely underflow */
 110     decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */
 111     dc.round=set->round;                     /* use supplied rounding */
 112     decNumberPlus(&dw, dn, &dc);             /* (round and check) */
 113     /* [this changes -0 to 0, so enforce the sign...] */
 114     dw.bits|=dn->bits&DECNEG;
 115     status=dc.status;                        /* save status */
 116     dn=&dw;                                  /* use the work number */
 117     } /* maybe out of range */
 118
 119   if (dn->bits&DECSPECIAL) {                      /* a special value */
 120     if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
 121      else {                                       /* sNaN or qNaN */
 122       if ((*dn->lsu!=0 || dn->digits>1)           /* non-zero coefficient */
 123        && (dn->digits<DECIMAL64_Pmax)) {          /* coefficient fits */
 124         decDigitsToDPD(dn, targar, 0);
 125         }
 126       if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
 127        else targhi|=DECIMAL_sNaN<<24;
 128       } /* a NaN */
 129     } /* special */
 130
 131    else { /* is finite */
 132     if (decNumberIsZero(dn)) {               /* is a zero */
 133       /* set and clamp exponent */
 134       if (dn->exponent<-DECIMAL64_Bias) {
 135         exp=0;                               /* low clamp */
 136         status|=DEC_Clamped;
 137         }
 138        else {
 139         exp=dn->exponent+DECIMAL64_Bias;     /* bias exponent */
 140         if (exp>DECIMAL64_Ehigh) {           /* top clamp */
 141           exp=DECIMAL64_Ehigh;
 142           status|=DEC_Clamped;
 143           }
 144         }
 145       comb=(exp>>5) & 0x18;             /* msd=0, exp top 2 bits .. */
 146       }
 147      else {                             /* non-zero finite number */
 148       uInt msd;                         /* work */
 149       Int pad=0;                        /* coefficient pad digits */
 150
 151       /* the dn is known to fit, but it may need to be padded */
 152       exp=(uInt)(dn->exponent+DECIMAL64_Bias);    /* bias exponent */
 153       if (exp>DECIMAL64_Ehigh) {                  /* fold-down case */
 154         pad=exp-DECIMAL64_Ehigh;
 155         exp=DECIMAL64_Ehigh;                      /* [to maximum] */
 156         status|=DEC_Clamped;
 157         }
 158
 159       /* fastpath common case */
 160       if (DECDPUN==3 && pad==0) {
 161         uInt dpd[6]={0,0,0,0,0,0};
 162         uInt i;
 163         Int d=dn->digits;
 164         for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
 165         targlo =dpd[0];
 166         targlo|=dpd[1]<<10;
 167         targlo|=dpd[2]<<20;
 168         if (dn->digits>6) {
 169           targlo|=dpd[3]<<30;
 170           targhi =dpd[3]>>2;
 171           targhi|=dpd[4]<<8;
 172           }
 173         msd=dpd[5];                /* [did not really need conversion] */
 174         }
 175        else { /* general case */
 176         decDigitsToDPD(dn, targar, pad);
 177         /* save and clear the top digit */
 178         msd=targhi>>18;
 179         targhi&=0x0003ffff;
 180         }
 181
 182       /* create the combination field */
 183       if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
 184              else comb=((exp>>5) & 0x18) | msd;
 185       }
 186     targhi|=comb<<26;              /* add combination field .. */
 187     targhi|=(exp&0xff)<<18;        /* .. and exponent continuation */
 188     } /* finite */
 189
 190   if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
 191
 192   /* now write to storage; this is now always endian */
 193   pu=(uInt *)d64->bytes;           /* overlay */
 194   if (DECLITEND) {
 195     pu[0]=targar[0];               /* directly store the low int */
 196     pu[1]=targar[1];               /* then the high int */
 197     }
 198    else {
 199     pu[0]=targar[1];               /* directly store the high int */
 200     pu[1]=targar[0];               /* then the low int */
 201     }
 202
 203   if (status!=0) decContextSetStatus(set, status); /* pass on status */
 204   /* decimal64Show(d64); */
 205   return d64;
 206   } /* decimal64FromNumber */
 207
 208 /* ------------------------------------------------------------------ */
 209 /* decimal64ToNumber -- convert decimal64 to decNumber                */
 210 /*   d64 is the source decimal64                                      */
 211 /*   dn is the target number, with appropriate space                  */
 212 /* No error is possible.                                              */
 213 /* ------------------------------------------------------------------ */
 214 decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {
 215   uInt msd;                        /* coefficient MSD */
 216   uInt exp;                        /* exponent top two bits */
 217   uInt comb;                       /* combination field */
 218   const uInt *pu;                  /* work */
 219   Int  need;                       /* .. */
 220   uInt sourar[2];                  /* source 64-bit */
 221   #define sourhi sourar[1]         /* name the word with the sign */
 222   #define sourlo sourar[0]         /* and the lower word */
 223
 224   /* load source from storage; this is endian */
 225   pu=(const uInt *)d64->bytes;     /* overlay */
 226   if (DECLITEND) {
 227     sourlo=pu[0];                  /* directly load the low int */
 228     sourhi=pu[1];                  /* then the high int */
 229     }
 230    else {
 231     sourhi=pu[0];                  /* directly load the high int */
 232     sourlo=pu[1];                  /* then the low int */
 233     }
 234
 235   comb=(sourhi>>26)&0x1f;          /* combination field */
 236
 237   decNumberZero(dn);               /* clean number */
 238   if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
 239
 240   msd=COMBMSD[comb];               /* decode the combination field */
 241   exp=COMBEXP[comb];               /* .. */
 242
 243   if (exp==3) {                    /* is a special */
 244     if (msd==0) {
 245       dn->bits|=DECINF;
 246       return dn;                   /* no coefficient needed */
 247       }
 248     else if (sourhi&0x02000000) dn->bits|=DECSNAN;
 249     else dn->bits|=DECNAN;
 250     msd=0;                         /* no top digit */
 251     }
 252    else {                          /* is a finite number */
 253     dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */
 254     }
 255
 256   /* get the coefficient */
 257   sourhi&=0x0003ffff;              /* clean coefficient continuation */
 258   if (msd) {                       /* non-zero msd */
 259     sourhi|=msd<<18;               /* prefix to coefficient */
 260     need=6;                        /* process 6 declets */
 261     }
 262    else { /* msd=0 */
 263     if (!sourhi) {                 /* top word 0 */
 264       if (!sourlo) return dn;      /* easy: coefficient is 0 */
 265       need=3;                      /* process at least 3 declets */
 266       if (sourlo&0xc0000000) need++; /* process 4 declets */
 267       /* [could reduce some more, here] */
 268       }
 269      else {                        /* some bits in top word, msd=0 */
 270       need=4;                      /* process at least 4 declets */
 271       if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */
 272       }
 273     } /*msd=0 */
 274
 275   decDigitsFromDPD(dn, sourar, need);   /* process declets */
 276   return dn;
 277   } /* decimal64ToNumber */
 278
 279
 280 /* ------------------------------------------------------------------ */
 281 /* to-scientific-string -- conversion to numeric string               */
 282 /* to-engineering-string -- conversion to numeric string              */
 283 /*                                                                    */
 284 /*   decimal64ToString(d64, string);                                  */
 285 /*   decimal64ToEngString(d64, string);                               */
 286 /*                                                                    */
 287 /*  d64 is the decimal64 format number to convert                     */
 288 /*  string is the string where the result will be laid out            */
 289 /*                                                                    */
 290 /*  string must be at least 24 characters                             */
 291 /*                                                                    */
 292 /*  No error is possible, and no status can be set.                   */
 293 /* ------------------------------------------------------------------ */
 294 char * decimal64ToEngString(const decimal64 *d64, char *string){
 295   decNumber dn;                         /* work */
 296   decimal64ToNumber(d64, &dn);
 297   decNumberToEngString(&dn, string);
 298   return string;
 299   } /* decimal64ToEngString */
 300
 301 char * decimal64ToString(const decimal64 *d64, char *string){
 302   uInt msd;                        /* coefficient MSD */
 303   Int  exp;                        /* exponent top two bits or full */
 304   uInt comb;                       /* combination field */
 305   char *cstart;                    /* coefficient start */
 306   char *c;                         /* output pointer in string */
 307   const uInt *pu;                  /* work */
 308   char *s, *t;                     /* .. (source, target) */
 309   Int  dpd;                        /* .. */
 310   Int  pre, e;                     /* .. */
 311   const uByte *u;                  /* .. */
 312
 313   uInt sourar[2];                  /* source 64-bit */
 314   #define sourhi sourar[1]         /* name the word with the sign */
 315   #define sourlo sourar[0]         /* and the lower word */
 316
 317   /* load source from storage; this is endian */
 318   pu=(const uInt *)d64->bytes;     /* overlay */
 319   if (DECLITEND) {
 320     sourlo=pu[0];                  /* directly load the low int */
 321     sourhi=pu[1];                  /* then the high int */
 322     }
 323    else {
 324     sourhi=pu[0];                  /* directly load the high int */
 325     sourlo=pu[1];                  /* then the low int */
 326     }
 327
 328   c=string;                        /* where result will go */
 329   if (((Int)sourhi)<0) *c++='-';   /* handle sign */
 330
 331   comb=(sourhi>>26)&0x1f;          /* combination field */
 332   msd=COMBMSD[comb];               /* decode the combination field */
 333   exp=COMBEXP[comb];               /* .. */
 334
 335   if (exp==3) {
 336     if (msd==0) {                  /* infinity */
 337       strcpy(c,   "Inf");
 338       strcpy(c+3, "inity");
 339       return string;               /* easy */
 340       }
 341     if (sourhi&0x02000000) *c++='s'; /* sNaN */
 342     strcpy(c, "NaN");              /* complete word */
 343     c+=3;                          /* step past */
 344     if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */
 345     /* otherwise drop through to add integer; set correct exp */
 346     exp=0; msd=0;                  /* setup for following code */
 347     }
 348    else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;
 349
 350   /* convert 16 digits of significand to characters */
 351   cstart=c;                        /* save start of coefficient */
 352   if (msd) *c++='0'+(char)msd;     /* non-zero most significant digit */
 353
 354   /* Now decode the declets.  After extracting each one, it is */
 355   /* decoded to binary and then to a 4-char sequence by table lookup; */
 356   /* the 4-chars are a 1-char length (significant digits, except 000 */
 357   /* has length 0).  This allows us to left-align the first declet */
 358   /* with non-zero content, then remaining ones are full 3-char */
 359   /* length.  We use fixed-length memcpys because variable-length */
 360   /* causes a subroutine call in GCC.  (These are length 4 for speed */
 361   /* and are safe because the array has an extra terminator byte.) */
 362   #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4];                   \
 363                    if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}      \
 364                     else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}
 365
 366   dpd=(sourhi>>8)&0x3ff;                     /* declet 1 */
 367   dpd2char;
 368   dpd=((sourhi&0xff)<<2) | (sourlo>>30);     /* declet 2 */
 369   dpd2char;
 370   dpd=(sourlo>>20)&0x3ff;                    /* declet 3 */
 371   dpd2char;
 372   dpd=(sourlo>>10)&0x3ff;                    /* declet 4 */
 373   dpd2char;
 374   dpd=(sourlo)&0x3ff;                        /* declet 5 */
 375   dpd2char;
 376
 377   if (c==cstart) *c++='0';         /* all zeros -- make 0 */
 378
 379   if (exp==0) {                    /* integer or NaN case -- easy */
 380     *c='\0';                       /* terminate */
 381     return string;
 382     }
 383
 384   /* non-0 exponent */
 385   e=0;                             /* assume no E */
 386   pre=c-cstart+exp;
 387   /* [here, pre-exp is the digits count (==1 for zero)] */
 388   if (exp>0 || pre<-5) {           /* need exponential form */
 389     e=pre-1;                       /* calculate E value */
 390     pre=1;                         /* assume one digit before '.' */
 391     } /* exponential form */
 392
 393   /* modify the coefficient, adding 0s, '.', and E+nn as needed */
 394   s=c-1;                           /* source (LSD) */
 395   if (pre>0) {                     /* ddd.ddd (plain), perhaps with E */
 396     char *dotat=cstart+pre;
 397     if (dotat<c) {                 /* if embedded dot needed... */
 398       t=c;                              /* target */
 399       for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
 400       *t='.';                           /* insert the dot */
 401       c++;                              /* length increased by one */
 402       }
 403
 404     /* finally add the E-part, if needed; it will never be 0, and has */
 405     /* a maximum length of 3 digits */
 406     if (e!=0) {
 407       *c++='E';                    /* starts with E */
 408       *c++='+';                    /* assume positive */
 409       if (e<0) {
 410         *(c-1)='-';                /* oops, need '-' */
 411         e=-e;                      /* uInt, please */
 412         }
 413       u=&BIN2CHAR[e*4];            /* -> length byte */
 414       memcpy(c, u+4-*u, 4);        /* copy fixed 4 characters [is safe] */
 415       c+=*u;                       /* bump pointer appropriately */
 416       }
 417     *c='\0';                       /* add terminator */
 418     /*printf("res %s\n", string); */
 419     return string;
 420     } /* pre>0 */
 421
 422   /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
 423   t=c+1-pre;
 424   *(t+1)='\0';                          /* can add terminator now */
 425   for (; s>=cstart; s--, t--) *t=*s;    /* shift whole coefficient right */
 426   c=cstart;
 427   *c++='0';                             /* always starts with 0. */
 428   *c++='.';
 429   for (; pre<0; pre++) *c++='0';        /* add any 0's after '.' */
 430   /*printf("res %s\n", string); */
 431   return string;
 432   } /* decimal64ToString */
 433
 434 /* ------------------------------------------------------------------ */
 435 /* to-number -- conversion from numeric string                        */
 436 /*                                                                    */
 437 /*   decimal64FromString(result, string, set);                        */
 438 /*                                                                    */
 439 /*  result  is the decimal64 format number which gets the result of   */
 440 /*          the conversion                                            */
 441 /*  *string is the character string which should contain a valid      */
 442 /*          number (which may be a special value)                     */
 443 /*  set     is the context                                            */
 444 /*                                                                    */
 445 /* The context is supplied to this routine is used for error handling */
 446 /* (setting of status and traps) and for the rounding mode, only.     */
 447 /* If an error occurs, the result will be a valid decimal64 NaN.      */
 448 /* ------------------------------------------------------------------ */
 449 decimal64 * decimal64FromString(decimal64 *result, const char *string,
 450                                 decContext *set) {
 451   decContext dc;                             /* work */
 452   decNumber dn;                              /* .. */
 453
 454   decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */
 455   dc.round=set->round;                        /* use supplied rounding */
 456
 457   decNumberFromString(&dn, string, &dc);     /* will round if needed */
 458
 459   decimal64FromNumber(result, &dn, &dc);
 460   if (dc.status!=0) {                        /* something happened */
 461     decContextSetStatus(set, dc.status);     /* .. pass it on */
 462     }
 463   return result;
 464   } /* decimal64FromString */
 465
 466 /* ------------------------------------------------------------------ */
 467 /* decimal64IsCanonical -- test whether encoding is canonical         */
 468 /*   d64 is the source decimal64                                      */
 469 /*   returns 1 if the encoding of d64 is canonical, 0 otherwise       */
 470 /* No error is possible.                                              */
 471 /* ------------------------------------------------------------------ */
 472 uint32_t decimal64IsCanonical(const decimal64 *d64) {
 473   decNumber dn;                         /* work */
 474   decimal64 canon;                      /* .. */
 475   decContext dc;                        /* .. */
 476   decContextDefault(&dc, DEC_INIT_DECIMAL64);
 477   decimal64ToNumber(d64, &dn);
 478   decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
 479   return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
 480   } /* decimal64IsCanonical */
 481
 482 /* ------------------------------------------------------------------ */
 483 /* decimal64Canonical -- copy an encoding, ensuring it is canonical   */
 484 /*   d64 is the source decimal64                                      */
 485 /*   result is the target (may be the same decimal64)                 */
 486 /*   returns result                                                   */
 487 /* No error is possible.                                              */
 488 /* ------------------------------------------------------------------ */
 489 decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
 490   decNumber dn;                         /* work */
 491   decContext dc;                        /* .. */
 492   decContextDefault(&dc, DEC_INIT_DECIMAL64);
 493   decimal64ToNumber(d64, &dn);
 494   decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */
 495   return result;
 496   } /* decimal64Canonical */
 497
 498 #if DECTRACE || DECCHECK
 499 /* Macros for accessing decimal64 fields.  These assume the
 500    argument is a reference (pointer) to the decimal64 structure,
 501    and the decimal64 is in network byte order (big-endian) */
 502 /* Get sign */
 503 #define decimal64Sign(d)       ((unsigned)(d)->bytes[0]>>7)
 504
 505 /* Get combination field */
 506 #define decimal64Comb(d)       (((d)->bytes[0] & 0x7c)>>2)
 507
 508 /* Get exponent continuation [does not remove bias] */
 509 #define decimal64ExpCon(d)     ((((d)->bytes[0] & 0x03)<<6)           \
 510                              | ((unsigned)(d)->bytes[1]>>2))
 511
 512 /* Set sign [this assumes sign previously 0] */
 513 #define decimal64SetSign(d, b) {                                      \
 514   (d)->bytes[0]|=((unsigned)(b)<<7);}
 515
 516 /* Set exponent continuation [does not apply bias] */
 517 /* This assumes range has been checked and exponent previously 0; */
 518 /* type of exponent must be unsigned */
 519 #define decimal64SetExpCon(d, e) {                                    \
 520   (d)->bytes[0]|=(uint8_t)((e)>>6);                                   \
 521   (d)->bytes[1]|=(uint8_t)(((e)&0x3F)<<2);}
 522
 523 /* ------------------------------------------------------------------ */
 524 /* decimal64Show -- display a decimal64 in hexadecimal [debug aid]    */
 525 /*   d64 -- the number to show                                        */
 526 /* ------------------------------------------------------------------ */
 527 /* Also shows sign/cob/expconfields extracted */
 528 void decimal64Show(const decimal64 *d64) {
 529   char buf[DECIMAL64_Bytes*2+1];
 530   Int i, j=0;
 531
 532   if (DECLITEND) {
 533     for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
 534       sprintf(&buf[j], "%02x", d64->bytes[7-i]);
 535       }
 536     printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
 537            d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
 538            ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
 539     }
 540    else { /* big-endian */
 541     for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
 542       sprintf(&buf[j], "%02x", d64->bytes[i]);
 543       }
 544     printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
 545            decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
 546     }
 547   } /* decimal64Show */
 548 #endif
 549
 550 /* ================================================================== */
 551 /* Shared utility routines and tables                                 */
 552 /* ================================================================== */
 553 /* define and include the conversion tables to use for shared code */
 554 #if DECDPUN==3
 555   #define DEC_DPD2BIN 1
 556 #else
 557   #define DEC_DPD2BCD 1
 558 #endif
 559 #include "libdecnumber/decDPD.h"
 560
 561 /* The maximum number of decNumberUnits needed for a working copy of */
 562 /* the units array is the ceiling of digits/DECDPUN, where digits is */
 563 /* the maximum number of digits in any of the formats for which this */
 564 /* is used.  decimal128.h must not be included in this module, so, as */
 565 /* a very special case, that number is defined as a literal here. */
 566 #define DECMAX754   34
 567 #define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)
 568
 569 /* ------------------------------------------------------------------ */
 570 /* Combination field lookup tables (uInts to save measurable work)    */
 571 /*                                                                    */
 572 /*      COMBEXP - 2-bit most-significant-bits of exponent             */
 573 /*                [11 if an Infinity or NaN]                          */
 574 /*      COMBMSD - 4-bit most-significant-digit                        */
 575 /*                [0=Infinity, 1=NaN if COMBEXP=11]                   */
 576 /*                                                                    */
 577 /* Both are indexed by the 5-bit combination field (0-31)             */
 578 /* ------------------------------------------------------------------ */
 579 const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
 580                         1, 1, 1, 1, 1, 1, 1, 1,
 581                         2, 2, 2, 2, 2, 2, 2, 2,
 582                         0, 0, 1, 1, 2, 2, 3, 3};
 583 const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,
 584                         0, 1, 2, 3, 4, 5, 6, 7,
 585                         0, 1, 2, 3, 4, 5, 6, 7,
 586                         8, 9, 8, 9, 8, 9, 0, 1};
 587
 588 /* ------------------------------------------------------------------ */
 589 /* decDigitsToDPD -- pack coefficient into DPD form                   */
 590 /*                                                                    */
 591 /*   dn   is the source number (assumed valid, max DECMAX754 digits)  */
 592 /*   targ is 1, 2, or 4-element uInt array, which the caller must     */
 593 /*        have cleared to zeros                                       */
 594 /*   shift is the number of 0 digits to add on the right (normally 0) */
 595 /*                                                                    */
 596 /* The coefficient must be known small enough to fit.  The full       */
 597 /* coefficient is copied, including the leading 'odd' digit.  This    */
 598 /* digit is retrieved and packed into the combination field by the    */
 599 /* caller.                                                            */
 600 /*                                                                    */
 601 /* The target uInts are altered only as necessary to receive the      */
 602 /* digits of the decNumber.  When more than one uInt is needed, they  */
 603 /* are filled from left to right (that is, the uInt at offset 0 will  */
 604 /* end up with the least-significant digits).                         */
 605 /*                                                                    */
 606 /* shift is used for 'fold-down' padding.                             */
 607 /*                                                                    */
 608 /* No error is possible.                                              */
 609 /* ------------------------------------------------------------------ */
 610 #if DECDPUN<=4
 611 /* Constant multipliers for divide-by-power-of five using reciprocal */
 612 /* multiply, after removing powers of 2 by shifting, and final shift */
 613 /* of 17 [we only need up to **4] */
 614 static const uInt multies[]={131073, 26215, 5243, 1049, 210};
 615 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
 616 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
 617 #endif
 618 void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
 619   Int  cut;                   /* work */
 620   Int  n;                     /* output bunch counter */
 621   Int  digits=dn->digits;     /* digit countdown */
 622   uInt dpd;                   /* densely packed decimal value */
 623   uInt bin;                   /* binary value 0-999 */
 624   uInt *uout=targ;            /* -> current output uInt */
 625   uInt  uoff=0;               /* -> current output offset [from right] */
 626   const Unit *inu=dn->lsu;    /* -> current input unit */
 627   Unit  uar[DECMAXUNITS];     /* working copy of units, iff shifted */
 628   #if DECDPUN!=3              /* not fast path */
 629     Unit in;                  /* current unit */
 630   #endif
 631
 632   if (shift!=0) {             /* shift towards most significant required */
 633     /* shift the units array to the left by pad digits and copy */
 634     /* [this code is a special case of decShiftToMost, which could */
 635     /* be used instead if exposed and the array were copied first] */
 636     const Unit *source;                 /* .. */
 637     Unit  *target, *first;              /* .. */
 638     uInt  next=0;                       /* work */
 639
 640     source=dn->lsu+D2U(digits)-1;       /* where msu comes from */
 641     target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
 642     cut=DECDPUN-MSUDIGITS(shift);       /* where to slice */
 643     if (cut==0) {                       /* unit-boundary case */
 644       for (; source>=dn->lsu; source--, target--) *target=*source;
 645       }
 646      else {
 647       first=uar+D2U(digits+shift)-1;    /* where msu will end up */
 648       for (; source>=dn->lsu; source--, target--) {
 649         /* split the source Unit and accumulate remainder for next */
 650         #if DECDPUN<=4
 651           uInt quot=QUOT10(*source, cut);
 652           uInt rem=*source-quot*DECPOWERS[cut];
 653           next+=quot;
 654         #else
 655           uInt rem=*source%DECPOWERS[cut];
 656           next+=*source/DECPOWERS[cut];
 657         #endif
 658         if (target<=first) *target=(Unit)next; /* write to target iff valid */
 659         next=rem*DECPOWERS[DECDPUN-cut];       /* save remainder for next Unit */
 660         }
 661       } /* shift-move */
 662     /* propagate remainder to one below and clear the rest */
 663     for (; target>=uar; target--) {
 664       *target=(Unit)next;
 665       next=0;
 666       }
 667     digits+=shift;                 /* add count (shift) of zeros added */
 668     inu=uar;                       /* use units in working array */
 669     }
 670
 671   /* now densely pack the coefficient into DPD declets */
 672
 673   #if DECDPUN!=3                   /* not fast path */
 674     in=*inu;                       /* current unit */
 675     cut=0;                         /* at lowest digit */
 676     bin=0;                         /* [keep compiler quiet] */
 677   #endif
 678
 679   for(n=0; digits>0; n++) {        /* each output bunch */
 680     #if DECDPUN==3                 /* fast path, 3-at-a-time */
 681       bin=*inu;                    /* 3 digits ready for convert */
 682       digits-=3;                   /* [may go negative] */
 683       inu++;                       /* may need another */
 684
 685     #else                          /* must collect digit-by-digit */
 686       Unit dig;                    /* current digit */
 687       Int j;                       /* digit-in-declet count */
 688       for (j=0; j<3; j++) {
 689         #if DECDPUN<=4
 690           Unit temp=(Unit)((uInt)(in*6554)>>16);
 691           dig=(Unit)(in-X10(temp));
 692           in=temp;
 693         #else
 694           dig=in%10;
 695           in=in/10;
 696         #endif
 697         if (j==0) bin=dig;
 698          else if (j==1)  bin+=X10(dig);
 699          else /* j==2 */ bin+=X100(dig);
 700         digits--;
 701         if (digits==0) break;      /* [also protects *inu below] */
 702         cut++;
 703         if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
 704         }
 705     #endif
 706     /* here there are 3 digits in bin, or have used all input digits */
 707
 708     dpd=BIN2DPD[bin];
 709
 710     /* write declet to uInt array */
 711     *uout|=dpd<<uoff;
 712     uoff+=10;
 713     if (uoff<32) continue;         /* no uInt boundary cross */
 714     uout++;
 715     uoff-=32;
 716     *uout|=dpd>>(10-uoff);         /* collect top bits */
 717     } /* n declets */
 718   return;
 719   } /* decDigitsToDPD */
 720
 721 /* ------------------------------------------------------------------ */
 722 /* decDigitsFromDPD -- unpack a format's coefficient                  */
 723 /*                                                                    */
 724 /*   dn is the target number, with 7, 16, or 34-digit space.          */
 725 /*   sour is a 1, 2, or 4-element uInt array containing only declets  */
 726 /*   declets is the number of (right-aligned) declets in sour to      */
 727 /*     be processed.  This may be 1 more than the obvious number in   */
 728 /*     a format, as any top digit is prefixed to the coefficient      */
 729 /*     continuation field.  It also may be as small as 1, as the      */
 730 /*     caller may pre-process leading zero declets.                   */
 731 /*                                                                    */
 732 /* When doing the 'extra declet' case care is taken to avoid writing  */
 733 /* extra digits when there are leading zeros, as these could overflow */
 734 /* the units array when DECDPUN is not 3.                             */
 735 /*                                                                    */
 736 /* The target uInts are used only as necessary to process declets     */
 737 /* declets into the decNumber.  When more than one uInt is needed,    */
 738 /* they are used from left to right (that is, the uInt at offset 0    */
 739 /* provides the least-significant digits).                            */
 740 /*                                                                    */
 741 /* dn->digits is set, but not the sign or exponent.                   */
 742 /* No error is possible [the redundant 888 codes are allowed].        */
 743 /* ------------------------------------------------------------------ */
 744 void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
 745
 746   uInt  dpd;                       /* collector for 10 bits */
 747   Int   n;                         /* counter */
 748   Unit  *uout=dn->lsu;             /* -> current output unit */
 749   Unit  *last=uout;                /* will be unit containing msd */
 750   const uInt *uin=sour;            /* -> current input uInt */
 751   uInt  uoff=0;                    /* -> current input offset [from right] */
 752
 753   #if DECDPUN!=3
 754   uInt  bcd;                       /* BCD result */
 755   uInt  nibble;                    /* work */
 756   Unit  out=0;                     /* accumulator */
 757   Int   cut=0;                     /* power of ten in current unit */
 758   #endif
 759   #if DECDPUN>4
 760   uInt const *pow;                 /* work */
 761   #endif
 762
 763   /* Expand the densely-packed integer, right to left */
 764   for (n=declets-1; n>=0; n--) {   /* count down declets of 10 bits */
 765     dpd=*uin>>uoff;
 766     uoff+=10;
 767     if (uoff>32) {                 /* crossed uInt boundary */
 768       uin++;
 769       uoff-=32;
 770       dpd|=*uin<<(10-uoff);        /* get waiting bits */
 771       }
 772     dpd&=0x3ff;                    /* clear uninteresting bits */
 773
 774   #if DECDPUN==3
 775     if (dpd==0) *uout=0;
 776      else {
 777       *uout=DPD2BIN[dpd];          /* convert 10 bits to binary 0-999 */
 778       last=uout;                   /* record most significant unit */
 779       }
 780     uout++;
 781     } /* n */
 782
 783   #else /* DECDPUN!=3 */
 784     if (dpd==0) {                  /* fastpath [e.g., leading zeros] */
 785       /* write out three 0 digits (nibbles); out may have digit(s) */
 786       cut++;
 787       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 788       if (n==0) break;             /* [as below, works even if MSD=0] */
 789       cut++;
 790       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 791       cut++;
 792       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 793       continue;
 794       }
 795
 796     bcd=DPD2BCD[dpd];              /* convert 10 bits to 12 bits BCD */
 797
 798     /* now accumulate the 3 BCD nibbles into units */
 799     nibble=bcd & 0x00f;
 800     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 801     cut++;
 802     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 803     bcd>>=4;
 804
 805     /* if this is the last declet and the remaining nibbles in bcd */
 806     /* are 00 then process no more nibbles, because this could be */
 807     /* the 'odd' MSD declet and writing any more Units would then */
 808     /* overflow the unit array */
 809     if (n==0 && !bcd) break;
 810
 811     nibble=bcd & 0x00f;
 812     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 813     cut++;
 814     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 815     bcd>>=4;
 816
 817     nibble=bcd & 0x00f;
 818     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 819     cut++;
 820     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 821     } /* n */
 822   if (cut!=0) {                         /* some more left over */
 823     *uout=out;                          /* write out final unit */
 824     if (out) last=uout;                 /* and note if non-zero */
 825     }
 826   #endif
 827
 828   /* here, last points to the most significant unit with digits; */
 829   /* inspect it to get the final digits count -- this is essentially */
 830   /* the same code as decGetDigits in decNumber.c */
 831   dn->digits=(last-dn->lsu)*DECDPUN+1;  /* floor of digits, plus */
 832                                         /* must be at least 1 digit */
 833   #if DECDPUN>1
 834   if (*last<10) return;                 /* common odd digit or 0 */
 835   dn->digits++;                         /* must be 2 at least */
 836   #if DECDPUN>2
 837   if (*last<100) return;                /* 10-99 */
 838   dn->digits++;                         /* must be 3 at least */
 839   #if DECDPUN>3
 840   if (*last<1000) return;               /* 100-999 */
 841   dn->digits++;                         /* must be 4 at least */
 842   #if DECDPUN>4
 843   for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
 844   #endif
 845   #endif
 846   #endif
 847   #endif
 848   return;
 849   } /*decDigitsFromDPD */