libdecnumber/dpd/decimal64.c

   1 /* Decimal 64-bit format module for the decNumber C Library.
   2    Copyright (C) 2005-2017 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 3, or (at your option) any later
  10    version.
  11
  12    GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  13    WARRANTY; without even the implied warranty of MERCHANTABILITY or
  14    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  15    for more details.
  16
  17 Under Section 7 of GPL version 3, you are granted additional
  18 permissions described in the GCC Runtime Library Exception, version
  19 3.1, as published by the Free Software Foundation.
  20
  21 You should have received a copy of the GNU General Public License and
  22 a copy of the GCC Runtime Library Exception along with this program;
  23 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  24 <http://www.gnu.org/licenses/>.  */
  25
  26 /* ------------------------------------------------------------------ */
  27 /* Decimal 64-bit format module                                       */
  28 /* ------------------------------------------------------------------ */
  29 /* This module comprises the routines for decimal64 format numbers.   */
  30 /* Conversions are supplied to and from decNumber and String.         */
  31 /*                                                                    */
  32 /* This is used when decNumber provides operations, either for all    */
  33 /* operations or as a proxy between decNumber and decSingle.          */
  34 /*                                                                    */
  35 /* Error handling is the same as decNumber (qv.).                     */
  36 /* ------------------------------------------------------------------ */
  37 #include <string.h>           /* [for memset/memcpy] */
  38 #include <stdio.h>            /* [for printf] */
  39
  40 #include "dconfig.h"          /* GCC definitions */
  41 #define  DECNUMDIGITS 16      /* make decNumbers with space for 16 */
  42 #include "decNumber.h"        /* base number library */
  43 #include "decNumberLocal.h"   /* decNumber local types, etc. */
  44 #include "decimal64.h"        /* our primary include */
  45
  46 /* Utility routines and tables [in decimal64.c]; externs for C++ */
  47 extern const uInt COMBEXP[32], COMBMSD[32];
  48 extern const uShort DPD2BIN[1024];
  49 extern const uShort BIN2DPD[1000];
  50 extern const uByte  BIN2CHAR[4001];
  51
  52 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
  53 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
  54
  55 #if DECTRACE || DECCHECK
  56 void decimal64Show(const decimal64 *);            /* for debug */
  57 extern void decNumberShow(const decNumber *);     /* .. */
  58 #endif
  59
  60 /* Useful macro */
  61 /* Clear a structure (e.g., a decNumber) */
  62 #define DEC_clear(d) memset(d, 0, sizeof(*d))
  63
  64 /* define and include the tables to use for conversions */
  65 #define DEC_BIN2CHAR 1
  66 #define DEC_DPD2BIN  1
  67 #define DEC_BIN2DPD  1             /* used for all sizes */
  68 #include "decDPD.h"                /* lookup tables */
  69
  70 /* ------------------------------------------------------------------ */
  71 /* decimal64FromNumber -- convert decNumber to decimal64              */
  72 /*                                                                    */
  73 /*   ds is the target decimal64                                       */
  74 /*   dn is the source number (assumed valid)                          */
  75 /*   set is the context, used only for reporting errors               */
  76 /*                                                                    */
  77 /* The set argument is used only for status reporting and for the     */
  78 /* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */
  79 /* digits or an overflow is detected).  If the exponent is out of the */
  80 /* valid range then Overflow or Underflow will be raised.             */
  81 /* After Underflow a subnormal result is possible.                    */
  82 /*                                                                    */
  83 /* DEC_Clamped is set if the number has to be 'folded down' to fit,   */
  84 /* by reducing its exponent and multiplying the coefficient by a      */
  85 /* power of ten, or if the exponent on a zero had to be clamped.      */
  86 /* ------------------------------------------------------------------ */
  87 decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,
  88                                 decContext *set) {
  89   uInt status=0;                   /* status accumulator */
  90   Int ae;                          /* adjusted exponent */
  91   decNumber  dw;                   /* work */
  92   decContext dc;                   /* .. */
  93   uInt comb, exp;                  /* .. */
  94   uInt uiwork;                     /* for macros */
  95   uInt targar[2]={0, 0};           /* target 64-bit */
  96   #define targhi targar[1]         /* name the word with the sign */
  97   #define targlo targar[0]         /* and the other */
  98
  99   /* If the number has too many digits, or the exponent could be */
 100   /* out of range then reduce the number under the appropriate */
 101   /* constraints.  This could push the number to Infinity or zero, */
 102   /* so this check and rounding must be done before generating the */
 103   /* decimal64] */
 104   ae=dn->exponent+dn->digits-1;              /* [0 if special] */
 105   if (dn->digits>DECIMAL64_Pmax              /* too many digits */
 106    || ae>DECIMAL64_Emax                      /* likely overflow */
 107    || ae<DECIMAL64_Emin) {                   /* likely underflow */
 108     decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */
 109     dc.round=set->round;                     /* use supplied rounding */
 110     decNumberPlus(&dw, dn, &dc);             /* (round and check) */
 111     /* [this changes -0 to 0, so enforce the sign...] */
 112     dw.bits|=dn->bits&DECNEG;
 113     status=dc.status;                        /* save status */
 114     dn=&dw;                                  /* use the work number */
 115     } /* maybe out of range */
 116
 117   if (dn->bits&DECSPECIAL) {                      /* a special value */
 118     if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
 119      else {                                       /* sNaN or qNaN */
 120       if ((*dn->lsu!=0 || dn->digits>1)           /* non-zero coefficient */
 121        && (dn->digits<DECIMAL64_Pmax)) {          /* coefficient fits */
 122         decDigitsToDPD(dn, targar, 0);
 123         }
 124       if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
 125        else targhi|=DECIMAL_sNaN<<24;
 126       } /* a NaN */
 127     } /* special */
 128
 129    else { /* is finite */
 130     if (decNumberIsZero(dn)) {               /* is a zero */
 131       /* set and clamp exponent */
 132       if (dn->exponent<-DECIMAL64_Bias) {
 133         exp=0;                               /* low clamp */
 134         status|=DEC_Clamped;
 135         }
 136        else {
 137         exp=dn->exponent+DECIMAL64_Bias;     /* bias exponent */
 138         if (exp>DECIMAL64_Ehigh) {           /* top clamp */
 139           exp=DECIMAL64_Ehigh;
 140           status|=DEC_Clamped;
 141           }
 142         }
 143       comb=(exp>>5) & 0x18;             /* msd=0, exp top 2 bits .. */
 144       }
 145      else {                             /* non-zero finite number */
 146       uInt msd;                         /* work */
 147       Int pad=0;                        /* coefficient pad digits */
 148
 149       /* the dn is known to fit, but it may need to be padded */
 150       exp=(uInt)(dn->exponent+DECIMAL64_Bias);    /* bias exponent */
 151       if (exp>DECIMAL64_Ehigh) {                  /* fold-down case */
 152         pad=exp-DECIMAL64_Ehigh;
 153         exp=DECIMAL64_Ehigh;                      /* [to maximum] */
 154         status|=DEC_Clamped;
 155         }
 156
 157       /* fastpath common case */
 158       if (DECDPUN==3 && pad==0) {
 159         uInt dpd[6]={0,0,0,0,0,0};
 160         uInt i;
 161         Int d=dn->digits;
 162         for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
 163         targlo =dpd[0];
 164         targlo|=dpd[1]<<10;
 165         targlo|=dpd[2]<<20;
 166         if (dn->digits>6) {
 167           targlo|=dpd[3]<<30;
 168           targhi =dpd[3]>>2;
 169           targhi|=dpd[4]<<8;
 170           }
 171         msd=dpd[5];                /* [did not really need conversion] */
 172         }
 173        else { /* general case */
 174         decDigitsToDPD(dn, targar, pad);
 175         /* save and clear the top digit */
 176         msd=targhi>>18;
 177         targhi&=0x0003ffff;
 178         }
 179
 180       /* create the combination field */
 181       if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
 182              else comb=((exp>>5) & 0x18) | msd;
 183       }
 184     targhi|=comb<<26;              /* add combination field .. */
 185     targhi|=(exp&0xff)<<18;        /* .. and exponent continuation */
 186     } /* finite */
 187
 188   if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
 189
 190   /* now write to storage; this is now always endian */
 191   if (DECLITEND) {
 192     /* lo int then hi */
 193     UBFROMUI(d64->bytes,   targar[0]);
 194     UBFROMUI(d64->bytes+4, targar[1]);
 195     }
 196    else {
 197     /* hi int then lo */
 198     UBFROMUI(d64->bytes,   targar[1]);
 199     UBFROMUI(d64->bytes+4, targar[0]);
 200     }
 201
 202   if (status!=0) decContextSetStatus(set, status); /* pass on status */
 203   /* decimal64Show(d64); */
 204   return d64;
 205   } /* decimal64FromNumber */
 206
 207 /* ------------------------------------------------------------------ */
 208 /* decimal64ToNumber -- convert decimal64 to decNumber                */
 209 /*   d64 is the source decimal64                                      */
 210 /*   dn is the target number, with appropriate space                  */
 211 /* No error is possible.                                              */
 212 /* ------------------------------------------------------------------ */
 213 decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {
 214   uInt msd;                        /* coefficient MSD */
 215   uInt exp;                        /* exponent top two bits */
 216   uInt comb;                       /* combination field */
 217   Int  need;                       /* work */
 218   uInt uiwork;                     /* for macros */
 219   uInt sourar[2];                  /* source 64-bit */
 220   #define sourhi sourar[1]         /* name the word with the sign */
 221   #define sourlo sourar[0]         /* and the lower word */
 222
 223   /* load source from storage; this is endian */
 224   if (DECLITEND) {
 225     sourlo=UBTOUI(d64->bytes  );   /* directly load the low int */
 226     sourhi=UBTOUI(d64->bytes+4);   /* then the high int */
 227     }
 228    else {
 229     sourhi=UBTOUI(d64->bytes  );   /* directly load the high int */
 230     sourlo=UBTOUI(d64->bytes+4);   /* then the low int */
 231     }
 232
 233   comb=(sourhi>>26)&0x1f;          /* combination field */
 234
 235   decNumberZero(dn);               /* clean number */
 236   if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
 237
 238   msd=COMBMSD[comb];               /* decode the combination field */
 239   exp=COMBEXP[comb];               /* .. */
 240
 241   if (exp==3) {                    /* is a special */
 242     if (msd==0) {
 243       dn->bits|=DECINF;
 244       return dn;                   /* no coefficient needed */
 245       }
 246     else if (sourhi&0x02000000) dn->bits|=DECSNAN;
 247     else dn->bits|=DECNAN;
 248     msd=0;                         /* no top digit */
 249     }
 250    else {                          /* is a finite number */
 251     dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */
 252     }
 253
 254   /* get the coefficient */
 255   sourhi&=0x0003ffff;              /* clean coefficient continuation */
 256   if (msd) {                       /* non-zero msd */
 257     sourhi|=msd<<18;               /* prefix to coefficient */
 258     need=6;                        /* process 6 declets */
 259     }
 260    else { /* msd=0 */
 261     if (!sourhi) {                 /* top word 0 */
 262       if (!sourlo) return dn;      /* easy: coefficient is 0 */
 263       need=3;                      /* process at least 3 declets */
 264       if (sourlo&0xc0000000) need++; /* process 4 declets */
 265       /* [could reduce some more, here] */
 266       }
 267      else {                        /* some bits in top word, msd=0 */
 268       need=4;                      /* process at least 4 declets */
 269       if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */
 270       }
 271     } /*msd=0 */
 272
 273   decDigitsFromDPD(dn, sourar, need);   /* process declets */
 274   return dn;
 275   } /* decimal64ToNumber */
 276
 277
 278 /* ------------------------------------------------------------------ */
 279 /* to-scientific-string -- conversion to numeric string               */
 280 /* to-engineering-string -- conversion to numeric string              */
 281 /*                                                                    */
 282 /*   decimal64ToString(d64, string);                                  */
 283 /*   decimal64ToEngString(d64, string);                               */
 284 /*                                                                    */
 285 /*  d64 is the decimal64 format number to convert                     */
 286 /*  string is the string where the result will be laid out            */
 287 /*                                                                    */
 288 /*  string must be at least 24 characters                             */
 289 /*                                                                    */
 290 /*  No error is possible, and no status can be set.                   */
 291 /* ------------------------------------------------------------------ */
 292 char * decimal64ToEngString(const decimal64 *d64, char *string){
 293   decNumber dn;                         /* work */
 294   decimal64ToNumber(d64, &dn);
 295   decNumberToEngString(&dn, string);
 296   return string;
 297   } /* decimal64ToEngString */
 298
 299 char * decimal64ToString(const decimal64 *d64, char *string){
 300   uInt msd;                        /* coefficient MSD */
 301   Int  exp;                        /* exponent top two bits or full */
 302   uInt comb;                       /* combination field */
 303   char *cstart;                    /* coefficient start */
 304   char *c;                         /* output pointer in string */
 305   const uByte *u;                  /* work */
 306   char *s, *t;                     /* .. (source, target) */
 307   Int  dpd;                        /* .. */
 308   Int  pre, e;                     /* .. */
 309   uInt uiwork;                     /* for macros */
 310
 311   uInt sourar[2];                  /* source 64-bit */
 312   #define sourhi sourar[1]         /* name the word with the sign */
 313   #define sourlo sourar[0]         /* and the lower word */
 314
 315   /* load source from storage; this is endian */
 316   if (DECLITEND) {
 317     sourlo=UBTOUI(d64->bytes  );   /* directly load the low int */
 318     sourhi=UBTOUI(d64->bytes+4);   /* then the high int */
 319     }
 320    else {
 321     sourhi=UBTOUI(d64->bytes  );   /* directly load the high int */
 322     sourlo=UBTOUI(d64->bytes+4);   /* then the low int */
 323     }
 324
 325   c=string;                        /* where result will go */
 326   if (((Int)sourhi)<0) *c++='-';   /* handle sign */
 327
 328   comb=(sourhi>>26)&0x1f;          /* combination field */
 329   msd=COMBMSD[comb];               /* decode the combination field */
 330   exp=COMBEXP[comb];               /* .. */
 331
 332   if (exp==3) {
 333     if (msd==0) {                  /* infinity */
 334       strcpy(c,   "Inf");
 335       strcpy(c+3, "inity");
 336       return string;               /* easy */
 337       }
 338     if (sourhi&0x02000000) *c++='s'; /* sNaN */
 339     strcpy(c, "NaN");              /* complete word */
 340     c+=3;                          /* step past */
 341     if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */
 342     /* otherwise drop through to add integer; set correct exp */
 343     exp=0; msd=0;                  /* setup for following code */
 344     }
 345    else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;
 346
 347   /* convert 16 digits of significand to characters */
 348   cstart=c;                        /* save start of coefficient */
 349   if (msd) *c++='0'+(char)msd;     /* non-zero most significant digit */
 350
 351   /* Now decode the declets.  After extracting each one, it is */
 352   /* decoded to binary and then to a 4-char sequence by table lookup; */
 353   /* the 4-chars are a 1-char length (significant digits, except 000 */
 354   /* has length 0).  This allows us to left-align the first declet */
 355   /* with non-zero content, then remaining ones are full 3-char */
 356   /* length.  We use fixed-length memcpys because variable-length */
 357   /* causes a subroutine call in GCC.  (These are length 4 for speed */
 358   /* and are safe because the array has an extra terminator byte.) */
 359   #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4];                   \
 360                    if (c!=cstart) {memcpy(c, u+1, 4); c+=3;}      \
 361                     else if (*u)  {memcpy(c, u+4-*u, 4); c+=*u;}
 362
 363   dpd=(sourhi>>8)&0x3ff;                     /* declet 1 */
 364   dpd2char;
 365   dpd=((sourhi&0xff)<<2) | (sourlo>>30);     /* declet 2 */
 366   dpd2char;
 367   dpd=(sourlo>>20)&0x3ff;                    /* declet 3 */
 368   dpd2char;
 369   dpd=(sourlo>>10)&0x3ff;                    /* declet 4 */
 370   dpd2char;
 371   dpd=(sourlo)&0x3ff;                        /* declet 5 */
 372   dpd2char;
 373
 374   if (c==cstart) *c++='0';         /* all zeros -- make 0 */
 375
 376   if (exp==0) {                    /* integer or NaN case -- easy */
 377     *c='\0';                       /* terminate */
 378     return string;
 379     }
 380
 381   /* non-0 exponent */
 382   e=0;                             /* assume no E */
 383   pre=c-cstart+exp;
 384   /* [here, pre-exp is the digits count (==1 for zero)] */
 385   if (exp>0 || pre<-5) {           /* need exponential form */
 386     e=pre-1;                       /* calculate E value */
 387     pre=1;                         /* assume one digit before '.' */
 388     } /* exponential form */
 389
 390   /* modify the coefficient, adding 0s, '.', and E+nn as needed */
 391   s=c-1;                           /* source (LSD) */
 392   if (pre>0) {                     /* ddd.ddd (plain), perhaps with E */
 393     char *dotat=cstart+pre;
 394     if (dotat<c) {                 /* if embedded dot needed... */
 395       t=c;                              /* target */
 396       for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
 397       *t='.';                           /* insert the dot */
 398       c++;                              /* length increased by one */
 399       }
 400
 401     /* finally add the E-part, if needed; it will never be 0, and has */
 402     /* a maximum length of 3 digits */
 403     if (e!=0) {
 404       *c++='E';                    /* starts with E */
 405       *c++='+';                    /* assume positive */
 406       if (e<0) {
 407         *(c-1)='-';                /* oops, need '-' */
 408         e=-e;                      /* uInt, please */
 409         }
 410       u=&BIN2CHAR[e*4];            /* -> length byte */
 411       memcpy(c, u+4-*u, 4);        /* copy fixed 4 characters [is safe] */
 412       c+=*u;                       /* bump pointer appropriately */
 413       }
 414     *c='\0';                       /* add terminator */
 415     /*printf("res %s\n", string); */
 416     return string;
 417     } /* pre>0 */
 418
 419   /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
 420   t=c+1-pre;
 421   *(t+1)='\0';                          /* can add terminator now */
 422   for (; s>=cstart; s--, t--) *t=*s;    /* shift whole coefficient right */
 423   c=cstart;
 424   *c++='0';                             /* always starts with 0. */
 425   *c++='.';
 426   for (; pre<0; pre++) *c++='0';        /* add any 0's after '.' */
 427   /*printf("res %s\n", string); */
 428   return string;
 429   } /* decimal64ToString */
 430
 431 /* ------------------------------------------------------------------ */
 432 /* to-number -- conversion from numeric string                        */
 433 /*                                                                    */
 434 /*   decimal64FromString(result, string, set);                        */
 435 /*                                                                    */
 436 /*  result  is the decimal64 format number which gets the result of   */
 437 /*          the conversion                                            */
 438 /*  *string is the character string which should contain a valid      */
 439 /*          number (which may be a special value)                     */
 440 /*  set     is the context                                            */
 441 /*                                                                    */
 442 /* The context is supplied to this routine is used for error handling */
 443 /* (setting of status and traps) and for the rounding mode, only.     */
 444 /* If an error occurs, the result will be a valid decimal64 NaN.      */
 445 /* ------------------------------------------------------------------ */
 446 decimal64 * decimal64FromString(decimal64 *result, const char *string,
 447                                 decContext *set) {
 448   decContext dc;                             /* work */
 449   decNumber dn;                              /* .. */
 450
 451   decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */
 452   dc.round=set->round;                        /* use supplied rounding */
 453
 454   decNumberFromString(&dn, string, &dc);     /* will round if needed */
 455
 456   decimal64FromNumber(result, &dn, &dc);
 457   if (dc.status!=0) {                        /* something happened */
 458     decContextSetStatus(set, dc.status);     /* .. pass it on */
 459     }
 460   return result;
 461   } /* decimal64FromString */
 462
 463 /* ------------------------------------------------------------------ */
 464 /* decimal64IsCanonical -- test whether encoding is canonical         */
 465 /*   d64 is the source decimal64                                      */
 466 /*   returns 1 if the encoding of d64 is canonical, 0 otherwise       */
 467 /* No error is possible.                                              */
 468 /* ------------------------------------------------------------------ */
 469 uInt decimal64IsCanonical(const decimal64 *d64) {
 470   decNumber dn;                         /* work */
 471   decimal64 canon;                      /* .. */
 472   decContext dc;                        /* .. */
 473   decContextDefault(&dc, DEC_INIT_DECIMAL64);
 474   decimal64ToNumber(d64, &dn);
 475   decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
 476   return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
 477   } /* decimal64IsCanonical */
 478
 479 /* ------------------------------------------------------------------ */
 480 /* decimal64Canonical -- copy an encoding, ensuring it is canonical   */
 481 /*   d64 is the source decimal64                                      */
 482 /*   result is the target (may be the same decimal64)                 */
 483 /*   returns result                                                   */
 484 /* No error is possible.                                              */
 485 /* ------------------------------------------------------------------ */
 486 decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
 487   decNumber dn;                         /* work */
 488   decContext dc;                        /* .. */
 489   decContextDefault(&dc, DEC_INIT_DECIMAL64);
 490   decimal64ToNumber(d64, &dn);
 491   decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */
 492   return result;
 493   } /* decimal64Canonical */
 494
 495 #if DECTRACE || DECCHECK
 496 /* Macros for accessing decimal64 fields.  These assume the
 497    argument is a reference (pointer) to the decimal64 structure,
 498    and the decimal64 is in network byte order (big-endian) */
 499 /* Get sign */
 500 #define decimal64Sign(d)       ((unsigned)(d)->bytes[0]>>7)
 501
 502 /* Get combination field */
 503 #define decimal64Comb(d)       (((d)->bytes[0] & 0x7c)>>2)
 504
 505 /* Get exponent continuation [does not remove bias] */
 506 #define decimal64ExpCon(d)     ((((d)->bytes[0] & 0x03)<<6)           \
 507                              | ((unsigned)(d)->bytes[1]>>2))
 508
 509 /* Set sign [this assumes sign previously 0] */
 510 #define decimal64SetSign(d, b) {                                      \
 511   (d)->bytes[0]|=((unsigned)(b)<<7);}
 512
 513 /* Set exponent continuation [does not apply bias] */
 514 /* This assumes range has been checked and exponent previously 0; */
 515 /* type of exponent must be unsigned */
 516 #define decimal64SetExpCon(d, e) {                                    \
 517   (d)->bytes[0]|=(uByte)((e)>>6);                                     \
 518   (d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);}
 519
 520 /* ------------------------------------------------------------------ */
 521 /* decimal64Show -- display a decimal64 in hexadecimal [debug aid]    */
 522 /*   d64 -- the number to show                                        */
 523 /* ------------------------------------------------------------------ */
 524 /* Also shows sign/cob/expconfields extracted */
 525 void decimal64Show(const decimal64 *d64) {
 526   char buf[DECIMAL64_Bytes*2+1];
 527   Int i, j=0;
 528
 529   if (DECLITEND) {
 530     for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
 531       sprintf(&buf[j], "%02x", d64->bytes[7-i]);
 532       }
 533     printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
 534            d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
 535            ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
 536     }
 537    else { /* big-endian */
 538     for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
 539       sprintf(&buf[j], "%02x", d64->bytes[i]);
 540       }
 541     printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
 542            decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
 543     }
 544   } /* decimal64Show */
 545 #endif
 546
 547 /* ================================================================== */
 548 /* Shared utility routines and tables                                 */
 549 /* ================================================================== */
 550 /* define and include the conversion tables to use for shared code */
 551 #if DECDPUN==3
 552   #define DEC_DPD2BIN 1
 553 #else
 554   #define DEC_DPD2BCD 1
 555 #endif
 556 #include "decDPD.h"           /* lookup tables */
 557
 558 /* The maximum number of decNumberUnits needed for a working copy of */
 559 /* the units array is the ceiling of digits/DECDPUN, where digits is */
 560 /* the maximum number of digits in any of the formats for which this */
 561 /* is used.  decimal128.h must not be included in this module, so, as */
 562 /* a very special case, that number is defined as a literal here. */
 563 #define DECMAX754   34
 564 #define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)
 565
 566 /* ------------------------------------------------------------------ */
 567 /* Combination field lookup tables (uInts to save measurable work)    */
 568 /*                                                                    */
 569 /*      COMBEXP - 2-bit most-significant-bits of exponent             */
 570 /*                [11 if an Infinity or NaN]                          */
 571 /*      COMBMSD - 4-bit most-significant-digit                        */
 572 /*                [0=Infinity, 1=NaN if COMBEXP=11]                   */
 573 /*                                                                    */
 574 /* Both are indexed by the 5-bit combination field (0-31)             */
 575 /* ------------------------------------------------------------------ */
 576 const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
 577                         1, 1, 1, 1, 1, 1, 1, 1,
 578                         2, 2, 2, 2, 2, 2, 2, 2,
 579                         0, 0, 1, 1, 2, 2, 3, 3};
 580 const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,
 581                         0, 1, 2, 3, 4, 5, 6, 7,
 582                         0, 1, 2, 3, 4, 5, 6, 7,
 583                         8, 9, 8, 9, 8, 9, 0, 1};
 584
 585 /* ------------------------------------------------------------------ */
 586 /* decDigitsToDPD -- pack coefficient into DPD form                   */
 587 /*                                                                    */
 588 /*   dn   is the source number (assumed valid, max DECMAX754 digits)  */
 589 /*   targ is 1, 2, or 4-element uInt array, which the caller must     */
 590 /*        have cleared to zeros                                       */
 591 /*   shift is the number of 0 digits to add on the right (normally 0) */
 592 /*                                                                    */
 593 /* The coefficient must be known small enough to fit.  The full       */
 594 /* coefficient is copied, including the leading 'odd' digit.  This    */
 595 /* digit is retrieved and packed into the combination field by the    */
 596 /* caller.                                                            */
 597 /*                                                                    */
 598 /* The target uInts are altered only as necessary to receive the      */
 599 /* digits of the decNumber.  When more than one uInt is needed, they  */
 600 /* are filled from left to right (that is, the uInt at offset 0 will  */
 601 /* end up with the least-significant digits).                         */
 602 /*                                                                    */
 603 /* shift is used for 'fold-down' padding.                             */
 604 /*                                                                    */
 605 /* No error is possible.                                              */
 606 /* ------------------------------------------------------------------ */
 607 #if DECDPUN<=4
 608 /* Constant multipliers for divide-by-power-of five using reciprocal */
 609 /* multiply, after removing powers of 2 by shifting, and final shift */
 610 /* of 17 [we only need up to **4] */
 611 static const uInt multies[]={131073, 26215, 5243, 1049, 210};
 612 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
 613 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
 614 #endif
 615 void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
 616   Int  cut;                   /* work */
 617   Int  n;                     /* output bunch counter */
 618   Int  digits=dn->digits;     /* digit countdown */
 619   uInt dpd;                   /* densely packed decimal value */
 620   uInt bin;                   /* binary value 0-999 */
 621   uInt *uout=targ;            /* -> current output uInt */
 622   uInt  uoff=0;               /* -> current output offset [from right] */
 623   const Unit *inu=dn->lsu;    /* -> current input unit */
 624   Unit  uar[DECMAXUNITS];     /* working copy of units, iff shifted */
 625   #if DECDPUN!=3              /* not fast path */
 626     Unit in;                  /* current unit */
 627   #endif
 628
 629   if (shift!=0) {             /* shift towards most significant required */
 630     /* shift the units array to the left by pad digits and copy */
 631     /* [this code is a special case of decShiftToMost, which could */
 632     /* be used instead if exposed and the array were copied first] */
 633     const Unit *source;                 /* .. */
 634     Unit  *target, *first;              /* .. */
 635     uInt  next=0;                       /* work */
 636
 637     source=dn->lsu+D2U(digits)-1;       /* where msu comes from */
 638     target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
 639     cut=DECDPUN-MSUDIGITS(shift);       /* where to slice */
 640     if (cut==0) {                       /* unit-boundary case */
 641       for (; source>=dn->lsu; source--, target--) *target=*source;
 642       }
 643      else {
 644       first=uar+D2U(digits+shift)-1;    /* where msu will end up */
 645       for (; source>=dn->lsu; source--, target--) {
 646         /* split the source Unit and accumulate remainder for next */
 647         #if DECDPUN<=4
 648           uInt quot=QUOT10(*source, cut);
 649           uInt rem=*source-quot*DECPOWERS[cut];
 650           next+=quot;
 651         #else
 652           uInt rem=*source%DECPOWERS[cut];
 653           next+=*source/DECPOWERS[cut];
 654         #endif
 655         if (target<=first) *target=(Unit)next; /* write to target iff valid */
 656         next=rem*DECPOWERS[DECDPUN-cut];       /* save remainder for next Unit */
 657         }
 658       } /* shift-move */
 659     /* propagate remainder to one below and clear the rest */
 660     for (; target>=uar; target--) {
 661       *target=(Unit)next;
 662       next=0;
 663       }
 664     digits+=shift;                 /* add count (shift) of zeros added */
 665     inu=uar;                       /* use units in working array */
 666     }
 667
 668   /* now densely pack the coefficient into DPD declets */
 669
 670   #if DECDPUN!=3                   /* not fast path */
 671     in=*inu;                       /* current unit */
 672     cut=0;                         /* at lowest digit */
 673     bin=0;                         /* [keep compiler quiet] */
 674   #endif
 675
 676   for(n=0; digits>0; n++) {        /* each output bunch */
 677     #if DECDPUN==3                 /* fast path, 3-at-a-time */
 678       bin=*inu;                    /* 3 digits ready for convert */
 679       digits-=3;                   /* [may go negative] */
 680       inu++;                       /* may need another */
 681
 682     #else                          /* must collect digit-by-digit */
 683       Unit dig;                    /* current digit */
 684       Int j;                       /* digit-in-declet count */
 685       for (j=0; j<3; j++) {
 686         #if DECDPUN<=4
 687           Unit temp=(Unit)((uInt)(in*6554)>>16);
 688           dig=(Unit)(in-X10(temp));
 689           in=temp;
 690         #else
 691           dig=in%10;
 692           in=in/10;
 693         #endif
 694         if (j==0) bin=dig;
 695          else if (j==1)  bin+=X10(dig);
 696          else /* j==2 */ bin+=X100(dig);
 697         digits--;
 698         if (digits==0) break;      /* [also protects *inu below] */
 699         cut++;
 700         if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
 701         }
 702     #endif
 703     /* here there are 3 digits in bin, or have used all input digits */
 704
 705     dpd=BIN2DPD[bin];
 706
 707     /* write declet to uInt array */
 708     *uout|=dpd<<uoff;
 709     uoff+=10;
 710     if (uoff<32) continue;         /* no uInt boundary cross */
 711     uout++;
 712     uoff-=32;
 713     *uout|=dpd>>(10-uoff);         /* collect top bits */
 714     } /* n declets */
 715   return;
 716   } /* decDigitsToDPD */
 717
 718 /* ------------------------------------------------------------------ */
 719 /* decDigitsFromDPD -- unpack a format's coefficient                  */
 720 /*                                                                    */
 721 /*   dn is the target number, with 7, 16, or 34-digit space.          */
 722 /*   sour is a 1, 2, or 4-element uInt array containing only declets  */
 723 /*   declets is the number of (right-aligned) declets in sour to      */
 724 /*     be processed.  This may be 1 more than the obvious number in   */
 725 /*     a format, as any top digit is prefixed to the coefficient      */
 726 /*     continuation field.  It also may be as small as 1, as the      */
 727 /*     caller may pre-process leading zero declets.                   */
 728 /*                                                                    */
 729 /* When doing the 'extra declet' case care is taken to avoid writing  */
 730 /* extra digits when there are leading zeros, as these could overflow */
 731 /* the units array when DECDPUN is not 3.                             */
 732 /*                                                                    */
 733 /* The target uInts are used only as necessary to process declets     */
 734 /* declets into the decNumber.  When more than one uInt is needed,    */
 735 /* they are used from left to right (that is, the uInt at offset 0    */
 736 /* provides the least-significant digits).                            */
 737 /*                                                                    */
 738 /* dn->digits is set, but not the sign or exponent.                   */
 739 /* No error is possible [the redundant 888 codes are allowed].        */
 740 /* ------------------------------------------------------------------ */
 741 void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
 742
 743   uInt  dpd;                       /* collector for 10 bits */
 744   Int   n;                         /* counter */
 745   Unit  *uout=dn->lsu;             /* -> current output unit */
 746   Unit  *last=uout;                /* will be unit containing msd */
 747   const uInt *uin=sour;            /* -> current input uInt */
 748   uInt  uoff=0;                    /* -> current input offset [from right] */
 749
 750   #if DECDPUN!=3
 751   uInt  bcd;                       /* BCD result */
 752   uInt  nibble;                    /* work */
 753   Unit  out=0;                     /* accumulator */
 754   Int   cut=0;                     /* power of ten in current unit */
 755   #endif
 756   #if DECDPUN>4
 757   uInt const *pow;                 /* work */
 758   #endif
 759
 760   /* Expand the densely-packed integer, right to left */
 761   for (n=declets-1; n>=0; n--) {   /* count down declets of 10 bits */
 762     dpd=*uin>>uoff;
 763     uoff+=10;
 764     if (uoff>32) {                 /* crossed uInt boundary */
 765       uin++;
 766       uoff-=32;
 767       dpd|=*uin<<(10-uoff);        /* get waiting bits */
 768       }
 769     dpd&=0x3ff;                    /* clear uninteresting bits */
 770
 771   #if DECDPUN==3
 772     if (dpd==0) *uout=0;
 773      else {
 774       *uout=DPD2BIN[dpd];          /* convert 10 bits to binary 0-999 */
 775       last=uout;                   /* record most significant unit */
 776       }
 777     uout++;
 778     } /* n */
 779
 780   #else /* DECDPUN!=3 */
 781     if (dpd==0) {                  /* fastpath [e.g., leading zeros] */
 782       /* write out three 0 digits (nibbles); out may have digit(s) */
 783       cut++;
 784       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 785       if (n==0) break;             /* [as below, works even if MSD=0] */
 786       cut++;
 787       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 788       cut++;
 789       if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 790       continue;
 791       }
 792
 793     bcd=DPD2BCD[dpd];              /* convert 10 bits to 12 bits BCD */
 794
 795     /* now accumulate the 3 BCD nibbles into units */
 796     nibble=bcd & 0x00f;
 797     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 798     cut++;
 799     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 800     bcd>>=4;
 801
 802     /* if this is the last declet and the remaining nibbles in bcd */
 803     /* are 00 then process no more nibbles, because this could be */
 804     /* the 'odd' MSD declet and writing any more Units would then */
 805     /* overflow the unit array */
 806     if (n==0 && !bcd) break;
 807
 808     nibble=bcd & 0x00f;
 809     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 810     cut++;
 811     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 812     bcd>>=4;
 813
 814     nibble=bcd & 0x00f;
 815     if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
 816     cut++;
 817     if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
 818     } /* n */
 819   if (cut!=0) {                         /* some more left over */
 820     *uout=out;                          /* write out final unit */
 821     if (out) last=uout;                 /* and note if non-zero */
 822     }
 823   #endif
 824
 825   /* here, last points to the most significant unit with digits; */
 826   /* inspect it to get the final digits count -- this is essentially */
 827   /* the same code as decGetDigits in decNumber.c */
 828   dn->digits=(last-dn->lsu)*DECDPUN+1;  /* floor of digits, plus */
 829                                         /* must be at least 1 digit */
 830   #if DECDPUN>1
 831   if (*last<10) return;                 /* common odd digit or 0 */
 832   dn->digits++;                         /* must be 2 at least */
 833   #if DECDPUN>2
 834   if (*last<100) return;                /* 10-99 */
 835   dn->digits++;                         /* must be 3 at least */
 836   #if DECDPUN>3
 837   if (*last<1000) return;               /* 100-999 */
 838   dn->digits++;                         /* must be 4 at least */
 839   #if DECDPUN>4
 840   for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
 841   #endif
 842   #endif
 843   #endif
 844   #endif
 845   return;
 846   } /*decDigitsFromDPD */