1 /* Decimal 64-bit format module for the decNumber C Library.
2 Copyright (C) 2005-2023 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 digits=dn->digits; /* digit countdown */
618 uInt dpd; /* densely packed decimal value */
619 uInt bin; /* binary value 0-999 */
620 uInt *uout=targ; /* -> current output uInt */
621 uInt uoff=0; /* -> current output offset [from right] */
622 const Unit *inu=dn->lsu; /* -> current input unit */
623 Unit uar[DECMAXUNITS]; /* working copy of units, iff shifted */
624 #if DECDPUN!=3 /* not fast path */
625 Unit in; /* current unit */
626 #endif
627
628 if (shift!=0) { /* shift towards most significant required */
629 /* shift the units array to the left by pad digits and copy */
630 /* [this code is a special case of decShiftToMost, which could */
631 /* be used instead if exposed and the array were copied first] */
632 const Unit *source; /* .. */
633 Unit *target, *first; /* .. */
634 uInt next=0; /* work */
635
636 source=dn->lsu+D2U(digits)-1; /* where msu comes from */
637 target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
638 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
639 if (cut==0) { /* unit-boundary case */
640 for (; source>=dn->lsu; source--, target--) *target=*source;
641 }
642 else {
643 first=uar+D2U(digits+shift)-1; /* where msu will end up */
644 for (; source>=dn->lsu; source--, target--) {
645 /* split the source Unit and accumulate remainder for next */
646 #if DECDPUN<=4
647 uInt quot=QUOT10(*source, cut);
648 uInt rem=*source-quot*DECPOWERS[cut];
649 next+=quot;
650 #else
651 uInt rem=*source%DECPOWERS[cut];
652 next+=*source/DECPOWERS[cut];
653 #endif
654 if (target<=first) *target=(Unit)next; /* write to target iff valid */
655 next=rem*DECPOWERS[DECDPUN-cut]; /* save remainder for next Unit */
656 }
657 } /* shift-move */
658 /* propagate remainder to one below and clear the rest */
659 for (; target>=uar; target--) {
660 *target=(Unit)next;
661 next=0;
662 }
663 digits+=shift; /* add count (shift) of zeros added */
664 inu=uar; /* use units in working array */
665 }
666
667 /* now densely pack the coefficient into DPD declets */
668
669 #if DECDPUN!=3 /* not fast path */
670 in=*inu; /* current unit */
671 cut=0; /* at lowest digit */
672 bin=0; /* [keep compiler quiet] */
673 #endif
674
675 for(; digits>0;) { /* each output bunch */
676 #if DECDPUN==3 /* fast path, 3-at-a-time */
677 bin=*inu; /* 3 digits ready for convert */
678 digits-=3; /* [may go negative] */
679 inu++; /* may need another */
680
681 #else /* must collect digit-by-digit */
682 Unit dig; /* current digit */
683 Int j; /* digit-in-declet count */
684 for (j=0; j<3; j++) {
685 #if DECDPUN<=4
686 Unit temp=(Unit)((uInt)(in*6554)>>16);
687 dig=(Unit)(in-X10(temp));
688 in=temp;
689 #else
690 dig=in%10;
691 in=in/10;
692 #endif
693 if (j==0) bin=dig;
694 else if (j==1) bin+=X10(dig);
695 else /* j==2 */ bin+=X100(dig);
696 digits--;
697 if (digits==0) break; /* [also protects *inu below] */
698 cut++;
699 if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
700 }
701 #endif
702 /* here there are 3 digits in bin, or have used all input digits */
703
704 dpd=BIN2DPD[bin];
705
706 /* write declet to uInt array */
707 *uout|=dpd<<uoff;
708 uoff+=10;
709 if (uoff<32) continue; /* no uInt boundary cross */
710 uout++;
711 uoff-=32;
712 *uout|=dpd>>(10-uoff); /* collect top bits */
713 } /* n declets */
714 return;
715 } /* decDigitsToDPD */
716
717 /* ------------------------------------------------------------------ */
718 /* decDigitsFromDPD -- unpack a format's coefficient */
719 /* */
720 /* dn is the target number, with 7, 16, or 34-digit space. */
721 /* sour is a 1, 2, or 4-element uInt array containing only declets */
722 /* declets is the number of (right-aligned) declets in sour to */
723 /* be processed. This may be 1 more than the obvious number in */
724 /* a format, as any top digit is prefixed to the coefficient */
725 /* continuation field. It also may be as small as 1, as the */
726 /* caller may pre-process leading zero declets. */
727 /* */
728 /* When doing the 'extra declet' case care is taken to avoid writing */
729 /* extra digits when there are leading zeros, as these could overflow */
730 /* the units array when DECDPUN is not 3. */
731 /* */
732 /* The target uInts are used only as necessary to process declets */
733 /* declets into the decNumber. When more than one uInt is needed, */
734 /* they are used from left to right (that is, the uInt at offset 0 */
735 /* provides the least-significant digits). */
736 /* */
737 /* dn->digits is set, but not the sign or exponent. */
738 /* No error is possible [the redundant 888 codes are allowed]. */
739 /* ------------------------------------------------------------------ */
740 void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
741
742 uInt dpd; /* collector for 10 bits */
743 Int n; /* counter */
744 Unit *uout=dn->lsu; /* -> current output unit */
745 Unit *last=uout; /* will be unit containing msd */
746 const uInt *uin=sour; /* -> current input uInt */
747 uInt uoff=0; /* -> current input offset [from right] */
748
749 #if DECDPUN!=3
750 uInt bcd; /* BCD result */
751 uInt nibble; /* work */
752 Unit out=0; /* accumulator */
753 Int cut=0; /* power of ten in current unit */
754 #endif
755 #if DECDPUN>4
756 uInt const *pow; /* work */
757 #endif
758
759 /* Expand the densely-packed integer, right to left */
760 for (n=declets-1; n>=0; n--) { /* count down declets of 10 bits */
761 dpd=*uin>>uoff;
762 uoff+=10;
763 if (uoff>32) { /* crossed uInt boundary */
764 uin++;
765 uoff-=32;
766 dpd|=*uin<<(10-uoff); /* get waiting bits */
767 }
768 dpd&=0x3ff; /* clear uninteresting bits */
769
770 #if DECDPUN==3
771 if (dpd==0) *uout=0;
772 else {
773 *uout=DPD2BIN[dpd]; /* convert 10 bits to binary 0-999 */
774 last=uout; /* record most significant unit */
775 }
776 uout++;
777 } /* n */
778
779 #else /* DECDPUN!=3 */
780 if (dpd==0) { /* fastpath [e.g., leading zeros] */
781 /* write out three 0 digits (nibbles); out may have digit(s) */
782 cut++;
783 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
784 if (n==0) break; /* [as below, works even if MSD=0] */
785 cut++;
786 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
787 cut++;
788 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
789 continue;
790 }
791
792 bcd=DPD2BCD[dpd]; /* convert 10 bits to 12 bits BCD */
793
794 /* now accumulate the 3 BCD nibbles into units */
795 nibble=bcd & 0x00f;
796 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
797 cut++;
798 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
799 bcd>>=4;
800
801 /* if this is the last declet and the remaining nibbles in bcd */
802 /* are 00 then process no more nibbles, because this could be */
803 /* the 'odd' MSD declet and writing any more Units would then */
804 /* overflow the unit array */
805 if (n==0 && !bcd) break;
806
807 nibble=bcd & 0x00f;
808 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
809 cut++;
810 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
811 bcd>>=4;
812
813 nibble=bcd & 0x00f;
814 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
815 cut++;
816 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
817 } /* n */
818 if (cut!=0) { /* some more left over */
819 *uout=out; /* write out final unit */
820 if (out) last=uout; /* and note if non-zero */
821 }
822 #endif
823
824 /* here, last points to the most significant unit with digits; */
825 /* inspect it to get the final digits count -- this is essentially */
826 /* the same code as decGetDigits in decNumber.c */
827 dn->digits=(last-dn->lsu)*DECDPUN+1; /* floor of digits, plus */
828 /* must be at least 1 digit */
829 #if DECDPUN>1
830 if (*last<10) return; /* common odd digit or 0 */
831 dn->digits++; /* must be 2 at least */
832 #if DECDPUN>2
833 if (*last<100) return; /* 10-99 */
834 dn->digits++; /* must be 3 at least */
835 #if DECDPUN>3
836 if (*last<1000) return; /* 100-999 */
837 dn->digits++; /* must be 4 at least */
838 #if DECDPUN>4
839 for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
840 #endif
841 #endif
842 #endif
843 #endif
844 return;
845 } /*decDigitsFromDPD */