1 /* Common code for fixed-size types in the decNumber C Library.
2 Copyright (C) 2007-2018 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 /* decCommon.c -- common code for all three fixed-size types */
28 /* ------------------------------------------------------------------ */
29 /* This module comprises code that is shared between all the formats */
30 /* (decSingle, decDouble, and decQuad); it includes set and extract */
31 /* of format components, widening, narrowing, and string conversions. */
32 /* */
33 /* Unlike decNumber, parameterization takes place at compile time */
34 /* rather than at runtime. The parameters are set in the decDouble.c */
35 /* (etc.) files, which then include this one to produce the compiled */
36 /* code. The functions here, therefore, are code shared between */
37 /* multiple formats. */
38 /* ------------------------------------------------------------------ */
39 /* Names here refer to decFloat rather than to decDouble, etc., and */
40 /* the functions are in strict alphabetical order. */
41 /* Constants, tables, and debug function(s) are included only for QUAD */
42 /* (which will always be compiled if DOUBLE or SINGLE are used). */
43 /* */
44 /* Whenever a decContext is used, only the status may be set (using */
45 /* OR) or the rounding mode read; all other fields are ignored and */
46 /* untouched. */
47
48 #include "decCommonSymbols.h"
49
50 /* names for simpler testing and default context */
51 #if DECPMAX==7
52 #define SINGLE 1
53 #define DOUBLE 0
54 #define QUAD 0
55 #define DEFCONTEXT DEC_INIT_DECIMAL32
56 #elif DECPMAX==16
57 #define SINGLE 0
58 #define DOUBLE 1
59 #define QUAD 0
60 #define DEFCONTEXT DEC_INIT_DECIMAL64
61 #elif DECPMAX==34
62 #define SINGLE 0
63 #define DOUBLE 0
64 #define QUAD 1
65 #define DEFCONTEXT DEC_INIT_DECIMAL128
66 #else
67 #error Unexpected DECPMAX value
68 #endif
69
70 /* Assertions */
71
72 #if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34
73 #error Unexpected Pmax (DECPMAX) value for this module
74 #endif
75
76 /* Assert facts about digit characters, etc. */
77 #if ('9'&0x0f)!=9
78 #error This module assumes characters are of the form 0b....nnnn
79 /* where .... are don't care 4 bits and nnnn is 0000 through 1001 */
80 #endif
81 #if ('9'&0xf0)==('.'&0xf0)
82 #error This module assumes '.' has a different mask than a digit
83 #endif
84
85 /* Assert ToString lay-out conditions */
86 #if DECSTRING<DECPMAX+9
87 #error ToString needs at least 8 characters for lead-in and dot
88 #endif
89 #if DECPMAX+DECEMAXD+5 > DECSTRING
90 #error Exponent form can be too long for ToString to lay out safely
91 #endif
92 #if DECEMAXD > 4
93 #error Exponent form is too long for ToString to lay out
94 /* Note: code for up to 9 digits exists in archives [decOct] */
95 #endif
96
97 /* Private functions used here and possibly in decBasic.c, etc. */
98 static decFloat * decFinalize(decFloat *, bcdnum *, decContext *);
99 static Flag decBiStr(const char *, const char *, const char *);
100
101 /* Macros and private tables; those which are not format-dependent */
102 /* are only included if decQuad is being built. */
103
104 /* ------------------------------------------------------------------ */
105 /* Combination field lookup tables (uInts to save measurable work) */
106 /* */
107 /* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */
108 /* 10), shifted left for format, or DECFLOAT_Inf/NaN */
109 /* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */
110 /* DECCOMBMSD - 4-bit most-significant-digit */
111 /* [0 if the index is a special (Infinity or NaN)] */
112 /* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */
113 /* (placed in uInt so no shift is needed) */
114 /* */
115 /* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */
116 /* and 5-bit combination field (0-63, the second half of the table */
117 /* identical to the first half) */
118 /* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */
119 /* */
120 /* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */
121 /* only included once, when QUAD is being built */
122 /* ------------------------------------------------------------------ */
123 static const uInt DECCOMBEXP[64]={
124 0, 0, 0, 0, 0, 0, 0, 0,
125 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
126 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
127 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
128 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
129 0, 0, 1<<DECECONL, 1<<DECECONL,
130 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN,
131 0, 0, 0, 0, 0, 0, 0, 0,
132 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
133 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
134 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
135 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
136 0, 0, 1<<DECECONL, 1<<DECECONL,
137 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN};
138 #if !QUAD
139 static const uInt DECCOMBWEXP[64]={
140 0, 0, 0, 0, 0, 0, 0, 0,
141 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
142 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
143 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
144 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
145 0, 0, 1<<DECWECONL, 1<<DECWECONL,
146 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN,
147 0, 0, 0, 0, 0, 0, 0, 0,
148 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
149 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
150 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
151 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
152 0, 0, 1<<DECWECONL, 1<<DECWECONL,
153 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN};
154 #endif
155
156 #if QUAD
157 const uInt DECCOMBMSD[64]={
158 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
159 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0,
160 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
161 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0};
162
163 const uInt DECCOMBFROM[48]={
164 0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000,
165 0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000,
166 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000,
167 0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000,
168 0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
169 0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000,
170 0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000,
171 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
172
173 /* ------------------------------------------------------------------ */
174 /* Request and include the tables to use for conversions */
175 /* ------------------------------------------------------------------ */
176 #define DEC_BCD2DPD 1 /* 0-0x999 -> DPD */
177 #define DEC_BIN2DPD 1 /* 0-999 -> DPD */
178 #define DEC_BIN2BCD8 1 /* 0-999 -> ddd, len */
179 #define DEC_DPD2BCD8 1 /* DPD -> ddd, len */
180 #define DEC_DPD2BIN 1 /* DPD -> 0-999 */
181 #define DEC_DPD2BINK 1 /* DPD -> 0-999000 */
182 #define DEC_DPD2BINM 1 /* DPD -> 0-999000000 */
183 #include "decDPD.h" /* source of the lookup tables */
184
185 #endif
186
187 /* ----------------------------------------------------------------- */
188 /* decBiStr -- compare string with pairwise options */
189 /* */
190 /* targ is the string to compare */
191 /* str1 is one of the strings to compare against (length may be 0) */
192 /* str2 is the other; it must be the same length as str1 */
193 /* */
194 /* returns 1 if strings compare equal, (that is, targ is the same */
195 /* length as str1 and str2, and each character of targ is in one */
196 /* of str1 or str2 in the corresponding position), or 0 otherwise */
197 /* */
198 /* This is used for generic caseless compare, including the awkward */
199 /* case of the Turkish dotted and dotless Is. Use as (for example): */
200 /* if (decBiStr(test, "mike", "MIKE")) ... */
201 /* ----------------------------------------------------------------- */
decBiStr(const char * targ,const char * str1,const char * str2)202 static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
203 for (;;targ++, str1++, str2++) {
204 if (*targ!=*str1 && *targ!=*str2) return 0;
205 /* *targ has a match in one (or both, if terminator) */
206 if (*targ=='\0') break;
207 } /* forever */
208 return 1;
209 } /* decBiStr */
210
211 /* ------------------------------------------------------------------ */
212 /* decFinalize -- adjust and store a final result */
213 /* */
214 /* df is the decFloat format number which gets the final result */
215 /* num is the descriptor of the number to be checked and encoded */
216 /* [its values, including the coefficient, may be modified] */
217 /* set is the context to use */
218 /* returns df */
219 /* */
220 /* The num descriptor may point to a bcd8 string of any length; this */
221 /* string may have leading insignificant zeros. If it has more than */
222 /* DECPMAX digits then the final digit can be a round-for-reround */
223 /* digit (i.e., it may include a sticky bit residue). */
224 /* */
225 /* The exponent (q) may be one of the codes for a special value and */
226 /* can be up to 999999999 for conversion from string. */
227 /* */
228 /* No error is possible, but Inexact, Underflow, and/or Overflow may */
229 /* be set. */
230 /* ------------------------------------------------------------------ */
231 /* Constant whose size varies with format; also the check for surprises */
232 static uByte allnines[DECPMAX]=
233 #if SINGLE
234 {9, 9, 9, 9, 9, 9, 9};
235 #elif DOUBLE
236 {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
237 #elif QUAD
238 {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
239 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
240 #endif
241
decFinalize(decFloat * df,bcdnum * num,decContext * set)242 static decFloat * decFinalize(decFloat *df, bcdnum *num,
243 decContext *set) {
244 uByte *ub; /* work */
245 uInt dpd; /* .. */
246 uInt uiwork; /* for macros */
247 uByte *umsd=num->msd; /* local copy */
248 uByte *ulsd=num->lsd; /* .. */
249 uInt encode; /* encoding accumulator */
250 Int length; /* coefficient length */
251
252 #if DECCHECK
253 Int clen=ulsd-umsd+1;
254 #if QUAD
255 #define COEXTRA 2 /* extra-long coefficent */
256 #else
257 #define COEXTRA 0
258 #endif
259 if (clen<1 || clen>DECPMAX*3+2+COEXTRA)
260 printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen);
261 if (num->sign!=0 && num->sign!=DECFLOAT_Sign)
262 printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign);
263 if (!EXPISSPECIAL(num->exponent)
264 && (num->exponent>1999999999 || num->exponent<-1999999999))
265 printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent);
266 /* decShowNum(num, "final"); */
267 #endif
268
269 /* A special will have an 'exponent' which is very positive and a */
270 /* coefficient < DECPMAX */
271 length=(uInt)(ulsd-umsd+1); /* coefficient length */
272
273 if (!NUMISSPECIAL(num)) {
274 Int drop; /* digits to be dropped */
275 /* skip leading insignificant zeros to calculate an exact length */
276 /* [this is quite expensive] */
277 if (*umsd==0) {
278 for (; umsd+3<ulsd && UBTOUI(umsd)==0;) umsd+=4;
279 for (; *umsd==0 && umsd<ulsd;) umsd++;
280 length=ulsd-umsd+1; /* recalculate */
281 }
282 drop=MAXI(length-DECPMAX, DECQTINY-num->exponent);
283 /* drop can now be > digits for bottom-clamp (subnormal) cases */
284 if (drop>0) { /* rounding needed */
285 /* (decFloatQuantize has very similar code to this, so any */
286 /* changes may need to be made there, too) */
287 uByte *roundat; /* -> re-round digit */
288 uByte reround; /* reround value */
289 /* printf("Rounding; drop=%ld\n", (LI)drop); */
290
291 num->exponent+=drop; /* always update exponent */
292
293 /* Three cases here: */
294 /* 1. new LSD is in coefficient (almost always) */
295 /* 2. new LSD is digit to left of coefficient (so MSD is */
296 /* round-for-reround digit) */
297 /* 3. new LSD is to left of case 2 (whole coefficient is sticky) */
298 /* [duplicate check-stickies code to save a test] */
299 /* [by-digit check for stickies as runs of zeros are rare] */
300 if (drop<length) { /* NB lengths not addresses */
301 roundat=umsd+length-drop;
302 reround=*roundat;
303 for (ub=roundat+1; ub<=ulsd; ub++) {
304 if (*ub!=0) { /* non-zero to be discarded */
305 reround=DECSTICKYTAB[reround]; /* apply sticky bit */
306 break; /* [remainder don't-care] */
307 }
308 } /* check stickies */
309 ulsd=roundat-1; /* new LSD */
310 }
311 else { /* edge case */
312 if (drop==length) {
313 roundat=umsd;
314 reround=*roundat;
315 }
316 else {
317 roundat=umsd-1;
318 reround=0;
319 }
320 for (ub=roundat+1; ub<=ulsd; ub++) {
321 if (*ub!=0) { /* non-zero to be discarded */
322 reround=DECSTICKYTAB[reround]; /* apply sticky bit */
323 break; /* [remainder don't-care] */
324 }
325 } /* check stickies */
326 *umsd=0; /* coefficient is a 0 */
327 ulsd=umsd; /* .. */
328 }
329
330 if (reround!=0) { /* discarding non-zero */
331 uInt bump=0;
332 set->status|=DEC_Inexact;
333 /* if adjusted exponent [exp+digits-1] is < EMIN then num is */
334 /* subnormal -- so raise Underflow */
335 if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN)
336 set->status|=DEC_Underflow;
337
338 /* next decide whether increment of the coefficient is needed */
339 if (set->round==DEC_ROUND_HALF_EVEN) { /* fastpath slowest case */
340 if (reround>5) bump=1; /* >0.5 goes up */
341 else if (reround==5) /* exactly 0.5000 .. */
342 bump=*ulsd & 0x01; /* .. up iff [new] lsd is odd */
343 } /* r-h-e */
344 else switch (set->round) {
345 case DEC_ROUND_DOWN: {
346 /* no change */
347 break;} /* r-d */
348 case DEC_ROUND_HALF_DOWN: {
349 if (reround>5) bump=1;
350 break;} /* r-h-d */
351 case DEC_ROUND_HALF_UP: {
352 if (reround>=5) bump=1;
353 break;} /* r-h-u */
354 case DEC_ROUND_UP: {
355 if (reround>0) bump=1;
356 break;} /* r-u */
357 case DEC_ROUND_CEILING: {
358 /* same as _UP for positive numbers, and as _DOWN for negatives */
359 if (!num->sign && reround>0) bump=1;
360 break;} /* r-c */
361 case DEC_ROUND_FLOOR: {
362 /* same as _UP for negative numbers, and as _DOWN for positive */
363 /* [negative reround cannot occur on 0] */
364 if (num->sign && reround>0) bump=1;
365 break;} /* r-f */
366 case DEC_ROUND_05UP: {
367 if (reround>0) { /* anything out there is 'sticky' */
368 /* bump iff lsd=0 or 5; this cannot carry so it could be */
369 /* effected immediately with no bump -- but the code */
370 /* is clearer if this is done the same way as the others */
371 if (*ulsd==0 || *ulsd==5) bump=1;
372 }
373 break;} /* r-r */
374 default: { /* e.g., DEC_ROUND_MAX */
375 set->status|=DEC_Invalid_context;
376 #if DECCHECK
377 printf("Unknown rounding mode: %ld\n", (LI)set->round);
378 #endif
379 break;}
380 } /* switch (not r-h-e) */
381 /* printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); */
382
383 if (bump!=0) { /* need increment */
384 /* increment the coefficient; this might end up with 1000... */
385 /* (after the all nines case) */
386 ub=ulsd;
387 for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) {
388 UBFROMUI(ub-3, 0); /* to 00000000 */
389 }
390 /* [note ub could now be to left of msd, and it is not safe */
391 /* to write to the the left of the msd] */
392 /* now at most 3 digits left to non-9 (usually just the one) */
393 for (; ub>=umsd; *ub=0, ub--) {
394 if (*ub==9) continue; /* carry */
395 *ub+=1;
396 break;
397 }
398 if (ub<umsd) { /* had all-nines */
399 *umsd=1; /* coefficient to 1000... */
400 /* usually the 1000... coefficient can be used as-is */
401 if ((ulsd-umsd+1)==DECPMAX) {
402 num->exponent++;
403 }
404 else {
405 /* if coefficient is shorter than Pmax then num is */
406 /* subnormal, so extend it; this is safe as drop>0 */
407 /* (or, if the coefficient was supplied above, it could */
408 /* not be 9); this may make the result normal. */
409 ulsd++;
410 *ulsd=0;
411 /* [exponent unchanged] */
412 #if DECCHECK
413 if (num->exponent!=DECQTINY) /* sanity check */
414 printf("decFinalize: bad all-nines extend [^%ld, %ld]\n",
415 (LI)num->exponent, (LI)(ulsd-umsd+1));
416 #endif
417 } /* subnormal extend */
418 } /* had all-nines */
419 } /* bump needed */
420 } /* inexact rounding */
421
422 length=ulsd-umsd+1; /* recalculate (may be <DECPMAX) */
423 } /* need round (drop>0) */
424
425 /* The coefficient will now fit and has final length unless overflow */
426 /* decShowNum(num, "rounded"); */
427
428 /* if exponent is >=emax may have to clamp, overflow, or fold-down */
429 if (num->exponent>DECEMAX-(DECPMAX-1)) { /* is edge case */
430 /* printf("overflow checks...\n"); */
431 if (*ulsd==0 && ulsd==umsd) { /* have zero */
432 num->exponent=DECEMAX-(DECPMAX-1); /* clamp to max */
433 }
434 else if ((num->exponent+length-1)>DECEMAX) { /* > Nmax */
435 /* Overflow -- these could go straight to encoding, here, but */
436 /* instead num is adjusted to keep the code cleaner */
437 Flag needmax=0; /* 1 for finite result */
438 set->status|=(DEC_Overflow | DEC_Inexact);
439 switch (set->round) {
440 case DEC_ROUND_DOWN: {
441 needmax=1; /* never Infinity */
442 break;} /* r-d */
443 case DEC_ROUND_05UP: {
444 needmax=1; /* never Infinity */
445 break;} /* r-05 */
446 case DEC_ROUND_CEILING: {
447 if (num->sign) needmax=1; /* Infinity iff non-negative */
448 break;} /* r-c */
449 case DEC_ROUND_FLOOR: {
450 if (!num->sign) needmax=1; /* Infinity iff negative */
451 break;} /* r-f */
452 default: break; /* Infinity in all other cases */
453 }
454 if (!needmax) { /* easy .. set Infinity */
455 num->exponent=DECFLOAT_Inf;
456 *umsd=0; /* be clean: coefficient to 0 */
457 ulsd=umsd; /* .. */
458 }
459 else { /* return Nmax */
460 umsd=allnines; /* use constant array */
461 ulsd=allnines+DECPMAX-1;
462 num->exponent=DECEMAX-(DECPMAX-1);
463 }
464 }
465 else { /* no overflow but non-zero and may have to fold-down */
466 Int shift=num->exponent-(DECEMAX-(DECPMAX-1));
467 if (shift>0) { /* fold-down needed */
468 /* fold down needed; must copy to buffer in order to pad */
469 /* with zeros safely; fortunately this is not the worst case */
470 /* path because cannot have had a round */
471 uByte buffer[ROUNDUP(DECPMAX+3, 4)]; /* [+3 allows uInt padding] */
472 uByte *s=umsd; /* source */
473 uByte *t=buffer; /* safe target */
474 uByte *tlsd=buffer+(ulsd-umsd)+shift; /* target LSD */
475 /* printf("folddown shift=%ld\n", (LI)shift); */
476 for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s));
477 for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); /* pad 0s */
478 num->exponent-=shift;
479 umsd=buffer;
480 ulsd=tlsd;
481 }
482 } /* fold-down? */
483 length=ulsd-umsd+1; /* recalculate length */
484 } /* high-end edge case */
485 } /* finite number */
486
487 /*------------------------------------------------------------------*/
488 /* At this point the result will properly fit the decFloat */
489 /* encoding, and it can be encoded with no possibility of error */
490 /*------------------------------------------------------------------*/
491 /* Following code does not alter coefficient (could be allnines array) */
492
493 /* fast path possible when DECPMAX digits */
494 if (length==DECPMAX) {
495 return decFloatFromBCD(df, num->exponent, umsd, num->sign);
496 } /* full-length */
497
498 /* slower path when not a full-length number; must care about length */
499 /* [coefficient length here will be < DECPMAX] */
500 if (!NUMISSPECIAL(num)) { /* is still finite */
501 /* encode the combination field and exponent continuation */
502 uInt uexp=(uInt)(num->exponent+DECBIAS); /* biased exponent */
503 uInt code=(uexp>>DECECONL)<<4; /* top two bits of exp */
504 /* [msd==0] */
505 /* look up the combination field and make high word */
506 encode=DECCOMBFROM[code]; /* indexed by (0-2)*16+msd */
507 encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; /* exponent continuation */
508 }
509 else encode=num->exponent; /* special [already in word] */
510 encode|=num->sign; /* add sign */
511
512 /* private macro to extract a declet, n (where 0<=n<DECLETS and 0 */
513 /* refers to the declet from the least significant three digits) */
514 /* and put the corresponding DPD code into dpd. Access to umsd and */
515 /* ulsd (pointers to the most and least significant digit of the */
516 /* variable-length coefficient) is assumed, along with use of a */
517 /* working pointer, uInt *ub. */
518 /* As not full-length then chances are there are many leading zeros */
519 /* [and there may be a partial triad] */
520 #define getDPDt(dpd, n) ub=ulsd-(3*(n))-2; \
521 if (ub<umsd-2) dpd=0; \
522 else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \
523 else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];}
524
525 /* place the declets in the encoding words and copy to result (df), */
526 /* according to endianness; in all cases complete the sign word */
527 /* first */
528 #if DECPMAX==7
529 getDPDt(dpd, 1);
530 encode|=dpd<<10;
531 getDPDt(dpd, 0);
532 encode|=dpd;
533 DFWORD(df, 0)=encode; /* just the one word */
534
535 #elif DECPMAX==16
536 getDPDt(dpd, 4); encode|=dpd<<8;
537 getDPDt(dpd, 3); encode|=dpd>>2;
538 DFWORD(df, 0)=encode;
539 encode=dpd<<30;
540 getDPDt(dpd, 2); encode|=dpd<<20;
541 getDPDt(dpd, 1); encode|=dpd<<10;
542 getDPDt(dpd, 0); encode|=dpd;
543 DFWORD(df, 1)=encode;
544
545 #elif DECPMAX==34
546 getDPDt(dpd,10); encode|=dpd<<4;
547 getDPDt(dpd, 9); encode|=dpd>>6;
548 DFWORD(df, 0)=encode;
549
550 encode=dpd<<26;
551 getDPDt(dpd, 8); encode|=dpd<<16;
552 getDPDt(dpd, 7); encode|=dpd<<6;
553 getDPDt(dpd, 6); encode|=dpd>>4;
554 DFWORD(df, 1)=encode;
555
556 encode=dpd<<28;
557 getDPDt(dpd, 5); encode|=dpd<<18;
558 getDPDt(dpd, 4); encode|=dpd<<8;
559 getDPDt(dpd, 3); encode|=dpd>>2;
560 DFWORD(df, 2)=encode;
561
562 encode=dpd<<30;
563 getDPDt(dpd, 2); encode|=dpd<<20;
564 getDPDt(dpd, 1); encode|=dpd<<10;
565 getDPDt(dpd, 0); encode|=dpd;
566 DFWORD(df, 3)=encode;
567 #endif
568
569 /* printf("Status: %08lx\n", (LI)set->status); */
570 /* decFloatShow(df, "final2"); */
571 return df;
572 } /* decFinalize */
573
574 /* ------------------------------------------------------------------ */
575 /* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */
576 /* */
577 /* df is the target decFloat */
578 /* exp is the in-range unbiased exponent, q, or a special value in */
579 /* the form returned by decFloatGetExponent */
580 /* bcdar holds DECPMAX digits to set the coefficient from, one */
581 /* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
582 /* if df is a NaN; all are ignored if df is infinite. */
583 /* All bytes must be in 0-9; results are undefined otherwise. */
584 /* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
585 /* returns df, which will be canonical */
586 /* */
587 /* No error is possible, and no status will be set. */
588 /* ------------------------------------------------------------------ */
decFloatFromBCD(decFloat * df,Int exp,const uByte * bcdar,Int sig)589 decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar,
590 Int sig) {
591 uInt encode, dpd; /* work */
592 const uByte *ub; /* .. */
593
594 if (EXPISSPECIAL(exp)) encode=exp|sig;/* specials already encoded */
595 else { /* is finite */
596 /* encode the combination field and exponent continuation */
597 uInt uexp=(uInt)(exp+DECBIAS); /* biased exponent */
598 uInt code=(uexp>>DECECONL)<<4; /* top two bits of exp */
599 code+=bcdar[0]; /* add msd */
600 /* look up the combination field and make high word */
601 encode=DECCOMBFROM[code]|sig; /* indexed by (0-2)*16+msd */
602 encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; /* exponent continuation */
603 }
604
605 /* private macro to extract a declet, n (where 0<=n<DECLETS and 0 */
606 /* refers to the declet from the least significant three digits) */
607 /* and put the corresponding DPD code into dpd. */
608 /* Use of a working pointer, uInt *ub, is assumed. */
609
610 #define getDPDb(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2; \
611 dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
612
613 /* place the declets in the encoding words and copy to result (df), */
614 /* according to endianness; in all cases complete the sign word */
615 /* first */
616 #if DECPMAX==7
617 getDPDb(dpd, 1);
618 encode|=dpd<<10;
619 getDPDb(dpd, 0);
620 encode|=dpd;
621 DFWORD(df, 0)=encode; /* just the one word */
622
623 #elif DECPMAX==16
624 getDPDb(dpd, 4); encode|=dpd<<8;
625 getDPDb(dpd, 3); encode|=dpd>>2;
626 DFWORD(df, 0)=encode;
627 encode=dpd<<30;
628 getDPDb(dpd, 2); encode|=dpd<<20;
629 getDPDb(dpd, 1); encode|=dpd<<10;
630 getDPDb(dpd, 0); encode|=dpd;
631 DFWORD(df, 1)=encode;
632
633 #elif DECPMAX==34
634 getDPDb(dpd,10); encode|=dpd<<4;
635 getDPDb(dpd, 9); encode|=dpd>>6;
636 DFWORD(df, 0)=encode;
637
638 encode=dpd<<26;
639 getDPDb(dpd, 8); encode|=dpd<<16;
640 getDPDb(dpd, 7); encode|=dpd<<6;
641 getDPDb(dpd, 6); encode|=dpd>>4;
642 DFWORD(df, 1)=encode;
643
644 encode=dpd<<28;
645 getDPDb(dpd, 5); encode|=dpd<<18;
646 getDPDb(dpd, 4); encode|=dpd<<8;
647 getDPDb(dpd, 3); encode|=dpd>>2;
648 DFWORD(df, 2)=encode;
649
650 encode=dpd<<30;
651 getDPDb(dpd, 2); encode|=dpd<<20;
652 getDPDb(dpd, 1); encode|=dpd<<10;
653 getDPDb(dpd, 0); encode|=dpd;
654 DFWORD(df, 3)=encode;
655 #endif
656 /* decFloatShow(df, "fromB"); */
657 return df;
658 } /* decFloatFromBCD */
659
660 /* ------------------------------------------------------------------ */
661 /* decFloatFromPacked -- set decFloat from exponent and packed BCD */
662 /* */
663 /* df is the target decFloat */
664 /* exp is the in-range unbiased exponent, q, or a special value in */
665 /* the form returned by decFloatGetExponent */
666 /* packed holds DECPMAX packed decimal digits plus a sign nibble */
667 /* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */
668 /* and all except sign are ignored if df is infinite. For DOUBLE */
669 /* and QUAD the first (pad) nibble is also ignored in all cases. */
670 /* All coefficient nibbles must be in 0-9 and sign in A-F; results */
671 /* are undefined otherwise. */
672 /* returns df, which will be canonical */
673 /* */
674 /* No error is possible, and no status will be set. */
675 /* ------------------------------------------------------------------ */
decFloatFromPacked(decFloat * df,Int exp,const uByte * packed)676 decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) {
677 uByte bcdar[DECPMAX+2]; /* work [+1 for pad, +1 for sign] */
678 const uByte *ip; /* .. */
679 uByte *op; /* .. */
680 Int sig=0; /* sign */
681
682 /* expand coefficient and sign to BCDAR */
683 #if SINGLE
684 op=bcdar+1; /* no pad digit */
685 #else
686 op=bcdar; /* first (pad) digit ignored */
687 #endif
688 for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
689 *op++=*ip>>4;
690 *op++=(uByte)(*ip&0x0f); /* [final nibble is sign] */
691 }
692 op--; /* -> sign byte */
693 if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
694
695 if (EXPISSPECIAL(exp)) { /* Infinity or NaN */
696 if (!EXPISINF(exp)) bcdar[1]=0; /* a NaN: ignore MSD */
697 else memset(bcdar+1, 0, DECPMAX); /* Infinite: coefficient to 0 */
698 }
699 return decFloatFromBCD(df, exp, bcdar+1, sig);
700 } /* decFloatFromPacked */
701
702 /* ------------------------------------------------------------------ */
703 /* decFloatFromPackedChecked -- set from exponent and packed; checked */
704 /* */
705 /* df is the target decFloat */
706 /* exp is the in-range unbiased exponent, q, or a special value in */
707 /* the form returned by decFloatGetExponent */
708 /* packed holds DECPMAX packed decimal digits plus a sign nibble */
709 /* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */
710 /* and all digits must be 0 if df is infinite. For DOUBLE and */
711 /* QUAD the first (pad) nibble must be 0. */
712 /* All coefficient nibbles must be in 0-9 and sign in A-F. */
713 /* returns df, which will be canonical or NULL if any of the */
714 /* requirements are not met (if this case df is unchanged); that */
715 /* is, the input data must be as returned by decFloatToPacked, */
716 /* except that all six sign codes are accepted. */
717 /* */
718 /* No status will be set. */
719 /* ------------------------------------------------------------------ */
decFloatFromPackedChecked(decFloat * df,Int exp,const uByte * packed)720 decFloat * decFloatFromPackedChecked(decFloat *df, Int exp,
721 const uByte *packed) {
722 uByte bcdar[DECPMAX+2]; /* work [+1 for pad, +1 for sign] */
723 const uByte *ip; /* .. */
724 uByte *op; /* .. */
725 Int sig=0; /* sign */
726
727 /* expand coefficient and sign to BCDAR */
728 #if SINGLE
729 op=bcdar+1; /* no pad digit */
730 #else
731 op=bcdar; /* first (pad) digit here */
732 #endif
733 for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
734 *op=*ip>>4;
735 if (*op>9) return NULL;
736 op++;
737 *op=(uByte)(*ip&0x0f); /* [final nibble is sign] */
738 if (*op>9 && ip<packed+((DECPMAX+2)/2)-1) return NULL;
739 op++;
740 }
741 op--; /* -> sign byte */
742 if (*op<=9) return NULL; /* bad sign */
743 if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
744
745 #if !SINGLE
746 if (bcdar[0]!=0) return NULL; /* bad pad nibble */
747 #endif
748
749 if (EXPISNAN(exp)) { /* a NaN */
750 if (bcdar[1]!=0) return NULL; /* bad msd */
751 } /* NaN */
752 else if (EXPISINF(exp)) { /* is infinite */
753 Int i;
754 for (i=0; i<DECPMAX; i++) {
755 if (bcdar[i+1]!=0) return NULL; /* should be all zeros */
756 }
757 } /* infinity */
758 else { /* finite */
759 /* check the exponent is in range */
760 if (exp>DECEMAX-DECPMAX+1) return NULL;
761 if (exp<DECEMIN-DECPMAX+1) return NULL;
762 }
763 return decFloatFromBCD(df, exp, bcdar+1, sig);
764 } /* decFloatFromPacked */
765
766 /* ------------------------------------------------------------------ */
767 /* decFloatFromString -- conversion from numeric string */
768 /* */
769 /* result is the decFloat format number which gets the result of */
770 /* the conversion */
771 /* *string is the character string which should contain a valid */
772 /* number (which may be a special value), \0-terminated */
773 /* If there are too many significant digits in the */
774 /* coefficient it will be rounded. */
775 /* set is the context */
776 /* returns result */
777 /* */
778 /* The length of the coefficient and the size of the exponent are */
779 /* checked by this routine, so the correct error (Underflow or */
780 /* Overflow) can be reported or rounding applied, as necessary. */
781 /* */
782 /* There is no limit to the coefficient length for finite inputs; */
783 /* NaN payloads must be integers with no more than DECPMAX-1 digits. */
784 /* Exponents may have up to nine significant digits. */
785 /* */
786 /* If bad syntax is detected, the result will be a quiet NaN. */
787 /* ------------------------------------------------------------------ */
decFloatFromString(decFloat * result,const char * string,decContext * set)788 decFloat * decFloatFromString(decFloat *result, const char *string,
789 decContext *set) {
790 Int digits; /* count of digits in coefficient */
791 const char *dotchar=NULL; /* where dot was found [NULL if none] */
792 const char *cfirst=string; /* -> first character of decimal part */
793 const char *c; /* work */
794 uByte *ub; /* .. */
795 uInt uiwork; /* for macros */
796 bcdnum num; /* collects data for finishing */
797 uInt error=DEC_Conversion_syntax; /* assume the worst */
798 uByte buffer[ROUNDUP(DECSTRING+11, 8)]; /* room for most coefficents, */
799 /* some common rounding, +3, & pad */
800 #if DECTRACE
801 /* printf("FromString %s ...\n", string); */
802 #endif
803
804 for(;;) { /* once-only 'loop' */
805 num.sign=0; /* assume non-negative */
806 num.msd=buffer; /* MSD is here always */
807
808 /* detect and validate the coefficient, including any leading, */
809 /* trailing, or embedded '.' */
810 /* [could test four-at-a-time here (saving 10% for decQuads), */
811 /* but that risks storage violation because the position of the */
812 /* terminator is unknown] */
813 for (c=string;; c++) { /* -> input character */
814 if (((unsigned)(*c-'0'))<=9) continue; /* '0' through '9' is good */
815 if (*c=='\0') break; /* most common non-digit */
816 if (*c=='.') {
817 if (dotchar!=NULL) break; /* not first '.' */
818 dotchar=c; /* record offset into decimal part */
819 continue;}
820 if (c==string) { /* first in string... */
821 if (*c=='-') { /* valid - sign */
822 cfirst++;
823 num.sign=DECFLOAT_Sign;
824 continue;}
825 if (*c=='+') { /* valid + sign */
826 cfirst++;
827 continue;}
828 }
829 /* *c is not a digit, terminator, or a valid +, -, or '.' */
830 break;
831 } /* c loop */
832
833 digits=(uInt)(c-cfirst); /* digits (+1 if a dot) */
834
835 if (digits>0) { /* had digits and/or dot */
836 const char *clast=c-1; /* note last coefficient char position */
837 Int exp=0; /* exponent accumulator */
838 if (*c!='\0') { /* something follows the coefficient */
839 uInt edig; /* unsigned work */
840 /* had some digits and more to come; expect E[+|-]nnn now */
841 const char *firstexp; /* exponent first non-zero */
842 if (*c!='E' && *c!='e') break;
843 c++; /* to (optional) sign */
844 if (*c=='-' || *c=='+') c++; /* step over sign (c=clast+2) */
845 if (*c=='\0') break; /* no digits! (e.g., '1.2E') */
846 for (; *c=='0';) c++; /* skip leading zeros [even last] */
847 firstexp=c; /* remember start [maybe '\0'] */
848 /* gather exponent digits */
849 edig=(uInt)*c-(uInt)'0';
850 if (edig<=9) { /* [check not bad or terminator] */
851 exp+=edig; /* avoid initial X10 */
852 c++;
853 for (;; c++) {
854 edig=(uInt)*c-(uInt)'0';
855 if (edig>9) break;
856 exp=exp*10+edig;
857 }
858 }
859 /* if not now on the '\0', *c must not be a digit */
860 if (*c!='\0') break;
861
862 /* (this next test must be after the syntax checks) */
863 /* if definitely more than the possible digits for format then */
864 /* the exponent may have wrapped, so simply set it to a certain */
865 /* over/underflow value */
866 if (c>firstexp+DECEMAXD) exp=DECEMAX*2;
867 if (*(clast+2)=='-') exp=-exp; /* was negative */
868 } /* digits>0 */
869
870 if (dotchar!=NULL) { /* had a '.' */
871 digits--; /* remove from digits count */
872 if (digits==0) break; /* was dot alone: bad syntax */
873 exp-=(Int)(clast-dotchar); /* adjust exponent */
874 /* [the '.' can now be ignored] */
875 }
876 num.exponent=exp; /* exponent is good; store it */
877
878 /* Here when whole string has been inspected and syntax is good */
879 /* cfirst->first digit or dot, clast->last digit or dot */
880 error=0; /* no error possible now */
881
882 /* if the number of digits in the coefficient will fit in buffer */
883 /* then it can simply be converted to bcd8 and copied -- decFinalize */
884 /* will take care of leading zeros and rounding; the buffer is big */
885 /* enough for all canonical coefficients, including 0.00000nn... */
886 ub=buffer;
887 if (digits<=(Int)(sizeof(buffer)-3)) { /* [-3 allows by-4s copy] */
888 c=cfirst;
889 if (dotchar!=NULL) { /* a dot to worry about */
890 if (*(c+1)=='.') { /* common canonical case */
891 *ub++=(uByte)(*c-'0'); /* copy leading digit */
892 c+=2; /* prepare to handle rest */
893 }
894 else for (; c<=clast;) { /* '.' could be anywhere */
895 /* as usual, go by fours when safe; NB it has been asserted */
896 /* that a '.' does not have the same mask as a digit */
897 if (c<=clast-3 /* safe for four */
898 && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { /* test four */
899 UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); /* to BCD8 */
900 ub+=4;
901 c+=4;
902 continue;
903 }
904 if (*c=='.') { /* found the dot */
905 c++; /* step over it .. */
906 break; /* .. and handle the rest */
907 }
908 *ub++=(uByte)(*c++-'0');
909 }
910 } /* had dot */
911 /* Now no dot; do this by fours (where safe) */
912 for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f);
913 for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0');
914 num.lsd=buffer+digits-1; /* record new LSD */
915 } /* fits */
916
917 else { /* too long for buffer */
918 /* [This is a rare and unusual case; arbitrary-length input] */
919 /* strip leading zeros [but leave final 0 if all 0's] */
920 if (*cfirst=='.') cfirst++; /* step past dot at start */
921 if (*cfirst=='0') { /* [cfirst always -> digit] */
922 for (; cfirst<clast; cfirst++) {
923 if (*cfirst!='0') { /* non-zero found */
924 if (*cfirst=='.') continue; /* [ignore] */
925 break; /* done */
926 }
927 digits--; /* 0 stripped */
928 } /* cfirst */
929 } /* at least one leading 0 */
930
931 /* the coefficient is now as short as possible, but may still */
932 /* be too long; copy up to Pmax+1 digits to the buffer, then */
933 /* just record any non-zeros (set round-for-reround digit) */
934 for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) {
935 /* (see commentary just above) */
936 if (c<=clast-3 /* safe for four */
937 && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { /* four digits */
938 UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); /* to BCD8 */
939 ub+=4;
940 c+=3; /* [will become 4] */
941 continue;
942 }
943 if (*c=='.') continue; /* [ignore] */
944 *ub++=(uByte)(*c-'0');
945 }
946 ub--; /* -> LSD */
947 for (; c<=clast; c++) { /* inspect remaining chars */
948 if (*c!='0') { /* sticky bit needed */
949 if (*c=='.') continue; /* [ignore] */
950 *ub=DECSTICKYTAB[*ub]; /* update round-for-reround */
951 break; /* no need to look at more */
952 }
953 }
954 num.lsd=ub; /* record LSD */
955 /* adjust exponent for dropped digits */
956 num.exponent+=digits-(Int)(ub-buffer+1);
957 } /* too long for buffer */
958 } /* digits or dot */
959
960 else { /* no digits or dot were found */
961 if (*c=='\0') break; /* nothing to come is bad */
962 /* only Infinities and NaNs are allowed, here */
963 buffer[0]=0; /* default a coefficient of 0 */
964 num.lsd=buffer; /* .. */
965 if (decBiStr(c, "infinity", "INFINITY")
966 || decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf;
967 else { /* should be a NaN */
968 num.exponent=DECFLOAT_qNaN; /* assume quiet NaN */
969 if (*c=='s' || *c=='S') { /* probably an sNaN */
970 c++;
971 num.exponent=DECFLOAT_sNaN; /* assume is in fact sNaN */
972 }
973 if (*c!='N' && *c!='n') break; /* check caseless "NaN" */
974 c++;
975 if (*c!='a' && *c!='A') break; /* .. */
976 c++;
977 if (*c!='N' && *c!='n') break; /* .. */
978 c++;
979 /* now either nothing, or nnnn payload (no dots), expected */
980 /* -> start of integer, and skip leading 0s [including plain 0] */
981 for (cfirst=c; *cfirst=='0';) cfirst++;
982 if (*cfirst!='\0') { /* not empty or all-0, payload */
983 /* payload found; check all valid digits and copy to buffer as bcd8 */
984 ub=buffer;
985 for (c=cfirst;; c++, ub++) {
986 if ((unsigned)(*c-'0')>9) break; /* quit if not 0-9 */
987 if (c-cfirst==DECPMAX-1) break; /* too many digits */
988 *ub=(uByte)(*c-'0'); /* good bcd8 */
989 }
990 if (*c!='\0') break; /* not all digits, or too many */
991 num.lsd=ub-1; /* record new LSD */
992 }
993 } /* NaN or sNaN */
994 error=0; /* syntax is OK */
995 break; /* done with specials */
996 } /* digits=0 (special expected) */
997 break;
998 } /* [for(;;) break] */
999
1000 /* decShowNum(&num, "fromStr"); */
1001
1002 if (error!=0) {
1003 set->status|=error;
1004 num.exponent=DECFLOAT_qNaN; /* set up quiet NaN */
1005 num.sign=0; /* .. with 0 sign */
1006 buffer[0]=0; /* .. and coefficient */
1007 num.lsd=buffer; /* .. */
1008 /* decShowNum(&num, "oops"); */
1009 }
1010
1011 /* decShowNum(&num, "dffs"); */
1012 decFinalize(result, &num, set); /* round, check, and lay out */
1013 /* decFloatShow(result, "fromString"); */
1014 return result;
1015 } /* decFloatFromString */
1016
1017 /* ------------------------------------------------------------------ */
1018 /* decFloatFromWider -- conversion from next-wider format */
1019 /* */
1020 /* result is the decFloat format number which gets the result of */
1021 /* the conversion */
1022 /* wider is the decFloatWider format number which will be narrowed */
1023 /* set is the context */
1024 /* returns result */
1025 /* */
1026 /* Narrowing can cause rounding, overflow, etc., but not Invalid */
1027 /* operation (sNaNs are copied and do not signal). */
1028 /* ------------------------------------------------------------------ */
1029 /* narrow-to is not possible for decQuad format numbers; simply omit */
1030 #if !QUAD
decFloatFromWider(decFloat * result,const decFloatWider * wider,decContext * set)1031 decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider,
1032 decContext *set) {
1033 bcdnum num; /* collects data for finishing */
1034 uByte bcdar[DECWPMAX]; /* room for wider coefficient */
1035 uInt widerhi=DFWWORD(wider, 0); /* top word */
1036 Int exp;
1037
1038 GETWCOEFF(wider, bcdar);
1039
1040 num.msd=bcdar; /* MSD is here always */
1041 num.lsd=bcdar+DECWPMAX-1; /* LSD is here always */
1042 num.sign=widerhi&0x80000000; /* extract sign [DECFLOAT_Sign=Neg] */
1043
1044 /* decode the wider combination field to exponent */
1045 exp=DECCOMBWEXP[widerhi>>26]; /* decode from wider combination field */
1046 /* if it is a special there's nothing to do unless sNaN; if it's */
1047 /* finite then add the (wider) exponent continuation and unbias */
1048 if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; /* include sNaN selector */
1049 else exp+=GETWECON(wider)-DECWBIAS;
1050 num.exponent=exp;
1051
1052 /* decShowNum(&num, "dffw"); */
1053 return decFinalize(result, &num, set);/* round, check, and lay out */
1054 } /* decFloatFromWider */
1055 #endif
1056
1057 /* ------------------------------------------------------------------ */
1058 /* decFloatGetCoefficient -- get coefficient as BCD8 */
1059 /* */
1060 /* df is the decFloat from which to extract the coefficient */
1061 /* bcdar is where DECPMAX bytes will be written, one BCD digit in */
1062 /* each byte (BCD8 encoding); if df is a NaN the first byte will */
1063 /* be zero, and if it is infinite they will all be zero */
1064 /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
1065 /* 0 otherwise) */
1066 /* */
1067 /* No error is possible, and no status will be set. If df is a */
1068 /* special value the array is set to zeros (for Infinity) or to the */
1069 /* payload of a qNaN or sNaN. */
1070 /* ------------------------------------------------------------------ */
decFloatGetCoefficient(const decFloat * df,uByte * bcdar)1071 Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) {
1072 if (DFISINF(df)) memset(bcdar, 0, DECPMAX);
1073 else {
1074 GETCOEFF(df, bcdar); /* use macro */
1075 if (DFISNAN(df)) bcdar[0]=0; /* MSD needs correcting */
1076 }
1077 return DFISSIGNED(df);
1078 } /* decFloatGetCoefficient */
1079
1080 /* ------------------------------------------------------------------ */
1081 /* decFloatGetExponent -- get unbiased exponent */
1082 /* */
1083 /* df is the decFloat from which to extract the exponent */
1084 /* returns the exponent, q. */
1085 /* */
1086 /* No error is possible, and no status will be set. If df is a */
1087 /* special value the first seven bits of the decFloat are returned, */
1088 /* left adjusted and with the first (sign) bit set to 0 (followed by */
1089 /* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */
1090 /* ------------------------------------------------------------------ */
decFloatGetExponent(const decFloat * df)1091 Int decFloatGetExponent(const decFloat *df) {
1092 if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000;
1093 return GETEXPUN(df);
1094 } /* decFloatGetExponent */
1095
1096 /* ------------------------------------------------------------------ */
1097 /* decFloatSetCoefficient -- set coefficient from BCD8 */
1098 /* */
1099 /* df is the target decFloat (and source of exponent/special value) */
1100 /* bcdar holds DECPMAX digits to set the coefficient from, one */
1101 /* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
1102 /* if df is a NaN; all are ignored if df is infinite. */
1103 /* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
1104 /* returns df, which will be canonical */
1105 /* */
1106 /* No error is possible, and no status will be set. */
1107 /* ------------------------------------------------------------------ */
decFloatSetCoefficient(decFloat * df,const uByte * bcdar,Int sig)1108 decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar,
1109 Int sig) {
1110 uInt exp; /* for exponent */
1111 uByte bcdzero[DECPMAX]; /* for infinities */
1112
1113 /* Exponent/special code is extracted from df */
1114 if (DFISSPECIAL(df)) {
1115 exp=DFWORD(df, 0)&0x7e000000;
1116 if (DFISINF(df)) {
1117 memset(bcdzero, 0, DECPMAX);
1118 return decFloatFromBCD(df, exp, bcdzero, sig);
1119 }
1120 }
1121 else exp=GETEXPUN(df);
1122 return decFloatFromBCD(df, exp, bcdar, sig);
1123 } /* decFloatSetCoefficient */
1124
1125 /* ------------------------------------------------------------------ */
1126 /* decFloatSetExponent -- set exponent or special value */
1127 /* */
1128 /* df is the target decFloat (and source of coefficient/payload) */
1129 /* set is the context for reporting status */
1130 /* exp is the unbiased exponent, q, or a special value in the form */
1131 /* returned by decFloatGetExponent */
1132 /* returns df, which will be canonical */
1133 /* */
1134 /* No error is possible, but Overflow or Underflow might occur. */
1135 /* ------------------------------------------------------------------ */
decFloatSetExponent(decFloat * df,decContext * set,Int exp)1136 decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) {
1137 uByte bcdcopy[DECPMAX]; /* for coefficient */
1138 bcdnum num; /* work */
1139 num.exponent=exp;
1140 num.sign=decFloatGetCoefficient(df, bcdcopy); /* extract coefficient */
1141 if (DFISSPECIAL(df)) { /* MSD or more needs correcting */
1142 if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX);
1143 bcdcopy[0]=0;
1144 }
1145 num.msd=bcdcopy;
1146 num.lsd=bcdcopy+DECPMAX-1;
1147 return decFinalize(df, &num, set);
1148 } /* decFloatSetExponent */
1149
1150 /* ------------------------------------------------------------------ */
1151 /* decFloatRadix -- returns the base (10) */
1152 /* */
1153 /* df is any decFloat of this format */
1154 /* ------------------------------------------------------------------ */
decFloatRadix(const decFloat * df)1155 uInt decFloatRadix(const decFloat *df) {
1156 if (df) return 10; /* to placate compiler */
1157 return 10;
1158 } /* decFloatRadix */
1159
1160 #if (DECCHECK || DECTRACE)
1161 /* ------------------------------------------------------------------ */
1162 /* decFloatShow -- printf a decFloat in hexadecimal and decimal */
1163 /* df is the decFloat to show */
1164 /* tag is a tag string displayed with the number */
1165 /* */
1166 /* This is a debug aid; the precise format of the string may change. */
1167 /* ------------------------------------------------------------------ */
decFloatShow(const decFloat * df,const char * tag)1168 void decFloatShow(const decFloat *df, const char *tag) {
1169 char hexbuf[DECBYTES*2+DECBYTES/4+1]; /* NB blank after every fourth */
1170 char buff[DECSTRING]; /* for value in decimal */
1171 Int i, j=0;
1172
1173 for (i=0; i<DECBYTES; i++) {
1174 #if DECLITEND
1175 sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]);
1176 #else
1177 sprintf(&hexbuf[j], "%02x", df->bytes[i]);
1178 #endif
1179 j+=2;
1180 /* the next line adds blank (and terminator) after final pair, too */
1181 if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;}
1182 }
1183 decFloatToString(df, buff);
1184 printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff);
1185 return;
1186 } /* decFloatShow */
1187 #endif
1188
1189 /* ------------------------------------------------------------------ */
1190 /* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */
1191 /* */
1192 /* df is the source decFloat */
1193 /* exp will be set to the unbiased exponent, q, or to a special */
1194 /* value in the form returned by decFloatGetExponent */
1195 /* bcdar is where DECPMAX bytes will be written, one BCD digit in */
1196 /* each byte (BCD8 encoding); if df is a NaN the first byte will */
1197 /* be zero, and if it is infinite they will all be zero */
1198 /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
1199 /* 0 otherwise) */
1200 /* */
1201 /* No error is possible, and no status will be set. */
1202 /* ------------------------------------------------------------------ */
decFloatToBCD(const decFloat * df,Int * exp,uByte * bcdar)1203 Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) {
1204 if (DFISINF(df)) {
1205 memset(bcdar, 0, DECPMAX);
1206 *exp=DFWORD(df, 0)&0x7e000000;
1207 }
1208 else {
1209 GETCOEFF(df, bcdar); /* use macro */
1210 if (DFISNAN(df)) {
1211 bcdar[0]=0; /* MSD needs correcting */
1212 *exp=DFWORD(df, 0)&0x7e000000;
1213 }
1214 else { /* finite */
1215 *exp=GETEXPUN(df);
1216 }
1217 }
1218 return DFISSIGNED(df);
1219 } /* decFloatToBCD */
1220
1221 /* ------------------------------------------------------------------ */
1222 /* decFloatToEngString -- conversion to numeric string, engineering */
1223 /* */
1224 /* df is the decFloat format number to convert */
1225 /* string is the string where the result will be laid out */
1226 /* */
1227 /* string must be at least DECPMAX+9 characters (the worst case is */
1228 /* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
1229 /* DECEMAXD<=4); this condition is asserted above */
1230 /* */
1231 /* No error is possible, and no status will be set */
1232 /* ------------------------------------------------------------------ */
decFloatToEngString(const decFloat * df,char * string)1233 char * decFloatToEngString(const decFloat *df, char *string){
1234 uInt msd; /* coefficient MSD */
1235 Int exp; /* exponent top two bits or full */
1236 uInt comb; /* combination field */
1237 char *cstart; /* coefficient start */
1238 char *c; /* output pointer in string */
1239 char *s, *t; /* .. (source, target) */
1240 Int pre, e; /* work */
1241 const uByte *u; /* .. */
1242 uInt uiwork; /* for macros [one compiler needs */
1243 /* volatile here to avoid bug, but */
1244 /* that doubles execution time] */
1245
1246 /* Source words; macro handles endianness */
1247 uInt sourhi=DFWORD(df, 0); /* word with sign */
1248 #if DECPMAX==16
1249 uInt sourlo=DFWORD(df, 1);
1250 #elif DECPMAX==34
1251 uInt sourmh=DFWORD(df, 1);
1252 uInt sourml=DFWORD(df, 2);
1253 uInt sourlo=DFWORD(df, 3);
1254 #endif
1255
1256 c=string; /* where result will go */
1257 if (((Int)sourhi)<0) *c++='-'; /* handle sign */
1258 comb=sourhi>>26; /* sign+combination field */
1259 msd=DECCOMBMSD[comb]; /* decode the combination field */
1260 exp=DECCOMBEXP[comb]; /* .. */
1261
1262 if (EXPISSPECIAL(exp)) { /* special */
1263 if (exp==DECFLOAT_Inf) { /* infinity */
1264 strcpy(c, "Inf");
1265 strcpy(c+3, "inity");
1266 return string; /* easy */
1267 }
1268 if (sourhi&0x02000000) *c++='s'; /* sNaN */
1269 strcpy(c, "NaN"); /* complete word */
1270 c+=3; /* step past */
1271 /* quick exit if the payload is zero */
1272 #if DECPMAX==7
1273 if ((sourhi&0x000fffff)==0) return string;
1274 #elif DECPMAX==16
1275 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
1276 #elif DECPMAX==34
1277 if (sourlo==0 && sourml==0 && sourmh==0
1278 && (sourhi&0x00003fff)==0) return string;
1279 #endif
1280 /* otherwise drop through to add integer; set correct exp etc. */
1281 exp=0; msd=0; /* setup for following code */
1282 }
1283 else { /* complete exponent; top two bits are in place */
1284 exp+=GETECON(df)-DECBIAS; /* .. + continuation and unbias */
1285 }
1286
1287 /* convert the digits of the significand to characters */
1288 cstart=c; /* save start of coefficient */
1289 if (msd) *c++=(char)('0'+(char)msd); /* non-zero most significant digit */
1290
1291 /* Decode the declets. After extracting each declet, it is */
1292 /* decoded to a 4-uByte sequence by table lookup; the four uBytes */
1293 /* are the three encoded BCD8 digits followed by a 1-byte length */
1294 /* (significant digits, except that 000 has length 0). This allows */
1295 /* us to left-align the first declet with non-zero content, then */
1296 /* the remaining ones are full 3-char length. Fixed-length copies */
1297 /* are used because variable-length memcpy causes a subroutine call */
1298 /* in at least two compilers. (The copies are length 4 for speed */
1299 /* and are safe because the last item in the array is of length */
1300 /* three and has the length byte following.) */
1301 #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
1302 if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
1303 else if (*(u+3)) { \
1304 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
1305
1306 #if DECPMAX==7
1307 dpd2char(sourhi>>10); /* declet 1 */
1308 dpd2char(sourhi); /* declet 2 */
1309
1310 #elif DECPMAX==16
1311 dpd2char(sourhi>>8); /* declet 1 */
1312 dpd2char((sourhi<<2) | (sourlo>>30)); /* declet 2 */
1313 dpd2char(sourlo>>20); /* declet 3 */
1314 dpd2char(sourlo>>10); /* declet 4 */
1315 dpd2char(sourlo); /* declet 5 */
1316
1317 #elif DECPMAX==34
1318 dpd2char(sourhi>>4); /* declet 1 */
1319 dpd2char((sourhi<<6) | (sourmh>>26)); /* declet 2 */
1320 dpd2char(sourmh>>16); /* declet 3 */
1321 dpd2char(sourmh>>6); /* declet 4 */
1322 dpd2char((sourmh<<4) | (sourml>>28)); /* declet 5 */
1323 dpd2char(sourml>>18); /* declet 6 */
1324 dpd2char(sourml>>8); /* declet 7 */
1325 dpd2char((sourml<<2) | (sourlo>>30)); /* declet 8 */
1326 dpd2char(sourlo>>20); /* declet 9 */
1327 dpd2char(sourlo>>10); /* declet 10 */
1328 dpd2char(sourlo); /* declet 11 */
1329 #endif
1330
1331 if (c==cstart) *c++='0'; /* all zeros, empty -- make "0" */
1332
1333 if (exp==0) { /* integer or NaN case -- easy */
1334 *c='\0'; /* terminate */
1335 return string;
1336 }
1337 /* non-0 exponent */
1338
1339 e=0; /* assume no E */
1340 pre=(Int)(c-cstart)+exp; /* length+exp [c->LSD+1] */
1341 /* [here, pre-exp is the digits count (==1 for zero)] */
1342
1343 if (exp>0 || pre<-5) { /* need exponential form */
1344 e=pre-1; /* calculate E value */
1345 pre=1; /* assume one digit before '.' */
1346 if (e!=0) { /* engineering: may need to adjust */
1347 Int adj; /* adjustment */
1348 /* The C remainder operator is undefined for negative numbers, so */
1349 /* a positive remainder calculation must be used here */
1350 if (e<0) {
1351 adj=(-e)%3;
1352 if (adj!=0) adj=3-adj;
1353 }
1354 else { /* e>0 */
1355 adj=e%3;
1356 }
1357 e=e-adj;
1358 /* if dealing with zero still produce an exponent which is a */
1359 /* multiple of three, as expected, but there will only be the */
1360 /* one zero before the E, still. Otherwise note the padding. */
1361 if (!DFISZERO(df)) pre+=adj;
1362 else { /* is zero */
1363 if (adj!=0) { /* 0.00Esnn needed */
1364 e=e+3;
1365 pre=-(2-adj);
1366 }
1367 } /* zero */
1368 } /* engineering adjustment */
1369 } /* exponential form */
1370 /* printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp); */
1371
1372 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
1373 if (pre>0) { /* ddd.ddd (plain), perhaps with E */
1374 /* or dd00 padding for engineering */
1375 char *dotat=cstart+pre;
1376 if (dotat<c) { /* if embedded dot needed... */
1377 /* move by fours; there must be space for junk at the end */
1378 /* because there is still space for exponent */
1379 s=dotat+ROUNDDOWN4(c-dotat); /* source */
1380 t=s+1; /* target */
1381 /* open the gap [cannot use memcpy] */
1382 for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
1383 *dotat='.';
1384 c++; /* length increased by one */
1385 } /* need dot? */
1386 else for (; c<dotat; c++) *c='0'; /* pad for engineering */
1387 } /* pre>0 */
1388 else {
1389 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have
1390 E, but only for 0.00E+3 kind of case -- with plenty of spare
1391 space in this case */
1392 pre=-pre+2; /* gap width, including "0." */
1393 t=cstart+ROUNDDOWN4(c-cstart)+pre; /* preferred first target point */
1394 /* backoff if too far to the right */
1395 if (t>string+DECSTRING-5) t=string+DECSTRING-5; /* adjust to fit */
1396 /* now shift the entire coefficient to the right, being careful not */
1397 /* to access to the left of string [cannot use memcpy] */
1398 for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
1399 /* for Quads and Singles there may be a character or two left... */
1400 s+=3; /* where next would come from */
1401 for(; s>=cstart; s--, t--) *(t+3)=*(s);
1402 /* now have fill 0. through 0.00000; use overlaps to avoid tests */
1403 if (pre>=4) {
1404 memcpy(cstart+pre-4, "0000", 4);
1405 memcpy(cstart, "0.00", 4);
1406 }
1407 else { /* 2 or 3 */
1408 *(cstart+pre-1)='0';
1409 memcpy(cstart, "0.", 2);
1410 }
1411 c+=pre; /* to end */
1412 }
1413
1414 /* finally add the E-part, if needed; it will never be 0, and has */
1415 /* a maximum length of 3 or 4 digits (asserted above) */
1416 if (e!=0) {
1417 memcpy(c, "E+", 2); /* starts with E, assume + */
1418 c++;
1419 if (e<0) {
1420 *c='-'; /* oops, need '-' */
1421 e=-e; /* uInt, please */
1422 }
1423 c++;
1424 /* Three-character exponents are easy; 4-character a little trickier */
1425 #if DECEMAXD<=3
1426 u=&BIN2BCD8[e*4]; /* -> 3 digits + length byte */
1427 /* copy fixed 4 characters [is safe], starting at non-zero */
1428 /* and with character mask to convert BCD to char */
1429 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
1430 c+=*(u+3); /* bump pointer appropriately */
1431 #elif DECEMAXD==4
1432 if (e<1000) { /* 3 (or fewer) digits case */
1433 u=&BIN2BCD8[e*4]; /* -> 3 digits + length byte */
1434 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); /* [as above] */
1435 c+=*(u+3); /* bump pointer appropriately */
1436 }
1437 else { /* 4-digits */
1438 Int thou=((e>>3)*1049)>>17; /* e/1000 */
1439 Int rem=e-(1000*thou); /* e%1000 */
1440 *c++=(char)('0'+(char)thou); /* the thousands digit */
1441 u=&BIN2BCD8[rem*4]; /* -> 3 digits + length byte */
1442 UBFROMUI(c, UBTOUI(u)|CHARMASK);/* copy fixed 3+1 characters [is safe] */
1443 c+=3; /* bump pointer, always 3 digits */
1444 }
1445 #endif
1446 }
1447 *c='\0'; /* terminate */
1448 /*printf("res %s\n", string); */
1449 return string;
1450 } /* decFloatToEngString */
1451
1452 /* ------------------------------------------------------------------ */
1453 /* decFloatToPacked -- convert decFloat to Packed decimal + exponent */
1454 /* */
1455 /* df is the source decFloat */
1456 /* exp will be set to the unbiased exponent, q, or to a special */
1457 /* value in the form returned by decFloatGetExponent */
1458 /* packed is where DECPMAX nibbles will be written with the sign as */
1459 /* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */
1460 /* of zero, and an infinity is all zeros. decDouble and decQuad */
1461 /* have a additional leading zero nibble, leading to result */
1462 /* lengths of 4, 9, and 18 bytes. */
1463 /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
1464 /* 0 otherwise) */
1465 /* */
1466 /* No error is possible, and no status will be set. */
1467 /* ------------------------------------------------------------------ */
decFloatToPacked(const decFloat * df,Int * exp,uByte * packed)1468 Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) {
1469 uByte bcdar[DECPMAX+2]; /* work buffer */
1470 uByte *ip=bcdar, *op=packed; /* work pointers */
1471 if (DFISINF(df)) {
1472 memset(bcdar, 0, DECPMAX+2);
1473 *exp=DECFLOAT_Inf;
1474 }
1475 else {
1476 GETCOEFF(df, bcdar+1); /* use macro */
1477 if (DFISNAN(df)) {
1478 bcdar[1]=0; /* MSD needs clearing */
1479 *exp=DFWORD(df, 0)&0x7e000000;
1480 }
1481 else { /* finite */
1482 *exp=GETEXPUN(df);
1483 }
1484 }
1485 /* now pack; coefficient currently at bcdar+1 */
1486 #if SINGLE
1487 ip++; /* ignore first byte */
1488 #else
1489 *ip=0; /* need leading zero */
1490 #endif
1491 /* set final byte to Packed BCD sign value */
1492 bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS);
1493 /* pack an even number of bytes... */
1494 for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) {
1495 *op=(uByte)((*ip<<4)+*(ip+1));
1496 }
1497 return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0);
1498 } /* decFloatToPacked */
1499
1500 /* ------------------------------------------------------------------ */
1501 /* decFloatToString -- conversion to numeric string */
1502 /* */
1503 /* df is the decFloat format number to convert */
1504 /* string is the string where the result will be laid out */
1505 /* */
1506 /* string must be at least DECPMAX+9 characters (the worst case is */
1507 /* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
1508 /* DECEMAXD<=4); this condition is asserted above */
1509 /* */
1510 /* No error is possible, and no status will be set */
1511 /* ------------------------------------------------------------------ */
decFloatToString(const decFloat * df,char * string)1512 char * decFloatToString(const decFloat *df, char *string){
1513 uInt msd; /* coefficient MSD */
1514 Int exp; /* exponent top two bits or full */
1515 uInt comb; /* combination field */
1516 char *cstart; /* coefficient start */
1517 char *c; /* output pointer in string */
1518 char *s, *t; /* .. (source, target) */
1519 Int pre, e; /* work */
1520 const uByte *u; /* .. */
1521 uInt uiwork; /* for macros [one compiler needs */
1522 /* volatile here to avoid bug, but */
1523 /* that doubles execution time] */
1524
1525 /* Source words; macro handles endianness */
1526 uInt sourhi=DFWORD(df, 0); /* word with sign */
1527 #if DECPMAX==16
1528 uInt sourlo=DFWORD(df, 1);
1529 #elif DECPMAX==34
1530 uInt sourmh=DFWORD(df, 1);
1531 uInt sourml=DFWORD(df, 2);
1532 uInt sourlo=DFWORD(df, 3);
1533 #endif
1534
1535 c=string; /* where result will go */
1536 if (((Int)sourhi)<0) *c++='-'; /* handle sign */
1537 comb=sourhi>>26; /* sign+combination field */
1538 msd=DECCOMBMSD[comb]; /* decode the combination field */
1539 exp=DECCOMBEXP[comb]; /* .. */
1540
1541 if (!EXPISSPECIAL(exp)) { /* finite */
1542 /* complete exponent; top two bits are in place */
1543 exp+=GETECON(df)-DECBIAS; /* .. + continuation and unbias */
1544 }
1545 else { /* IS special */
1546 if (exp==DECFLOAT_Inf) { /* infinity */
1547 strcpy(c, "Infinity");
1548 return string; /* easy */
1549 }
1550 if (sourhi&0x02000000) *c++='s'; /* sNaN */
1551 strcpy(c, "NaN"); /* complete word */
1552 c+=3; /* step past */
1553 /* quick exit if the payload is zero */
1554 #if DECPMAX==7
1555 if ((sourhi&0x000fffff)==0) return string;
1556 #elif DECPMAX==16
1557 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
1558 #elif DECPMAX==34
1559 if (sourlo==0 && sourml==0 && sourmh==0
1560 && (sourhi&0x00003fff)==0) return string;
1561 #endif
1562 /* otherwise drop through to add integer; set correct exp etc. */
1563 exp=0; msd=0; /* setup for following code */
1564 }
1565
1566 /* convert the digits of the significand to characters */
1567 cstart=c; /* save start of coefficient */
1568 if (msd) *c++=(char)('0'+(char)msd); /* non-zero most significant digit */
1569
1570 /* Decode the declets. After extracting each declet, it is */
1571 /* decoded to a 4-uByte sequence by table lookup; the four uBytes */
1572 /* are the three encoded BCD8 digits followed by a 1-byte length */
1573 /* (significant digits, except that 000 has length 0). This allows */
1574 /* us to left-align the first declet with non-zero content, then */
1575 /* the remaining ones are full 3-char length. Fixed-length copies */
1576 /* are used because variable-length memcpy causes a subroutine call */
1577 /* in at least two compilers. (The copies are length 4 for speed */
1578 /* and are safe because the last item in the array is of length */
1579 /* three and has the length byte following.) */
1580 #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
1581 if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
1582 else if (*(u+3)) { \
1583 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
1584
1585 #if DECPMAX==7
1586 dpd2char(sourhi>>10); /* declet 1 */
1587 dpd2char(sourhi); /* declet 2 */
1588
1589 #elif DECPMAX==16
1590 dpd2char(sourhi>>8); /* declet 1 */
1591 dpd2char((sourhi<<2) | (sourlo>>30)); /* declet 2 */
1592 dpd2char(sourlo>>20); /* declet 3 */
1593 dpd2char(sourlo>>10); /* declet 4 */
1594 dpd2char(sourlo); /* declet 5 */
1595
1596 #elif DECPMAX==34
1597 dpd2char(sourhi>>4); /* declet 1 */
1598 dpd2char((sourhi<<6) | (sourmh>>26)); /* declet 2 */
1599 dpd2char(sourmh>>16); /* declet 3 */
1600 dpd2char(sourmh>>6); /* declet 4 */
1601 dpd2char((sourmh<<4) | (sourml>>28)); /* declet 5 */
1602 dpd2char(sourml>>18); /* declet 6 */
1603 dpd2char(sourml>>8); /* declet 7 */
1604 dpd2char((sourml<<2) | (sourlo>>30)); /* declet 8 */
1605 dpd2char(sourlo>>20); /* declet 9 */
1606 dpd2char(sourlo>>10); /* declet 10 */
1607 dpd2char(sourlo); /* declet 11 */
1608 #endif
1609
1610 if (c==cstart) *c++='0'; /* all zeros, empty -- make "0" */
1611
1612 /*[This fast path is valid but adds 3-5 cycles to worst case length] */
1613 /*if (exp==0) { // integer or NaN case -- easy */
1614 /* *c='\0'; // terminate */
1615 /* return string; */
1616 /* } */
1617
1618 e=0; /* assume no E */
1619 pre=(Int)(c-cstart)+exp; /* length+exp [c->LSD+1] */
1620 /* [here, pre-exp is the digits count (==1 for zero)] */
1621
1622 if (exp>0 || pre<-5) { /* need exponential form */
1623 e=pre-1; /* calculate E value */
1624 pre=1; /* assume one digit before '.' */
1625 } /* exponential form */
1626
1627 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
1628 if (pre>0) { /* ddd.ddd (plain), perhaps with E */
1629 char *dotat=cstart+pre;
1630 if (dotat<c) { /* if embedded dot needed... */
1631 /* [memmove is a disaster, here] */
1632 /* move by fours; there must be space for junk at the end */
1633 /* because exponent is still possible */
1634 s=dotat+ROUNDDOWN4(c-dotat); /* source */
1635 t=s+1; /* target */
1636 /* open the gap [cannot use memcpy] */
1637 for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
1638 *dotat='.';
1639 c++; /* length increased by one */
1640 } /* need dot? */
1641
1642 /* finally add the E-part, if needed; it will never be 0, and has */
1643 /* a maximum length of 3 or 4 digits (asserted above) */
1644 if (e!=0) {
1645 memcpy(c, "E+", 2); /* starts with E, assume + */
1646 c++;
1647 if (e<0) {
1648 *c='-'; /* oops, need '-' */
1649 e=-e; /* uInt, please */
1650 }
1651 c++;
1652 /* Three-character exponents are easy; 4-character a little trickier */
1653 #if DECEMAXD<=3
1654 u=&BIN2BCD8[e*4]; /* -> 3 digits + length byte */
1655 /* copy fixed 4 characters [is safe], starting at non-zero */
1656 /* and with character mask to convert BCD to char */
1657 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
1658 c+=*(u+3); /* bump pointer appropriately */
1659 #elif DECEMAXD==4
1660 if (e<1000) { /* 3 (or fewer) digits case */
1661 u=&BIN2BCD8[e*4]; /* -> 3 digits + length byte */
1662 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); /* [as above] */
1663 c+=*(u+3); /* bump pointer appropriately */
1664 }
1665 else { /* 4-digits */
1666 Int thou=((e>>3)*1049)>>17; /* e/1000 */
1667 Int rem=e-(1000*thou); /* e%1000 */
1668 *c++=(char)('0'+(char)thou); /* the thousands digit */
1669 u=&BIN2BCD8[rem*4]; /* -> 3 digits + length byte */
1670 UBFROMUI(c, UBTOUI(u)|CHARMASK); /* copy fixed 3+1 characters [is safe] */
1671 c+=3; /* bump pointer, always 3 digits */
1672 }
1673 #endif
1674 }
1675 *c='\0'; /* add terminator */
1676 /*printf("res %s\n", string); */
1677 return string;
1678 } /* pre>0 */
1679
1680 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
1681 /* Surprisingly, this is close to being the worst-case path, so the */
1682 /* shift is done by fours; this is a little tricky because the */
1683 /* rightmost character to be written must not be beyond where the */
1684 /* rightmost terminator could be -- so backoff to not touch */
1685 /* terminator position if need be (this can make exact alignments */
1686 /* for full Doubles, but in some cases needs care not to access too */
1687 /* far to the left) */
1688
1689 pre=-pre+2; /* gap width, including "0." */
1690 t=cstart+ROUNDDOWN4(c-cstart)+pre; /* preferred first target point */
1691 /* backoff if too far to the right */
1692 if (t>string+DECSTRING-5) t=string+DECSTRING-5; /* adjust to fit */
1693 /* now shift the entire coefficient to the right, being careful not */
1694 /* to access to the left of string [cannot use memcpy] */
1695 for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
1696 /* for Quads and Singles there may be a character or two left... */
1697 s+=3; /* where next would come from */
1698 for(; s>=cstart; s--, t--) *(t+3)=*(s);
1699 /* now have fill 0. through 0.00000; use overlaps to avoid tests */
1700 if (pre>=4) {
1701 memcpy(cstart+pre-4, "0000", 4);
1702 memcpy(cstart, "0.00", 4);
1703 }
1704 else { /* 2 or 3 */
1705 *(cstart+pre-1)='0';
1706 memcpy(cstart, "0.", 2);
1707 }
1708 *(c+pre)='\0'; /* terminate */
1709 return string;
1710 } /* decFloatToString */
1711
1712 /* ------------------------------------------------------------------ */
1713 /* decFloatToWider -- conversion to next-wider format */
1714 /* */
1715 /* source is the decFloat format number which gets the result of */
1716 /* the conversion */
1717 /* wider is the decFloatWider format number which will be narrowed */
1718 /* returns wider */
1719 /* */
1720 /* Widening is always exact; no status is set (sNaNs are copied and */
1721 /* do not signal). The result will be canonical if the source is, */
1722 /* and may or may not be if the source is not. */
1723 /* ------------------------------------------------------------------ */
1724 /* widening is not possible for decQuad format numbers; simply omit */
1725 #if !QUAD
decFloatToWider(const decFloat * source,decFloatWider * wider)1726 decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) {
1727 uInt msd;
1728
1729 /* Construct and copy the sign word */
1730 if (DFISSPECIAL(source)) {
1731 /* copy sign, combination, and first bit of exponent (sNaN selector) */
1732 DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000;
1733 msd=0;
1734 }
1735 else { /* is finite number */
1736 uInt exp=GETEXPUN(source)+DECWBIAS; /* get unbiased exponent and rebias */
1737 uInt code=(exp>>DECWECONL)<<29; /* set two bits of exp [msd=0] */
1738 code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; /* add exponent continuation */
1739 code|=DFWORD(source, 0)&0x80000000; /* add sign */
1740 DFWWORD(wider, 0)=code; /* .. and place top word in wider */
1741 msd=GETMSD(source); /* get source coefficient MSD [0-9] */
1742 }
1743 /* Copy the coefficient and clear any 'unused' words to left */
1744 #if SINGLE
1745 DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20);
1746 #elif DOUBLE
1747 DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18);
1748 DFWWORD(wider, 3)=DFWORD(source, 1);
1749 DFWWORD(wider, 1)=0;
1750 #endif
1751 return wider;
1752 } /* decFloatToWider */
1753 #endif
1754
1755 /* ------------------------------------------------------------------ */
1756 /* decFloatVersion -- return package version string */
1757 /* */
1758 /* returns a constant string describing this package */
1759 /* ------------------------------------------------------------------ */
decFloatVersion(void)1760 const char *decFloatVersion(void) {
1761 return DECVERSION;
1762 } /* decFloatVersion */
1763
1764 /* ------------------------------------------------------------------ */
1765 /* decFloatZero -- set to canonical (integer) zero */
1766 /* */
1767 /* df is the decFloat format number to integer +0 (q=0, c=+0) */
1768 /* returns df */
1769 /* */
1770 /* No error is possible, and no status can be set. */
1771 /* ------------------------------------------------------------------ */
decFloatZero(decFloat * df)1772 decFloat * decFloatZero(decFloat *df){
1773 DFWORD(df, 0)=ZEROWORD; /* set appropriate top word */
1774 #if DOUBLE || QUAD
1775 DFWORD(df, 1)=0;
1776 #if QUAD
1777 DFWORD(df, 2)=0;
1778 DFWORD(df, 3)=0;
1779 #endif
1780 #endif
1781 /* decFloatShow(df, "zero"); */
1782 return df;
1783 } /* decFloatZero */
1784
1785 /* ------------------------------------------------------------------ */
1786 /* Private generic function (not format-specific) for development use */
1787 /* ------------------------------------------------------------------ */
1788 /* This is included once only, for all to use */
1789 #if QUAD && (DECCHECK || DECTRACE)
1790 /* ---------------------------------------------------------------- */
1791 /* decShowNum -- display bcd8 number in debug form */
1792 /* */
1793 /* num is the bcdnum to display */
1794 /* tag is a string to label the display */
1795 /* ---------------------------------------------------------------- */
decShowNum(const bcdnum * num,const char * tag)1796 void decShowNum(const bcdnum *num, const char *tag) {
1797 const char *csign="+"; /* sign character */
1798 uByte *ub; /* work */
1799 uInt uiwork; /* for macros */
1800 if (num->sign==DECFLOAT_Sign) csign="-";
1801
1802 printf(">%s> ", tag);
1803 if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign);
1804 else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign);
1805 else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign);
1806 else { /* finite */
1807 char qbuf[10]; /* for right-aligned q */
1808 char *c; /* work */
1809 const uByte *u; /* .. */
1810 Int e=num->exponent; /* .. exponent */
1811 strcpy(qbuf, "q=");
1812 c=&qbuf[2]; /* where exponent will go */
1813 /* lay out the exponent */
1814 if (e<0) {
1815 *c++='-'; /* add '-' */
1816 e=-e; /* uInt, please */
1817 }
1818 #if DECEMAXD>4
1819 #error Exponent form is too long for ShowNum to lay out
1820 #endif
1821 if (e==0) *c++='0'; /* 0-length case */
1822 else if (e<1000) { /* 3 (or fewer) digits case */
1823 u=&BIN2BCD8[e*4]; /* -> 3 digits + length byte */
1824 UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); /* [as above] */
1825 c+=*(u+3); /* bump pointer appropriately */
1826 }
1827 else { /* 4-digits */
1828 Int thou=((e>>3)*1049)>>17; /* e/1000 */
1829 Int rem=e-(1000*thou); /* e%1000 */
1830 *c++=(char)('0'+(char)thou); /* the thousands digit */
1831 u=&BIN2BCD8[rem*4]; /* -> 3 digits + length byte */
1832 UBFROMUI(c, UBTOUI(u)|CHARMASK); /* copy fixed 3+1 characters [is safe] */
1833 c+=3; /* bump pointer, always 3 digits */
1834 }
1835 *c='\0'; /* add terminator */
1836 printf("%7s c=%s", qbuf, csign);
1837 }
1838
1839 if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) {
1840 for (ub=num->msd; ub<=num->lsd; ub++) { /* coefficient... */
1841 printf("%1x", *ub);
1842 if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); /* 4-space */
1843 }
1844 }
1845 printf("\n");
1846 } /* decShowNum */
1847 #endif
1848