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[qemu/ar7.git] / libdecnumber / dpd / decimal128.c
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1 /* Decimal 128-bit format module for the decNumber C Library.
2 Copyright (C) 2005, 2007 Free Software Foundation, Inc.
3 Contributed by IBM Corporation. Author Mike Cowlishaw.
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 2, or (at your option) any later
10 version.
12 In addition to the permissions in the GNU General Public License,
13 the Free Software Foundation gives you unlimited permission to link
14 the compiled version of this file into combinations with other
15 programs, and to distribute those combinations without any
16 restriction coming from the use of this file. (The General Public
17 License restrictions do apply in other respects; for example, they
18 cover modification of the file, and distribution when not linked
19 into a combine executable.)
21 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
22 WARRANTY; without even the implied warranty of MERCHANTABILITY or
23 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
24 for more details.
26 You should have received a copy of the GNU General Public License
27 along with GCC; see the file COPYING. If not, write to the Free
28 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
29 02110-1301, USA. */
31 /* ------------------------------------------------------------------ */
32 /* Decimal 128-bit format module */
33 /* ------------------------------------------------------------------ */
34 /* This module comprises the routines for decimal128 format numbers. */
35 /* Conversions are supplied to and from decNumber and String. */
36 /* */
37 /* This is used when decNumber provides operations, either for all */
38 /* operations or as a proxy between decNumber and decSingle. */
39 /* */
40 /* Error handling is the same as decNumber (qv.). */
41 /* ------------------------------------------------------------------ */
42 #include <string.h> /* [for memset/memcpy] */
43 #include <stdio.h> /* [for printf] */
45 #include "libdecnumber/dconfig.h"
46 #define DECNUMDIGITS 34 /* make decNumbers with space for 34 */
47 #include "libdecnumber/decNumber.h"
48 #include "libdecnumber/decNumberLocal.h"
49 #include "libdecnumber/dpd/decimal128.h"
51 /* Utility routines and tables [in decimal64.c] */
52 extern const uInt COMBEXP[32], COMBMSD[32];
53 extern const uByte BIN2CHAR[4001];
55 extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
56 extern void decDigitsToDPD(const decNumber *, uInt *, Int);
58 #if DECTRACE || DECCHECK
59 void decimal128Show(const decimal128 *); /* for debug */
60 extern void decNumberShow(const decNumber *); /* .. */
61 #endif
63 /* Useful macro */
64 /* Clear a structure (e.g., a decNumber) */
65 #define DEC_clear(d) memset(d, 0, sizeof(*d))
67 /* ------------------------------------------------------------------ */
68 /* decimal128FromNumber -- convert decNumber to decimal128 */
69 /* */
70 /* ds is the target decimal128 */
71 /* dn is the source number (assumed valid) */
72 /* set is the context, used only for reporting errors */
73 /* */
74 /* The set argument is used only for status reporting and for the */
75 /* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
76 /* digits or an overflow is detected). If the exponent is out of the */
77 /* valid range then Overflow or Underflow will be raised. */
78 /* After Underflow a subnormal result is possible. */
79 /* */
80 /* DEC_Clamped is set if the number has to be 'folded down' to fit, */
81 /* by reducing its exponent and multiplying the coefficient by a */
82 /* power of ten, or if the exponent on a zero had to be clamped. */
83 /* ------------------------------------------------------------------ */
84 decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,
85 decContext *set) {
86 uInt status=0; /* status accumulator */
87 Int ae; /* adjusted exponent */
88 decNumber dw; /* work */
89 decContext dc; /* .. */
90 uInt *pu; /* .. */
91 uInt comb, exp; /* .. */
92 uInt targar[4]={0,0,0,0}; /* target 128-bit */
93 #define targhi targar[3] /* name the word with the sign */
94 #define targmh targar[2] /* name the words */
95 #define targml targar[1] /* .. */
96 #define targlo targar[0] /* .. */
98 /* If the number has too many digits, or the exponent could be */
99 /* out of range then reduce the number under the appropriate */
100 /* constraints. This could push the number to Infinity or zero, */
101 /* so this check and rounding must be done before generating the */
102 /* decimal128] */
103 ae=dn->exponent+dn->digits-1; /* [0 if special] */
104 if (dn->digits>DECIMAL128_Pmax /* too many digits */
105 || ae>DECIMAL128_Emax /* likely overflow */
106 || ae<DECIMAL128_Emin) { /* likely underflow */
107 decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
108 dc.round=set->round; /* use supplied rounding */
109 decNumberPlus(&dw, dn, &dc); /* (round and check) */
110 /* [this changes -0 to 0, so enforce the sign...] */
111 dw.bits|=dn->bits&DECNEG;
112 status=dc.status; /* save status */
113 dn=&dw; /* use the work number */
114 } /* maybe out of range */
116 if (dn->bits&DECSPECIAL) { /* a special value */
117 if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
118 else { /* sNaN or qNaN */
119 if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */
120 && (dn->digits<DECIMAL128_Pmax)) { /* coefficient fits */
121 decDigitsToDPD(dn, targar, 0);
123 if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
124 else targhi|=DECIMAL_sNaN<<24;
125 } /* a NaN */
126 } /* special */
128 else { /* is finite */
129 if (decNumberIsZero(dn)) { /* is a zero */
130 /* set and clamp exponent */
131 if (dn->exponent<-DECIMAL128_Bias) {
132 exp=0; /* low clamp */
133 status|=DEC_Clamped;
135 else {
136 exp=dn->exponent+DECIMAL128_Bias; /* bias exponent */
137 if (exp>DECIMAL128_Ehigh) { /* top clamp */
138 exp=DECIMAL128_Ehigh;
139 status|=DEC_Clamped;
142 comb=(exp>>9) & 0x18; /* msd=0, exp top 2 bits .. */
144 else { /* non-zero finite number */
145 uInt msd; /* work */
146 Int pad=0; /* coefficient pad digits */
148 /* the dn is known to fit, but it may need to be padded */
149 exp=(uInt)(dn->exponent+DECIMAL128_Bias); /* bias exponent */
150 if (exp>DECIMAL128_Ehigh) { /* fold-down case */
151 pad=exp-DECIMAL128_Ehigh;
152 exp=DECIMAL128_Ehigh; /* [to maximum] */
153 status|=DEC_Clamped;
156 /* [fastpath for common case is not a win, here] */
157 decDigitsToDPD(dn, targar, pad);
158 /* save and clear the top digit */
159 msd=targhi>>14;
160 targhi&=0x00003fff;
162 /* create the combination field */
163 if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
164 else comb=((exp>>9) & 0x18) | msd;
166 targhi|=comb<<26; /* add combination field .. */
167 targhi|=(exp&0xfff)<<14; /* .. and exponent continuation */
168 } /* finite */
170 if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
172 /* now write to storage; this is endian */
173 pu=(uInt *)d128->bytes; /* overlay */
174 if (DECLITEND) {
175 pu[0]=targlo; /* directly store the low int */
176 pu[1]=targml; /* then the mid-low */
177 pu[2]=targmh; /* then the mid-high */
178 pu[3]=targhi; /* then the high int */
180 else {
181 pu[0]=targhi; /* directly store the high int */
182 pu[1]=targmh; /* then the mid-high */
183 pu[2]=targml; /* then the mid-low */
184 pu[3]=targlo; /* then the low int */
187 if (status!=0) decContextSetStatus(set, status); /* pass on status */
188 /* decimal128Show(d128); */
189 return d128;
190 } /* decimal128FromNumber */
192 /* ------------------------------------------------------------------ */
193 /* decimal128ToNumber -- convert decimal128 to decNumber */
194 /* d128 is the source decimal128 */
195 /* dn is the target number, with appropriate space */
196 /* No error is possible. */
197 /* ------------------------------------------------------------------ */
198 decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {
199 uInt msd; /* coefficient MSD */
200 uInt exp; /* exponent top two bits */
201 uInt comb; /* combination field */
202 const uInt *pu; /* work */
203 Int need; /* .. */
204 uInt sourar[4]; /* source 128-bit */
205 #define sourhi sourar[3] /* name the word with the sign */
206 #define sourmh sourar[2] /* and the mid-high word */
207 #define sourml sourar[1] /* and the mod-low word */
208 #define sourlo sourar[0] /* and the lowest word */
210 /* load source from storage; this is endian */
211 pu=(const uInt *)d128->bytes; /* overlay */
212 if (DECLITEND) {
213 sourlo=pu[0]; /* directly load the low int */
214 sourml=pu[1]; /* then the mid-low */
215 sourmh=pu[2]; /* then the mid-high */
216 sourhi=pu[3]; /* then the high int */
218 else {
219 sourhi=pu[0]; /* directly load the high int */
220 sourmh=pu[1]; /* then the mid-high */
221 sourml=pu[2]; /* then the mid-low */
222 sourlo=pu[3]; /* then the low int */
225 comb=(sourhi>>26)&0x1f; /* combination field */
227 decNumberZero(dn); /* clean number */
228 if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
230 msd=COMBMSD[comb]; /* decode the combination field */
231 exp=COMBEXP[comb]; /* .. */
233 if (exp==3) { /* is a special */
234 if (msd==0) {
235 dn->bits|=DECINF;
236 return dn; /* no coefficient needed */
238 else if (sourhi&0x02000000) dn->bits|=DECSNAN;
239 else dn->bits|=DECNAN;
240 msd=0; /* no top digit */
242 else { /* is a finite number */
243 dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
246 /* get the coefficient */
247 sourhi&=0x00003fff; /* clean coefficient continuation */
248 if (msd) { /* non-zero msd */
249 sourhi|=msd<<14; /* prefix to coefficient */
250 need=12; /* process 12 declets */
252 else { /* msd=0 */
253 if (sourhi) need=11; /* declets to process */
254 else if (sourmh) need=10;
255 else if (sourml) need=7;
256 else if (sourlo) need=4;
257 else return dn; /* easy: coefficient is 0 */
258 } /*msd=0 */
260 decDigitsFromDPD(dn, sourar, need); /* process declets */
261 /* decNumberShow(dn); */
262 return dn;
263 } /* decimal128ToNumber */
265 /* ------------------------------------------------------------------ */
266 /* to-scientific-string -- conversion to numeric string */
267 /* to-engineering-string -- conversion to numeric string */
268 /* */
269 /* decimal128ToString(d128, string); */
270 /* decimal128ToEngString(d128, string); */
271 /* */
272 /* d128 is the decimal128 format number to convert */
273 /* string is the string where the result will be laid out */
274 /* */
275 /* string must be at least 24 characters */
276 /* */
277 /* No error is possible, and no status can be set. */
278 /* ------------------------------------------------------------------ */
279 char * decimal128ToEngString(const decimal128 *d128, char *string){
280 decNumber dn; /* work */
281 decimal128ToNumber(d128, &dn);
282 decNumberToEngString(&dn, string);
283 return string;
284 } /* decimal128ToEngString */
286 char * decimal128ToString(const decimal128 *d128, char *string){
287 uInt msd; /* coefficient MSD */
288 Int exp; /* exponent top two bits or full */
289 uInt comb; /* combination field */
290 char *cstart; /* coefficient start */
291 char *c; /* output pointer in string */
292 const uInt *pu; /* work */
293 char *s, *t; /* .. (source, target) */
294 Int dpd; /* .. */
295 Int pre, e; /* .. */
296 const uByte *u; /* .. */
298 uInt sourar[4]; /* source 128-bit */
299 #define sourhi sourar[3] /* name the word with the sign */
300 #define sourmh sourar[2] /* and the mid-high word */
301 #define sourml sourar[1] /* and the mod-low word */
302 #define sourlo sourar[0] /* and the lowest word */
304 /* load source from storage; this is endian */
305 pu=(const uInt *)d128->bytes; /* overlay */
306 if (DECLITEND) {
307 sourlo=pu[0]; /* directly load the low int */
308 sourml=pu[1]; /* then the mid-low */
309 sourmh=pu[2]; /* then the mid-high */
310 sourhi=pu[3]; /* then the high int */
312 else {
313 sourhi=pu[0]; /* directly load the high int */
314 sourmh=pu[1]; /* then the mid-high */
315 sourml=pu[2]; /* then the mid-low */
316 sourlo=pu[3]; /* then the low int */
319 c=string; /* where result will go */
320 if (((Int)sourhi)<0) *c++='-'; /* handle sign */
322 comb=(sourhi>>26)&0x1f; /* combination field */
323 msd=COMBMSD[comb]; /* decode the combination field */
324 exp=COMBEXP[comb]; /* .. */
326 if (exp==3) {
327 if (msd==0) { /* infinity */
328 strcpy(c, "Inf");
329 strcpy(c+3, "inity");
330 return string; /* easy */
332 if (sourhi&0x02000000) *c++='s'; /* sNaN */
333 strcpy(c, "NaN"); /* complete word */
334 c+=3; /* step past */
335 if (sourlo==0 && sourml==0 && sourmh==0
336 && (sourhi&0x0003ffff)==0) return string; /* zero payload */
337 /* otherwise drop through to add integer; set correct exp */
338 exp=0; msd=0; /* setup for following code */
340 else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
342 /* convert 34 digits of significand to characters */
343 cstart=c; /* save start of coefficient */
344 if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */
346 /* Now decode the declets. After extracting each one, it is */
347 /* decoded to binary and then to a 4-char sequence by table lookup; */
348 /* the 4-chars are a 1-char length (significant digits, except 000 */
349 /* has length 0). This allows us to left-align the first declet */
350 /* with non-zero content, then remaining ones are full 3-char */
351 /* length. We use fixed-length memcpys because variable-length */
352 /* causes a subroutine call in GCC. (These are length 4 for speed */
353 /* and are safe because the array has an extra terminator byte.) */
354 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
355 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
356 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
357 dpd=(sourhi>>4)&0x3ff; /* declet 1 */
358 dpd2char;
359 dpd=((sourhi&0xf)<<6) | (sourmh>>26); /* declet 2 */
360 dpd2char;
361 dpd=(sourmh>>16)&0x3ff; /* declet 3 */
362 dpd2char;
363 dpd=(sourmh>>6)&0x3ff; /* declet 4 */
364 dpd2char;
365 dpd=((sourmh&0x3f)<<4) | (sourml>>28); /* declet 5 */
366 dpd2char;
367 dpd=(sourml>>18)&0x3ff; /* declet 6 */
368 dpd2char;
369 dpd=(sourml>>8)&0x3ff; /* declet 7 */
370 dpd2char;
371 dpd=((sourml&0xff)<<2) | (sourlo>>30); /* declet 8 */
372 dpd2char;
373 dpd=(sourlo>>20)&0x3ff; /* declet 9 */
374 dpd2char;
375 dpd=(sourlo>>10)&0x3ff; /* declet 10 */
376 dpd2char;
377 dpd=(sourlo)&0x3ff; /* declet 11 */
378 dpd2char;
380 if (c==cstart) *c++='0'; /* all zeros -- make 0 */
382 if (exp==0) { /* integer or NaN case -- easy */
383 *c='\0'; /* terminate */
384 return string;
387 /* non-0 exponent */
388 e=0; /* assume no E */
389 pre=c-cstart+exp;
390 /* [here, pre-exp is the digits count (==1 for zero)] */
391 if (exp>0 || pre<-5) { /* need exponential form */
392 e=pre-1; /* calculate E value */
393 pre=1; /* assume one digit before '.' */
394 } /* exponential form */
396 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
397 s=c-1; /* source (LSD) */
398 if (pre>0) { /* ddd.ddd (plain), perhaps with E */
399 char *dotat=cstart+pre;
400 if (dotat<c) { /* if embedded dot needed... */
401 t=c; /* target */
402 for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
403 *t='.'; /* insert the dot */
404 c++; /* length increased by one */
407 /* finally add the E-part, if needed; it will never be 0, and has */
408 /* a maximum length of 4 digits */
409 if (e!=0) {
410 *c++='E'; /* starts with E */
411 *c++='+'; /* assume positive */
412 if (e<0) {
413 *(c-1)='-'; /* oops, need '-' */
414 e=-e; /* uInt, please */
416 if (e<1000) { /* 3 (or fewer) digits case */
417 u=&BIN2CHAR[e*4]; /* -> length byte */
418 memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */
419 c+=*u; /* bump pointer appropriately */
421 else { /* 4-digits */
422 Int thou=((e>>3)*1049)>>17; /* e/1000 */
423 Int rem=e-(1000*thou); /* e%1000 */
424 *c++='0'+(char)thou;
425 u=&BIN2CHAR[rem*4]; /* -> length byte */
426 memcpy(c, u+1, 4); /* copy fixed 3+1 characters [is safe] */
427 c+=3; /* bump pointer, always 3 digits */
430 *c='\0'; /* add terminator */
431 /*printf("res %s\n", string); */
432 return string;
433 } /* pre>0 */
435 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
436 t=c+1-pre;
437 *(t+1)='\0'; /* can add terminator now */
438 for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */
439 c=cstart;
440 *c++='0'; /* always starts with 0. */
441 *c++='.';
442 for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */
443 /*printf("res %s\n", string); */
444 return string;
445 } /* decimal128ToString */
447 /* ------------------------------------------------------------------ */
448 /* to-number -- conversion from numeric string */
449 /* */
450 /* decimal128FromString(result, string, set); */
451 /* */
452 /* result is the decimal128 format number which gets the result of */
453 /* the conversion */
454 /* *string is the character string which should contain a valid */
455 /* number (which may be a special value) */
456 /* set is the context */
457 /* */
458 /* The context is supplied to this routine is used for error handling */
459 /* (setting of status and traps) and for the rounding mode, only. */
460 /* If an error occurs, the result will be a valid decimal128 NaN. */
461 /* ------------------------------------------------------------------ */
462 decimal128 * decimal128FromString(decimal128 *result, const char *string,
463 decContext *set) {
464 decContext dc; /* work */
465 decNumber dn; /* .. */
467 decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */
468 dc.round=set->round; /* use supplied rounding */
470 decNumberFromString(&dn, string, &dc); /* will round if needed */
471 decimal128FromNumber(result, &dn, &dc);
472 if (dc.status!=0) { /* something happened */
473 decContextSetStatus(set, dc.status); /* .. pass it on */
475 return result;
476 } /* decimal128FromString */
478 /* ------------------------------------------------------------------ */
479 /* decimal128IsCanonical -- test whether encoding is canonical */
480 /* d128 is the source decimal128 */
481 /* returns 1 if the encoding of d128 is canonical, 0 otherwise */
482 /* No error is possible. */
483 /* ------------------------------------------------------------------ */
484 uint32_t decimal128IsCanonical(const decimal128 *d128) {
485 decNumber dn; /* work */
486 decimal128 canon; /* .. */
487 decContext dc; /* .. */
488 decContextDefault(&dc, DEC_INIT_DECIMAL128);
489 decimal128ToNumber(d128, &dn);
490 decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
491 return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
492 } /* decimal128IsCanonical */
494 /* ------------------------------------------------------------------ */
495 /* decimal128Canonical -- copy an encoding, ensuring it is canonical */
496 /* d128 is the source decimal128 */
497 /* result is the target (may be the same decimal128) */
498 /* returns result */
499 /* No error is possible. */
500 /* ------------------------------------------------------------------ */
501 decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {
502 decNumber dn; /* work */
503 decContext dc; /* .. */
504 decContextDefault(&dc, DEC_INIT_DECIMAL128);
505 decimal128ToNumber(d128, &dn);
506 decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */
507 return result;
508 } /* decimal128Canonical */
510 #if DECTRACE || DECCHECK
511 /* Macros for accessing decimal128 fields. These assume the argument
512 is a reference (pointer) to the decimal128 structure, and the
513 decimal128 is in network byte order (big-endian) */
514 /* Get sign */
515 #define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7)
517 /* Get combination field */
518 #define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2)
520 /* Get exponent continuation [does not remove bias] */
521 #define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \
522 | ((unsigned)(d)->bytes[1]<<2) \
523 | ((unsigned)(d)->bytes[2]>>6))
525 /* Set sign [this assumes sign previously 0] */
526 #define decimal128SetSign(d, b) { \
527 (d)->bytes[0]|=((unsigned)(b)<<7);}
529 /* Set exponent continuation [does not apply bias] */
530 /* This assumes range has been checked and exponent previously 0; */
531 /* type of exponent must be unsigned */
532 #define decimal128SetExpCon(d, e) { \
533 (d)->bytes[0]|=(uint8_t)((e)>>10); \
534 (d)->bytes[1] =(uint8_t)(((e)&0x3fc)>>2); \
535 (d)->bytes[2]|=(uint8_t)(((e)&0x03)<<6);}
537 /* ------------------------------------------------------------------ */
538 /* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */
539 /* d128 -- the number to show */
540 /* ------------------------------------------------------------------ */
541 /* Also shows sign/cob/expconfields extracted */
542 void decimal128Show(const decimal128 *d128) {
543 char buf[DECIMAL128_Bytes*2+1];
544 Int i, j=0;
546 if (DECLITEND) {
547 for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
548 sprintf(&buf[j], "%02x", d128->bytes[15-i]);
550 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
551 d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
552 ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|
553 (d128->bytes[13]>>6));
555 else {
556 for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
557 sprintf(&buf[j], "%02x", d128->bytes[i]);
559 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
560 decimal128Sign(d128), decimal128Comb(d128),
561 decimal128ExpCon(d128));
563 } /* decimal128Show */
564 #endif