1 /* Decimal 128-bit format module for the decNumber C Library.
2 Copyright (C) 2005-2013 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 3, or (at your option) any later
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
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.
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/>. */
26 /* ------------------------------------------------------------------ */
27 /* Decimal 128-bit format module */
28 /* ------------------------------------------------------------------ */
29 /* This module comprises the routines for decimal128 format numbers. */
30 /* Conversions are supplied to and from decNumber and String. */
32 /* This is used when decNumber provides operations, either for all */
33 /* operations or as a proxy between decNumber and decSingle. */
35 /* Error handling is the same as decNumber (qv.). */
36 /* ------------------------------------------------------------------ */
37 #include <string.h> /* [for memset/memcpy] */
38 #include <stdio.h> /* [for printf] */
40 #include "dconfig.h" /* GCC definitions */
41 #define DECNUMDIGITS 34 /* make decNumbers with space for 34 */
42 #include "decNumber.h" /* base number library */
43 #include "decNumberLocal.h" /* decNumber local types, etc. */
44 #include "decimal128.h" /* our primary include */
46 /* Utility routines and tables [in decimal64.c] */
47 extern const uInt COMBEXP
[32], COMBMSD
[32];
48 extern const uShort DPD2BIN
[1024];
49 extern const uShort BIN2DPD
[1000]; /* [not used] */
50 extern const uByte BIN2CHAR
[4001];
52 extern void decDigitsFromDPD(decNumber
*, const uInt
*, Int
);
53 extern void decDigitsToDPD(const decNumber
*, uInt
*, Int
);
55 #if DECTRACE || DECCHECK
56 void decimal128Show(const decimal128
*); /* for debug */
57 extern void decNumberShow(const decNumber
*); /* .. */
61 /* Clear a structure (e.g., a decNumber) */
62 #define DEC_clear(d) memset(d, 0, sizeof(*d))
64 /* ------------------------------------------------------------------ */
65 /* decimal128FromNumber -- convert decNumber to decimal128 */
67 /* ds is the target decimal128 */
68 /* dn is the source number (assumed valid) */
69 /* set is the context, used only for reporting errors */
71 /* The set argument is used only for status reporting and for the */
72 /* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
73 /* digits or an overflow is detected). If the exponent is out of the */
74 /* valid range then Overflow or Underflow will be raised. */
75 /* After Underflow a subnormal result is possible. */
77 /* DEC_Clamped is set if the number has to be 'folded down' to fit, */
78 /* by reducing its exponent and multiplying the coefficient by a */
79 /* power of ten, or if the exponent on a zero had to be clamped. */
80 /* ------------------------------------------------------------------ */
81 decimal128
* decimal128FromNumber(decimal128
*d128
, const decNumber
*dn
,
83 uInt status
=0; /* status accumulator */
84 Int ae
; /* adjusted exponent */
85 decNumber dw
; /* work */
86 decContext dc
; /* .. */
87 uInt comb
, exp
; /* .. */
88 uInt uiwork
; /* for macros */
89 uInt targar
[4]={0,0,0,0}; /* target 128-bit */
90 #define targhi targar[3] /* name the word with the sign */
91 #define targmh targar[2] /* name the words */
92 #define targml targar[1] /* .. */
93 #define targlo targar[0] /* .. */
95 /* If the number has too many digits, or the exponent could be */
96 /* out of range then reduce the number under the appropriate */
97 /* constraints. This could push the number to Infinity or zero, */
98 /* so this check and rounding must be done before generating the */
100 ae
=dn
->exponent
+dn
->digits
-1; /* [0 if special] */
101 if (dn
->digits
>DECIMAL128_Pmax
/* too many digits */
102 || ae
>DECIMAL128_Emax
/* likely overflow */
103 || ae
<DECIMAL128_Emin
) { /* likely underflow */
104 decContextDefault(&dc
, DEC_INIT_DECIMAL128
); /* [no traps] */
105 dc
.round
=set
->round
; /* use supplied rounding */
106 decNumberPlus(&dw
, dn
, &dc
); /* (round and check) */
107 /* [this changes -0 to 0, so enforce the sign...] */
108 dw
.bits
|=dn
->bits
&DECNEG
;
109 status
=dc
.status
; /* save status */
110 dn
=&dw
; /* use the work number */
111 } /* maybe out of range */
113 if (dn
->bits
&DECSPECIAL
) { /* a special value */
114 if (dn
->bits
&DECINF
) targhi
=DECIMAL_Inf
<<24;
115 else { /* sNaN or qNaN */
116 if ((*dn
->lsu
!=0 || dn
->digits
>1) /* non-zero coefficient */
117 && (dn
->digits
<DECIMAL128_Pmax
)) { /* coefficient fits */
118 decDigitsToDPD(dn
, targar
, 0);
120 if (dn
->bits
&DECNAN
) targhi
|=DECIMAL_NaN
<<24;
121 else targhi
|=DECIMAL_sNaN
<<24;
125 else { /* is finite */
126 if (decNumberIsZero(dn
)) { /* is a zero */
127 /* set and clamp exponent */
128 if (dn
->exponent
<-DECIMAL128_Bias
) {
129 exp
=0; /* low clamp */
133 exp
=dn
->exponent
+DECIMAL128_Bias
; /* bias exponent */
134 if (exp
>DECIMAL128_Ehigh
) { /* top clamp */
135 exp
=DECIMAL128_Ehigh
;
139 comb
=(exp
>>9) & 0x18; /* msd=0, exp top 2 bits .. */
141 else { /* non-zero finite number */
143 Int pad
=0; /* coefficient pad digits */
145 /* the dn is known to fit, but it may need to be padded */
146 exp
=(uInt
)(dn
->exponent
+DECIMAL128_Bias
); /* bias exponent */
147 if (exp
>DECIMAL128_Ehigh
) { /* fold-down case */
148 pad
=exp
-DECIMAL128_Ehigh
;
149 exp
=DECIMAL128_Ehigh
; /* [to maximum] */
153 /* [fastpath for common case is not a win, here] */
154 decDigitsToDPD(dn
, targar
, pad
);
155 /* save and clear the top digit */
159 /* create the combination field */
160 if (msd
>=8) comb
=0x18 | ((exp
>>11) & 0x06) | (msd
& 0x01);
161 else comb
=((exp
>>9) & 0x18) | msd
;
163 targhi
|=comb
<<26; /* add combination field .. */
164 targhi
|=(exp
&0xfff)<<14; /* .. and exponent continuation */
167 if (dn
->bits
&DECNEG
) targhi
|=0x80000000; /* add sign bit */
169 /* now write to storage; this is endian */
172 UBFROMUI(d128
->bytes
, targlo
);
173 UBFROMUI(d128
->bytes
+4, targml
);
174 UBFROMUI(d128
->bytes
+8, targmh
);
175 UBFROMUI(d128
->bytes
+12, targhi
);
179 UBFROMUI(d128
->bytes
, targhi
);
180 UBFROMUI(d128
->bytes
+4, targmh
);
181 UBFROMUI(d128
->bytes
+8, targml
);
182 UBFROMUI(d128
->bytes
+12, targlo
);
185 if (status
!=0) decContextSetStatus(set
, status
); /* pass on status */
186 /* decimal128Show(d128); */
188 } /* decimal128FromNumber */
190 /* ------------------------------------------------------------------ */
191 /* decimal128ToNumber -- convert decimal128 to decNumber */
192 /* d128 is the source decimal128 */
193 /* dn is the target number, with appropriate space */
194 /* No error is possible. */
195 /* ------------------------------------------------------------------ */
196 decNumber
* decimal128ToNumber(const decimal128
*d128
, decNumber
*dn
) {
197 uInt msd
; /* coefficient MSD */
198 uInt exp
; /* exponent top two bits */
199 uInt comb
; /* combination field */
201 uInt uiwork
; /* for macros */
202 uInt sourar
[4]; /* source 128-bit */
203 #define sourhi sourar[3] /* name the word with the sign */
204 #define sourmh sourar[2] /* and the mid-high word */
205 #define sourml sourar[1] /* and the mod-low word */
206 #define sourlo sourar[0] /* and the lowest word */
208 /* load source from storage; this is endian */
210 sourlo
=UBTOUI(d128
->bytes
); /* directly load the low int */
211 sourml
=UBTOUI(d128
->bytes
+4 ); /* then the mid-low */
212 sourmh
=UBTOUI(d128
->bytes
+8 ); /* then the mid-high */
213 sourhi
=UBTOUI(d128
->bytes
+12); /* then the high int */
216 sourhi
=UBTOUI(d128
->bytes
); /* directly load the high int */
217 sourmh
=UBTOUI(d128
->bytes
+4 ); /* then the mid-high */
218 sourml
=UBTOUI(d128
->bytes
+8 ); /* then the mid-low */
219 sourlo
=UBTOUI(d128
->bytes
+12); /* then the low int */
222 comb
=(sourhi
>>26)&0x1f; /* combination field */
224 decNumberZero(dn
); /* clean number */
225 if (sourhi
&0x80000000) dn
->bits
=DECNEG
; /* set sign if negative */
227 msd
=COMBMSD
[comb
]; /* decode the combination field */
228 exp
=COMBEXP
[comb
]; /* .. */
230 if (exp
==3) { /* is a special */
233 return dn
; /* no coefficient needed */
235 else if (sourhi
&0x02000000) dn
->bits
|=DECSNAN
;
236 else dn
->bits
|=DECNAN
;
237 msd
=0; /* no top digit */
239 else { /* is a finite number */
240 dn
->exponent
=(exp
<<12)+((sourhi
>>14)&0xfff)-DECIMAL128_Bias
; /* unbiased */
243 /* get the coefficient */
244 sourhi
&=0x00003fff; /* clean coefficient continuation */
245 if (msd
) { /* non-zero msd */
246 sourhi
|=msd
<<14; /* prefix to coefficient */
247 need
=12; /* process 12 declets */
250 if (sourhi
) need
=11; /* declets to process */
251 else if (sourmh
) need
=10;
252 else if (sourml
) need
=7;
253 else if (sourlo
) need
=4;
254 else return dn
; /* easy: coefficient is 0 */
257 decDigitsFromDPD(dn
, sourar
, need
); /* process declets */
258 /* decNumberShow(dn); */
260 } /* decimal128ToNumber */
262 /* ------------------------------------------------------------------ */
263 /* to-scientific-string -- conversion to numeric string */
264 /* to-engineering-string -- conversion to numeric string */
266 /* decimal128ToString(d128, string); */
267 /* decimal128ToEngString(d128, string); */
269 /* d128 is the decimal128 format number to convert */
270 /* string is the string where the result will be laid out */
272 /* string must be at least 24 characters */
274 /* No error is possible, and no status can be set. */
275 /* ------------------------------------------------------------------ */
276 char * decimal128ToEngString(const decimal128
*d128
, char *string
){
277 decNumber dn
; /* work */
278 decimal128ToNumber(d128
, &dn
);
279 decNumberToEngString(&dn
, string
);
281 } /* decimal128ToEngString */
283 char * decimal128ToString(const decimal128
*d128
, char *string
){
284 uInt msd
; /* coefficient MSD */
285 Int exp
; /* exponent top two bits or full */
286 uInt comb
; /* combination field */
287 char *cstart
; /* coefficient start */
288 char *c
; /* output pointer in string */
289 const uByte
*u
; /* work */
290 char *s
, *t
; /* .. (source, target) */
293 uInt uiwork
; /* for macros */
295 uInt sourar
[4]; /* source 128-bit */
296 #define sourhi sourar[3] /* name the word with the sign */
297 #define sourmh sourar[2] /* and the mid-high word */
298 #define sourml sourar[1] /* and the mod-low word */
299 #define sourlo sourar[0] /* and the lowest word */
301 /* load source from storage; this is endian */
303 sourlo
=UBTOUI(d128
->bytes
); /* directly load the low int */
304 sourml
=UBTOUI(d128
->bytes
+4 ); /* then the mid-low */
305 sourmh
=UBTOUI(d128
->bytes
+8 ); /* then the mid-high */
306 sourhi
=UBTOUI(d128
->bytes
+12); /* then the high int */
309 sourhi
=UBTOUI(d128
->bytes
); /* directly load the high int */
310 sourmh
=UBTOUI(d128
->bytes
+4 ); /* then the mid-high */
311 sourml
=UBTOUI(d128
->bytes
+8 ); /* then the mid-low */
312 sourlo
=UBTOUI(d128
->bytes
+12); /* then the low int */
315 c
=string
; /* where result will go */
316 if (((Int
)sourhi
)<0) *c
++='-'; /* handle sign */
318 comb
=(sourhi
>>26)&0x1f; /* combination field */
319 msd
=COMBMSD
[comb
]; /* decode the combination field */
320 exp
=COMBEXP
[comb
]; /* .. */
323 if (msd
==0) { /* infinity */
325 strcpy(c
+3, "inity");
326 return string
; /* easy */
328 if (sourhi
&0x02000000) *c
++='s'; /* sNaN */
329 strcpy(c
, "NaN"); /* complete word */
330 c
+=3; /* step past */
331 if (sourlo
==0 && sourml
==0 && sourmh
==0
332 && (sourhi
&0x0003ffff)==0) return string
; /* zero payload */
333 /* otherwise drop through to add integer; set correct exp */
334 exp
=0; msd
=0; /* setup for following code */
336 else exp
=(exp
<<12)+((sourhi
>>14)&0xfff)-DECIMAL128_Bias
; /* unbiased */
338 /* convert 34 digits of significand to characters */
339 cstart
=c
; /* save start of coefficient */
340 if (msd
) *c
++='0'+(char)msd
; /* non-zero most significant digit */
342 /* Now decode the declets. After extracting each one, it is */
343 /* decoded to binary and then to a 4-char sequence by table lookup; */
344 /* the 4-chars are a 1-char length (significant digits, except 000 */
345 /* has length 0). This allows us to left-align the first declet */
346 /* with non-zero content, then remaining ones are full 3-char */
347 /* length. We use fixed-length memcpys because variable-length */
348 /* causes a subroutine call in GCC. (These are length 4 for speed */
349 /* and are safe because the array has an extra terminator byte.) */
350 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
351 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
352 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
353 dpd
=(sourhi
>>4)&0x3ff; /* declet 1 */
355 dpd
=((sourhi
&0xf)<<6) | (sourmh
>>26); /* declet 2 */
357 dpd
=(sourmh
>>16)&0x3ff; /* declet 3 */
359 dpd
=(sourmh
>>6)&0x3ff; /* declet 4 */
361 dpd
=((sourmh
&0x3f)<<4) | (sourml
>>28); /* declet 5 */
363 dpd
=(sourml
>>18)&0x3ff; /* declet 6 */
365 dpd
=(sourml
>>8)&0x3ff; /* declet 7 */
367 dpd
=((sourml
&0xff)<<2) | (sourlo
>>30); /* declet 8 */
369 dpd
=(sourlo
>>20)&0x3ff; /* declet 9 */
371 dpd
=(sourlo
>>10)&0x3ff; /* declet 10 */
373 dpd
=(sourlo
)&0x3ff; /* declet 11 */
376 if (c
==cstart
) *c
++='0'; /* all zeros -- make 0 */
378 if (exp
==0) { /* integer or NaN case -- easy */
379 *c
='\0'; /* terminate */
384 e
=0; /* assume no E */
386 /* [here, pre-exp is the digits count (==1 for zero)] */
387 if (exp
>0 || pre
<-5) { /* need exponential form */
388 e
=pre
-1; /* calculate E value */
389 pre
=1; /* assume one digit before '.' */
390 } /* exponential form */
392 /* modify the coefficient, adding 0s, '.', and E+nn as needed */
393 s
=c
-1; /* source (LSD) */
394 if (pre
>0) { /* ddd.ddd (plain), perhaps with E */
395 char *dotat
=cstart
+pre
;
396 if (dotat
<c
) { /* if embedded dot needed... */
398 for (; s
>=dotat
; s
--, t
--) *t
=*s
; /* open the gap; leave t at gap */
399 *t
='.'; /* insert the dot */
400 c
++; /* length increased by one */
403 /* finally add the E-part, if needed; it will never be 0, and has */
404 /* a maximum length of 4 digits */
406 *c
++='E'; /* starts with E */
407 *c
++='+'; /* assume positive */
409 *(c
-1)='-'; /* oops, need '-' */
410 e
=-e
; /* uInt, please */
412 if (e
<1000) { /* 3 (or fewer) digits case */
413 u
=&BIN2CHAR
[e
*4]; /* -> length byte */
414 memcpy(c
, u
+4-*u
, 4); /* copy fixed 4 characters [is safe] */
415 c
+=*u
; /* bump pointer appropriately */
417 else { /* 4-digits */
418 Int thou
=((e
>>3)*1049)>>17; /* e/1000 */
419 Int rem
=e
-(1000*thou
); /* e%1000 */
421 u
=&BIN2CHAR
[rem
*4]; /* -> length byte */
422 memcpy(c
, u
+1, 4); /* copy fixed 3+1 characters [is safe] */
423 c
+=3; /* bump pointer, always 3 digits */
426 *c
='\0'; /* add terminator */
427 /*printf("res %s\n", string); */
431 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
433 *(t
+1)='\0'; /* can add terminator now */
434 for (; s
>=cstart
; s
--, t
--) *t
=*s
; /* shift whole coefficient right */
436 *c
++='0'; /* always starts with 0. */
438 for (; pre
<0; pre
++) *c
++='0'; /* add any 0's after '.' */
439 /*printf("res %s\n", string); */
441 } /* decimal128ToString */
443 /* ------------------------------------------------------------------ */
444 /* to-number -- conversion from numeric string */
446 /* decimal128FromString(result, string, set); */
448 /* result is the decimal128 format number which gets the result of */
450 /* *string is the character string which should contain a valid */
451 /* number (which may be a special value) */
452 /* set is the context */
454 /* The context is supplied to this routine is used for error handling */
455 /* (setting of status and traps) and for the rounding mode, only. */
456 /* If an error occurs, the result will be a valid decimal128 NaN. */
457 /* ------------------------------------------------------------------ */
458 decimal128
* decimal128FromString(decimal128
*result
, const char *string
,
460 decContext dc
; /* work */
461 decNumber dn
; /* .. */
463 decContextDefault(&dc
, DEC_INIT_DECIMAL128
); /* no traps, please */
464 dc
.round
=set
->round
; /* use supplied rounding */
466 decNumberFromString(&dn
, string
, &dc
); /* will round if needed */
467 decimal128FromNumber(result
, &dn
, &dc
);
468 if (dc
.status
!=0) { /* something happened */
469 decContextSetStatus(set
, dc
.status
); /* .. pass it on */
472 } /* decimal128FromString */
474 /* ------------------------------------------------------------------ */
475 /* decimal128IsCanonical -- test whether encoding is canonical */
476 /* d128 is the source decimal128 */
477 /* returns 1 if the encoding of d128 is canonical, 0 otherwise */
478 /* No error is possible. */
479 /* ------------------------------------------------------------------ */
480 uInt
decimal128IsCanonical(const decimal128
*d128
) {
481 decNumber dn
; /* work */
482 decimal128 canon
; /* .. */
483 decContext dc
; /* .. */
484 decContextDefault(&dc
, DEC_INIT_DECIMAL128
);
485 decimal128ToNumber(d128
, &dn
);
486 decimal128FromNumber(&canon
, &dn
, &dc
);/* canon will now be canonical */
487 return memcmp(d128
, &canon
, DECIMAL128_Bytes
)==0;
488 } /* decimal128IsCanonical */
490 /* ------------------------------------------------------------------ */
491 /* decimal128Canonical -- copy an encoding, ensuring it is canonical */
492 /* d128 is the source decimal128 */
493 /* result is the target (may be the same decimal128) */
495 /* No error is possible. */
496 /* ------------------------------------------------------------------ */
497 decimal128
* decimal128Canonical(decimal128
*result
, const decimal128
*d128
) {
498 decNumber dn
; /* work */
499 decContext dc
; /* .. */
500 decContextDefault(&dc
, DEC_INIT_DECIMAL128
);
501 decimal128ToNumber(d128
, &dn
);
502 decimal128FromNumber(result
, &dn
, &dc
);/* result will now be canonical */
504 } /* decimal128Canonical */
506 #if DECTRACE || DECCHECK
507 /* Macros for accessing decimal128 fields. These assume the argument
508 is a reference (pointer) to the decimal128 structure, and the
509 decimal128 is in network byte order (big-endian) */
511 #define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7)
513 /* Get combination field */
514 #define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2)
516 /* Get exponent continuation [does not remove bias] */
517 #define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \
518 | ((unsigned)(d)->bytes[1]<<2) \
519 | ((unsigned)(d)->bytes[2]>>6))
521 /* Set sign [this assumes sign previously 0] */
522 #define decimal128SetSign(d, b) { \
523 (d)->bytes[0]|=((unsigned)(b)<<7);}
525 /* Set exponent continuation [does not apply bias] */
526 /* This assumes range has been checked and exponent previously 0; */
527 /* type of exponent must be unsigned */
528 #define decimal128SetExpCon(d, e) { \
529 (d)->bytes[0]|=(uByte)((e)>>10); \
530 (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \
531 (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);}
533 /* ------------------------------------------------------------------ */
534 /* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */
535 /* d128 -- the number to show */
536 /* ------------------------------------------------------------------ */
537 /* Also shows sign/cob/expconfields extracted */
538 void decimal128Show(const decimal128
*d128
) {
539 char buf
[DECIMAL128_Bytes
*2+1];
543 for (i
=0; i
<DECIMAL128_Bytes
; i
++, j
+=2) {
544 sprintf(&buf
[j
], "%02x", d128
->bytes
[15-i
]);
546 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf
,
547 d128
->bytes
[15]>>7, (d128
->bytes
[15]>>2)&0x1f,
548 ((d128
->bytes
[15]&0x3)<<10)|(d128
->bytes
[14]<<2)|
549 (d128
->bytes
[13]>>6));
552 for (i
=0; i
<DECIMAL128_Bytes
; i
++, j
+=2) {
553 sprintf(&buf
[j
], "%02x", d128
->bytes
[i
]);
555 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf
,
556 decimal128Sign(d128
), decimal128Comb(d128
),
557 decimal128ExpCon(d128
));
559 } /* decimal128Show */
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