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c906108c SS |
1 | /* This is a software floating point library which can be used instead of |
2 | the floating point routines in libgcc1.c for targets without hardware | |
3 | floating point. */ | |
4 | ||
7b6bb8da JB |
5 | /* Copyright (C) 1994, 2007, 2008, 2009, 2010, 2011 |
6 | Free Software Foundation, Inc. | |
c906108c | 7 | |
4744ac1b JB |
8 | This program is free software; you can redistribute it and/or modify |
9 | it under the terms of the GNU General Public License as published by | |
10 | the Free Software Foundation; either version 3 of the License, or | |
11 | (at your option) any later version. | |
c906108c | 12 | |
4744ac1b JB |
13 | This program is distributed in the hope that it will be useful, |
14 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
16 | GNU General Public License for more details. | |
c906108c SS |
17 | |
18 | You should have received a copy of the GNU General Public License | |
4744ac1b | 19 | along with this program. If not, see <http://www.gnu.org/licenses/>. */ |
c906108c SS |
20 | |
21 | /* As a special exception, if you link this library with other files, | |
22 | some of which are compiled with GCC, to produce an executable, | |
23 | this library does not by itself cause the resulting executable | |
24 | to be covered by the GNU General Public License. | |
25 | This exception does not however invalidate any other reasons why | |
26 | the executable file might be covered by the GNU General Public License. */ | |
27 | ||
28 | /* This implements IEEE 754 format arithmetic, but does not provide a | |
29 | mechanism for setting the rounding mode, or for generating or handling | |
30 | exceptions. | |
31 | ||
32 | The original code by Steve Chamberlain, hacked by Mark Eichin and Jim | |
33 | Wilson, all of Cygnus Support. */ | |
34 | ||
35 | /* The intended way to use this file is to make two copies, add `#define FLOAT' | |
36 | to one copy, then compile both copies and add them to libgcc.a. */ | |
37 | ||
38 | /* The following macros can be defined to change the behaviour of this file: | |
39 | FLOAT: Implement a `float', aka SFmode, fp library. If this is not | |
40 | defined, then this file implements a `double', aka DFmode, fp library. | |
41 | FLOAT_ONLY: Used with FLOAT, to implement a `float' only library, i.e. | |
42 | don't include float->double conversion which requires the double library. | |
43 | This is useful only for machines which can't support doubles, e.g. some | |
44 | 8-bit processors. | |
45 | CMPtype: Specify the type that floating point compares should return. | |
46 | This defaults to SItype, aka int. | |
47 | US_SOFTWARE_GOFAST: This makes all entry points use the same names as the | |
48 | US Software goFast library. If this is not defined, the entry points use | |
49 | the same names as libgcc1.c. | |
50 | _DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding | |
51 | two integers to the FLO_union_type. | |
52 | NO_NANS: Disable nan and infinity handling | |
53 | SMALL_MACHINE: Useful when operations on QIs and HIs are faster | |
54 | than on an SI */ | |
55 | ||
56 | #ifndef SFtype | |
57 | typedef SFtype __attribute__ ((mode (SF))); | |
58 | #endif | |
59 | #ifndef DFtype | |
60 | typedef DFtype __attribute__ ((mode (DF))); | |
61 | #endif | |
62 | ||
63 | #ifndef HItype | |
64 | typedef int HItype __attribute__ ((mode (HI))); | |
65 | #endif | |
66 | #ifndef SItype | |
67 | typedef int SItype __attribute__ ((mode (SI))); | |
68 | #endif | |
69 | #ifndef DItype | |
70 | typedef int DItype __attribute__ ((mode (DI))); | |
71 | #endif | |
72 | ||
73 | /* The type of the result of a fp compare */ | |
74 | #ifndef CMPtype | |
75 | #define CMPtype SItype | |
76 | #endif | |
77 | ||
78 | #ifndef UHItype | |
79 | typedef unsigned int UHItype __attribute__ ((mode (HI))); | |
80 | #endif | |
81 | #ifndef USItype | |
82 | typedef unsigned int USItype __attribute__ ((mode (SI))); | |
83 | #endif | |
84 | #ifndef UDItype | |
85 | typedef unsigned int UDItype __attribute__ ((mode (DI))); | |
86 | #endif | |
87 | ||
88 | #define MAX_SI_INT ((SItype) ((unsigned) (~0)>>1)) | |
89 | #define MAX_USI_INT ((USItype) ~0) | |
90 | ||
91 | ||
92 | #ifdef FLOAT_ONLY | |
93 | #define NO_DI_MODE | |
94 | #endif | |
95 | ||
96 | #ifdef FLOAT | |
97 | # define NGARDS 7L | |
98 | # define GARDROUND 0x3f | |
99 | # define GARDMASK 0x7f | |
100 | # define GARDMSB 0x40 | |
101 | # define EXPBITS 8 | |
102 | # define EXPBIAS 127 | |
103 | # define FRACBITS 23 | |
104 | # define EXPMAX (0xff) | |
105 | # define QUIET_NAN 0x100000L | |
106 | # define FRAC_NBITS 32 | |
107 | # define FRACHIGH 0x80000000L | |
108 | # define FRACHIGH2 0xc0000000L | |
109 | typedef USItype fractype; | |
110 | typedef UHItype halffractype; | |
111 | typedef SFtype FLO_type; | |
112 | typedef SItype intfrac; | |
113 | ||
114 | #else | |
115 | # define PREFIXFPDP dp | |
116 | # define PREFIXSFDF df | |
117 | # define NGARDS 8L | |
118 | # define GARDROUND 0x7f | |
119 | # define GARDMASK 0xff | |
120 | # define GARDMSB 0x80 | |
121 | # define EXPBITS 11 | |
122 | # define EXPBIAS 1023 | |
123 | # define FRACBITS 52 | |
124 | # define EXPMAX (0x7ff) | |
125 | # define QUIET_NAN 0x8000000000000LL | |
126 | # define FRAC_NBITS 64 | |
127 | # define FRACHIGH 0x8000000000000000LL | |
128 | # define FRACHIGH2 0xc000000000000000LL | |
129 | typedef UDItype fractype; | |
130 | typedef USItype halffractype; | |
131 | typedef DFtype FLO_type; | |
132 | typedef DItype intfrac; | |
133 | #endif | |
134 | ||
135 | #ifdef US_SOFTWARE_GOFAST | |
136 | # ifdef FLOAT | |
137 | # define add fpadd | |
138 | # define sub fpsub | |
139 | # define multiply fpmul | |
140 | # define divide fpdiv | |
141 | # define compare fpcmp | |
142 | # define si_to_float sitofp | |
143 | # define float_to_si fptosi | |
144 | # define float_to_usi fptoui | |
145 | # define negate __negsf2 | |
146 | # define sf_to_df fptodp | |
147 | # define dptofp dptofp | |
148 | #else | |
149 | # define add dpadd | |
150 | # define sub dpsub | |
151 | # define multiply dpmul | |
152 | # define divide dpdiv | |
153 | # define compare dpcmp | |
154 | # define si_to_float litodp | |
155 | # define float_to_si dptoli | |
156 | # define float_to_usi dptoul | |
157 | # define negate __negdf2 | |
158 | # define df_to_sf dptofp | |
159 | #endif | |
160 | #else | |
161 | # ifdef FLOAT | |
162 | # define add __addsf3 | |
163 | # define sub __subsf3 | |
164 | # define multiply __mulsf3 | |
165 | # define divide __divsf3 | |
166 | # define compare __cmpsf2 | |
167 | # define _eq_f2 __eqsf2 | |
168 | # define _ne_f2 __nesf2 | |
169 | # define _gt_f2 __gtsf2 | |
170 | # define _ge_f2 __gesf2 | |
171 | # define _lt_f2 __ltsf2 | |
172 | # define _le_f2 __lesf2 | |
173 | # define si_to_float __floatsisf | |
174 | # define float_to_si __fixsfsi | |
175 | # define float_to_usi __fixunssfsi | |
176 | # define negate __negsf2 | |
177 | # define sf_to_df __extendsfdf2 | |
178 | #else | |
179 | # define add __adddf3 | |
180 | # define sub __subdf3 | |
181 | # define multiply __muldf3 | |
182 | # define divide __divdf3 | |
183 | # define compare __cmpdf2 | |
184 | # define _eq_f2 __eqdf2 | |
185 | # define _ne_f2 __nedf2 | |
186 | # define _gt_f2 __gtdf2 | |
187 | # define _ge_f2 __gedf2 | |
188 | # define _lt_f2 __ltdf2 | |
189 | # define _le_f2 __ledf2 | |
190 | # define si_to_float __floatsidf | |
191 | # define float_to_si __fixdfsi | |
192 | # define float_to_usi __fixunsdfsi | |
193 | # define negate __negdf2 | |
194 | # define df_to_sf __truncdfsf2 | |
195 | # endif | |
196 | #endif | |
197 | ||
198 | ||
199 | #ifndef INLINE | |
200 | #define INLINE __inline__ | |
201 | #endif | |
202 | ||
203 | /* Preserve the sticky-bit when shifting fractions to the right. */ | |
204 | #define LSHIFT(a) { a = (a & 1) | (a >> 1); } | |
205 | ||
206 | /* numeric parameters */ | |
207 | /* F_D_BITOFF is the number of bits offset between the MSB of the mantissa | |
208 | of a float and of a double. Assumes there are only two float types. | |
209 | (double::FRAC_BITS+double::NGARGS-(float::FRAC_BITS-float::NGARDS)) | |
210 | */ | |
211 | #define F_D_BITOFF (52+8-(23+7)) | |
212 | ||
213 | ||
214 | #define NORMAL_EXPMIN (-(EXPBIAS)+1) | |
215 | #define IMPLICIT_1 (1LL<<(FRACBITS+NGARDS)) | |
216 | #define IMPLICIT_2 (1LL<<(FRACBITS+1+NGARDS)) | |
217 | ||
218 | /* common types */ | |
219 | ||
220 | typedef enum | |
221 | { | |
222 | CLASS_SNAN, | |
223 | CLASS_QNAN, | |
224 | CLASS_ZERO, | |
225 | CLASS_NUMBER, | |
226 | CLASS_INFINITY | |
227 | } fp_class_type; | |
228 | ||
229 | typedef struct | |
230 | { | |
231 | #ifdef SMALL_MACHINE | |
232 | char class; | |
233 | unsigned char sign; | |
234 | short normal_exp; | |
235 | #else | |
236 | fp_class_type class; | |
237 | unsigned int sign; | |
238 | int normal_exp; | |
239 | #endif | |
240 | ||
241 | union | |
242 | { | |
243 | fractype ll; | |
244 | halffractype l[2]; | |
245 | } fraction; | |
246 | } fp_number_type; | |
247 | ||
248 | typedef union | |
249 | { | |
250 | FLO_type value; | |
251 | #ifdef _DEBUG_BITFLOAT | |
252 | int l[2]; | |
253 | #endif | |
254 | struct | |
255 | { | |
256 | #ifndef FLOAT_BIT_ORDER_MISMATCH | |
257 | unsigned int sign:1 __attribute__ ((packed)); | |
258 | unsigned int exp:EXPBITS __attribute__ ((packed)); | |
259 | fractype fraction:FRACBITS __attribute__ ((packed)); | |
260 | #else | |
261 | fractype fraction:FRACBITS __attribute__ ((packed)); | |
262 | unsigned int exp:EXPBITS __attribute__ ((packed)); | |
263 | unsigned int sign:1 __attribute__ ((packed)); | |
264 | #endif | |
265 | } | |
266 | bits; | |
267 | } | |
268 | FLO_union_type; | |
269 | ||
270 | ||
271 | /* end of header */ | |
272 | ||
273 | /* IEEE "special" number predicates */ | |
274 | ||
275 | #ifdef NO_NANS | |
276 | ||
277 | #define nan() 0 | |
278 | #define isnan(x) 0 | |
279 | #define isinf(x) 0 | |
280 | #else | |
281 | ||
282 | INLINE | |
283 | static fp_number_type * | |
284 | nan () | |
285 | { | |
286 | static fp_number_type thenan; | |
287 | ||
288 | return &thenan; | |
289 | } | |
290 | ||
291 | INLINE | |
292 | static int | |
293 | isnan ( fp_number_type * x) | |
294 | { | |
295 | return x->class == CLASS_SNAN || x->class == CLASS_QNAN; | |
296 | } | |
297 | ||
298 | INLINE | |
299 | static int | |
300 | isinf ( fp_number_type * x) | |
301 | { | |
302 | return x->class == CLASS_INFINITY; | |
303 | } | |
304 | ||
305 | #endif | |
306 | ||
307 | INLINE | |
308 | static int | |
309 | iszero ( fp_number_type * x) | |
310 | { | |
311 | return x->class == CLASS_ZERO; | |
312 | } | |
313 | ||
314 | INLINE | |
315 | static void | |
316 | flip_sign ( fp_number_type * x) | |
317 | { | |
318 | x->sign = !x->sign; | |
319 | } | |
320 | ||
321 | static FLO_type | |
322 | pack_d ( fp_number_type * src) | |
323 | { | |
324 | FLO_union_type dst; | |
325 | fractype fraction = src->fraction.ll; /* wasn't unsigned before? */ | |
326 | ||
327 | dst.bits.sign = src->sign; | |
328 | ||
329 | if (isnan (src)) | |
330 | { | |
331 | dst.bits.exp = EXPMAX; | |
332 | dst.bits.fraction = src->fraction.ll; | |
333 | if (src->class == CLASS_QNAN || 1) | |
334 | { | |
335 | dst.bits.fraction |= QUIET_NAN; | |
336 | } | |
337 | } | |
338 | else if (isinf (src)) | |
339 | { | |
340 | dst.bits.exp = EXPMAX; | |
341 | dst.bits.fraction = 0; | |
342 | } | |
343 | else if (iszero (src)) | |
344 | { | |
345 | dst.bits.exp = 0; | |
346 | dst.bits.fraction = 0; | |
347 | } | |
348 | else if (fraction == 0) | |
349 | { | |
350 | dst.value = 0; | |
351 | } | |
352 | else | |
353 | { | |
354 | if (src->normal_exp < NORMAL_EXPMIN) | |
355 | { | |
356 | /* This number's exponent is too low to fit into the bits | |
357 | available in the number, so we'll store 0 in the exponent and | |
358 | shift the fraction to the right to make up for it. */ | |
359 | ||
360 | int shift = NORMAL_EXPMIN - src->normal_exp; | |
361 | ||
362 | dst.bits.exp = 0; | |
363 | ||
364 | if (shift > FRAC_NBITS - NGARDS) | |
365 | { | |
366 | /* No point shifting, since it's more that 64 out. */ | |
367 | fraction = 0; | |
368 | } | |
369 | else | |
370 | { | |
371 | /* Shift by the value */ | |
372 | fraction >>= shift; | |
373 | } | |
374 | fraction >>= NGARDS; | |
375 | dst.bits.fraction = fraction; | |
376 | } | |
377 | else if (src->normal_exp > EXPBIAS) | |
378 | { | |
379 | dst.bits.exp = EXPMAX; | |
380 | dst.bits.fraction = 0; | |
381 | } | |
382 | else | |
383 | { | |
384 | dst.bits.exp = src->normal_exp + EXPBIAS; | |
385 | /* IF the gard bits are the all zero, but the first, then we're | |
386 | half way between two numbers, choose the one which makes the | |
387 | lsb of the answer 0. */ | |
388 | if ((fraction & GARDMASK) == GARDMSB) | |
389 | { | |
390 | if (fraction & (1 << NGARDS)) | |
391 | fraction += GARDROUND + 1; | |
392 | } | |
393 | else | |
394 | { | |
395 | /* Add a one to the guards to round up */ | |
396 | fraction += GARDROUND; | |
397 | } | |
398 | if (fraction >= IMPLICIT_2) | |
399 | { | |
400 | fraction >>= 1; | |
401 | dst.bits.exp += 1; | |
402 | } | |
403 | fraction >>= NGARDS; | |
404 | dst.bits.fraction = fraction; | |
405 | } | |
406 | } | |
407 | return dst.value; | |
408 | } | |
409 | ||
410 | static void | |
411 | unpack_d (FLO_union_type * src, fp_number_type * dst) | |
412 | { | |
413 | fractype fraction = src->bits.fraction; | |
414 | ||
415 | dst->sign = src->bits.sign; | |
416 | if (src->bits.exp == 0) | |
417 | { | |
418 | /* Hmm. Looks like 0 */ | |
419 | if (fraction == 0) | |
420 | { | |
421 | /* tastes like zero */ | |
422 | dst->class = CLASS_ZERO; | |
423 | } | |
424 | else | |
425 | { | |
426 | /* Zero exponent with non zero fraction - it's denormalized, | |
427 | so there isn't a leading implicit one - we'll shift it so | |
428 | it gets one. */ | |
429 | dst->normal_exp = src->bits.exp - EXPBIAS + 1; | |
430 | fraction <<= NGARDS; | |
431 | ||
432 | dst->class = CLASS_NUMBER; | |
433 | #if 1 | |
434 | while (fraction < IMPLICIT_1) | |
435 | { | |
436 | fraction <<= 1; | |
437 | dst->normal_exp--; | |
438 | } | |
439 | #endif | |
440 | dst->fraction.ll = fraction; | |
441 | } | |
442 | } | |
443 | else if (src->bits.exp == EXPMAX) | |
444 | { | |
445 | /* Huge exponent*/ | |
446 | if (fraction == 0) | |
447 | { | |
448 | /* Attached to a zero fraction - means infinity */ | |
449 | dst->class = CLASS_INFINITY; | |
450 | } | |
451 | else | |
452 | { | |
453 | /* Non zero fraction, means nan */ | |
454 | if (dst->sign) | |
455 | { | |
456 | dst->class = CLASS_SNAN; | |
457 | } | |
458 | else | |
459 | { | |
460 | dst->class = CLASS_QNAN; | |
461 | } | |
462 | /* Keep the fraction part as the nan number */ | |
463 | dst->fraction.ll = fraction; | |
464 | } | |
465 | } | |
466 | else | |
467 | { | |
468 | /* Nothing strange about this number */ | |
469 | dst->normal_exp = src->bits.exp - EXPBIAS; | |
470 | dst->class = CLASS_NUMBER; | |
471 | dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1; | |
472 | } | |
473 | } | |
474 | ||
475 | static fp_number_type * | |
476 | _fpadd_parts (fp_number_type * a, | |
477 | fp_number_type * b, | |
478 | fp_number_type * tmp) | |
479 | { | |
480 | intfrac tfraction; | |
481 | ||
482 | /* Put commonly used fields in local variables. */ | |
483 | int a_normal_exp; | |
484 | int b_normal_exp; | |
485 | fractype a_fraction; | |
486 | fractype b_fraction; | |
487 | ||
488 | if (isnan (a)) | |
489 | { | |
490 | return a; | |
491 | } | |
492 | if (isnan (b)) | |
493 | { | |
494 | return b; | |
495 | } | |
496 | if (isinf (a)) | |
497 | { | |
498 | /* Adding infinities with opposite signs yields a NaN. */ | |
499 | if (isinf (b) && a->sign != b->sign) | |
500 | return nan (); | |
501 | return a; | |
502 | } | |
503 | if (isinf (b)) | |
504 | { | |
505 | return b; | |
506 | } | |
507 | if (iszero (b)) | |
508 | { | |
509 | return a; | |
510 | } | |
511 | if (iszero (a)) | |
512 | { | |
513 | return b; | |
514 | } | |
515 | ||
516 | /* Got two numbers. shift the smaller and increment the exponent till | |
517 | they're the same */ | |
518 | { | |
519 | int diff; | |
520 | ||
521 | a_normal_exp = a->normal_exp; | |
522 | b_normal_exp = b->normal_exp; | |
523 | a_fraction = a->fraction.ll; | |
524 | b_fraction = b->fraction.ll; | |
525 | ||
526 | diff = a_normal_exp - b_normal_exp; | |
527 | ||
528 | if (diff < 0) | |
529 | diff = -diff; | |
530 | if (diff < FRAC_NBITS) | |
531 | { | |
532 | /* ??? This does shifts one bit at a time. Optimize. */ | |
533 | while (a_normal_exp > b_normal_exp) | |
534 | { | |
535 | b_normal_exp++; | |
536 | LSHIFT (b_fraction); | |
537 | } | |
538 | while (b_normal_exp > a_normal_exp) | |
539 | { | |
540 | a_normal_exp++; | |
541 | LSHIFT (a_fraction); | |
542 | } | |
543 | } | |
544 | else | |
545 | { | |
546 | /* Somethings's up.. choose the biggest */ | |
547 | if (a_normal_exp > b_normal_exp) | |
548 | { | |
549 | b_normal_exp = a_normal_exp; | |
550 | b_fraction = 0; | |
551 | } | |
552 | else | |
553 | { | |
554 | a_normal_exp = b_normal_exp; | |
555 | a_fraction = 0; | |
556 | } | |
557 | } | |
558 | } | |
559 | ||
560 | if (a->sign != b->sign) | |
561 | { | |
562 | if (a->sign) | |
563 | { | |
564 | tfraction = -a_fraction + b_fraction; | |
565 | } | |
566 | else | |
567 | { | |
568 | tfraction = a_fraction - b_fraction; | |
569 | } | |
570 | if (tfraction > 0) | |
571 | { | |
572 | tmp->sign = 0; | |
573 | tmp->normal_exp = a_normal_exp; | |
574 | tmp->fraction.ll = tfraction; | |
575 | } | |
576 | else | |
577 | { | |
578 | tmp->sign = 1; | |
579 | tmp->normal_exp = a_normal_exp; | |
580 | tmp->fraction.ll = -tfraction; | |
581 | } | |
582 | /* and renormalize it */ | |
583 | ||
584 | while (tmp->fraction.ll < IMPLICIT_1 && tmp->fraction.ll) | |
585 | { | |
586 | tmp->fraction.ll <<= 1; | |
587 | tmp->normal_exp--; | |
588 | } | |
589 | } | |
590 | else | |
591 | { | |
592 | tmp->sign = a->sign; | |
593 | tmp->normal_exp = a_normal_exp; | |
594 | tmp->fraction.ll = a_fraction + b_fraction; | |
595 | } | |
596 | tmp->class = CLASS_NUMBER; | |
597 | /* Now the fraction is added, we have to shift down to renormalize the | |
598 | number */ | |
599 | ||
600 | if (tmp->fraction.ll >= IMPLICIT_2) | |
601 | { | |
602 | LSHIFT (tmp->fraction.ll); | |
603 | tmp->normal_exp++; | |
604 | } | |
605 | return tmp; | |
606 | ||
607 | } | |
608 | ||
609 | FLO_type | |
610 | add (FLO_type arg_a, FLO_type arg_b) | |
611 | { | |
612 | fp_number_type a; | |
613 | fp_number_type b; | |
614 | fp_number_type tmp; | |
615 | fp_number_type *res; | |
616 | ||
617 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
618 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
619 | ||
620 | res = _fpadd_parts (&a, &b, &tmp); | |
621 | ||
622 | return pack_d (res); | |
623 | } | |
624 | ||
625 | FLO_type | |
626 | sub (FLO_type arg_a, FLO_type arg_b) | |
627 | { | |
628 | fp_number_type a; | |
629 | fp_number_type b; | |
630 | fp_number_type tmp; | |
631 | fp_number_type *res; | |
632 | ||
633 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
634 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
635 | ||
636 | b.sign ^= 1; | |
637 | ||
638 | res = _fpadd_parts (&a, &b, &tmp); | |
639 | ||
640 | return pack_d (res); | |
641 | } | |
642 | ||
643 | static fp_number_type * | |
644 | _fpmul_parts ( fp_number_type * a, | |
645 | fp_number_type * b, | |
646 | fp_number_type * tmp) | |
647 | { | |
648 | fractype low = 0; | |
649 | fractype high = 0; | |
650 | ||
651 | if (isnan (a)) | |
652 | { | |
653 | a->sign = a->sign != b->sign; | |
654 | return a; | |
655 | } | |
656 | if (isnan (b)) | |
657 | { | |
658 | b->sign = a->sign != b->sign; | |
659 | return b; | |
660 | } | |
661 | if (isinf (a)) | |
662 | { | |
663 | if (iszero (b)) | |
664 | return nan (); | |
665 | a->sign = a->sign != b->sign; | |
666 | return a; | |
667 | } | |
668 | if (isinf (b)) | |
669 | { | |
670 | if (iszero (a)) | |
671 | { | |
672 | return nan (); | |
673 | } | |
674 | b->sign = a->sign != b->sign; | |
675 | return b; | |
676 | } | |
677 | if (iszero (a)) | |
678 | { | |
679 | a->sign = a->sign != b->sign; | |
680 | return a; | |
681 | } | |
682 | if (iszero (b)) | |
683 | { | |
684 | b->sign = a->sign != b->sign; | |
685 | return b; | |
686 | } | |
687 | ||
688 | /* Calculate the mantissa by multiplying both 64bit numbers to get a | |
689 | 128 bit number */ | |
690 | { | |
691 | fractype x = a->fraction.ll; | |
692 | fractype ylow = b->fraction.ll; | |
693 | fractype yhigh = 0; | |
694 | int bit; | |
695 | ||
696 | #if defined(NO_DI_MODE) | |
697 | { | |
698 | /* ??? This does multiplies one bit at a time. Optimize. */ | |
699 | for (bit = 0; bit < FRAC_NBITS; bit++) | |
700 | { | |
701 | int carry; | |
702 | ||
703 | if (x & 1) | |
704 | { | |
705 | carry = (low += ylow) < ylow; | |
706 | high += yhigh + carry; | |
707 | } | |
708 | yhigh <<= 1; | |
709 | if (ylow & FRACHIGH) | |
710 | { | |
711 | yhigh |= 1; | |
712 | } | |
713 | ylow <<= 1; | |
714 | x >>= 1; | |
715 | } | |
716 | } | |
717 | #elif defined(FLOAT) | |
718 | { | |
719 | /* Multiplying two 32 bit numbers to get a 64 bit number on | |
720 | a machine with DI, so we're safe */ | |
721 | ||
722 | DItype answer = (DItype)(a->fraction.ll) * (DItype)(b->fraction.ll); | |
723 | ||
724 | high = answer >> 32; | |
725 | low = answer; | |
726 | } | |
727 | #else | |
728 | /* Doing a 64*64 to 128 */ | |
729 | { | |
730 | UDItype nl = a->fraction.ll & 0xffffffff; | |
731 | UDItype nh = a->fraction.ll >> 32; | |
732 | UDItype ml = b->fraction.ll & 0xffffffff; | |
733 | UDItype mh = b->fraction.ll >>32; | |
734 | UDItype pp_ll = ml * nl; | |
735 | UDItype pp_hl = mh * nl; | |
736 | UDItype pp_lh = ml * nh; | |
737 | UDItype pp_hh = mh * nh; | |
738 | UDItype res2 = 0; | |
739 | UDItype res0 = 0; | |
740 | UDItype ps_hh__ = pp_hl + pp_lh; | |
741 | if (ps_hh__ < pp_hl) | |
742 | res2 += 0x100000000LL; | |
743 | pp_hl = (ps_hh__ << 32) & 0xffffffff00000000LL; | |
744 | res0 = pp_ll + pp_hl; | |
745 | if (res0 < pp_ll) | |
746 | res2++; | |
747 | res2 += ((ps_hh__ >> 32) & 0xffffffffL) + pp_hh; | |
748 | high = res2; | |
749 | low = res0; | |
750 | } | |
751 | #endif | |
752 | } | |
753 | ||
754 | tmp->normal_exp = a->normal_exp + b->normal_exp; | |
755 | tmp->sign = a->sign != b->sign; | |
756 | #ifdef FLOAT | |
757 | tmp->normal_exp += 2; /* ??????????????? */ | |
758 | #else | |
759 | tmp->normal_exp += 4; /* ??????????????? */ | |
760 | #endif | |
761 | while (high >= IMPLICIT_2) | |
762 | { | |
763 | tmp->normal_exp++; | |
764 | if (high & 1) | |
765 | { | |
766 | low >>= 1; | |
767 | low |= FRACHIGH; | |
768 | } | |
769 | high >>= 1; | |
770 | } | |
771 | while (high < IMPLICIT_1) | |
772 | { | |
773 | tmp->normal_exp--; | |
774 | ||
775 | high <<= 1; | |
776 | if (low & FRACHIGH) | |
777 | high |= 1; | |
778 | low <<= 1; | |
779 | } | |
780 | /* rounding is tricky. if we only round if it won't make us round later. */ | |
781 | #if 0 | |
782 | if (low & FRACHIGH2) | |
783 | { | |
784 | if (((high & GARDMASK) != GARDMSB) | |
785 | && (((high + 1) & GARDMASK) == GARDMSB)) | |
786 | { | |
787 | /* don't round, it gets done again later. */ | |
788 | } | |
789 | else | |
790 | { | |
791 | high++; | |
792 | } | |
793 | } | |
794 | #endif | |
795 | if ((high & GARDMASK) == GARDMSB) | |
796 | { | |
797 | if (high & (1 << NGARDS)) | |
798 | { | |
799 | /* half way, so round to even */ | |
800 | high += GARDROUND + 1; | |
801 | } | |
802 | else if (low) | |
803 | { | |
804 | /* but we really weren't half way */ | |
805 | high += GARDROUND + 1; | |
806 | } | |
807 | } | |
808 | tmp->fraction.ll = high; | |
809 | tmp->class = CLASS_NUMBER; | |
810 | return tmp; | |
811 | } | |
812 | ||
813 | FLO_type | |
814 | multiply (FLO_type arg_a, FLO_type arg_b) | |
815 | { | |
816 | fp_number_type a; | |
817 | fp_number_type b; | |
818 | fp_number_type tmp; | |
819 | fp_number_type *res; | |
820 | ||
821 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
822 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
823 | ||
824 | res = _fpmul_parts (&a, &b, &tmp); | |
825 | ||
826 | return pack_d (res); | |
827 | } | |
828 | ||
829 | static fp_number_type * | |
830 | _fpdiv_parts (fp_number_type * a, | |
831 | fp_number_type * b, | |
832 | fp_number_type * tmp) | |
833 | { | |
834 | fractype low = 0; | |
835 | fractype high = 0; | |
836 | fractype r0, r1, y0, y1, bit; | |
837 | fractype q; | |
838 | fractype numerator; | |
839 | fractype denominator; | |
840 | fractype quotient; | |
841 | fractype remainder; | |
842 | ||
843 | if (isnan (a)) | |
844 | { | |
845 | return a; | |
846 | } | |
847 | if (isnan (b)) | |
848 | { | |
849 | return b; | |
850 | } | |
851 | if (isinf (a) || iszero (a)) | |
852 | { | |
853 | if (a->class == b->class) | |
854 | return nan (); | |
855 | return a; | |
856 | } | |
857 | a->sign = a->sign ^ b->sign; | |
858 | ||
859 | if (isinf (b)) | |
860 | { | |
861 | a->fraction.ll = 0; | |
862 | a->normal_exp = 0; | |
863 | return a; | |
864 | } | |
865 | if (iszero (b)) | |
866 | { | |
867 | a->class = CLASS_INFINITY; | |
868 | return b; | |
869 | } | |
870 | ||
871 | /* Calculate the mantissa by multiplying both 64bit numbers to get a | |
872 | 128 bit number */ | |
873 | { | |
874 | int carry; | |
875 | intfrac d0, d1; /* weren't unsigned before ??? */ | |
876 | ||
877 | /* quotient = | |
878 | ( numerator / denominator) * 2^(numerator exponent - denominator exponent) | |
879 | */ | |
880 | ||
881 | a->normal_exp = a->normal_exp - b->normal_exp; | |
882 | numerator = a->fraction.ll; | |
883 | denominator = b->fraction.ll; | |
884 | ||
885 | if (numerator < denominator) | |
886 | { | |
887 | /* Fraction will be less than 1.0 */ | |
888 | numerator *= 2; | |
889 | a->normal_exp--; | |
890 | } | |
891 | bit = IMPLICIT_1; | |
892 | quotient = 0; | |
893 | /* ??? Does divide one bit at a time. Optimize. */ | |
894 | while (bit) | |
895 | { | |
896 | if (numerator >= denominator) | |
897 | { | |
898 | quotient |= bit; | |
899 | numerator -= denominator; | |
900 | } | |
901 | bit >>= 1; | |
902 | numerator *= 2; | |
903 | } | |
904 | ||
905 | if ((quotient & GARDMASK) == GARDMSB) | |
906 | { | |
907 | if (quotient & (1 << NGARDS)) | |
908 | { | |
909 | /* half way, so round to even */ | |
910 | quotient += GARDROUND + 1; | |
911 | } | |
912 | else if (numerator) | |
913 | { | |
914 | /* but we really weren't half way, more bits exist */ | |
915 | quotient += GARDROUND + 1; | |
916 | } | |
917 | } | |
918 | ||
919 | a->fraction.ll = quotient; | |
920 | return (a); | |
921 | } | |
922 | } | |
923 | ||
924 | FLO_type | |
925 | divide (FLO_type arg_a, FLO_type arg_b) | |
926 | { | |
927 | fp_number_type a; | |
928 | fp_number_type b; | |
929 | fp_number_type tmp; | |
930 | fp_number_type *res; | |
931 | ||
932 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
933 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
934 | ||
935 | res = _fpdiv_parts (&a, &b, &tmp); | |
936 | ||
937 | return pack_d (res); | |
938 | } | |
939 | ||
940 | /* according to the demo, fpcmp returns a comparison with 0... thus | |
941 | a<b -> -1 | |
942 | a==b -> 0 | |
943 | a>b -> +1 | |
944 | */ | |
945 | ||
946 | static int | |
947 | _fpcmp_parts (fp_number_type * a, fp_number_type * b) | |
948 | { | |
949 | #if 0 | |
950 | /* either nan -> unordered. Must be checked outside of this routine. */ | |
951 | if (isnan (a) && isnan (b)) | |
952 | { | |
953 | return 1; /* still unordered! */ | |
954 | } | |
955 | #endif | |
956 | ||
957 | if (isnan (a) || isnan (b)) | |
958 | { | |
959 | return 1; /* how to indicate unordered compare? */ | |
960 | } | |
961 | if (isinf (a) && isinf (b)) | |
962 | { | |
963 | /* +inf > -inf, but +inf != +inf */ | |
964 | /* b \a| +inf(0)| -inf(1) | |
965 | ______\+--------+-------- | |
966 | +inf(0)| a==b(0)| a<b(-1) | |
967 | -------+--------+-------- | |
968 | -inf(1)| a>b(1) | a==b(0) | |
969 | -------+--------+-------- | |
970 | So since unordered must be non zero, just line up the columns... | |
971 | */ | |
972 | return b->sign - a->sign; | |
973 | } | |
974 | /* but not both... */ | |
975 | if (isinf (a)) | |
976 | { | |
977 | return a->sign ? -1 : 1; | |
978 | } | |
979 | if (isinf (b)) | |
980 | { | |
981 | return b->sign ? 1 : -1; | |
982 | } | |
983 | if (iszero (a) && iszero (b)) | |
984 | { | |
985 | return 0; | |
986 | } | |
987 | if (iszero (a)) | |
988 | { | |
989 | return b->sign ? 1 : -1; | |
990 | } | |
991 | if (iszero (b)) | |
992 | { | |
993 | return a->sign ? -1 : 1; | |
994 | } | |
995 | /* now both are "normal". */ | |
996 | if (a->sign != b->sign) | |
997 | { | |
998 | /* opposite signs */ | |
999 | return a->sign ? -1 : 1; | |
1000 | } | |
1001 | /* same sign; exponents? */ | |
1002 | if (a->normal_exp > b->normal_exp) | |
1003 | { | |
1004 | return a->sign ? -1 : 1; | |
1005 | } | |
1006 | if (a->normal_exp < b->normal_exp) | |
1007 | { | |
1008 | return a->sign ? 1 : -1; | |
1009 | } | |
1010 | /* same exponents; check size. */ | |
1011 | if (a->fraction.ll > b->fraction.ll) | |
1012 | { | |
1013 | return a->sign ? -1 : 1; | |
1014 | } | |
1015 | if (a->fraction.ll < b->fraction.ll) | |
1016 | { | |
1017 | return a->sign ? 1 : -1; | |
1018 | } | |
1019 | /* after all that, they're equal. */ | |
1020 | return 0; | |
1021 | } | |
1022 | ||
1023 | CMPtype | |
1024 | compare (FLO_type arg_a, FLO_type arg_b) | |
1025 | { | |
1026 | fp_number_type a; | |
1027 | fp_number_type b; | |
1028 | ||
1029 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1030 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1031 | ||
1032 | return _fpcmp_parts (&a, &b); | |
1033 | } | |
1034 | ||
1035 | #ifndef US_SOFTWARE_GOFAST | |
1036 | ||
1037 | /* These should be optimized for their specific tasks someday. */ | |
1038 | ||
1039 | CMPtype | |
1040 | _eq_f2 (FLO_type arg_a, FLO_type arg_b) | |
1041 | { | |
1042 | fp_number_type a; | |
1043 | fp_number_type b; | |
1044 | ||
1045 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1046 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1047 | ||
1048 | if (isnan (&a) || isnan (&b)) | |
1049 | return 1; /* false, truth == 0 */ | |
1050 | ||
1051 | return _fpcmp_parts (&a, &b) ; | |
1052 | } | |
1053 | ||
1054 | CMPtype | |
1055 | _ne_f2 (FLO_type arg_a, FLO_type arg_b) | |
1056 | { | |
1057 | fp_number_type a; | |
1058 | fp_number_type b; | |
1059 | ||
1060 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1061 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1062 | ||
1063 | if (isnan (&a) || isnan (&b)) | |
1064 | return 1; /* true, truth != 0 */ | |
1065 | ||
1066 | return _fpcmp_parts (&a, &b) ; | |
1067 | } | |
1068 | ||
1069 | CMPtype | |
1070 | _gt_f2 (FLO_type arg_a, FLO_type arg_b) | |
1071 | { | |
1072 | fp_number_type a; | |
1073 | fp_number_type b; | |
1074 | ||
1075 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1076 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1077 | ||
1078 | if (isnan (&a) || isnan (&b)) | |
1079 | return -1; /* false, truth > 0 */ | |
1080 | ||
1081 | return _fpcmp_parts (&a, &b); | |
1082 | } | |
1083 | ||
1084 | CMPtype | |
1085 | _ge_f2 (FLO_type arg_a, FLO_type arg_b) | |
1086 | { | |
1087 | fp_number_type a; | |
1088 | fp_number_type b; | |
1089 | ||
1090 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1091 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1092 | ||
1093 | if (isnan (&a) || isnan (&b)) | |
1094 | return -1; /* false, truth >= 0 */ | |
1095 | return _fpcmp_parts (&a, &b) ; | |
1096 | } | |
1097 | ||
1098 | CMPtype | |
1099 | _lt_f2 (FLO_type arg_a, FLO_type arg_b) | |
1100 | { | |
1101 | fp_number_type a; | |
1102 | fp_number_type b; | |
1103 | ||
1104 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1105 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1106 | ||
1107 | if (isnan (&a) || isnan (&b)) | |
1108 | return 1; /* false, truth < 0 */ | |
1109 | ||
1110 | return _fpcmp_parts (&a, &b); | |
1111 | } | |
1112 | ||
1113 | CMPtype | |
1114 | _le_f2 (FLO_type arg_a, FLO_type arg_b) | |
1115 | { | |
1116 | fp_number_type a; | |
1117 | fp_number_type b; | |
1118 | ||
1119 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1120 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1121 | ||
1122 | if (isnan (&a) || isnan (&b)) | |
1123 | return 1; /* false, truth <= 0 */ | |
1124 | ||
1125 | return _fpcmp_parts (&a, &b) ; | |
1126 | } | |
1127 | ||
1128 | #endif /* ! US_SOFTWARE_GOFAST */ | |
1129 | ||
1130 | FLO_type | |
1131 | si_to_float (SItype arg_a) | |
1132 | { | |
1133 | fp_number_type in; | |
1134 | ||
1135 | in.class = CLASS_NUMBER; | |
1136 | in.sign = arg_a < 0; | |
1137 | if (!arg_a) | |
1138 | { | |
1139 | in.class = CLASS_ZERO; | |
1140 | } | |
1141 | else | |
1142 | { | |
1143 | in.normal_exp = FRACBITS + NGARDS; | |
1144 | if (in.sign) | |
1145 | { | |
1146 | /* Special case for minint, since there is no +ve integer | |
1147 | representation for it */ | |
1148 | if (arg_a == 0x80000000) | |
1149 | { | |
1150 | return -2147483648.0; | |
1151 | } | |
1152 | in.fraction.ll = (-arg_a); | |
1153 | } | |
1154 | else | |
1155 | in.fraction.ll = arg_a; | |
1156 | ||
1157 | while (in.fraction.ll < (1LL << (FRACBITS + NGARDS))) | |
1158 | { | |
1159 | in.fraction.ll <<= 1; | |
1160 | in.normal_exp -= 1; | |
1161 | } | |
1162 | } | |
1163 | return pack_d (&in); | |
1164 | } | |
1165 | ||
1166 | SItype | |
1167 | float_to_si (FLO_type arg_a) | |
1168 | { | |
1169 | fp_number_type a; | |
1170 | SItype tmp; | |
1171 | ||
1172 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1173 | if (iszero (&a)) | |
1174 | return 0; | |
1175 | if (isnan (&a)) | |
1176 | return 0; | |
1177 | /* get reasonable MAX_SI_INT... */ | |
1178 | if (isinf (&a)) | |
1179 | return a.sign ? MAX_SI_INT : (-MAX_SI_INT)-1; | |
1180 | /* it is a number, but a small one */ | |
1181 | if (a.normal_exp < 0) | |
1182 | return 0; | |
1183 | if (a.normal_exp > 30) | |
1184 | return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT; | |
1185 | tmp = a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp); | |
1186 | return a.sign ? (-tmp) : (tmp); | |
1187 | } | |
1188 | ||
1189 | #ifdef US_SOFTWARE_GOFAST | |
1190 | /* While libgcc2.c defines its own __fixunssfsi and __fixunsdfsi routines, | |
1191 | we also define them for GOFAST because the ones in libgcc2.c have the | |
1192 | wrong names and I'd rather define these here and keep GOFAST CYG-LOC's | |
1193 | out of libgcc2.c. We can't define these here if not GOFAST because then | |
1194 | there'd be duplicate copies. */ | |
1195 | ||
1196 | USItype | |
1197 | float_to_usi (FLO_type arg_a) | |
1198 | { | |
1199 | fp_number_type a; | |
1200 | ||
1201 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1202 | if (iszero (&a)) | |
1203 | return 0; | |
1204 | if (isnan (&a)) | |
1205 | return 0; | |
1206 | /* get reasonable MAX_USI_INT... */ | |
1207 | if (isinf (&a)) | |
1208 | return a.sign ? MAX_USI_INT : 0; | |
1209 | /* it is a negative number */ | |
1210 | if (a.sign) | |
1211 | return 0; | |
1212 | /* it is a number, but a small one */ | |
1213 | if (a.normal_exp < 0) | |
1214 | return 0; | |
1215 | if (a.normal_exp > 31) | |
1216 | return MAX_USI_INT; | |
1217 | else if (a.normal_exp > (FRACBITS + NGARDS)) | |
1218 | return a.fraction.ll << ((FRACBITS + NGARDS) - a.normal_exp); | |
1219 | else | |
1220 | return a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp); | |
1221 | } | |
1222 | #endif | |
1223 | ||
1224 | FLO_type | |
1225 | negate (FLO_type arg_a) | |
1226 | { | |
1227 | fp_number_type a; | |
1228 | ||
1229 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1230 | flip_sign (&a); | |
1231 | return pack_d (&a); | |
1232 | } | |
1233 | ||
1234 | #ifdef FLOAT | |
1235 | ||
1236 | SFtype | |
1237 | __make_fp(fp_class_type class, | |
1238 | unsigned int sign, | |
1239 | int exp, | |
1240 | USItype frac) | |
1241 | { | |
1242 | fp_number_type in; | |
1243 | ||
1244 | in.class = class; | |
1245 | in.sign = sign; | |
1246 | in.normal_exp = exp; | |
1247 | in.fraction.ll = frac; | |
1248 | return pack_d (&in); | |
1249 | } | |
1250 | ||
1251 | #ifndef FLOAT_ONLY | |
1252 | ||
1253 | /* This enables one to build an fp library that supports float but not double. | |
1254 | Otherwise, we would get an undefined reference to __make_dp. | |
1255 | This is needed for some 8-bit ports that can't handle well values that | |
1256 | are 8-bytes in size, so we just don't support double for them at all. */ | |
1257 | ||
1258 | extern DFtype __make_dp (fp_class_type, unsigned int, int, UDItype frac); | |
1259 | ||
1260 | DFtype | |
1261 | sf_to_df (SFtype arg_a) | |
1262 | { | |
1263 | fp_number_type in; | |
1264 | ||
1265 | unpack_d ((FLO_union_type *) & arg_a, &in); | |
1266 | return __make_dp (in.class, in.sign, in.normal_exp, | |
1267 | ((UDItype) in.fraction.ll) << F_D_BITOFF); | |
1268 | } | |
1269 | ||
1270 | #endif | |
1271 | #endif | |
1272 | ||
1273 | #ifndef FLOAT | |
1274 | ||
1275 | extern SFtype __make_fp (fp_class_type, unsigned int, int, USItype); | |
1276 | ||
1277 | DFtype | |
1278 | __make_dp (fp_class_type class, unsigned int sign, int exp, UDItype frac) | |
1279 | { | |
1280 | fp_number_type in; | |
1281 | ||
1282 | in.class = class; | |
1283 | in.sign = sign; | |
1284 | in.normal_exp = exp; | |
1285 | in.fraction.ll = frac; | |
1286 | return pack_d (&in); | |
1287 | } | |
1288 | ||
1289 | SFtype | |
1290 | df_to_sf (DFtype arg_a) | |
1291 | { | |
1292 | fp_number_type in; | |
1293 | ||
1294 | unpack_d ((FLO_union_type *) & arg_a, &in); | |
1295 | return __make_fp (in.class, in.sign, in.normal_exp, | |
1296 | in.fraction.ll >> F_D_BITOFF); | |
1297 | } | |
1298 | ||
1299 | #endif |