forked from gcc-mirror/gcc
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathfp-bit.c
1646 lines (1445 loc) · 36.6 KB
/
fp-bit.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/* This is a software floating point library which can be used
for targets without hardware floating point.
Copyright (C) 1994-2017 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
/* This implements IEEE 754 format arithmetic, but does not provide a
mechanism for setting the rounding mode, or for generating or handling
exceptions.
The original code by Steve Chamberlain, hacked by Mark Eichin and Jim
Wilson, all of Cygnus Support. */
/* The intended way to use this file is to make two copies, add `#define FLOAT'
to one copy, then compile both copies and add them to libgcc.a. */
#include "tconfig.h"
#include "coretypes.h"
#include "tm.h"
#include "libgcc_tm.h"
#include "fp-bit.h"
/* The following macros can be defined to change the behavior of this file:
FLOAT: Implement a `float', aka SFmode, fp library. If this is not
defined, then this file implements a `double', aka DFmode, fp library.
FLOAT_ONLY: Used with FLOAT, to implement a `float' only library, i.e.
don't include float->double conversion which requires the double library.
This is useful only for machines which can't support doubles, e.g. some
8-bit processors.
CMPtype: Specify the type that floating point compares should return.
This defaults to SItype, aka int.
_DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding
two integers to the FLO_union_type.
NO_DENORMALS: Disable handling of denormals.
NO_NANS: Disable nan and infinity handling
SMALL_MACHINE: Useful when operations on QIs and HIs are faster
than on an SI */
/* We don't currently support extended floats (long doubles) on machines
without hardware to deal with them.
These stubs are just to keep the linker from complaining about unresolved
references which can be pulled in from libio & libstdc++, even if the
user isn't using long doubles. However, they may generate an unresolved
external to abort if abort is not used by the function, and the stubs
are referenced from within libc, since libgcc goes before and after the
system library. */
#ifdef DECLARE_LIBRARY_RENAMES
DECLARE_LIBRARY_RENAMES
#endif
#ifdef EXTENDED_FLOAT_STUBS
extern void abort (void);
void __extendsfxf2 (void) { abort(); }
void __extenddfxf2 (void) { abort(); }
void __truncxfdf2 (void) { abort(); }
void __truncxfsf2 (void) { abort(); }
void __fixxfsi (void) { abort(); }
void __floatsixf (void) { abort(); }
void __addxf3 (void) { abort(); }
void __subxf3 (void) { abort(); }
void __mulxf3 (void) { abort(); }
void __divxf3 (void) { abort(); }
void __negxf2 (void) { abort(); }
void __eqxf2 (void) { abort(); }
void __nexf2 (void) { abort(); }
void __gtxf2 (void) { abort(); }
void __gexf2 (void) { abort(); }
void __lexf2 (void) { abort(); }
void __ltxf2 (void) { abort(); }
void __extendsftf2 (void) { abort(); }
void __extenddftf2 (void) { abort(); }
void __trunctfdf2 (void) { abort(); }
void __trunctfsf2 (void) { abort(); }
void __fixtfsi (void) { abort(); }
void __floatsitf (void) { abort(); }
void __addtf3 (void) { abort(); }
void __subtf3 (void) { abort(); }
void __multf3 (void) { abort(); }
void __divtf3 (void) { abort(); }
void __negtf2 (void) { abort(); }
void __eqtf2 (void) { abort(); }
void __netf2 (void) { abort(); }
void __gttf2 (void) { abort(); }
void __getf2 (void) { abort(); }
void __letf2 (void) { abort(); }
void __lttf2 (void) { abort(); }
#else /* !EXTENDED_FLOAT_STUBS, rest of file */
/* IEEE "special" number predicates */
#ifdef NO_NANS
#define nan() 0
#define isnan(x) 0
#define isinf(x) 0
#else
#if defined L_thenan_sf
const fp_number_type __thenan_sf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined L_thenan_df
const fp_number_type __thenan_df = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined L_thenan_tf
const fp_number_type __thenan_tf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined TFLOAT
extern const fp_number_type __thenan_tf;
#elif defined FLOAT
extern const fp_number_type __thenan_sf;
#else
extern const fp_number_type __thenan_df;
#endif
INLINE
static const fp_number_type *
makenan (void)
{
#ifdef TFLOAT
return & __thenan_tf;
#elif defined FLOAT
return & __thenan_sf;
#else
return & __thenan_df;
#endif
}
INLINE
static int
isnan (const fp_number_type *x)
{
return __builtin_expect (x->class == CLASS_SNAN || x->class == CLASS_QNAN,
0);
}
INLINE
static int
isinf (const fp_number_type * x)
{
return __builtin_expect (x->class == CLASS_INFINITY, 0);
}
#endif /* NO_NANS */
INLINE
static int
iszero (const fp_number_type * x)
{
return x->class == CLASS_ZERO;
}
INLINE
static void
flip_sign ( fp_number_type * x)
{
x->sign = !x->sign;
}
/* Count leading zeroes in N. */
INLINE
static int
clzusi (USItype n)
{
extern int __clzsi2 (USItype);
if (sizeof (USItype) == sizeof (unsigned int))
return __builtin_clz (n);
else if (sizeof (USItype) == sizeof (unsigned long))
return __builtin_clzl (n);
else if (sizeof (USItype) == sizeof (unsigned long long))
return __builtin_clzll (n);
else
return __clzsi2 (n);
}
extern FLO_type pack_d (const fp_number_type * );
#if defined(L_pack_df) || defined(L_pack_sf) || defined(L_pack_tf)
FLO_type
pack_d (const fp_number_type *src)
{
FLO_union_type dst;
fractype fraction = src->fraction.ll; /* wasn't unsigned before? */
int sign = src->sign;
int exp = 0;
if (isnan (src))
{
exp = EXPMAX;
/* Restore the NaN's payload. */
fraction >>= NGARDS;
fraction &= QUIET_NAN - 1;
if (src->class == CLASS_QNAN || 1)
{
#ifdef QUIET_NAN_NEGATED
/* The quiet/signaling bit remains unset. */
/* Make sure the fraction has a non-zero value. */
if (fraction == 0)
fraction |= QUIET_NAN - 1;
#else
/* Set the quiet/signaling bit. */
fraction |= QUIET_NAN;
#endif
}
}
else if (isinf (src))
{
exp = EXPMAX;
fraction = 0;
}
else if (iszero (src))
{
exp = 0;
fraction = 0;
}
else if (fraction == 0)
{
exp = 0;
}
else
{
if (__builtin_expect (src->normal_exp < NORMAL_EXPMIN, 0))
{
#ifdef NO_DENORMALS
/* Go straight to a zero representation if denormals are not
supported. The denormal handling would be harmless but
isn't unnecessary. */
exp = 0;
fraction = 0;
#else /* NO_DENORMALS */
/* This number's exponent is too low to fit into the bits
available in the number, so we'll store 0 in the exponent and
shift the fraction to the right to make up for it. */
int shift = NORMAL_EXPMIN - src->normal_exp;
exp = 0;
if (shift > FRAC_NBITS - NGARDS)
{
/* No point shifting, since it's more that 64 out. */
fraction = 0;
}
else
{
int lowbit = (fraction & (((fractype)1 << shift) - 1)) ? 1 : 0;
fraction = (fraction >> shift) | lowbit;
}
if ((fraction & GARDMASK) == GARDMSB)
{
if ((fraction & (1 << NGARDS)))
fraction += GARDROUND + 1;
}
else
{
/* Add to the guards to round up. */
fraction += GARDROUND;
}
/* Perhaps the rounding means we now need to change the
exponent, because the fraction is no longer denormal. */
if (fraction >= IMPLICIT_1)
{
exp += 1;
}
fraction >>= NGARDS;
#endif /* NO_DENORMALS */
}
else if (__builtin_expect (src->normal_exp > EXPBIAS, 0))
{
exp = EXPMAX;
fraction = 0;
}
else
{
exp = src->normal_exp + EXPBIAS;
/* IF the gard bits are the all zero, but the first, then we're
half way between two numbers, choose the one which makes the
lsb of the answer 0. */
if ((fraction & GARDMASK) == GARDMSB)
{
if (fraction & (1 << NGARDS))
fraction += GARDROUND + 1;
}
else
{
/* Add a one to the guards to round up */
fraction += GARDROUND;
}
if (fraction >= IMPLICIT_2)
{
fraction >>= 1;
exp += 1;
}
fraction >>= NGARDS;
}
}
/* We previously used bitfields to store the number, but this doesn't
handle little/big endian systems conveniently, so use shifts and
masks */
#ifdef FLOAT_BIT_ORDER_MISMATCH
dst.bits.fraction = fraction;
dst.bits.exp = exp;
dst.bits.sign = sign;
#else
# if defined TFLOAT && defined HALFFRACBITS
{
halffractype high, low, unity;
int lowsign, lowexp;
unity = (halffractype) 1 << HALFFRACBITS;
/* Set HIGH to the high double's significand, masking out the implicit 1.
Set LOW to the low double's full significand. */
high = (fraction >> (FRACBITS - HALFFRACBITS)) & (unity - 1);
low = fraction & (unity * 2 - 1);
/* Get the initial sign and exponent of the low double. */
lowexp = exp - HALFFRACBITS - 1;
lowsign = sign;
/* HIGH should be rounded like a normal double, making |LOW| <=
0.5 ULP of HIGH. Assume round-to-nearest. */
if (exp < EXPMAX)
if (low > unity || (low == unity && (high & 1) == 1))
{
/* Round HIGH up and adjust LOW to match. */
high++;
if (high == unity)
{
/* May make it infinite, but that's OK. */
high = 0;
exp++;
}
low = unity * 2 - low;
lowsign ^= 1;
}
high |= (halffractype) exp << HALFFRACBITS;
high |= (halffractype) sign << (HALFFRACBITS + EXPBITS);
if (exp == EXPMAX || exp == 0 || low == 0)
low = 0;
else
{
while (lowexp > 0 && low < unity)
{
low <<= 1;
lowexp--;
}
if (lowexp <= 0)
{
halffractype roundmsb, round;
int shift;
shift = 1 - lowexp;
roundmsb = (1 << (shift - 1));
round = low & ((roundmsb << 1) - 1);
low >>= shift;
lowexp = 0;
if (round > roundmsb || (round == roundmsb && (low & 1) == 1))
{
low++;
if (low == unity)
/* LOW rounds up to the smallest normal number. */
lowexp++;
}
}
low &= unity - 1;
low |= (halffractype) lowexp << HALFFRACBITS;
low |= (halffractype) lowsign << (HALFFRACBITS + EXPBITS);
}
dst.value_raw = ((fractype) high << HALFSHIFT) | low;
}
# else
dst.value_raw = fraction & ((((fractype)1) << FRACBITS) - (fractype)1);
dst.value_raw |= ((fractype) (exp & ((1 << EXPBITS) - 1))) << FRACBITS;
dst.value_raw |= ((fractype) (sign & 1)) << (FRACBITS | EXPBITS);
# endif
#endif
#if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
#ifdef TFLOAT
{
qrtrfractype tmp1 = dst.words[0];
qrtrfractype tmp2 = dst.words[1];
dst.words[0] = dst.words[3];
dst.words[1] = dst.words[2];
dst.words[2] = tmp2;
dst.words[3] = tmp1;
}
#else
{
halffractype tmp = dst.words[0];
dst.words[0] = dst.words[1];
dst.words[1] = tmp;
}
#endif
#endif
return dst.value;
}
#endif
#if defined(L_unpack_df) || defined(L_unpack_sf) || defined(L_unpack_tf)
void
unpack_d (FLO_union_type * src, fp_number_type * dst)
{
/* We previously used bitfields to store the number, but this doesn't
handle little/big endian systems conveniently, so use shifts and
masks */
fractype fraction;
int exp;
int sign;
#if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
FLO_union_type swapped;
#ifdef TFLOAT
swapped.words[0] = src->words[3];
swapped.words[1] = src->words[2];
swapped.words[2] = src->words[1];
swapped.words[3] = src->words[0];
#else
swapped.words[0] = src->words[1];
swapped.words[1] = src->words[0];
#endif
src = &swapped;
#endif
#ifdef FLOAT_BIT_ORDER_MISMATCH
fraction = src->bits.fraction;
exp = src->bits.exp;
sign = src->bits.sign;
#else
# if defined TFLOAT && defined HALFFRACBITS
{
halffractype high, low;
high = src->value_raw >> HALFSHIFT;
low = src->value_raw & (((fractype)1 << HALFSHIFT) - 1);
fraction = high & ((((fractype)1) << HALFFRACBITS) - 1);
fraction <<= FRACBITS - HALFFRACBITS;
exp = ((int)(high >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
sign = ((int)(high >> (((HALFFRACBITS + EXPBITS))))) & 1;
if (exp != EXPMAX && exp != 0 && low != 0)
{
int lowexp = ((int)(low >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
int lowsign = ((int)(low >> (((HALFFRACBITS + EXPBITS))))) & 1;
int shift;
fractype xlow;
xlow = low & ((((fractype)1) << HALFFRACBITS) - 1);
if (lowexp)
xlow |= (((halffractype)1) << HALFFRACBITS);
else
lowexp = 1;
shift = (FRACBITS - HALFFRACBITS) - (exp - lowexp);
if (shift > 0)
xlow <<= shift;
else if (shift < 0)
xlow >>= -shift;
if (sign == lowsign)
fraction += xlow;
else if (fraction >= xlow)
fraction -= xlow;
else
{
/* The high part is a power of two but the full number is lower.
This code will leave the implicit 1 in FRACTION, but we'd
have added that below anyway. */
fraction = (((fractype) 1 << FRACBITS) - xlow) << 1;
exp--;
}
}
}
# else
fraction = src->value_raw & ((((fractype)1) << FRACBITS) - 1);
exp = ((int)(src->value_raw >> FRACBITS)) & ((1 << EXPBITS) - 1);
sign = ((int)(src->value_raw >> (FRACBITS + EXPBITS))) & 1;
# endif
#endif
dst->sign = sign;
if (exp == 0)
{
/* Hmm. Looks like 0 */
if (fraction == 0
#ifdef NO_DENORMALS
|| 1
#endif
)
{
/* tastes like zero */
dst->class = CLASS_ZERO;
}
else
{
/* Zero exponent with nonzero fraction - it's denormalized,
so there isn't a leading implicit one - we'll shift it so
it gets one. */
dst->normal_exp = exp - EXPBIAS + 1;
fraction <<= NGARDS;
dst->class = CLASS_NUMBER;
#if 1
while (fraction < IMPLICIT_1)
{
fraction <<= 1;
dst->normal_exp--;
}
#endif
dst->fraction.ll = fraction;
}
}
else if (__builtin_expect (exp == EXPMAX, 0))
{
/* Huge exponent*/
if (fraction == 0)
{
/* Attached to a zero fraction - means infinity */
dst->class = CLASS_INFINITY;
}
else
{
/* Nonzero fraction, means nan */
#ifdef QUIET_NAN_NEGATED
if ((fraction & QUIET_NAN) == 0)
#else
if (fraction & QUIET_NAN)
#endif
{
dst->class = CLASS_QNAN;
}
else
{
dst->class = CLASS_SNAN;
}
/* Now that we know which kind of NaN we got, discard the
quiet/signaling bit, but do preserve the NaN payload. */
fraction &= ~QUIET_NAN;
dst->fraction.ll = fraction << NGARDS;
}
}
else
{
/* Nothing strange about this number */
dst->normal_exp = exp - EXPBIAS;
dst->class = CLASS_NUMBER;
dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1;
}
}
#endif /* L_unpack_df || L_unpack_sf */
#if defined(L_addsub_sf) || defined(L_addsub_df) || defined(L_addsub_tf)
static const fp_number_type *
_fpadd_parts (fp_number_type * a,
fp_number_type * b,
fp_number_type * tmp)
{
intfrac tfraction;
/* Put commonly used fields in local variables. */
int a_normal_exp;
int b_normal_exp;
fractype a_fraction;
fractype b_fraction;
if (isnan (a))
{
return a;
}
if (isnan (b))
{
return b;
}
if (isinf (a))
{
/* Adding infinities with opposite signs yields a NaN. */
if (isinf (b) && a->sign != b->sign)
return makenan ();
return a;
}
if (isinf (b))
{
return b;
}
if (iszero (b))
{
if (iszero (a))
{
*tmp = *a;
tmp->sign = a->sign & b->sign;
return tmp;
}
return a;
}
if (iszero (a))
{
return b;
}
/* Got two numbers. shift the smaller and increment the exponent till
they're the same */
{
int diff;
int sdiff;
a_normal_exp = a->normal_exp;
b_normal_exp = b->normal_exp;
a_fraction = a->fraction.ll;
b_fraction = b->fraction.ll;
diff = a_normal_exp - b_normal_exp;
sdiff = diff;
if (diff < 0)
diff = -diff;
if (diff < FRAC_NBITS)
{
if (sdiff > 0)
{
b_normal_exp += diff;
LSHIFT (b_fraction, diff);
}
else if (sdiff < 0)
{
a_normal_exp += diff;
LSHIFT (a_fraction, diff);
}
}
else
{
/* Somethings's up.. choose the biggest */
if (a_normal_exp > b_normal_exp)
{
b_normal_exp = a_normal_exp;
b_fraction = 0;
}
else
{
a_normal_exp = b_normal_exp;
a_fraction = 0;
}
}
}
if (a->sign != b->sign)
{
if (a->sign)
{
tfraction = -a_fraction + b_fraction;
}
else
{
tfraction = a_fraction - b_fraction;
}
if (tfraction >= 0)
{
tmp->sign = 0;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = tfraction;
}
else
{
tmp->sign = 1;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = -tfraction;
}
/* and renormalize it */
while (tmp->fraction.ll < IMPLICIT_1 && tmp->fraction.ll)
{
tmp->fraction.ll <<= 1;
tmp->normal_exp--;
}
}
else
{
tmp->sign = a->sign;
tmp->normal_exp = a_normal_exp;
tmp->fraction.ll = a_fraction + b_fraction;
}
tmp->class = CLASS_NUMBER;
/* Now the fraction is added, we have to shift down to renormalize the
number */
if (tmp->fraction.ll >= IMPLICIT_2)
{
LSHIFT (tmp->fraction.ll, 1);
tmp->normal_exp++;
}
return tmp;
}
FLO_type
add (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
const fp_number_type *res;
FLO_union_type au, bu;
au.value = arg_a;
bu.value = arg_b;
unpack_d (&au, &a);
unpack_d (&bu, &b);
res = _fpadd_parts (&a, &b, &tmp);
return pack_d (res);
}
FLO_type
sub (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
const fp_number_type *res;
FLO_union_type au, bu;
au.value = arg_a;
bu.value = arg_b;
unpack_d (&au, &a);
unpack_d (&bu, &b);
b.sign ^= 1;
res = _fpadd_parts (&a, &b, &tmp);
return pack_d (res);
}
#endif /* L_addsub_sf || L_addsub_df */
#if defined(L_mul_sf) || defined(L_mul_df) || defined(L_mul_tf)
static inline __attribute__ ((__always_inline__)) const fp_number_type *
_fpmul_parts ( fp_number_type * a,
fp_number_type * b,
fp_number_type * tmp)
{
fractype low = 0;
fractype high = 0;
if (isnan (a))
{
a->sign = a->sign != b->sign;
return a;
}
if (isnan (b))
{
b->sign = a->sign != b->sign;
return b;
}
if (isinf (a))
{
if (iszero (b))
return makenan ();
a->sign = a->sign != b->sign;
return a;
}
if (isinf (b))
{
if (iszero (a))
{
return makenan ();
}
b->sign = a->sign != b->sign;
return b;
}
if (iszero (a))
{
a->sign = a->sign != b->sign;
return a;
}
if (iszero (b))
{
b->sign = a->sign != b->sign;
return b;
}
/* Calculate the mantissa by multiplying both numbers to get a
twice-as-wide number. */
{
#if defined(NO_DI_MODE) || defined(TFLOAT)
{
fractype x = a->fraction.ll;
fractype ylow = b->fraction.ll;
fractype yhigh = 0;
int bit;
/* ??? This does multiplies one bit at a time. Optimize. */
for (bit = 0; bit < FRAC_NBITS; bit++)
{
int carry;
if (x & 1)
{
carry = (low += ylow) < ylow;
high += yhigh + carry;
}
yhigh <<= 1;
if (ylow & FRACHIGH)
{
yhigh |= 1;
}
ylow <<= 1;
x >>= 1;
}
}
#elif defined(FLOAT)
/* Multiplying two USIs to get a UDI, we're safe. */
{
UDItype answer = (UDItype)a->fraction.ll * (UDItype)b->fraction.ll;
high = answer >> BITS_PER_SI;
low = answer;
}
#else
/* fractype is DImode, but we need the result to be twice as wide.
Assuming a widening multiply from DImode to TImode is not
available, build one by hand. */
{
USItype nl = a->fraction.ll;
USItype nh = a->fraction.ll >> BITS_PER_SI;
USItype ml = b->fraction.ll;
USItype mh = b->fraction.ll >> BITS_PER_SI;
UDItype pp_ll = (UDItype) ml * nl;
UDItype pp_hl = (UDItype) mh * nl;
UDItype pp_lh = (UDItype) ml * nh;
UDItype pp_hh = (UDItype) mh * nh;
UDItype res2 = 0;
UDItype res0 = 0;
UDItype ps_hh__ = pp_hl + pp_lh;
if (ps_hh__ < pp_hl)
res2 += (UDItype)1 << BITS_PER_SI;
pp_hl = (UDItype)(USItype)ps_hh__ << BITS_PER_SI;
res0 = pp_ll + pp_hl;
if (res0 < pp_ll)
res2++;
res2 += (ps_hh__ >> BITS_PER_SI) + pp_hh;
high = res2;
low = res0;
}
#endif
}
tmp->normal_exp = a->normal_exp + b->normal_exp
+ FRAC_NBITS - (FRACBITS + NGARDS);
tmp->sign = a->sign != b->sign;
while (high >= IMPLICIT_2)
{
tmp->normal_exp++;
if (high & 1)
{
low >>= 1;
low |= FRACHIGH;
}
high >>= 1;
}
while (high < IMPLICIT_1)
{
tmp->normal_exp--;
high <<= 1;
if (low & FRACHIGH)
high |= 1;
low <<= 1;
}
if ((high & GARDMASK) == GARDMSB)
{
if (high & (1 << NGARDS))
{
/* Because we're half way, we would round to even by adding
GARDROUND + 1, except that's also done in the packing
function, and rounding twice will lose precision and cause
the result to be too far off. Example: 32-bit floats with
bit patterns 0xfff * 0x3f800400 ~= 0xfff (less than 0.5ulp
off), not 0x1000 (more than 0.5ulp off). */
}
else if (low)
{
/* We're a further than half way by a small amount corresponding
to the bits set in "low". Knowing that, we round here and
not in pack_d, because there we don't have "low" available
anymore. */
high += GARDROUND + 1;
/* Avoid further rounding in pack_d. */
high &= ~(fractype) GARDMASK;
}
}
tmp->fraction.ll = high;
tmp->class = CLASS_NUMBER;
return tmp;
}
FLO_type
multiply (FLO_type arg_a, FLO_type arg_b)
{
fp_number_type a;
fp_number_type b;
fp_number_type tmp;
const fp_number_type *res;
FLO_union_type au, bu;
au.value = arg_a;
bu.value = arg_b;
unpack_d (&au, &a);
unpack_d (&bu, &b);
res = _fpmul_parts (&a, &b, &tmp);
return pack_d (res);
}
#endif /* L_mul_sf || L_mul_df || L_mul_tf */
#if defined(L_div_sf) || defined(L_div_df) || defined(L_div_tf)
static inline __attribute__ ((__always_inline__)) const fp_number_type *
_fpdiv_parts (fp_number_type * a,
fp_number_type * b)
{
fractype bit;
fractype numerator;
fractype denominator;
fractype quotient;
if (isnan (a))
{
return a;
}
if (isnan (b))
{
return b;
}
a->sign = a->sign ^ b->sign;
if (isinf (a) || iszero (a))
{
if (a->class == b->class)
return makenan ();
return a;
}
if (isinf (b))
{
a->fraction.ll = 0;
a->normal_exp = 0;
return a;
}
if (iszero (b))
{
a->class = CLASS_INFINITY;
return a;
}
/* Calculate the mantissa by multiplying both 64bit numbers to get a
128 bit number */
{
/* quotient =
( numerator / denominator) * 2^(numerator exponent - denominator exponent)
*/
a->normal_exp = a->normal_exp - b->normal_exp;
numerator = a->fraction.ll;
denominator = b->fraction.ll;
if (numerator < denominator)
{
/* Fraction will be less than 1.0 */