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
|
/******************************************************************************
Copyright (c) 2007-2024, Intel Corp.
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of Intel Corporation nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
THE POSSIBILITY OF SUCH DAMAGE.
******************************************************************************/
#include <stdio.h>
/* File: dpml_ux_ops.c */
/*
** Facility:
**
** DPML
**
** Abstract:
**
** This file contains source code for the basic operations used in the
** unpacked x-float library that are independent of word size: pack,
** unpack, addsub and normalize
**
** Modification History:
**
** 1-001 Version 1. RNH 01-Sep-95
** 1-002 Made PACK and UNPACK take error information. RNH 17-Sep-95
** 1-003 Adding missing return value in UNPACK2. RNH 09-May-98
** 1-004 Modified FFS_AND_SHIFT and PACK to respect signed zeros;
** Changed the representation of the default connonical NaN
** RNH 29-Jun-07
**
*/
#include "dpml_ux.h"
/* Pick up packed constant table */
#undef INSTANTIATE_TABLE
#undef INSTANTIATE_DEFINES
#define INSTANTIATE_TABLE 1
#define INSTANTIATE_DEFINES 0
#include STR(DPML_UX_CONS_FILE_NAME)
/*
** The FFS_AND_SHIFT routine finds the most significant non-zero bit in an
** UX_FLOAT value and aligns it with the MSB of a normalized UX_FLOAT value.
** The flags argument controls the interpretation of the input argument.
** If flags is one of FFS_CVT_WORD or FFS_CVT_U_WORD, then the high fraction
** digit is assumed to be signed of unsigned word and all other fields are
** assumed to be undefined.
*/
WORD
FFS_AND_SHIFT ( UX_FLOAT * argument, U_WORD flags)
{
WORD shift, cshift, num_digits, cnt;
UX_SIGN_TYPE sign;
UX_EXPONENT_TYPE exponent;
UX_FRACTION_DIGIT_TYPE msd, lsd OTHER_DIGITS;
D_UNION u;
msd = G_UX_MSD(argument);
if (FFS_NORMALIZE == flags)
{ /* Do a quick check for a normalized argument */
exponent = G_UX_EXPONENT(argument);
if ((UX_SIGNED_FRACTION_DIGIT_TYPE) msd < 0)
return 0;
}
else
{
sign = 0;
exponent = BITS_PER_UX_FRACTION_DIGIT_TYPE;
if ((FFS_CVT_WORD == flags) &&
((UX_SIGNED_FRACTION_DIGIT_TYPE) msd < 0))
{
sign = UX_SIGN_BIT;
msd = -msd;
}
P_UX_MSD(argument, msd);
CLR_UX_LOW_FRACTION(argument);
P_UX_SIGN(argument, sign);
}
lsd = G_UX_LSD(argument);
G_UX_OTHER_DIGITS(argument);
num_digits = NUM_UX_FRACTION_DIGITS;
cnt = 0;
do {
if (msd)
goto find_shift;
DIGIT_SHIFT_FRACTION_LEFT(lsd, msd);
cnt += BITS_PER_UX_FRACTION_DIGIT_TYPE;
} while (--num_digits);
/*
** If we get here, we had a zero fraction. Set the exponent field
** accordingly, force the sign to positive and return.
*/
P_UX_EXPONENT(argument, UX_ZERO_EXPONENT);
P_UX_SIGN(argument, 0);
return cnt;
find_shift:
/* Quick check to see if its already normalized */
if ((UX_SIGNED_FRACTION_DIGIT_TYPE) msd >= 0)
{ /* The high bit is not set, see if any of the next four are set */
shift = (msd >> (BITS_PER_UX_FRACTION_DIGIT_TYPE - 6)) & 0x1e;
if (shift)
/* Figure out which bit is set by "table look-up" */
shift = ((((3 << 2*1) |
(2 << 2*2) |
(2 << 2*3) |
(1 << 2*4) |
(1 << 2*5) |
(1 << 2*6) |
(1 << 2*7) ) >> shift) & 0x3) + 1;
else
/*
** Get shift by converting to floating point and extracting the
** then exponent field. In the 64 bit case, make sure there is
** rounding on the convert.
*/
{
if (BITS_PER_UX_FRACTION_DIGIT_TYPE == 32)
u.f = (double) msd;
else
{
UX_FRACTION_DIGIT_TYPE itmp;
itmp = msd & ~0xff;
itmp = itmp ? itmp : msd;
u.f = (double) itmp;
}
shift = (BITS_PER_UX_FRACTION_DIGIT_TYPE - 1 + D_EXP_BIAS - D_NORM)
- (u.D_SIGNED_HI_WORD >> D_EXP_POS) ;
}
cshift = BITS_PER_UX_FRACTION_DIGIT_TYPE - shift;
BIT_SHIFT_FRACTION_LEFT(lsd, msd, shift, cshift);
cnt += shift;
}
P_UX_MSD(argument, msd);
P_UX_OTHER_DIGITS(argument);
P_UX_LSD(argument, lsd);
P_UX_EXPONENT(argument, exponent - cnt);
return cnt;
}
/*
** The ADDSUB routine add and/or subtracts two unpacked x-float values.
** The logic to determine the larger value is driven by the exponent fields
** only, so that it may be necessary to explicitly normalize the operands
** prior to calling ADDSUB. The flags argument allow for producing the
** sum, difference or both for signed or unsigned values
*/
#define DO_NORMALIZATION (2*NO_NORMALIZATION)
void
ADDSUB ( UX_FLOAT * x, UX_FLOAT *y, U_WORD flags, UX_FLOAT * result)
{
WORD shift, cshift, cnt, op, tmp1, tmp2;
UX_FLOAT * ux_tmp, ux_save;
UX_SIGN_TYPE sign;
UX_EXPONENT_TYPE exponent;
UX_FRACTION_DIGIT_TYPE msd, lsd, tmp_digit, carry OTHER_DIGITS;
/*
** See if we are doing an implicit addition or subtraction. This logic
** depends upon ADD = 0 and SUB = 1
*/
# if (ADD != 0) || (SUB != 1)
# error "Must have ADD = 0 and SUB = 1"
# endif
sign = G_UX_SIGN(x);
op = flags << (BITS_PER_UX_SIGN_TYPE - 1);
tmp1 = (op^sign)^G_UX_SIGN(y);
tmp2 = flags & MAGNITUDE_ONLY;
sign = tmp2 ? 0 : sign;
op = tmp2 ? op : tmp1;
op = (op >> (BITS_PER_UX_SIGN_TYPE - 1)) & 1;
/*
** Determine larger value, call it x and the smaller y. In the process
** keep track of whether or not a swap takes place so that we can get
** the correct sign of the second result on a combined operation
*/
exponent = G_UX_EXPONENT(x);
shift = exponent - G_UX_EXPONENT(y);
P_UX_SIGN(&ux_save, 0);
if (shift < 0)
{
ux_tmp = x;
x = y;
y = ux_tmp;
shift = -shift;
exponent += shift;
P_UX_SIGN(&ux_save, UX_SIGN_BIT);
sign ^= ((op == ADD) ? 0 : UX_SIGN_BIT);
}
/* Now align digits of the smaller value */
lsd = G_UX_LSD(y);
G_UX_OTHER_DIGITS(y);
msd = G_UX_MSD(y);
cnt = NUM_UX_FRACTION_DIGITS;
do {
cshift = BITS_PER_UX_FRACTION_DIGIT_TYPE - shift;
if (cshift > 0)
goto bit_shift;
DIGIT_SHIFT_FRACTION_RIGHT(lsd, msd);
shift = -cshift;
} while (--cnt);
/*
** If we get here, there was a *VERY* big alignment shift, so we
** copy the answer to the result
*/
UX_COPY(x, result);
P_UX_SIGN(result, sign);
if ((flags & 0x2))
{
result++;
UX_COPY(x, result);
P_UX_SIGN(result, sign ^ G_UX_SIGN(&ux_save));
}
return;
bit_shift:
if (shift)
BIT_SHIFT_FRACTION_RIGHT(lsd, msd, shift, cshift);
/*
** Save shifted value in case we are dealing with an ADD_SUB op
*/
P_UX_MSD(&ux_save, msd);
P_UX_LSD(&ux_save, lsd);
P_UX_OTHER_DIGITS(&ux_save);
/*
** Now do the operation. The purpose of the do-loop is to ease processing
** of the ADD_SUB and SUB_ADD cases.
*/
do {
tmp_digit = G_UX_LSD(x);
if (op == ADD)
{
/*
** Addition code. Turn off normalization
*/
flags &= (DO_NORMALIZATION - 1);
lsd += tmp_digit;
carry = (lsd < tmp_digit);
# if NUM_UX_FRACTION_DIGITS == 4
tmp_digit = G_UX_FRACTION_DIGIT(x, 2);
_F2 += + carry;
carry = (_F2 < carry);
_F2 += tmp_digit;
carry += (_F2 < tmp_digit);
tmp_digit = G_UX_FRACTION_DIGIT(x, 1);
_F1 += carry;
carry = (_F1 < carry);
_F1 += tmp_digit;
carry += (_F1 < tmp_digit);
# endif
tmp_digit = G_UX_MSD(x);
msd += carry;
carry = (msd < carry);
msd += tmp_digit;
carry += (msd < tmp_digit);
/* If carry is set, we need to normalizes fraction field */
if (carry)
{
BIT_SHIFT_FRACTION_RIGHT(lsd, msd, 1,
BITS_PER_UX_FRACTION_DIGIT_TYPE - 1);
msd |= UX_MSB;
exponent++;
}
}
else
{
/*
** Subtraction code. Set normalization flag
*/
flags -= NO_NORMALIZATION;
carry = (lsd > tmp_digit);
lsd = tmp_digit - lsd;
# if NUM_UX_FRACTION_DIGITS == 4
tmp_digit = G_UX_FRACTION_DIGIT(x, 2);
_F2 += carry;
carry = (_F2 < carry);
_F2 = tmp_digit - _F2;
carry += (tmp_digit < _F2);
tmp_digit = G_UX_FRACTION_DIGIT(x, 1);
_F1 += carry;
carry = (_F1 < carry);
_F1 = tmp_digit - _F1;
carry += (tmp_digit < _F1);
# endif
tmp_digit = G_UX_MSD(x);
msd += carry;
carry = (msd < carry);
msd = tmp_digit - msd;
carry += (tmp_digit < msd);
/*
** If carry is set, we guessed wrong about which was larger so
** negate the result
*/
if (carry)
{
sign ^= UX_SIGN_BIT;
P_UX_SIGN(&ux_save, UX_SIGN_BIT);
lsd = -lsd;
carry = (lsd == 0) ? 0 : -1;
# if NUM_UX_FRACTION_DIGITS == 4
_F2 = carry - F2;
carry = (_F2 == 0) ? carry : -1;
_F3 = carry - F3;
carry = (_F3 == 0) ? carry : -1;
# endif
msd = carry - msd;
}
}
P_UX_MSD(result, msd);
P_UX_LSD(result, lsd);
P_UX_OTHER_DIGITS(result);
P_UX_EXPONENT(result, exponent);
P_UX_SIGN(result, sign);
if (flags & DO_NORMALIZATION)
NORMALIZE(result);
if (0 == (flags & 0x2))
/* Single op. Quit now */
break;
/* This is a dual op. Do the second part */
op = 1 - op;
flags ^= 0x2;
result ++;
msd = G_UX_MSD(&ux_save);
lsd = G_UX_LSD(&ux_save);
G_UX_OTHER_DIGITS(&ux_save);
sign ^= G_UX_SIGN(&ux_save);
exponent = G_UX_EXPONENT(x);
} while (1);
}
/*
** UNPACK_X_OR_Y unpacks one of two x-float arguments and handles any
** special FP classes based on the class_to_action_map. If the second
** argument, y, is non-zero, it is unpacked, otherwise the first argument is
** unpacked.
*/
#define SHIFT F_EXP_WIDTH
#define CSHIFT (BITS_PER_UX_FRACTION_DIGIT_TYPE - F_EXP_WIDTH)
/*
** The following macro changes/definitions are required to get the standard
** exception dispatcher interface macros to work
*/
#undef F_TYPE
#define F_TYPE _X_FLOAT
#undef P_EXCPTN_VALUE_x
#define P_EXCPTN_VALUE_x(x,v) x.ld = *((F_TYPE *) v)
#define TYPE_MASK MAKE_MASK(TYPE_WIDTH-1, TYPE_POS)
#undef ADD_ERR_CODE_TYPE
#define ADD_ERR_CODE_TYPE(e) (((F_TYPE_ENUM << TYPE_POS) & TYPE_MASK) \
| ((e) & (~TYPE_MASK)))
WORD
UNPACK_X_OR_Y(
_X_FLOAT * packed_x,
_X_FLOAT * packed_y,
UX_FLOAT * unpacked_argument,
U_WORD const * class_to_action_map,
_X_FLOAT * packed_result
OPT_EXCEPTION_INFO_DECLARATION)
{
WORD fp_class, sign, action, disp, index, action_index, map_element,
shift, index_limit;
UX_FRACTION_DIGIT_TYPE exponent_digit, cur_digit, next_digit, inf_nan,
zero_denorm, fract_bits, * digit_ptr;
UX_EXPONENT_TYPE exponent;
_X_FLOAT * packed_value, * packed_argument, *tmp_ptr;
EXCEPTION_RECORD_DECLARATION
# if (BITS_PER_WORD == 32)
WORD tmp;
# endif
/*
** Start unpacking the argument by fetching the exponent word and
** decomposing it into its sign, exponent and high fraction bit components
*/
index_limit = (packed_y != 0);
packed_argument = index_limit ? packed_y : packed_x;
IF_OPTNL_ERROR_INFO( EXCPTN_INFO->args[index_limit] = packed_argument);
exponent_digit = G_X_DIGIT( packed_argument, 0);
cur_digit = UX_MSB;
P_UX_SIGN(unpacked_argument, (exponent_digit & cur_digit) >>
(BITS_PER_UX_FRACTION_DIGIT_TYPE - BITS_PER_UX_SIGN_TYPE));
P_UX_EXPONENT(unpacked_argument,
((exponent_digit >> F_EXP_POS) & MAKE_MASK( F_EXP_WIDTH, 0))
- F_EXP_BIAS + 1);
cur_digit |= (exponent_digit << SHIFT);
/*
** Now get the remaining fraction bits, align them, and put them into
** the unpacked argument. While we're fetching the fraction bits, generate
** the logical 'or' of all of them to be used for the classification
** logic later on.
*/
next_digit = G_X_DIGIT( packed_argument, 1);
fract_bits = cur_digit + cur_digit;
cur_digit |= (next_digit >> CSHIFT);
P_UX_MSD( unpacked_argument, cur_digit);
cur_digit = next_digit << SHIFT;
fract_bits |= next_digit;
# if (BITS_PER_WORD == 32)
next_digit = G_X_DIGIT( packed_argument, 2);
cur_digit |= (next_digit >> CSHIFT);
P_UX_FRACTION_DIGIT( unpacked_argument, 1, cur_digit);
cur_digit = next_digit << SHIFT;
fract_bits |= next_digit;
next_digit = G_X_DIGIT( packed_argument, 3);
cur_digit |= (next_digit >> CSHIFT);
P_UX_FRACTION_DIGIT( unpacked_argument, 2, cur_digit);
cur_digit = next_digit << SHIFT;
fract_bits |= next_digit;
# endif
P_UX_LSD( unpacked_argument, cur_digit);
/*
** We've unpacked the argument, now start the classification process
*/
zero_denorm = exponent_digit - F_HIDDEN_BIT_MASK;
inf_nan = exponent_digit + F_HIDDEN_BIT_MASK;
sign = exponent_digit >> F_SIGN_BIT_POS;
fp_class = F_C_POS_NORM;
if ((WORD) (inf_nan ^ zero_denorm) < 0 )
{ /* Input argument is +/-0, +/-denorm, +/- Infinity, [SQ]NaN */
if ((WORD) (zero_denorm ^ exponent_digit) < 0)
{ /* argument was +/- zero or +/- denorm */
if (!fract_bits)
fp_class = F_C_POS_ZERO;
else
{ /* denorm, undo hidden bit, adjust exponent and normalize */
P_UX_MSD(unpacked_argument,
G_UX_MSD(unpacked_argument) - UX_MSB);
UX_INCR_EXPONENT(unpacked_argument, 1);
NORMALIZE(unpacked_argument);
fp_class = F_C_POS_DENORM;
}
}
else
{ /* argument was +/- Inf or [SQ]NaN */
if (!fract_bits)
fp_class = F_C_POS_INF;
else
{ /* NaN */
fp_class = F_C_SIG_NAN;
sign = exponent_digit >> (F_EXP_POS - 1) & 1;
}
}
}
fp_class += sign;
IF_OPTNL_ERROR_INFO( EXCPTN_INFO->arg_classes = (1 << fp_class));
/* Now get the class to action mapping index and action */
shift = fp_class*(INDEX_WIDTH + ACTION_WIDTH);
# if (BITS_PER_WORD == 64)
map_element = class_to_action_map[0];
action_index = map_element >> shift;
disp = map_element >> 60;
# else
map_element = class_to_action_map[0];
tmp = class_to_action_map[1];
if (fp_class < F_C_NEG_NORM)
action_index = map_element >> shift;
else
action_index = map_element >>
(shift - F_C_NEG_NORM*(INDEX_WIDTH + ACTION_WIDTH));
disp = ((map_element >> 31) & 0x6) |
((tmp >> 29) & 0x18);
# endif
index = action_index & INDEX_MASK;
action = (action_index >> ACTION_POS) & INDEX_MASK;
/* Leave now if all we have to do is unpack the argument */
if (action == RETURN_UNPACKED)
return fp_class;
//printf("UNPACK %llx, %llx\n", (long long)fp_class, index);
/*
** If index is not 0 or 1, then the base return value is in the class to
** action mapping table. Otherwise, the base value is the input argument
** or the auxiliary argument.
*/
if (index <= index_limit)
{
digit_ptr = (UX_FRACTION_DIGIT_TYPE *) (index == 0 ?
packed_x : packed_y);
}
else
{
index = WORDS_PER_CLASS_TO_ACTION_MAP*(disp & 0xf) + index - 1;
index = class_to_action_map[ index ];
digit_ptr = (UX_FRACTION_DIGIT_TYPE *)
& ((_X_FLOAT *) PACKED_CONSTANT_TABLE)[index];
//printf("UNPACK 3 %llx, %llx d= %llx, %llx\n", (long long)fp_class, index, digit_ptr[0],digit_ptr[1]);
}
/*
** If this is an error action, process the exception and get the final
** return value from the exception handler. Otherwise, manipulate
** the base value to get the final return value.
*/
if (action == RETURN_ERROR)
{
index = ADD_ERR_CODE_TYPE(index);
GET_EXCEPTION_RESULT_2(index, packed_x, packed_y, *packed_result);
}
else
{
exponent_digit = G_X_DIGIT(digit_ptr, MSD_NUM);
switch (action)
{
case RETURN_QUIET_NAN:
// exponent_digit &= (~SET_BIT(F_EXP_POS - 1));
exponent_digit |= (SET_BIT(F_EXP_POS - 1));
break;
case RETURN_NEGATIVE:
exponent_digit ^= (F_SIGN_BIT_MASK);
break;
case RETURN_ABSOLUTE:
exponent_digit &= (~F_SIGN_BIT_MASK);
break;
case RETURN_CPYSN_ARG_0:
exponent_digit = (exponent_digit & (~F_SIGN_BIT_MASK)) |
(G_X_DIGIT(packed_x, MSD_NUM) & F_SIGN_BIT_MASK);
break;
case RETURN_VALUE:
default:
break;
}
/* Copy the final result to the packed result and return */
P_X_DIGIT(packed_result, MSD_NUM, exponent_digit);
# if BITS_PER_WORD == 32
P_X_DIGIT(packed_result, 1, G_X_DIGIT(digit_ptr, 1));
P_X_DIGIT(packed_result, 2, G_X_DIGIT(digit_ptr, 2));
# endif
P_X_DIGIT(packed_result, LSD_NUM, G_X_DIGIT(digit_ptr, LSD_NUM));
}
return fp_class | ((U_WORD) 1 << (BITS_PER_WORD - 1));
}
/*
** UNPACK2 is an interface layer that deals with processing the input
** arguments for 2 argument functions. Basicly, this routine call
** UNPACK_X_OR_Y twice and processes the more complicated class_to_action
** mappings associated with two argument functions.
*/
WORD
UNPACK2(
_X_FLOAT * packed_x,
_X_FLOAT * packed_y,
UX_FLOAT * unpacked_x,
UX_FLOAT * unpacked_y,
U_WORD const * class_to_action_map,
_X_FLOAT * packed_result
OPT_EXCEPTION_INFO_DECLARATION)
{
WORD fp_class_x, fp_class_y, disp, shift;
IF_OPTNL_ERROR_INFO( U_WORD arg_classes; )
fp_class_x = UNPACK(
packed_x,
unpacked_x,
class_to_action_map,
packed_result
OPT_EXCEPTION_INFO_ARGUMENT );
if (0 > fp_class_x)
return fp_class_x;
/*
** Check for NULL second argument. This allows for UNPACK2 to
** process single arguments if it has to
*/
if ( ! packed_y )
return fp_class_x;
shift = F_C_CLASS_BIT_WIDTH*fp_class_x;
# if (BITS_PER_WORD == 64)
disp = (U_WORD) class_to_action_map[1];
# else
if (fp_class_x < (BITS_PER_WORD/F_C_CLASS_BIT_WIDTH))
disp = (U_WORD) class_to_action_map[2];
else
{
disp = (U_WORD) class_to_action_map[3];
shift -= (BITS_PER_WORD/F_C_CLASS_BIT_WIDTH);
}
# endif
disp = (disp >> (shift - 3)) & MAKE_MASK(F_C_CLASS_BIT_WIDTH, 3);
IF_OPTNL_ERROR_INFO( arg_classes = EXCPTN_INFO->arg_classes );
fp_class_y = UNPACK_X_OR_Y(
packed_x,
packed_y,
unpacked_y,
(U_WORD *) ((char *) class_to_action_map + disp),
packed_result
OPT_EXCEPTION_INFO_ARGUMENT);
IF_OPTNL_ERROR_INFO( EXCPTN_INFO->arg_classes |= arg_classes );
return fp_class_y | (fp_class_x << F_C_CLASS_BIT_WIDTH);
}
/*
** The PACK routine converts unpacked x-float arguments to packed and deals
** with any overflow, underflow or denorm conditions that might result.
*/
void
PACK (
UX_FLOAT * unpacked_result,
_X_FLOAT * packed_result,
U_WORD underflow_error,
U_WORD overflow_error
OPT_EXCEPTION_INFO_DECLARATION )
{
WORD shift, error_code;
UX_FLOAT tmp;
_X_FLOAT * x_ptr;
UX_EXPONENT_TYPE exponent;
UX_FRACTION_DIGIT_TYPE incr, tmp_digit, next_digit, current_digit,
* error_val_ptr;
EXCEPTION_RECORD_DECLARATION
/*
** Start by "normalizing" any denormal results. Also screen out any
** (encoded) zeros, since they screw up the rest of the logic
*/
NORMALIZE(unpacked_result);
exponent = G_UX_EXPONENT(unpacked_result);
if (exponent == UX_ZERO_EXPONENT)
{
next_digit = G_UX_SIGN(unpacked_result);
# if (NUM_UX_DIGITS == 4)
packed_result->digit[2] = 0;
packed_result->digit[3] = 0;
# else
next_digit <<= UX_SIGN_SHIFT;
# endif
//packed_result->digit[1] = 0;
// packed_result->digit[0] = 0;
P_X_DIGIT(packed_result, LSD_NUM, 0);
P_X_DIGIT(packed_result, 0, next_digit);
return;
}
shift = (F_MIN_BIN_EXP + 1) - exponent;
if (shift > 0)
{
SET_UX_FRACTION_TO_HALF(&tmp);
P_UX_EXPONENT(&tmp, exponent + shift);
P_UX_SIGN(&tmp, G_UX_SIGN(unpacked_result));
ADDSUB(&tmp, unpacked_result, ADD, unpacked_result);
/*
** We need to distinguish between zero, denoms and underflow here.
** In all cases, the fraction field will be correct. However, we
** need to adjust the exponent value to get the right exponent field.
*/
exponent = 1-F_EXP_BIAS;
if ((shift > F_PRECISION) &&
(shift != -(UX_ZERO_EXPONENT - F_MIN_BIN_EXP - 1)))
/* Force underflow */
exponent--;
}
/* Now round result and shift right */
incr = (UX_FRACTION_DIGIT_TYPE) 1 << (F_EXP_WIDTH - 1);
tmp_digit = G_UX_LSD(unpacked_result);
current_digit = tmp_digit + incr;
incr = (current_digit < incr);
current_digit >>= SHIFT;
tmp_digit = G_UX_2nd_LSD(unpacked_result);
next_digit = tmp_digit + incr;
incr = (next_digit < incr);
current_digit |= (next_digit << CSHIFT);
P_X_DIGIT(packed_result, LSD_NUM, current_digit);
current_digit = (next_digit >> SHIFT);
# if (NUM_UX_DIGITS == 4)
tmp_digit = G_UX_FRACTION_DIGIT(unpacked_result, 1);
next_digit = tmp_digit + incr;
incr = (next_digit < incr);
current_digit |= (next_digit << CSHIFT);
P_X_DIGIT(packed_result, 2, current_digit);
current_digit = (next_digit >> SHIFT);
tmp_digit = G_UX_FRACTION_DIGIT(unpacked_result, 0);
next_digit = tmp_digit + incr;
incr = (next_digit < incr);
current_digit |= (next_digit << CSHIFT);
P_X_DIGIT(packed_result, 1, current_digit);
current_digit = (next_digit >> SHIFT);
# endif
/*
** At this point, all of the fraction bits except the most significant
** have been written to the destination. Current_digit holds the most
** significant fraction (correctly aligned) and incr = 1 iff the rounded
** fraction is 1.
*/
if (incr)
{
exponent++;
current_digit = (UX_MSB >> SHIFT);
}
/* Finish packing and check for overflow and underflow */
/*
** Pack sign and exponent. Be careful to convert to UX_FRACTION_DIGIT_TYPE
** first. Adjust exponent to reflect hidden bit in fraction field
*/
tmp_digit = exponent + ((F_EXP_BIAS - 1) - 1);
current_digit += (tmp_digit << (CSHIFT - 1));
next_digit = G_UX_SIGN(unpacked_result);
current_digit |= (next_digit << UX_SIGN_SHIFT);
P_X_DIGIT(packed_result, 0, current_digit);
/* If no overflow or underflow, we're done */
if ( tmp_digit < (MAKE_MASK(F_EXP_WIDTH, 0) - 1) )
/* OK, no overflow or underflow. */
return;
/* Check for denorm and overflow/underflow processing */
if ( ++tmp_digit == 0 )
{
# define IEEE_SPECIAL_ENCODING_MASK ( (1 << F_C_QUIET_NAN) \
| (1 << F_C_SIG_NAN) \
| (1 << F_C_POS_INF) \
| (1 << F_C_NEG_INF) \
| (1 << F_C_POS_DENORM) \
| (1 << F_C_NEG_DENORM) )
# define INPUT_WAS_IEEE_SPECIAL_ENCODING \
((EXCPTN_INFO->arg_classes & IEEE_SPECIAL_ENCODING_MASK) != 0)
if (
IF_OPTNL_ERROR_INFO( INPUT_WAS_IEEE_SPECIAL_ENCODING || )
PROCESS_DENORMS )
return;
}
error_code = (exponent < 0) ? underflow_error : overflow_error;
error_code = ADD_ERR_CODE_TYPE(error_code);
GET_EXCEPTION_RESULT_2(error_code, packed_x, packed_y, *packed_result);
}
/*
** For very ill behaved polynomial evaluations, we introduce a "packed" form
** of the coefficients to be used by a less efficient evaluation routine
** that unpacks the coefficients and evaluates the polynomial via Horner's
** scheme by calling the add/sub and multiply routines.
**
** The special format used looks like:
**
** |<----------------------- 128 bits -------------------->|
** +---------------------------------------------------+---+-+
** | Normalized Fraction | K |s|
** +---------------------------------------------------+---+-+
** -->| w |<--
**
** where K is a biased scale field of w-bits and s is the sign bit. The
** width of the biased scale factor, w, and the actual bias depends on the
** coefficients. In general it is 4 bits or less.
**
** In a Horner's scheme evaluation of degree n, involving the coefficients
** c(k) and an argument x, the basic iteration (ignoring the signs) is of
** the form:
**
** T(n) <-- c(n)
** T(k) <-- c(k) + x*T(k+1) for k = n-1, n-2, ..., 1, 0
**
** If we consider the binary exponent and fraction fields of the c(k)'s
** separately we can write c[k] = 2^e(k)*f(k), where 1/2 <= f(k) < 1. We
** now define the k-th scale factor s(k) as
**
** s(0) = e(0)
** s(k) = e(k-1) - e(k) for k = 1, 2, ..., n
**
** Then consider the recursion:
**
** t(n) <-- 2^s(n)*f(n)
** t(k) <-- 2^s(k)*[f(k) + x*t(k+1)] for k = n-1, n-2, ..., 1, 0
**
** It can be shown by induction that t(k) = T(k)/2^e(k) for k >= 1 and that
** t(0) = T(0).
*/
#if NUM_UX_FRACTION_DIGITS == 2
# define COPY_MIDDLE_DIGITS(coef, ux)
#else
# define COPY_MIDDLE_DIGITS(coef, ux) \
P_UX_FRACTION_DIGIT(ux, 2, coef->digits[1]); \
P_UX_FRACTION_DIGIT(ux, 1, coef->digits[2])
#endif
#define UNPACK_COEF_TO_UX(coef, ux, mask, bias, scale, op) \
{ \
UX_FRACTION_DIGIT_TYPE lsd; \
\
P_UX_FRACTION_DIGIT(ux, 0, coef->digits[LSD_NUM]); \
COPY_MIDDLE_DIGITS(coef, ux); \
lsd = coef->digits[0]; \
P_UX_FRACTION_DIGIT(ux, LSD_NUM, lsd & ~mask); \
op = lsd & 1; \
scale = (((lsd >> 1) & mask) - bias); \
}
void
EVALUATE_PACKED_POLY( UX_FLOAT * argument, WORD degree, FIXED_128 * coefs,
U_WORD mask, WORD bias, UX_FLOAT * result)
{
WORD op;
UX_EXPONENT_TYPE scale;
UX_FLOAT tmp;
P_UX_SIGN(&tmp, 0);
P_UX_EXPONENT(&tmp, 0);
UNPACK_COEF_TO_UX(coefs, result, mask, bias, scale, op);
P_UX_SIGN(result, (op == ADD) ? 0 : UX_SIGN_BIT );
P_UX_EXPONENT(result, scale);
while (--degree >= 0)
{
MULTIPLY(argument, result, result);
NORMALIZE(result);
coefs++;
UNPACK_COEF_TO_UX(coefs, &tmp, mask, bias, scale, op);
ADDSUB(result, &tmp, op, result);
UX_INCR_EXPONENT(result, scale);
}
}
#if !defined GROUP
double D_GROUP_NAME( double x ) { return x; }
#endif
|
