forked from torvalds/linux
-
Notifications
You must be signed in to change notification settings - Fork 17
/
fp_util.S
1454 lines (1414 loc) · 35.5 KB
/
fp_util.S
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
/*
* fp_util.S
*
* Copyright Roman Zippel, 1997. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, and the entire permission notice in its entirety,
* including the disclaimer of warranties.
* 2. 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.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior
* written permission.
*
* ALTERNATIVELY, this product may be distributed under the terms of
* the GNU General Public License, in which case the provisions of the GPL are
* required INSTEAD OF the above restrictions. (This clause is
* necessary due to a potential bad interaction between the GPL and
* the restrictions contained in a BSD-style copyright.)
*
* THIS SOFTWARE IS PROVIDED ``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 AUTHOR 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 "fp_emu.h"
/*
* Here are lots of conversion and normalization functions mainly
* used by fp_scan.S
* Note that these functions are optimized for "normal" numbers,
* these are handled first and exit as fast as possible, this is
* especially important for fp_normalize_ext/fp_conv_ext2ext, as
* it's called very often.
* The register usage is optimized for fp_scan.S and which register
* is currently at that time unused, be careful if you want change
* something here. %d0 and %d1 is always usable, sometimes %d2 (or
* only the lower half) most function have to return the %a0
* unmodified, so that the caller can immediately reuse it.
*/
.globl fp_ill, fp_end
| exits from fp_scan:
| illegal instruction
fp_ill:
printf ,"fp_illegal\n"
rts
| completed instruction
fp_end:
tst.l (TASK_MM-8,%a2)
jmi 1f
tst.l (TASK_MM-4,%a2)
jmi 1f
tst.l (TASK_MM,%a2)
jpl 2f
1: printf ,"oops:%p,%p,%p\n",3,%a2@(TASK_MM-8),%a2@(TASK_MM-4),%a2@(TASK_MM)
2: clr.l %d0
rts
.globl fp_conv_long2ext, fp_conv_single2ext
.globl fp_conv_double2ext, fp_conv_ext2ext
.globl fp_normalize_ext, fp_normalize_double
.globl fp_normalize_single, fp_normalize_single_fast
.globl fp_conv_ext2double, fp_conv_ext2single
.globl fp_conv_ext2long, fp_conv_ext2short
.globl fp_conv_ext2byte
.globl fp_finalrounding_single, fp_finalrounding_single_fast
.globl fp_finalrounding_double
.globl fp_finalrounding, fp_finaltest, fp_final
/*
* First several conversion functions from a source operand
* into the extended format. Note, that only fp_conv_ext2ext
* normalizes the number and is always called after the other
* conversion functions, which only move the information into
* fp_ext structure.
*/
| fp_conv_long2ext:
|
| args: %d0 = source (32-bit long)
| %a0 = destination (ptr to struct fp_ext)
fp_conv_long2ext:
printf PCONV,"l2e: %p -> %p(",2,%d0,%a0
clr.l %d1 | sign defaults to zero
tst.l %d0
jeq fp_l2e_zero | is source zero?
jpl 1f | positive?
moveq #1,%d1
neg.l %d0
1: swap %d1
move.w #0x3fff+31,%d1
move.l %d1,(%a0)+ | set sign / exp
move.l %d0,(%a0)+ | set mantissa
clr.l (%a0)
subq.l #8,%a0 | restore %a0
printx PCONV,%a0@
printf PCONV,")\n"
rts
| source is zero
fp_l2e_zero:
clr.l (%a0)+
clr.l (%a0)+
clr.l (%a0)
subq.l #8,%a0
printx PCONV,%a0@
printf PCONV,")\n"
rts
| fp_conv_single2ext
| args: %d0 = source (single-precision fp value)
| %a0 = dest (struct fp_ext *)
fp_conv_single2ext:
printf PCONV,"s2e: %p -> %p(",2,%d0,%a0
move.l %d0,%d1
lsl.l #8,%d0 | shift mantissa
lsr.l #8,%d1 | exponent / sign
lsr.l #7,%d1
lsr.w #8,%d1
jeq fp_s2e_small | zero / denormal?
cmp.w #0xff,%d1 | NaN / Inf?
jeq fp_s2e_large
bset #31,%d0 | set explizit bit
add.w #0x3fff-0x7f,%d1 | re-bias the exponent.
9: move.l %d1,(%a0)+ | fp_ext.sign, fp_ext.exp
move.l %d0,(%a0)+ | high lword of fp_ext.mant
clr.l (%a0) | low lword = 0
subq.l #8,%a0
printx PCONV,%a0@
printf PCONV,")\n"
rts
| zeros and denormalized
fp_s2e_small:
| exponent is zero, so explizit bit is already zero too
tst.l %d0
jeq 9b
move.w #0x4000-0x7f,%d1
jra 9b
| infinities and NAN
fp_s2e_large:
bclr #31,%d0 | clear explizit bit
move.w #0x7fff,%d1
jra 9b
fp_conv_double2ext:
#ifdef FPU_EMU_DEBUG
getuser.l %a1@(0),%d0,fp_err_ua2,%a1
getuser.l %a1@(4),%d1,fp_err_ua2,%a1
printf PCONV,"d2e: %p%p -> %p(",3,%d0,%d1,%a0
#endif
getuser.l (%a1)+,%d0,fp_err_ua2,%a1
move.l %d0,%d1
lsl.l #8,%d0 | shift high mantissa
lsl.l #3,%d0
lsr.l #8,%d1 | exponent / sign
lsr.l #7,%d1
lsr.w #5,%d1
jeq fp_d2e_small | zero / denormal?
cmp.w #0x7ff,%d1 | NaN / Inf?
jeq fp_d2e_large
bset #31,%d0 | set explizit bit
add.w #0x3fff-0x3ff,%d1 | re-bias the exponent.
9: move.l %d1,(%a0)+ | fp_ext.sign, fp_ext.exp
move.l %d0,(%a0)+
getuser.l (%a1)+,%d0,fp_err_ua2,%a1
move.l %d0,%d1
lsl.l #8,%d0
lsl.l #3,%d0
move.l %d0,(%a0)
moveq #21,%d0
lsr.l %d0,%d1
or.l %d1,-(%a0)
subq.l #4,%a0
printx PCONV,%a0@
printf PCONV,")\n"
rts
| zeros and denormalized
fp_d2e_small:
| exponent is zero, so explizit bit is already zero too
tst.l %d0
jeq 9b
move.w #0x4000-0x3ff,%d1
jra 9b
| infinities and NAN
fp_d2e_large:
bclr #31,%d0 | clear explizit bit
move.w #0x7fff,%d1
jra 9b
| fp_conv_ext2ext:
| originally used to get longdouble from userspace, now it's
| called before arithmetic operations to make sure the number
| is normalized [maybe rename it?].
| args: %a0 = dest (struct fp_ext *)
| returns 0 in %d0 for a NaN, otherwise 1
fp_conv_ext2ext:
printf PCONV,"e2e: %p(",1,%a0
printx PCONV,%a0@
printf PCONV,"), "
move.l (%a0)+,%d0
cmp.w #0x7fff,%d0 | Inf / NaN?
jeq fp_e2e_large
move.l (%a0),%d0
jpl fp_e2e_small | zero / denorm?
| The high bit is set, so normalization is irrelevant.
fp_e2e_checkround:
subq.l #4,%a0
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
move.b (%a0),%d0
jne fp_e2e_round
#endif
printf PCONV,"%p(",1,%a0
printx PCONV,%a0@
printf PCONV,")\n"
moveq #1,%d0
rts
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
fp_e2e_round:
fp_set_sr FPSR_EXC_INEX2
clr.b (%a0)
move.w (FPD_RND,FPDATA),%d2
jne fp_e2e_roundother | %d2 == 0, round to nearest
tst.b %d0 | test guard bit
jpl 9f | zero is closer
btst #0,(11,%a0) | test lsb bit
jne fp_e2e_doroundup | round to infinity
lsl.b #1,%d0 | check low bits
jeq 9f | round to zero
fp_e2e_doroundup:
addq.l #1,(8,%a0)
jcc 9f
addq.l #1,(4,%a0)
jcc 9f
move.w #0x8000,(4,%a0)
addq.w #1,(2,%a0)
9: printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
fp_e2e_roundother:
subq.w #2,%d2
jcs 9b | %d2 < 2, round to zero
jhi 1f | %d2 > 2, round to +infinity
tst.b (1,%a0) | to -inf
jne fp_e2e_doroundup | negative, round to infinity
jra 9b | positive, round to zero
1: tst.b (1,%a0) | to +inf
jeq fp_e2e_doroundup | positive, round to infinity
jra 9b | negative, round to zero
#endif
| zeros and subnormals:
| try to normalize these anyway.
fp_e2e_small:
jne fp_e2e_small1 | high lword zero?
move.l (4,%a0),%d0
jne fp_e2e_small2
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
clr.l %d0
move.b (-4,%a0),%d0
jne fp_e2e_small3
#endif
| Genuine zero.
clr.w -(%a0)
subq.l #2,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
moveq #1,%d0
rts
| definitely subnormal, need to shift all 64 bits
fp_e2e_small1:
bfffo %d0{#0,#32},%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
1: move.w %d2,(%a0)+
move.w %d1,%d2
jeq fp_e2e_checkround
| fancy 64-bit double-shift begins here
lsl.l %d2,%d0
move.l %d0,(%a0)+
move.l (%a0),%d0
move.l %d0,%d1
lsl.l %d2,%d0
move.l %d0,(%a0)
neg.w %d2
and.w #0x1f,%d2
lsr.l %d2,%d1
or.l %d1,-(%a0)
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
fp_e2e_extra1:
clr.l %d0
move.b (-4,%a0),%d0
neg.w %d2
add.w #24,%d2
jcc 1f
clr.b (-4,%a0)
lsl.l %d2,%d0
or.l %d0,(4,%a0)
jra fp_e2e_checkround
1: addq.w #8,%d2
lsl.l %d2,%d0
move.b %d0,(-4,%a0)
lsr.l #8,%d0
or.l %d0,(4,%a0)
#endif
jra fp_e2e_checkround
| pathologically small subnormal
fp_e2e_small2:
bfffo %d0{#0,#32},%d1
add.w #32,%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Beyond pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
1: move.w %d2,(%a0)+
ext.l %d1
jeq fp_e2e_checkround
clr.l (4,%a0)
sub.w #32,%d2
jcs 1f
lsl.l %d1,%d0 | lower lword needs only to be shifted
move.l %d0,(%a0) | into the higher lword
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
clr.l %d0
move.b (-4,%a0),%d0
clr.b (-4,%a0)
neg.w %d1
add.w #32,%d1
bfins %d0,(%a0){%d1,#8}
#endif
jra fp_e2e_checkround
1: neg.w %d1 | lower lword is splitted between
bfins %d0,(%a0){%d1,#32} | higher and lower lword
#ifndef CONFIG_M68KFPU_EMU_EXTRAPREC
jra fp_e2e_checkround
#else
move.w %d1,%d2
jra fp_e2e_extra1
| These are extremely small numbers, that will mostly end up as zero
| anyway, so this is only important for correct rounding.
fp_e2e_small3:
bfffo %d0{#24,#8},%d1
add.w #40,%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
1: move.w %d2,(%a0)+
ext.l %d1
jeq fp_e2e_checkround
cmp.w #8,%d1
jcs 2f
1: clr.b (-4,%a0)
sub.w #64,%d1
jcs 1f
add.w #24,%d1
lsl.l %d1,%d0
move.l %d0,(%a0)
jra fp_e2e_checkround
1: neg.w %d1
bfins %d0,(%a0){%d1,#8}
jra fp_e2e_checkround
2: lsl.l %d1,%d0
move.b %d0,(-4,%a0)
lsr.l #8,%d0
move.b %d0,(7,%a0)
jra fp_e2e_checkround
#endif
1: move.l %d0,%d1 | lower lword is splitted between
lsl.l %d2,%d0 | higher and lower lword
move.l %d0,(%a0)
move.l %d1,%d0
neg.w %d2
add.w #32,%d2
lsr.l %d2,%d0
move.l %d0,-(%a0)
jra fp_e2e_checkround
| Infinities and NaNs
fp_e2e_large:
move.l (%a0)+,%d0
jne 3f
1: tst.l (%a0)
jne 4f
moveq #1,%d0
2: subq.l #8,%a0
printf PCONV,"%p(",1,%a0
printx PCONV,%a0@
printf PCONV,")\n"
rts
| we have maybe a NaN, shift off the highest bit
3: lsl.l #1,%d0
jeq 1b
| we have a NaN, clear the return value
4: clrl %d0
jra 2b
/*
* Normalization functions. Call these on the output of general
* FP operators, and before any conversion into the destination
* formats. fp_normalize_ext has always to be called first, the
* following conversion functions expect an already normalized
* number.
*/
| fp_normalize_ext:
| normalize an extended in extended (unpacked) format, basically
| it does the same as fp_conv_ext2ext, additionally it also does
| the necessary postprocessing checks.
| args: %a0 (struct fp_ext *)
| NOTE: it does _not_ modify %a0/%a1 and the upper word of %d2
fp_normalize_ext:
printf PNORM,"ne: %p(",1,%a0
printx PNORM,%a0@
printf PNORM,"), "
move.l (%a0)+,%d0
cmp.w #0x7fff,%d0 | Inf / NaN?
jeq fp_ne_large
move.l (%a0),%d0
jpl fp_ne_small | zero / denorm?
| The high bit is set, so normalization is irrelevant.
fp_ne_checkround:
subq.l #4,%a0
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
move.b (%a0),%d0
jne fp_ne_round
#endif
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
fp_ne_round:
fp_set_sr FPSR_EXC_INEX2
clr.b (%a0)
move.w (FPD_RND,FPDATA),%d2
jne fp_ne_roundother | %d2 == 0, round to nearest
tst.b %d0 | test guard bit
jpl 9f | zero is closer
btst #0,(11,%a0) | test lsb bit
jne fp_ne_doroundup | round to infinity
lsl.b #1,%d0 | check low bits
jeq 9f | round to zero
fp_ne_doroundup:
addq.l #1,(8,%a0)
jcc 9f
addq.l #1,(4,%a0)
jcc 9f
addq.w #1,(2,%a0)
move.w #0x8000,(4,%a0)
9: printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
fp_ne_roundother:
subq.w #2,%d2
jcs 9b | %d2 < 2, round to zero
jhi 1f | %d2 > 2, round to +infinity
tst.b (1,%a0) | to -inf
jne fp_ne_doroundup | negative, round to infinity
jra 9b | positive, round to zero
1: tst.b (1,%a0) | to +inf
jeq fp_ne_doroundup | positive, round to infinity
jra 9b | negative, round to zero
#endif
| Zeros and subnormal numbers
| These are probably merely subnormal, rather than "denormalized"
| numbers, so we will try to make them normal again.
fp_ne_small:
jne fp_ne_small1 | high lword zero?
move.l (4,%a0),%d0
jne fp_ne_small2
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
clr.l %d0
move.b (-4,%a0),%d0
jne fp_ne_small3
#endif
| Genuine zero.
clr.w -(%a0)
subq.l #2,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
| Subnormal.
fp_ne_small1:
bfffo %d0{#0,#32},%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
fp_set_sr FPSR_EXC_UNFL
1: move.w %d2,(%a0)+
move.w %d1,%d2
jeq fp_ne_checkround
| This is exactly the same 64-bit double shift as seen above.
lsl.l %d2,%d0
move.l %d0,(%a0)+
move.l (%a0),%d0
move.l %d0,%d1
lsl.l %d2,%d0
move.l %d0,(%a0)
neg.w %d2
and.w #0x1f,%d2
lsr.l %d2,%d1
or.l %d1,-(%a0)
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
fp_ne_extra1:
clr.l %d0
move.b (-4,%a0),%d0
neg.w %d2
add.w #24,%d2
jcc 1f
clr.b (-4,%a0)
lsl.l %d2,%d0
or.l %d0,(4,%a0)
jra fp_ne_checkround
1: addq.w #8,%d2
lsl.l %d2,%d0
move.b %d0,(-4,%a0)
lsr.l #8,%d0
or.l %d0,(4,%a0)
#endif
jra fp_ne_checkround
| May or may not be subnormal, if so, only 32 bits to shift.
fp_ne_small2:
bfffo %d0{#0,#32},%d1
add.w #32,%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Beyond pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
fp_set_sr FPSR_EXC_UNFL
1: move.w %d2,(%a0)+
ext.l %d1
jeq fp_ne_checkround
clr.l (4,%a0)
sub.w #32,%d1
jcs 1f
lsl.l %d1,%d0 | lower lword needs only to be shifted
move.l %d0,(%a0) | into the higher lword
#ifdef CONFIG_M68KFPU_EMU_EXTRAPREC
clr.l %d0
move.b (-4,%a0),%d0
clr.b (-4,%a0)
neg.w %d1
add.w #32,%d1
bfins %d0,(%a0){%d1,#8}
#endif
jra fp_ne_checkround
1: neg.w %d1 | lower lword is splitted between
bfins %d0,(%a0){%d1,#32} | higher and lower lword
#ifndef CONFIG_M68KFPU_EMU_EXTRAPREC
jra fp_ne_checkround
#else
move.w %d1,%d2
jra fp_ne_extra1
| These are extremely small numbers, that will mostly end up as zero
| anyway, so this is only important for correct rounding.
fp_ne_small3:
bfffo %d0{#24,#8},%d1
add.w #40,%d1
move.w -(%a0),%d2
sub.w %d1,%d2
jcc 1f
| Pathologically small, denormalize.
add.w %d2,%d1
clr.w %d2
1: move.w %d2,(%a0)+
ext.l %d1
jeq fp_ne_checkround
cmp.w #8,%d1
jcs 2f
1: clr.b (-4,%a0)
sub.w #64,%d1
jcs 1f
add.w #24,%d1
lsl.l %d1,%d0
move.l %d0,(%a0)
jra fp_ne_checkround
1: neg.w %d1
bfins %d0,(%a0){%d1,#8}
jra fp_ne_checkround
2: lsl.l %d1,%d0
move.b %d0,(-4,%a0)
lsr.l #8,%d0
move.b %d0,(7,%a0)
jra fp_ne_checkround
#endif
| Infinities and NaNs, again, same as above.
fp_ne_large:
move.l (%a0)+,%d0
jne 3f
1: tst.l (%a0)
jne 4f
2: subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
| we have maybe a NaN, shift off the highest bit
3: move.l %d0,%d1
lsl.l #1,%d1
jne 4f
clr.l (-4,%a0)
jra 1b
| we have a NaN, test if it is signaling
4: bset #30,%d0
jne 2b
fp_set_sr FPSR_EXC_SNAN
move.l %d0,(-4,%a0)
jra 2b
| these next two do rounding as per the IEEE standard.
| values for the rounding modes appear to be:
| 0: Round to nearest
| 1: Round to zero
| 2: Round to -Infinity
| 3: Round to +Infinity
| both functions expect that fp_normalize was already
| called (and extended argument is already normalized
| as far as possible), these are used if there is different
| rounding precision is selected and before converting
| into single/double
| fp_normalize_double:
| normalize an extended with double (52-bit) precision
| args: %a0 (struct fp_ext *)
fp_normalize_double:
printf PNORM,"nd: %p(",1,%a0
printx PNORM,%a0@
printf PNORM,"), "
move.l (%a0)+,%d2
tst.w %d2
jeq fp_nd_zero | zero / denormalized
cmp.w #0x7fff,%d2
jeq fp_nd_huge | NaN / infinitive.
sub.w #0x4000-0x3ff,%d2 | will the exponent fit?
jcs fp_nd_small | too small.
cmp.w #0x7fe,%d2
jcc fp_nd_large | too big.
addq.l #4,%a0
move.l (%a0),%d0 | low lword of mantissa
| now, round off the low 11 bits.
fp_nd_round:
moveq #21,%d1
lsl.l %d1,%d0 | keep 11 low bits.
jne fp_nd_checkround | Are they non-zero?
| nothing to do here
9: subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
| Be careful with the X bit! It contains the lsb
| from the shift above, it is needed for round to nearest.
fp_nd_checkround:
fp_set_sr FPSR_EXC_INEX2 | INEX2 bit
and.w #0xf800,(2,%a0) | clear bits 0-10
move.w (FPD_RND,FPDATA),%d2 | rounding mode
jne 2f | %d2 == 0, round to nearest
tst.l %d0 | test guard bit
jpl 9b | zero is closer
| here we test the X bit by adding it to %d2
clr.w %d2 | first set z bit, addx only clears it
addx.w %d2,%d2 | test lsb bit
| IEEE754-specified "round to even" behaviour. If the guard
| bit is set, then the number is odd, so rounding works like
| in grade-school arithmetic (i.e. 1.5 rounds to 2.0)
| Otherwise, an equal distance rounds towards zero, so as not
| to produce an odd number. This is strange, but it is what
| the standard says.
jne fp_nd_doroundup | round to infinity
lsl.l #1,%d0 | check low bits
jeq 9b | round to zero
fp_nd_doroundup:
| round (the mantissa, that is) towards infinity
add.l #0x800,(%a0)
jcc 9b | no overflow, good.
addq.l #1,-(%a0) | extend to high lword
jcc 1f | no overflow, good.
| Yow! we have managed to overflow the mantissa. Since this
| only happens when %d1 was 0xfffff800, it is now zero, so
| reset the high bit, and increment the exponent.
move.w #0x8000,(%a0)
addq.w #1,-(%a0)
cmp.w #0x43ff,(%a0)+ | exponent now overflown?
jeq fp_nd_large | yes, so make it infinity.
1: subq.l #4,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
2: subq.w #2,%d2
jcs 9b | %d2 < 2, round to zero
jhi 3f | %d2 > 2, round to +infinity
| Round to +Inf or -Inf. High word of %d2 contains the
| sign of the number, by the way.
swap %d2 | to -inf
tst.b %d2
jne fp_nd_doroundup | negative, round to infinity
jra 9b | positive, round to zero
3: swap %d2 | to +inf
tst.b %d2
jeq fp_nd_doroundup | positive, round to infinity
jra 9b | negative, round to zero
| Exponent underflow. Try to make a denormal, and set it to
| the smallest possible fraction if this fails.
fp_nd_small:
fp_set_sr FPSR_EXC_UNFL | set UNFL bit
move.w #0x3c01,(-2,%a0) | 2**-1022
neg.w %d2 | degree of underflow
cmp.w #32,%d2 | single or double shift?
jcc 1f
| Again, another 64-bit double shift.
move.l (%a0),%d0
move.l %d0,%d1
lsr.l %d2,%d0
move.l %d0,(%a0)+
move.l (%a0),%d0
lsr.l %d2,%d0
neg.w %d2
add.w #32,%d2
lsl.l %d2,%d1
or.l %d1,%d0
move.l (%a0),%d1
move.l %d0,(%a0)
| Check to see if we shifted off any significant bits
lsl.l %d2,%d1
jeq fp_nd_round | Nope, round.
bset #0,%d0 | Yes, so set the "sticky bit".
jra fp_nd_round | Now, round.
| Another 64-bit single shift and store
1: sub.w #32,%d2
cmp.w #32,%d2 | Do we really need to shift?
jcc 2f | No, the number is too small.
move.l (%a0),%d0
clr.l (%a0)+
move.l %d0,%d1
lsr.l %d2,%d0
neg.w %d2
add.w #32,%d2
| Again, check to see if we shifted off any significant bits.
tst.l (%a0)
jeq 1f
bset #0,%d0 | Sticky bit.
1: move.l %d0,(%a0)
lsl.l %d2,%d1
jeq fp_nd_round
bset #0,%d0
jra fp_nd_round
| Sorry, the number is just too small.
2: clr.l (%a0)+
clr.l (%a0)
moveq #1,%d0 | Smallest possible fraction,
jra fp_nd_round | round as desired.
| zero and denormalized
fp_nd_zero:
tst.l (%a0)+
jne 1f
tst.l (%a0)
jne 1f
subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts | zero. nothing to do.
| These are not merely subnormal numbers, but true denormals,
| i.e. pathologically small (exponent is 2**-16383) numbers.
| It is clearly impossible for even a normal extended number
| with that exponent to fit into double precision, so just
| write these ones off as "too darn small".
1: fp_set_sr FPSR_EXC_UNFL | Set UNFL bit
clr.l (%a0)
clr.l -(%a0)
move.w #0x3c01,-(%a0) | i.e. 2**-1022
addq.l #6,%a0
moveq #1,%d0
jra fp_nd_round | round.
| Exponent overflow. Just call it infinity.
fp_nd_large:
move.w #0x7ff,%d0
and.w (6,%a0),%d0
jeq 1f
fp_set_sr FPSR_EXC_INEX2
1: fp_set_sr FPSR_EXC_OVFL
move.w (FPD_RND,FPDATA),%d2
jne 3f | %d2 = 0 round to nearest
1: move.w #0x7fff,(-2,%a0)
clr.l (%a0)+
clr.l (%a0)
2: subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
3: subq.w #2,%d2
jcs 5f | %d2 < 2, round to zero
jhi 4f | %d2 > 2, round to +infinity
tst.b (-3,%a0) | to -inf
jne 1b
jra 5f
4: tst.b (-3,%a0) | to +inf
jeq 1b
5: move.w #0x43fe,(-2,%a0)
moveq #-1,%d0
move.l %d0,(%a0)+
move.w #0xf800,%d0
move.l %d0,(%a0)
jra 2b
| Infinities or NaNs
fp_nd_huge:
subq.l #4,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
| fp_normalize_single:
| normalize an extended with single (23-bit) precision
| args: %a0 (struct fp_ext *)
fp_normalize_single:
printf PNORM,"ns: %p(",1,%a0
printx PNORM,%a0@
printf PNORM,") "
addq.l #2,%a0
move.w (%a0)+,%d2
jeq fp_ns_zero | zero / denormalized
cmp.w #0x7fff,%d2
jeq fp_ns_huge | NaN / infinitive.
sub.w #0x4000-0x7f,%d2 | will the exponent fit?
jcs fp_ns_small | too small.
cmp.w #0xfe,%d2
jcc fp_ns_large | too big.
move.l (%a0)+,%d0 | get high lword of mantissa
fp_ns_round:
tst.l (%a0) | check the low lword
jeq 1f
| Set a sticky bit if it is non-zero. This should only
| affect the rounding in what would otherwise be equal-
| distance situations, which is what we want it to do.
bset #0,%d0
1: clr.l (%a0) | zap it from memory.
| now, round off the low 8 bits of the hi lword.
tst.b %d0 | 8 low bits.
jne fp_ns_checkround | Are they non-zero?
| nothing to do here
subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
fp_ns_checkround:
fp_set_sr FPSR_EXC_INEX2 | INEX2 bit
clr.b -(%a0) | clear low byte of high lword
subq.l #3,%a0
move.w (FPD_RND,FPDATA),%d2 | rounding mode
jne 2f | %d2 == 0, round to nearest
tst.b %d0 | test guard bit
jpl 9f | zero is closer
btst #8,%d0 | test lsb bit
| round to even behaviour, see above.
jne fp_ns_doroundup | round to infinity
lsl.b #1,%d0 | check low bits
jeq 9f | round to zero
fp_ns_doroundup:
| round (the mantissa, that is) towards infinity
add.l #0x100,(%a0)
jcc 9f | no overflow, good.
| Overflow. This means that the %d1 was 0xffffff00, so it
| is now zero. We will set the mantissa to reflect this, and
| increment the exponent (checking for overflow there too)
move.w #0x8000,(%a0)
addq.w #1,-(%a0)
cmp.w #0x407f,(%a0)+ | exponent now overflown?
jeq fp_ns_large | yes, so make it infinity.
9: subq.l #4,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
| check nondefault rounding modes
2: subq.w #2,%d2
jcs 9b | %d2 < 2, round to zero
jhi 3f | %d2 > 2, round to +infinity
tst.b (-3,%a0) | to -inf
jne fp_ns_doroundup | negative, round to infinity
jra 9b | positive, round to zero
3: tst.b (-3,%a0) | to +inf
jeq fp_ns_doroundup | positive, round to infinity
jra 9b | negative, round to zero
| Exponent underflow. Try to make a denormal, and set it to
| the smallest possible fraction if this fails.
fp_ns_small:
fp_set_sr FPSR_EXC_UNFL | set UNFL bit
move.w #0x3f81,(-2,%a0) | 2**-126
neg.w %d2 | degree of underflow
cmp.w #32,%d2 | single or double shift?
jcc 2f
| a 32-bit shift.
move.l (%a0),%d0
move.l %d0,%d1
lsr.l %d2,%d0
move.l %d0,(%a0)+
| Check to see if we shifted off any significant bits.
neg.w %d2
add.w #32,%d2
lsl.l %d2,%d1
jeq 1f
bset #0,%d0 | Sticky bit.
| Check the lower lword
1: tst.l (%a0)
jeq fp_ns_round
clr (%a0)
bset #0,%d0 | Sticky bit.
jra fp_ns_round
| Sorry, the number is just too small.
2: clr.l (%a0)+
clr.l (%a0)
moveq #1,%d0 | Smallest possible fraction,
jra fp_ns_round | round as desired.
| Exponent overflow. Just call it infinity.
fp_ns_large:
tst.b (3,%a0)
jeq 1f
fp_set_sr FPSR_EXC_INEX2
1: fp_set_sr FPSR_EXC_OVFL
move.w (FPD_RND,FPDATA),%d2
jne 3f | %d2 = 0 round to nearest
1: move.w #0x7fff,(-2,%a0)
clr.l (%a0)+
clr.l (%a0)
2: subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts
3: subq.w #2,%d2
jcs 5f | %d2 < 2, round to zero
jhi 4f | %d2 > 2, round to +infinity
tst.b (-3,%a0) | to -inf
jne 1b
jra 5f
4: tst.b (-3,%a0) | to +inf
jeq 1b
5: move.w #0x407e,(-2,%a0)
move.l #0xffffff00,(%a0)+
clr.l (%a0)
jra 2b
| zero and denormalized
fp_ns_zero:
tst.l (%a0)+
jne 1f
tst.l (%a0)
jne 1f
subq.l #8,%a0
printf PNORM,"%p(",1,%a0
printx PNORM,%a0@
printf PNORM,")\n"
rts | zero. nothing to do.
| These are not merely subnormal numbers, but true denormals,
| i.e. pathologically small (exponent is 2**-16383) numbers.
| It is clearly impossible for even a normal extended number
| with that exponent to fit into single precision, so just
| write these ones off as "too darn small".
1: fp_set_sr FPSR_EXC_UNFL | Set UNFL bit
clr.l (%a0)
clr.l -(%a0)
move.w #0x3f81,-(%a0) | i.e. 2**-126