Repository navigation
Expand file tree
/
Copy pathmath3.asm
More file actions
1379 lines (1193 loc) · 29.5 KB
/
Copy pathmath3.asm
File metadata and controls
1379 lines (1193 loc) · 29.5 KB
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
keep obj/math3
mcopy math3.macros
case on
****************************************************************
*
* Math3 - additional math routines from C23
*
* This code implements <math.h> functions added in C23.
*
****************************************************************
math3 private dummy segment
copy equates.asm
end
INVALID gequ $0001 exceptions
UNDERFLOW gequ $0002
OVERFLOW gequ $0004
DIVBYZERO gequ $0008
INEXACT gequ $0010
TONEAREST gequ 0 rounding directions
UPWARD gequ 1
DOWNWARD gequ 2
TOWARDZERO gequ 3
EXTENDED_PRECISION gequ 0 rounding precisions
DOUBLE_PRECISION gequ 1
SINGLE_PRECISION gequ 2
FADDX_OPWORD gequ $0000 opwords for certain SANE operations
FSUBX_OPWORD gequ $0002
FMULX_OPWORD gequ $0004
FDIVX_OPWORD gequ $0006
****************************************************************
*
* MathCommon3 - common work areas for the math library
*
****************************************************************
*
MathCommon3 privdata
;
; constant
;
pi dc h'35C2 6821 A2DA 0FC9 0040'
;
; temporary work space/return value
;
t1 ds 10
end
****************************************************************
*
* int __iscanonicall(long double x);
*
* Returns nonzero iff x has a canonical representation.
*
* This treats denormalized numbers or zeros that do not have
* the minimum exponent as non-canonical.
*
****************************************************************
*
__iscanonicall start
result equ 1 result value
csubroutine (10:x),2
stz result assume non-canonical
lda x+8 if e field is 0 or 32767 then
asl a
beq canonic x is canonical
cmp #32767*2
beq canonic
lda x+6 if i field is 1 then
bpl ret x is canonical
canonic inc result
ret creturn 2:result
end
****************************************************************
*
* int __iseqsig(long double x, long double y);
*
* Returns 1 if x==y, or 0 otherwise.
* Signals "invalid" if x or y is a NaN.
*
****************************************************************
*
__iseqsig start
jml ~EQUE
end
****************************************************************
*
* double acospi(double x);
*
* Computes acos(x)/pi.
*
****************************************************************
*
acospi start
acospif entry
acospil entry
using MathCommon3
csubroutine (10:x),0
pei (x+8) compute acos(x)
pei (x+6)
pei (x+4)
pei (x+2)
pei (x)
jsl acos
sta x
stx x+2
ldy #8 copy result to t1
lda [x],y
sta >t1+8
dey
dey
lda [x],y
sta >t1+6
dey
dey
lda [x],y
sta >t1+4
dey
dey
lda [x],y
sta >t1+2
lda [x]
sta >t1
ph4 #pi divide by pi
ph4 #t1
FDIVX
creturn 10:t1 return t1
end
****************************************************************
*
* double asinpi(double x);
*
* Computes asin(x)/pi.
*
****************************************************************
*
asinpi start
asinpif entry
asinpil entry
using MathCommon3
csubroutine (10:x),0
pei (x+8) compute asin(x)
pei (x+6)
pei (x+4)
pei (x+2)
pei (x)
jsl asin
sta x
stx x+2
ldy #8 copy result to t1
lda [x],y
sta >t1+8
dey
dey
lda [x],y
sta >t1+6
dey
dey
lda [x],y
sta >t1+4
dey
dey
lda [x],y
sta >t1+2
lda [x]
sta >t1
ph4 #pi divide by pi
ph4 #t1
FDIVX
creturn 10:t1 return t1
end
****************************************************************
*
* double atan2pi(double y, double x);
*
* Computes atan2(y,x)/pi.
*
****************************************************************
*
atan2pi start
atan2pif entry
atan2pil entry
using MathCommon3
csubroutine (10:y,10:x),0
pei (x+8) compute atan2(y,x)
pei (x+6)
pei (x+4)
pei (x+2)
pei (x)
pei (y+8)
pei (y+6)
pei (y+4)
pei (y+2)
pei (y)
jsl atan2
sta x
stx x+2
ldy #8 copy result to t1
lda [x],y
sta >t1+8
dey
dey
lda [x],y
sta >t1+6
dey
dey
lda [x],y
sta >t1+4
dey
dey
lda [x],y
sta >t1+2
lda [x]
sta >t1
ph4 #pi divide by pi
ph4 #t1
FDIVX
creturn 10:t1 return t1
end
****************************************************************
*
* atanpi - return arctan(x)/pi
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
atanpi start
atanpif entry
atanpil entry
using MathCommon3
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
phy
phx
ph4 #t1 compute the arc tangent
FATANX
ph4 #pi divide by pi
ph4 #t1
FDIVX
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* int canonicalize(double *cx, const double *x);
*
* Stores a canonical version of *x in *cx.
* Returns 0 to indicate success.
*
****************************************************************
*
canonicalize start
using MathCommon3
csubroutine (4:cx,4:x),0
ph4 <x
ph4 #t1
FD2X
ph4 #t1
ph4 <cx
FX2D
stz cx
creturn 2:cx
end
****************************************************************
*
* int canonicalizef(float *cx, const float *x);
*
* Stores a canonical version of *x in *cx.
* Returns 0 to indicate success.
*
****************************************************************
*
canonicalizef start
using MathCommon3
csubroutine (4:cx,4:x),0
ph4 <x
ph4 #t1
FS2X
ph4 #t1
ph4 <cx
FX2S
stz cx
creturn 2:cx
end
****************************************************************
*
* int canonicalizel(long double *cx, const long double *x);
*
* Stores a canonical version of *x in *cx.
* Returns 0 to indicate success.
*
****************************************************************
*
canonicalizel start
csubroutine (4:cx,4:x),0
ph4 <x
ph4 <cx
FX2X
stz cx
creturn 2:cx
end
****************************************************************
*
* double compoundn(double x, long long int n);
*
* Returns (1+x)^n (defined for x >= -1).
*
****************************************************************
*
compoundn start
compoundnf entry
compoundnl entry
using MathCommon3
csubroutine (10:x,8:n),0
phb
phk
plb
lda n+6 if n == LLONG_MIN
bpl use_fc2x
asl a
ora n
ora n+2
ora n+4
bne use_fc2x
lda llmin t1 = LLONG_MIN
sta t1
lda llmin+2
sta t1+2
lda llmin+4
sta t1+4
lda llmin+6
sta t1+6
lda llmin+8
sta t1+8
bra do_cmpnd else
use_fc2x tdc t1 = n (treated as comp)
clc
adc #n
pea 0
pha
ph4 #t1
FC2X
do_cmpnd tdc t1 = (1 + x) ^ n
clc
adc #x
pea 0
pha
ph4 #t1
ph4 #t1
FCOMPOUND
plb
creturn 10:t1 return t1
llmin dc e'-9223372036854775808' LLONG_MIN in extended format
end
****************************************************************
*
* double cospi(double x);
*
* Computes cos(x * pi)
*
****************************************************************
*
cospi start
cospif entry
cospil entry
using MathCommon3
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
phy
phx
ph4 #two divide by 2 and take remainder (-1..1)
ph4 #t1
FREMI
ph4 #pi multiply by pi
ph4 #t1
FMULX
ph4 #t1 compute the cosine
FCOSX
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
two dc i2'2'
end
****************************************************************
*
* double exp10(double x);
*
* Returns 10^x.
*
****************************************************************
*
exp10 start
exp10f entry
exp10l entry
using MathCommon3
csubroutine (10:x),0
phb
phk
plb
lda ten t1 = 10
sta t1
lda ten+2
sta t1+2
lda ten+4
sta t1+4
lda ten+6
sta t1+6
lda ten+8
sta t1+8
tdc t1 = 10 ^ x
clc
adc #x
pea 0
pha
ph4 #t1
FXPWRY
plb
creturn 10:t1 return t1
ten dc e'10'
end
****************************************************************
*
* double exp10m1(double x);
*
* Returns 10^x - 1.
*
****************************************************************
*
exp10m1 start
exp10m1f entry
exp10m1l entry
using MathCommon3
csubroutine (10:x),0
phb
phk
plb
lda x copy x to t1
sta t1
lda x+2
sta t1+2
lda x+4
sta t1+4
lda x+6
sta t1+6
lda x+8
sta t1+8
ph4 #log2_10 t1 = x * log2(10)
ph4 #t1
FMULX
ph4 #t1 t1 = 2^(x * log2(10)) - 1
FEXP21X
plb
creturn 10:t1 return t1
log2_10 dc e'3.32192809488736234787031942948939017586483139302458'
end
****************************************************************
*
* double exp2m1(double x);
*
* Returns 2^x - 1.
*
****************************************************************
*
exp2m1 start
exp2m1f entry
exp2m1l entry
using MathCommon3
csubroutine (10:x),0
phb
phk
plb
lda x copy x to t1
sta t1
lda x+2
sta t1+2
lda x+4
sta t1+4
lda x+6
sta t1+6
lda x+8
sta t1+8
ph4 #t1 t1 = 2^x - 1
FEXP21X
plb
creturn 10:t1 return t1
end
****************************************************************
*
* float fadd(double x, double y);
*
* Returns x+y, rounded to float precision.
*
****************************************************************
*
fadd start
faddl entry
lda #FADDX_OPWORD
ldx #SINGLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* double daddl(long double x, long double y);
*
* Returns x+y, rounded to double precision.
*
****************************************************************
*
daddl start
lda #FADDX_OPWORD
ldx #DOUBLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* float fsub(double x, double y);
*
* Returns x-y, rounded to float precision.
*
****************************************************************
*
fsub start
fsubl entry
lda #FSUBX_OPWORD
ldx #SINGLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* double dsubl(long double x, long double y);
*
* Returns x-y, rounded to double precision.
*
****************************************************************
*
dsubl start
lda #FSUBX_OPWORD
ldx #DOUBLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* float fmul(double x, double y);
*
* Returns x*y, rounded to float precision.
*
****************************************************************
*
fmul start
fmull entry
lda #FMULX_OPWORD
ldx #SINGLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* double dmull(long double x, long double y);
*
* Returns x*y, rounded to double precision.
*
****************************************************************
*
dmull start
lda #FMULX_OPWORD
ldx #DOUBLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* float fdiv(double x, double y);
*
* Returns x/y, rounded to float precision.
*
****************************************************************
*
fdiv start
fdivl entry
lda #FDIVX_OPWORD
ldx #SINGLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* double ddivl(long double x, long double y);
*
* Returns x/y, rounded to double precision.
*
****************************************************************
*
ddivl start
lda #FDIVX_OPWORD
ldx #DOUBLE_PRECISION*$40
jmp ~NarrowingBinop
end
****************************************************************
*
* ~NarrrowingBinop
*
* Do a binary operation, rounding to a narrower result type.
*
* Inputs:
* Two extended operands on stack
* A - Opword for the binary operation (+, -, *, /)
* X - Rounding precision, to be or'd into environment word
*
****************************************************************
*
~NarrowingBinop private
using MathCommon3
sta >opword
txa
sta >precision
csubroutine (10:x,10:y),0
FGETENV
phx save original environment
txa
and #$E020 clear halts, exceptions, precision
ora >precision set rounding precision
pha
FSETENV
lda x copy x to t1
sta >t1
lda x+2
sta >t1+2
lda x+4
sta >t1+4
lda x+6
sta >t1+6
lda x+8
sta >t1+8
tdc t1 = t1 OP y
clc
adc #y
pea 0
pha
ph4 #t1
lda >opword
pha
_SANEFP816
FPROCEXIT restore env & raise any new exceptions
creturn 10:t1 return t1
opword ds 2
precision ds 2
end
****************************************************************
*
* double fsqrt(double x);
*
* Returns sqrt(x), rounded to single precision.
*
* double dsqrtl(long double x);
*
* Returns sqrt(x), rounded to double precision.
*
****************************************************************
*
fsqrt start
fsqrtl entry
using MathCommon3
lda #SINGLE_PRECISION*$40
bra lb1
dsqrtl entry
lda #DOUBLE_PRECISION*$40
lb1 sta >precision
csubroutine (10:x),0
FGETENV
phx save original environment
txa
and #$E020 clear halts, exceptions, precision
ora >precision set rounding precision
pha
FSETENV
lda x copy x to t1
sta >t1
lda x+2
sta >t1+2
lda x+4
sta >t1+4
lda x+6
sta >t1+6
lda x+8
sta >t1+8
ph4 #t1 t1 = sqrt(t1)
FSQRTX
FPROCEXIT restore env & raise any new exceptions
creturn 10:t1 return t1
opword ds 2
precision ds 2
end
****************************************************************
*
* long llogb(double x);
*
* Returns the binary exponent of x (a signed integer value),
* treating denormalized numbers as if they were normalized.
* Handles inf/nan/0 cases specially.
*
****************************************************************
*
llogb start
llogbf entry
llogbl entry
csubroutine (10:x),0
tdc check for special cases
clc
adc #x
pea 0
pha
FCLASSX
txa
ldy #$7FFF
ldx #$FFFF
and #$FF
cmp #$FE if x is INF
beq special return LONG_MAX
lsr a
beq do_logb if x is 0 or NAN
inx return LONG_MIN
iny
special stx x
sty x+2
bra ret
do_logb tdc compute logb(x)
clc
adc #x
pea 0
pha
FLOGBX
tdc convert to long integer
clc
adc #x
pea 0
pha
pea 0
pha
FX2L
ret creturn 4:x return it
end
****************************************************************
*
* double log10p1(double x);
*
* Returns log10(1+x).
*
****************************************************************
*
log10p1 start
log10p1f entry
log10p1l entry
using MathCommon3
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
phy
phx
plb
ph4 #t1 t1 = log2(1+x)
FLOG21X
ph4 #log2_10 t1 = log2(1+x) / log2(10)
ph4 #t1
FDIVX
ldx #^t1 return a pointer to the result
lda #t1
rtl
log2_10 dc e'3.32192809488736234787031942948939017586483139302458'
end
****************************************************************
*
* double log2p1(double x);
*
* Returns log2(1+x).
*
****************************************************************
*
log2p1 start
log2p1f entry
log2p1l entry
using MathCommon3
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
phy
phx
plb
ph4 #t1 compute the value
FLOG21X
ldx #^t1 return a pointer to the result
lda #t1
rtl
end
****************************************************************
*
* double logp1(double x);
*
* Returns ln(1+x).
*
****************************************************************
*
logp1 start
logp1f entry
logp1l entry
jml log1p
end
****************************************************************
*
* double nextdown(double x);
* float nextdownf(float x);
* long double nextdownl(long double x);
* double nextup(double x);
* float nextupf(float x);
* long double nextupl(long double x);
*