Repository navigation
Expand file tree
/
Copy pathmath.asm
More file actions
1404 lines (1334 loc) · 31 KB
/
Copy pathmath.asm
File metadata and controls
1404 lines (1334 loc) · 31 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/math
mcopy math.macros
case on
****************************************************************
*
* Math - Math libraries for C
*
* This code implements the tables and subroutines needed to
* support the standard C library MATH.
*
* January 1989
* Mike Westerfield
*
* Copyright 1989
* Byte Works, Inc.
*
****************************************************************
*
Math start dummy segment
copy equates.asm
end
****************************************************************
*
* MathCommon - common work areas for the math library
*
****************************************************************
*
MathCommon privdata
;
; constants
;
pi dc h'35C2 6821 A2DA 0FC9 0040'
piover2 dc h'35C2 6821 A2DA 0FC9 FF3F'
quarter dc h'0000 0000 0000 0080 FD3F'
half dc h'0000 0000 0000 0080 FE3F'
one dc h'0000 0000 0000 0080 FF3F'
two dc h'0000 0000 0000 0080 0040'
;
; temporary work space
;
t1 ds 10
t2 ds 10
t3 ds 10
sign ds 2
orig ds 10 saved copy of input value
end
****************************************************************
*
* asin - return arcsin(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
asin start
using MathCommon
;
; Intialization
;
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
phy
phx
;
; do general initialization
;
move one,t3,#10 t3 := 1.0
lda t1 t2 := t1
sta t2
lda t1+2
sta t2+2
lda t1+4
sta t2+4
lda t1+6
sta t2+6
lda t1+8
sta t2+8
;
; if t2 >= 2^-33 then arcsine(t1) := atan(t1/sqrt(1-sqr(t2))
; else arssine(t1) := t1
;
and #$7FFF branch if the value is less than 2^-33
cmp #$3FDE
blt lb3
lda #t2 t2 := sqr(t2)
ldx #^t2
phx
pha
phx
pha
fmulx
ph4 #t2 t3 := t3-t2
ph4 #t3
fsubx
lb2 lda #t3 t3 := sqrt(t3)
ldx #^t3
phx
pha
phx
pha
fsqrtx
ph4 #t1 t1 := t1/t3
fdivx
ph4 #t1 t1 := atan(t1)
fatanx
lb3 jsr ~SetErrno check for a domain error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* acos - return arccosin(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
acos start
using MathCommon
;
; Intialization
;
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
phy
phx
;
; acos(t1) := 2*atan(sqrt((1-t1)/(1+t1)))
;
move one,t2,#10 t2 := 1
ph4 #t1 t2 := t2+t1
ph4 #t2
faddx
ph4 #one t1 := t1-1
ph4 #t1
fsubx
lda t1+8 t1 := -t1
eor #$8000
sta t1+8
ph4 #t2 t1 := t1/t2
ph4 #t1
fdivx
lda #t1 t1 := sqrt(t1)
ldx #^t1
phx
pha
phx
pha
fsqrtx
fatanx t1 := atan(t1)
ph4 #two t1 := t1*2
ph4 #t1
fmulx
jsr ~SetErrno check for a domain error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* atan - return arctan(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
atan start
using MathCommon
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
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* atan2 - return arctangent(y,x) scaled to -pi..pi
*
* Inputs:
* stack - extended numbers
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
atan2 start
using MathCommon
phb place the numbers in the work areas
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
pla
sta t2
pla
sta t2+2
pla
sta t2+4
pla
sta t2+6
pla
sta t2+8
phy
phx
;
; do special processing for x=0
;
lda t2+8 branch if x <> 0
and #$7FFF
ora t2+6
ora t2+4
ora t2+2
ora t2
bne lb2
lda t1+8 if y = 0, report a range error
and #$7FFF
ora t1+6
ora t1+4
ora t1+2
ora t1
bne lb1
lda #ERANGE
sta >errno
brl lb5
lb1 lda t1+8 return pi/2 with the sign of t1
and #$8000
ora piover2+8
sta t1+8
move piover2,t1,#8
bra lb5
;
; handle cases where x <> 0
;
lb2 lda t2+8 save the sign of t2 in sign
and #$8000
sta sign
lda t2+8 t2 := abs(t2)
and #$7FFF
sta t2+8
ph4 #t2 t1 := t1/t2
ph4 #t1
fdivx
ph4 #t1 t1 := arctan(t1)
fatanx
lda sign if t2 was less than zero then
beq lb5
ph4 #pi
ph4 #t1
lda t1+8 if t1 < 0 then
bpl lb3
faddx t1 := t1+pi
bra lb4
lb3 fsubx else t1 := t1-pi
lb4 lda t1+8 t1 := -t1
eor #$8000
sta t1+8
lb5 ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* ceil - round up
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
ceil start
using MathCommon
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
fgetenv set the rounding direction to round up
phx
txa
and #$3FFF
ora #$4000
pha
fsetenv
ph4 #t1
frintx round the number
fsetenv restore the environment
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* cos - return cos(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
cos start
using MathCommon
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 cosine
fcosx
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* cosh - return hyperbolic cosine(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
cosh start
using MathCommon
;
; Intialization
;
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta orig+8
and #$7FFF (take the absolute value now)
sta t1+8
phy
phx
;
; cosh(t1) := (0.5*exp(abs(t1)) + 0.25/(0.5*exp(abs(t1)))
;
ph4 #t1 t1 := exp(abs(t1))
fexpx
ph4 #half t1 := t1*0.5
ph4 #t1
fmulx
move quarter,t2,#10 t2 := 0.25
ph4 #t1 t2 := t2/t1
ph4 #t2
fdivx
ph4 #t2 t1 := t1+t2
ph4 #t1
faddx
jsr ~SetErrno check for a range error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* exp - return exp(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
exp start
using MathCommon
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
phy
phx
ph4 #t1 compute the exponent
fexpx
jsr ~SetErrno check for a range error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* fabs - absolute value of an extended number
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
fabs start
using MathCommon
phb
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
and #$7FFF
sta t1+8
phy
phx
plb
ldx #^t1
lda #t1
rtl
end
****************************************************************
*
* floor - round down
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
floor start
using MathCommon
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
fgetenv set the rounding direction to round down
phx
txa
and #$3FFF
ora #$8000
pha
fsetenv
ph4 #t1
frintx round the number
fsetenv restore the environment
ldx #^t1 return a pointer to the result
lda #t1
rtl
end
****************************************************************
*
* fmod - return the floating point remainder
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
fmod start
using MathCommon
phb place the numbers in the work areas
plx
ply
phk
plb
pla
sta t1
pla
sta t1+2
pla
sta t1+4
pla
sta t1+6
pla
sta t1+8
pla
sta t2
pla
sta t2+2
pla
sta t2+4
pla
sta t2+6
pla
sta t2+8
phy
phx
move t1,t3,#10 t3 := t1/t2
ph4 #t2
ph4 #t3
fdivx
ph4 #t3 t3 := trunc(t3)
ftintx
ph4 #t2 t3 = t3*t2
ph4 #t3
fmulx
ph4 #t3 t1 = t1-t3
ph4 #t1
fsubx
lb1 ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* frexp - split a number into a fracrion and exponent
*
* Inputs:
* x - number
* nptr - pointer to location to save integer
*
* Outputs:
* returns the address of the fraction
*
****************************************************************
*
frexp start
using MathCommon
csubroutine (10:x,4:nptr),0
phb
phk
plb
lda x+8 get the exponent
and #$7FFF
bne lb1 handle zero
sta [nptr]
bra lb2
lb1 sec
sbc #$3FFE
sta [nptr]
lda x+8 set the fraction range
and #$8000
ora #$3FFE
sta x+8
lb2 ldx #8 set up to return the result
lb3 lda x,X
sta t1,X
dex
dex
bpl lb3
lla nptr,t1
plb
creturn 4:nptr
end
****************************************************************
*
* ldexp - raise a number to an integer power of 2
*
* Inputs:
* x - number
* n - integer power of 2
*
* Outputs:
* returns the address of the result
*
****************************************************************
*
ldexp start
using MathCommon
csubroutine (10:x,2:n),0
phb
phk
plb
lda x+8 separate the sign from the exponent
and #$8000
sta sign
clc add the value to the exponent
lda x+8
and #$7FFF
adc n
bvs err
cmp #$7FFF check for a range error
blt lb1
err lda #ERANGE
sta >errno
bra lb2
lb1 ora sign replace the sign
sta x+8 save the exponent
lb2 ldx #8 set up to return the result
lb3 lda x,X
sta t1,X
dex
dex
bpl lb3
lla x,t1
plb
creturn 4:x
end
****************************************************************
*
* log - return ln(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
log start
using MathCommon
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
phy
phx
ph4 #t1 compute ln(x)
flnx
jsr ~SetErrno check for a domain or pole error
lb1 ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************
*
* log10 - return log(x)
*
* Inputs:
* stack - extended number
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
log10 start
using MathCommon
phb place the number in a work area
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
phy
phx
ph4 #t1 compute ln(x)
flnx
ph4 #ln10e convert from ln base e to log base 10
ph4 #t1
fmulx
jsr ~SetErrno check for a domain or pole error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
ln10e dc e'0.43429448190325182765'
end
****************************************************************
*
* modf - split a number into whole and fraction parts
*
* Inputs:
* x - number
* nptr - ptr to double to store integer part
*
* Outputs:
* returns the address of the result
*
****************************************************************
*
modf start
using MathCommon
csubroutine (10:x,4:nptr),0
phb
phk
plb
ldx #8 t1 := x
lb1 lda x,X t2 := x
sta t1,X
sta t2,X
dex
dex
bpl lb1
ph4 #t2 t2 := trunc(t2)
ftintx
ph4 #t2 t1 := t1-t2
ph4 #t1
fsubx
ph4 #t2 convert t2 to a double
ph4 #t3
fx2d
lb2 ldy #6
lb3 lda t3,Y return the integer part
sta [nptr],Y
dey
dey
bpl lb3
lla nptr,t1 set up to return the result
plb
creturn 4:nptr
end
****************************************************************
*
* pow - return x ** y
*
* Inputs:
* stack - extended numbers
*
* Outputs:
* X-A - addr of the result
*
****************************************************************
*
pow start
using MathCommon
phb place the numbers in the work areas
plx
ply
phk
plb
pla
sta t1
sta orig
pla
sta t1+2
sta orig+2
pla
sta t1+4
sta orig+4
pla
sta t1+6
sta orig+6
pla
sta t1+8
sta orig+8
pla
sta t2
pla
sta t2+2
pla
sta t2+4
pla
sta t2+6
pla
sta t2+8
phy
phx
ph4 #t2 t1 := t1 ** t2
ph4 #t1
fxpwry
jsr ~SetErrno2 check for a range error
ldx #^t1 return a pointer to the result
lda #t1
plb
rtl
end
****************************************************************