mirror of
https://github.com/cc65/cc65.git
synced 2024-12-25 17:29:50 +00:00
163 lines
3.9 KiB
ArmAsm
163 lines
3.9 KiB
ArmAsm
;
|
|
; Fixed point cosine/sine functions.
|
|
;
|
|
; int __fastcall__ _sin (unsigned x);
|
|
; int __fastcall__ _cos (unsigned x);
|
|
;
|
|
; Returns the cosine/sine for the given argument as angular degree.
|
|
; Valid argument range is 0..360 for both functions. They will return
|
|
; garbage if the argument is not in a valid range. Result is in 8.8 fixed
|
|
; point format, so $100 is 1.0 and $FF00 is -1.0.
|
|
;
|
|
;
|
|
; Ullrich von Bassewitz, 2009-10-29
|
|
;
|
|
|
|
.export __cos, __sin
|
|
|
|
|
|
; ---------------------------------------------------------------------------
|
|
; Sinus table covering values from 0..86° as 0.8 fixed point values. Values
|
|
; for 87..90° are actually 1.0 (= $100), will therefore not fit in the table
|
|
; and are covered specially in the code below.
|
|
|
|
.rodata
|
|
|
|
_sintab:
|
|
.byte $00, $04, $09, $0D, $12, $16, $1B, $1F, $24, $28
|
|
.byte $2C, $31, $35, $3A, $3E, $42, $47, $4B, $4F, $53
|
|
.byte $58, $5C, $60, $64, $68, $6C, $70, $74, $78, $7C
|
|
.byte $80, $84, $88, $8B, $8F, $93, $96, $9A, $9E, $A1
|
|
.byte $A5, $A8, $AB, $AF, $B2, $B5, $B8, $BB, $BE, $C1
|
|
.byte $C4, $C7, $CA, $CC, $CF, $D2, $D4, $D7, $D9, $DB
|
|
.byte $DE, $E0, $E2, $E4, $E6, $E8, $EA, $EC, $ED, $EF
|
|
.byte $F1, $F2, $F3, $F5, $F6, $F7, $F8, $F9, $FA, $FB
|
|
.byte $FC, $FD, $FE, $FE, $FF, $FF, $FF
|
|
|
|
|
|
|
|
; ---------------------------------------------------------------------------
|
|
; Cosine function. Is actually implemented as _cos(x) = _sin(x+90)
|
|
|
|
.code
|
|
|
|
__cos:
|
|
|
|
; _cos(x) = _sin(x+90)
|
|
|
|
clc
|
|
adc #90
|
|
bcc @L1
|
|
inx
|
|
|
|
; If x is now larger than 360, we need to subtract 360.
|
|
|
|
@L1: cpx #>360
|
|
bne @L2
|
|
cmp #<360
|
|
@L2: bcc __sin
|
|
|
|
sbc #<360
|
|
bcs @L3
|
|
dex
|
|
@L3: dex
|
|
|
|
; ---------------------------------------------------------------------------
|
|
; Sine function. Uses
|
|
;
|
|
; table lookup for 0..89°
|
|
; _sin(x) = _sin(180-x) for 90°..179°
|
|
; _sin(x) = -_sin(x-180) for 180..360°
|
|
;
|
|
; Plus special handling for the values missing in the table.
|
|
|
|
__sin:
|
|
|
|
; If the high byte is non zero, argument is > 255
|
|
|
|
cpx #0
|
|
bne L3
|
|
cmp #180
|
|
bcs L4
|
|
|
|
; 0..179°
|
|
|
|
cmp #90
|
|
bcc L1
|
|
|
|
; 90..179°. Value is identical to _sin(180-val). Carry is set on entry.
|
|
;
|
|
; 180-val := -val + 180.
|
|
; With
|
|
; -val := (val ^ $FF) + 1
|
|
; we get
|
|
; 180-val = (val ^ $FF) + 1 + 180
|
|
; Since carry is set, we can drop the "+ 1".
|
|
;
|
|
|
|
eor #$FF
|
|
adc #180 ; 180-val
|
|
|
|
; 0..89°. Values for 87..90° are actually 1.0. Since this format doesn't fit
|
|
; into the table, we have to check for it manually.
|
|
|
|
L1: cmp #87
|
|
bcc L2
|
|
|
|
; The value is 1.0
|
|
|
|
ldx #>(1 << 8)
|
|
lda #<(1 << 8)
|
|
rts
|
|
|
|
; 0..86°. Read the value from the table.
|
|
|
|
L2: tay
|
|
ldx #0
|
|
lda _sintab,y
|
|
rts
|
|
|
|
; 180..360°. _sin(x) = -_sin(x-180). Since the argument is in range 0..180
|
|
; after the subtraction, we don't need to handle the high byte.
|
|
|
|
L3: sec
|
|
L4: sbc #180
|
|
|
|
cmp #90
|
|
bcc L5
|
|
|
|
; 270..360°. Value is identical to -_sin(180-val). Carry is set on entry.
|
|
;
|
|
; 180-val := -val + 180.
|
|
; With
|
|
; -val := (val ^ $FF) + 1
|
|
; we get
|
|
; 180-val = (val ^ $FF) + 1 + 180
|
|
; Since carry is set, we can drop the "+ 1".
|
|
;
|
|
|
|
eor #$FF
|
|
adc #180 ; 180-val
|
|
|
|
; 180..269°. Values for 267..269° are actually -1.0. Since this format doesn't
|
|
; fit into the table, we have to check for it manually.
|
|
|
|
L5: ldx #$FF
|
|
cmp #87
|
|
bcc L6
|
|
|
|
; The value is -1.0
|
|
|
|
lda #<(-1 << 8)
|
|
rts
|
|
|
|
; 180..266°. Read the value from the table. Carry is clear on entry.
|
|
|
|
L6: tay
|
|
txa ; A = $FF
|
|
eor _sintab,y
|
|
adc #1
|
|
bcc L7
|
|
inx
|
|
L7: rts
|