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165 lines
3.9 KiB
ArmAsm
165 lines
3.9 KiB
ArmAsm
;
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; Fixed point cosine/sine functions.
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;
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; int __fastcall__ cc65_sin (unsigned x);
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; int __fastcall__ cc65_cos (unsigned x);
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;
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; Returns the cosine/sine for the given argument as angular degree.
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; Valid argument range is 0..360 for both functions. They will return
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; garbage if the argument is not in a valid range. Result is in 8.8 fixed
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; point format, so $100 is 1.0 and $FF00 is -1.0.
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;
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;
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; Ullrich von Bassewitz, 2009-10-29
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;
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.export _cc65_cos, _cc65_sin
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; ---------------------------------------------------------------------------
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; Sinus table covering values from 0..86° as 0.8 fixed point values. Values
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; for 87..90° are actually 1.0 (= $100), will therefore not fit in the table
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; and are covered specially in the code below.
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.rodata
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_cc65_sintab:
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.byte $00, $04, $09, $0D, $12, $16, $1B, $1F, $24, $28
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.byte $2C, $31, $35, $3A, $3E, $42, $47, $4B, $4F, $53
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.byte $58, $5C, $60, $64, $68, $6C, $70, $74, $78, $7C
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.byte $80, $84, $88, $8B, $8F, $93, $96, $9A, $9E, $A1
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.byte $A5, $A8, $AB, $AF, $B2, $B5, $B8, $BB, $BE, $C1
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.byte $C4, $C7, $CA, $CC, $CF, $D2, $D4, $D7, $D9, $DB
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.byte $DE, $E0, $E2, $E4, $E6, $E8, $EA, $EC, $ED, $EF
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.byte $F1, $F2, $F3, $F5, $F6, $F7, $F8, $F9, $FA, $FB
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.byte $FC, $FD, $FE, $FE, $FF, $FF, $FF
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; ---------------------------------------------------------------------------
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; Cosine function. Is actually implemented as cos(x) = sin(x+90)
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.code
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_cc65_cos:
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; cos(x) = sin(x+90)
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clc
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adc #90
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bcc @L1
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inx
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; If x is now larger than 360, we need to subtract 360.
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@L1: cpx #>360
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bne @L2
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cmp #<360
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@L2: bcc _cc65_sin
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sbc #<360
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bcs @L3
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dex
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@L3: dex
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; ---------------------------------------------------------------------------
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; Sine function. Uses
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;
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; table lookup for 0..89°
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; sin(x) = sin(180-x) for 90°..179°
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; sin(x) = -sin(x-180) for 180..360°
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;
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; Plus special handling for the values missing in the table.
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_cc65_sin:
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; If the high byte is non zero, argument is > 255
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cpx #0
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bne L3
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cmp #180
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bcs L4
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; 0..179°
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cmp #90
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bcc L1
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; 90..179°. Value is identical to sin(180-val). Carry is set on entry.
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;
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; 180-val := -val + 180.
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; With
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; -val := (val ^ $FF) + 1
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; we get
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; 180-val = (val ^ $FF) + 1 + 180
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; Since carry is set, we can drop the "+ 1".
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;
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eor #$FF
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adc #180 ; 180-val
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; 0..89°. Values for 87..90° are actually 1.0. Since this format doesn't fit
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; into the table, we have to check for it manually.
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L1: cmp #87
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bcc L2
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; The value is 1.0
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ldx #>(1 << 8)
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lda #<(1 << 8)
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rts
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; 0..86°. Read the value from the table.
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L2: tay
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ldx #0
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lda _cc65_sintab,y
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rts
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; 180..360°. sin(x) = -sin(x-180). Since the argument is in range 0..180
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; after the subtraction, we don't need to handle the high byte.
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L3: sec
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L4: sbc #180
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cmp #90
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bcc L5
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; 270..360°. Value is identical to -sin(180-val). Carry is set on entry.
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;
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; 180-val := -val + 180.
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; With
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; -val := (val ^ $FF) + 1
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; we get
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; 180-val = (val ^ $FF) + 1 + 180
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; Since carry is set, we can drop the "+ 1".
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;
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eor #$FF
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adc #180 ; 180-val
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; 180..269°. Values for 267..269° are actually -1.0. Since this format doesn't
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; fit into the table, we have to check for it manually.
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L5: ldx #$FF
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cmp #87
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bcc L6
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; The value is -1.0
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lda #<(-1 << 8)
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rts
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; 180..266°. Read the value from the table. Carry is clear on entry.
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L6: tay
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txa ; A = $FF
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eor _cc65_sintab,y
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adc #1
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bcc L7
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inx
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L7: rts
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