mirror of
https://github.com/irmen/prog8.git
synced 2024-11-22 15:33:02 +00:00
9438e996d7
Added math.lerpw() a LERP routine for words (to complement the existing math.lerp() for bytes) Described the LERP routines in the library chapter in the docs.
666 lines
18 KiB
Lua
666 lines
18 KiB
Lua
; Internal Math library routines - always included by the compiler
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; note: some functions you might expect here are builtin functions,
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; such as abs, sqrt, clamp, min, max for example.
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math {
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%option no_symbol_prefixing, ignore_unused
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asmsub sin8u(ubyte angle @A) clobbers(Y) -> ubyte @A {
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%asm {{
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tay
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lda _sinecos8u,y
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rts
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_sinecos8u .byte trunc(128.0 + 127.5 * sin(range(256+64) * rad(360.0/256.0)))
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; !notreached!
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}}
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}
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asmsub cos8u(ubyte angle @A) clobbers(Y) -> ubyte @A {
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%asm {{
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tay
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lda sin8u._sinecos8u+64,y
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rts
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}}
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}
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asmsub sin8(ubyte angle @A) clobbers(Y) -> byte @A {
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%asm {{
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tay
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lda _sinecos8,y
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rts
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_sinecos8 .char trunc(127.0 * sin(range(256+64) * rad(360.0/256.0)))
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; !notreached!
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}}
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}
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asmsub cos8(ubyte angle @A) clobbers(Y) -> byte @A {
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%asm {{
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tay
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lda sin8._sinecos8+64,y
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rts
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}}
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}
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asmsub sinr8u(ubyte radians @A) clobbers(Y) -> ubyte @A {
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%asm {{
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tay
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lda _sinecosR8u,y
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rts
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_sinecosR8u .byte trunc(128.0 + 127.5 * sin(range(180+45) * rad(360.0/180.0)))
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; !notreached!
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}}
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}
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asmsub cosr8u(ubyte radians @A) clobbers(Y) -> ubyte @A {
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%asm {{
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tay
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lda sinr8u._sinecosR8u+45,y
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rts
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}}
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}
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asmsub sinr8(ubyte radians @A) clobbers(Y) -> byte @A {
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%asm {{
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tay
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lda _sinecosR8,y
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rts
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_sinecosR8 .char trunc(127.0 * sin(range(180+45) * rad(360.0/180.0)))
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; !notreached!
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}}
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}
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asmsub cosr8(ubyte radians @A) clobbers(Y) -> byte @A {
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%asm {{
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tay
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lda sinr8._sinecosR8+45,y
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rts
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}}
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}
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asmsub rnd() clobbers(Y) -> ubyte @A {
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%asm {{
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jmp prog8_math.randbyte
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}}
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}
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asmsub rndw() -> uword @AY {
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%asm {{
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jmp prog8_math.randword
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}}
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}
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sub randrange(ubyte n) -> ubyte {
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; -- return random number uniformly distributed from 0 to n-1 (compensates for divisibility bias)
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cx16.r0H = 255 / n * n
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do {
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cx16.r0L = math.rnd()
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} until cx16.r0L < cx16.r0H
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return cx16.r0L % n
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}
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sub randrangew(uword n) -> uword {
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; -- return random number uniformly distributed from 0 to n-1 (compensates for divisibility bias)
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cx16.r1 = 65535 / n * n
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do {
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cx16.r0 = math.rndw()
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} until cx16.r0 < cx16.r1
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return cx16.r0 % n
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}
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asmsub rndseed(uword seed1 @AY, uword seed2 @R0) clobbers(A,Y) {
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; -- set new pseudo RNG's seed values. Defaults are: $00c2, $1137
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%asm {{
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sta prog8_math.randword.x1
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sty prog8_math.randword.c1
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lda cx16.r0L
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sta prog8_math.randword.a1
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lda cx16.r0H
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sta prog8_math.randword.b1
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rts
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}}
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}
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asmsub log2(ubyte value @A) -> ubyte @Y {
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%asm {{
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sta P8ZP_SCRATCH_B1
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lda #$80
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ldy #7
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- bit P8ZP_SCRATCH_B1
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beq +
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rts
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+ dey
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bne +
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rts
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+ lsr a
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bne -
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; !notreached!
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}}
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}
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asmsub log2w(uword value @AY) -> ubyte @Y {
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%asm {{
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sta P8ZP_SCRATCH_W1
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sty P8ZP_SCRATCH_W1+1
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lda #<$8000
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sta cx16.r0
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lda #>$8000
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sta cx16.r0+1
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ldy #15
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- lda P8ZP_SCRATCH_W1
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and cx16.r0
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sta P8ZP_SCRATCH_B1
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lda P8ZP_SCRATCH_W1+1
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and cx16.r0+1
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ora P8ZP_SCRATCH_B1
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beq +
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rts
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+ dey
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bne +
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rts
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+ lsr cx16.r0+1
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ror cx16.r0
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jmp -
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}}
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}
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asmsub mul16_last_upper() -> uword @AY {
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; This routine peeks into the internal 32 bits multiplication result buffer of the
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; 16*16 bits multiplication routine, to fetch the upper 16 bits of the last calculation.
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; Notes:
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; - to avoid interference it's best to fetch and store this value immediately after the multiplication expression.
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; for instance, simply printing a number may already result in new multiplication calls being performed
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; - not all multiplications in the source code result in an actual multiplication call:
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; some simpler multiplications will be optimized away into faster routines. These will not set the upper 16 bits at all!
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; - THE RESULT IS ONLY VALID IF THE MULTIPLICATION WAS DONE WITH UWORD ARGUMENTS (or two positive WORD arguments)
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; as soon as a negative word value (or 2) was used in the multiplication, these upper 16 bits are not valid!!
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; Suggestion (if you are on the Commander X16): use verafx.muls() to get a hardware accelerated 32 bit signed multplication.
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%asm {{
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lda prog8_math.multiply_words.result+2
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ldy prog8_math.multiply_words.result+3
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rts
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}}
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}
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sub direction_sc(byte x1, byte y1, byte x2, byte y2) -> ubyte {
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; From a pair of signed coordinates around the origin, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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cx16.r1sL = x2-x1 ; xdelta
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if_neg {
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cx16.r0L--
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cx16.r1sL = -cx16.r1sL
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}
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cx16.r2sL = y2-y1 ; ydelta
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if_neg {
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cx16.r0L-=2
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cx16.r2sL = -cx16.r2sL
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}
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return direction_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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sub direction(ubyte x1, ubyte y1, ubyte x2, ubyte y2) -> ubyte {
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; From a pair of positive coordinates, calculate discrete direction between 0 and 23 into A.
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cx16.r0L = 3 ; quadrant
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if x2>=x1 {
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cx16.r1L = x2-x1
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} else {
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cx16.r1L = x1-x2
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cx16.r0L--
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}
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if y2>=y1 {
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cx16.r2L = y2-y1
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} else {
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cx16.r2L = y1-y2
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cx16.r0L -= 2
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}
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return direction_qd(cx16.r0L, cx16.r1L, cx16.r2L)
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}
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asmsub direction_qd(ubyte quadrant @A, ubyte xdelta @X, ubyte ydelta @Y) -> ubyte @A {
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;Arctan https://github.com/dustmop/arctan24
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; From a pair of X/Y deltas (both >=0), and quadrant 0-3, calculate discrete direction between 0 and 23 into A.
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; .reg:a @in quadrant Number 0 to 3.
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; .reg:x @in x_delta Delta for x direction.
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; .reg:y @in y_delta Delta for y direction.
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; Returns A as the direction (0-23).
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%asm {{
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x_delta = cx16.r0L
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y_delta = cx16.r1L
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quadrant = cx16.r2L
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half_value = cx16.r3L
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region_number = cx16.r4L
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small = cx16.r5L
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large = cx16.r5H
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sta quadrant
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sty y_delta
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stx x_delta
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cpx y_delta
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bcs _XGreaterOrEqualY
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_XLessY:
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lda #16
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sta region_number
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stx small
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sty large
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bne _DetermineRegion
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_XGreaterOrEqualY:
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lda #0
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sta region_number
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stx large
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sty small
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_DetermineRegion:
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; set A = small * 2.5
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lda small
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lsr a
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sta half_value
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lda small
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asl a
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bcs _SmallerQuotient
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clc
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adc half_value
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bcs _SmallerQuotient
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cmp large
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bcc _LargerQuotient
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; S * 2.5 > L
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_SmallerQuotient:
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; set A = S * 1.25
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lsr half_value
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lda small
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clc
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adc half_value
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cmp large
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bcc _Region1 ; if S * 1.25 < L then goto Region1 (L / S > 1.25)
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bcs _Region0 ; (L / S < 1.25)
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; S * 2.5 < L
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_LargerQuotient:
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; set A = S * 7.5
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lda small
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asl a
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asl a
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asl a
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bcs _Region2
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sec
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sbc half_value
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cmp large
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bcc _Region3 ; if S * 7.5 < L then goto Region3 (L / S > 7.5)
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jmp _Region2 ; (L / S < 7.5)
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_Region0:
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; L / S < 1.25. d=3,9,15,21
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jmp _LookupResult
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_Region1:
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; 1.25 < L / S < 2.5. d=2,4,8,10,14,16,20,22
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lda region_number
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clc
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adc #4
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sta region_number
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bpl _LookupResult
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_Region2:
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; 2.5 < L / S < 7.5. d=1,5,7,11,13,17,19,23
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lda region_number
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clc
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adc #8
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sta region_number
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bpl _LookupResult
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_Region3:
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; 7.5 < L / S. d=0,6,12,18
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lda region_number
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clc
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adc #12
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sta region_number
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_LookupResult:
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lda quadrant
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clc
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adc region_number
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tax
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lda _quadrant_region_to_direction,x
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rts
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_quadrant_region_to_direction:
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.byte 9, 3,15,21
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.byte 10, 2,14,22
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.byte 11, 1,13,23
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.byte 12, 0,12, 0
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.byte 9, 3,15,21
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.byte 8, 4,16,20
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.byte 7, 5,17,19
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.byte 6, 6,18,18
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; !notreached!
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}}
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}
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asmsub atan2(ubyte x1 @R0, ubyte y1 @R1, ubyte x2 @R2, ubyte y2 @R3) -> ubyte @A {
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;; Calculate the angle, in a 256-degree circle, between two points into A.
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;; The points (x1, y1) and (x2, y2) have to use *unsigned coordinates only* from the positive quadrant in the carthesian plane!
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;; https://www.codebase64.org/doku.php?id=base:8bit_atan2_8-bit_angle
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;; This uses 2 large lookup tables so uses a lot of memory but is super fast.
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%asm {{
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x1 = cx16.r0L
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y1 = cx16.r1L
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x2 = cx16.r2L
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y2 = cx16.r3L
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octant = cx16.r4L ;; temporary zeropage variable
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lda x1
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sec
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sbc x2
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bcs *+4
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eor #$ff
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tax
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rol octant
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lda y1
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sec
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sbc y2
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bcs *+4
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eor #$ff
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tay
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rol octant
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lda log2_tab,x
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sec
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sbc log2_tab,y
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bcc *+4
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eor #$ff
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tax
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lda octant
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rol a
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and #%111
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tay
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lda atan_tab,x
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eor octant_adjust,y
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rts
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octant_adjust
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.byte %00111111 ;; x+,y+,|x|>|y|
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.byte %00000000 ;; x+,y+,|x|<|y|
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.byte %11000000 ;; x+,y-,|x|>|y|
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.byte %11111111 ;; x+,y-,|x|<|y|
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.byte %01000000 ;; x-,y+,|x|>|y|
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.byte %01111111 ;; x-,y+,|x|<|y|
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.byte %10111111 ;; x-,y-,|x|>|y|
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.byte %10000000 ;; x-,y-,|x|<|y|
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;;;;;;;; atan(2^(x/32))*128/pi ;;;;;;;;
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atan_tab
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$00,$00,$00
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.byte $00,$00,$00,$00,$00,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$01,$01,$01
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.byte $01,$01,$01,$01,$01,$02,$02,$02
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.byte $02,$02,$02,$02,$02,$02,$02,$02
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.byte $02,$02,$02,$02,$02,$02,$02,$02
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.byte $03,$03,$03,$03,$03,$03,$03,$03
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.byte $03,$03,$03,$03,$03,$04,$04,$04
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.byte $04,$04,$04,$04,$04,$04,$04,$04
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.byte $05,$05,$05,$05,$05,$05,$05,$05
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.byte $06,$06,$06,$06,$06,$06,$06,$06
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.byte $07,$07,$07,$07,$07,$07,$08,$08
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.byte $08,$08,$08,$08,$09,$09,$09,$09
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.byte $09,$0a,$0a,$0a,$0a,$0b,$0b,$0b
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.byte $0b,$0c,$0c,$0c,$0c,$0d,$0d,$0d
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.byte $0d,$0e,$0e,$0e,$0e,$0f,$0f,$0f
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.byte $10,$10,$10,$11,$11,$11,$12,$12
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.byte $12,$13,$13,$13,$14,$14,$15,$15
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.byte $15,$16,$16,$17,$17,$17,$18,$18
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.byte $19,$19,$19,$1a,$1a,$1b,$1b,$1c
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.byte $1c,$1c,$1d,$1d,$1e,$1e,$1f,$1f
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;;;;;;;; log2(x)*32 ;;;;;;;;
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log2_tab
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.byte $00,$00,$20,$32,$40,$4a,$52,$59
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.byte $60,$65,$6a,$6e,$72,$76,$79,$7d
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.byte $80,$82,$85,$87,$8a,$8c,$8e,$90
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.byte $92,$94,$96,$98,$99,$9b,$9d,$9e
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.byte $a0,$a1,$a2,$a4,$a5,$a6,$a7,$a9
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.byte $aa,$ab,$ac,$ad,$ae,$af,$b0,$b1
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.byte $b2,$b3,$b4,$b5,$b6,$b7,$b8,$b9
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.byte $b9,$ba,$bb,$bc,$bd,$bd,$be,$bf
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.byte $c0,$c0,$c1,$c2,$c2,$c3,$c4,$c4
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.byte $c5,$c6,$c6,$c7,$c7,$c8,$c9,$c9
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.byte $ca,$ca,$cb,$cc,$cc,$cd,$cd,$ce
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.byte $ce,$cf,$cf,$d0,$d0,$d1,$d1,$d2
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.byte $d2,$d3,$d3,$d4,$d4,$d5,$d5,$d5
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.byte $d6,$d6,$d7,$d7,$d8,$d8,$d9,$d9
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.byte $d9,$da,$da,$db,$db,$db,$dc,$dc
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.byte $dd,$dd,$dd,$de,$de,$de,$df,$df
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.byte $df,$e0,$e0,$e1,$e1,$e1,$e2,$e2
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.byte $e2,$e3,$e3,$e3,$e4,$e4,$e4,$e5
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.byte $e5,$e5,$e6,$e6,$e6,$e7,$e7,$e7
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.byte $e7,$e8,$e8,$e8,$e9,$e9,$e9,$ea
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.byte $ea,$ea,$ea,$eb,$eb,$eb,$ec,$ec
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.byte $ec,$ec,$ed,$ed,$ed,$ed,$ee,$ee
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.byte $ee,$ee,$ef,$ef,$ef,$ef,$f0,$f0
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.byte $f0,$f1,$f1,$f1,$f1,$f1,$f2,$f2
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.byte $f2,$f2,$f3,$f3,$f3,$f3,$f4,$f4
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.byte $f4,$f4,$f5,$f5,$f5,$f5,$f5,$f6
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.byte $f6,$f6,$f6,$f7,$f7,$f7,$f7,$f7
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.byte $f8,$f8,$f8,$f8,$f9,$f9,$f9,$f9
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.byte $f9,$fa,$fa,$fa,$fa,$fa,$fb,$fb
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.byte $fb,$fb,$fb,$fc,$fc,$fc,$fc,$fc
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.byte $fd,$fd,$fd,$fd,$fd,$fd,$fe,$fe
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.byte $fe,$fe,$fe,$ff,$ff,$ff,$ff,$ff
|
|
; !notreached!
|
|
}}
|
|
}
|
|
|
|
asmsub diff(ubyte v1 @A, ubyte v2 @Y) -> ubyte @A {
|
|
; -- returns the (absolute) difference, or distance, between the two bytes
|
|
%asm {{
|
|
sty P8ZP_SCRATCH_REG
|
|
sec
|
|
sbc P8ZP_SCRATCH_REG
|
|
bcs +
|
|
eor #255
|
|
inc a
|
|
+ rts
|
|
}}
|
|
}
|
|
|
|
asmsub diffw(uword w1 @R0, uword w2 @AY) -> uword @AY {
|
|
; -- returns the (absolute) difference, or distance, between the two words
|
|
%asm {{
|
|
sec
|
|
sbc cx16.r0L
|
|
sta cx16.r0L
|
|
tya
|
|
sbc cx16.r0H
|
|
sta cx16.r0H
|
|
bcs +
|
|
eor #255
|
|
sta cx16.r0H
|
|
lda cx16.r0L
|
|
eor #255
|
|
inc a
|
|
sta cx16.r0L
|
|
bne +
|
|
inc cx16.r0H
|
|
+ lda cx16.r0L
|
|
ldy cx16.r0H
|
|
rts
|
|
}}
|
|
}
|
|
|
|
sub crc16(uword data, uword length) -> uword {
|
|
; calculates the CRC16 (XMODEM) checksum of the buffer.
|
|
; There are also "streaming" crc16_start/update/end routines below, that allow you to calculate crc16 for data that doesn't fit in a single memory block.
|
|
crc16_start()
|
|
cx16.r13 = data
|
|
cx16.r14 = data+length
|
|
while cx16.r13!=cx16.r14 {
|
|
crc16_update(@(cx16.r13))
|
|
cx16.r13++
|
|
}
|
|
return crc16_end()
|
|
}
|
|
|
|
sub crc16_start() {
|
|
; start the "streaming" crc16
|
|
; note: tracks the crc16 checksum in cx16.r15!
|
|
; if your code uses that, it must save/restore it before calling this routine
|
|
cx16.r15 = 0
|
|
}
|
|
|
|
asmsub crc16_update(ubyte value @A) {
|
|
; update the "streaming" crc16 with next byte value
|
|
; note: tracks the crc16 checksum in cx16.r15!
|
|
; if your code uses that, it must save/restore it before calling this routine
|
|
%asm {{
|
|
eor cx16.r15H
|
|
sta cx16.r15H
|
|
ldy #8
|
|
- lda cx16.r15H
|
|
asl cx16.r15L
|
|
rol cx16.r15H
|
|
and #$80
|
|
beq +
|
|
lda cx16.r15H
|
|
eor #$10
|
|
sta cx16.r15H
|
|
lda cx16.r15L
|
|
eor #$21
|
|
sta cx16.r15L
|
|
+ dey
|
|
bne -
|
|
rts
|
|
}}
|
|
; orignal prog8 code was:
|
|
; cx16.r15H ^= value
|
|
; repeat 8 {
|
|
; if cx16.r15H & $80 !=0 {
|
|
; cx16.r15 <<=1
|
|
; cx16.r15 ^= $1021
|
|
; } else
|
|
; cx16.r15<<=1
|
|
; }
|
|
}
|
|
|
|
sub crc16_end() -> uword {
|
|
; finalize the "streaming" crc16, returns resulting crc16 value
|
|
return cx16.r15
|
|
}
|
|
|
|
sub crc32(uword data, uword length) {
|
|
; Calculates the CRC-32 (POSIX) checksum of the buffer.
|
|
; because prog8 doesn't have 32 bits integers, we have to split up the calculation over 2 words.
|
|
; result stored in cx16.r14 (low word) and cx16.r15 (high word)
|
|
; There are also "streaming" crc32_start/update/end routines below, that allow you to calculate crc32 for data that doesn't fit in a single memory block.
|
|
crc32_start()
|
|
cx16.r12 = data
|
|
cx16.r13 = data+length
|
|
while cx16.r12!=cx16.r13 {
|
|
crc32_update(@(cx16.r12))
|
|
cx16.r12++
|
|
}
|
|
crc32_end()
|
|
}
|
|
|
|
sub crc32_start() {
|
|
; start the "streaming" crc32
|
|
; note: tracks the crc32 checksum in cx16.r14 and cx16.r15!
|
|
; if your code uses these, it must save/restore them before calling this routine
|
|
cx16.r14 = cx16.r15 = 0
|
|
}
|
|
|
|
asmsub crc32_update(ubyte value @A) {
|
|
; update the "streaming" crc32 with next byte value
|
|
; note: tracks the crc32 checksum in cx16.r14 and cx16.r15!
|
|
; if your code uses these, it must save/restore them before calling this routine
|
|
%asm {{
|
|
eor cx16.r15H
|
|
sta cx16.r15H
|
|
ldy #8
|
|
- lda cx16.r15H
|
|
asl cx16.r14L
|
|
rol cx16.r14H
|
|
rol cx16.r15L
|
|
rol cx16.r15H
|
|
and #$80
|
|
beq +
|
|
lda cx16.r15H
|
|
eor #$04
|
|
sta cx16.r15H
|
|
lda cx16.r15L
|
|
eor #$c1
|
|
sta cx16.r15L
|
|
lda cx16.r14H
|
|
eor #$1d
|
|
sta cx16.r14H
|
|
lda cx16.r14L
|
|
eor #$b7
|
|
sta cx16.r14L
|
|
+ dey
|
|
bne -
|
|
rts
|
|
}}
|
|
; original prog8 code:
|
|
; cx16.r15H ^= value
|
|
; repeat 8 {
|
|
; if cx16.r15H & $80 !=0 {
|
|
; cx16.r14 <<= 1
|
|
; rol(cx16.r15)
|
|
; cx16.r15 ^= $04c1
|
|
; cx16.r14 ^= $1db7
|
|
; }
|
|
; else {
|
|
; cx16.r14 <<= 1
|
|
; rol(cx16.r15)
|
|
; }
|
|
; }
|
|
|
|
}
|
|
|
|
sub crc32_end() {
|
|
; finalize the "streaming" crc32
|
|
; result stored in cx16.r14 (low word) and cx16.r15 (high word)
|
|
cx16.r15 ^= $ffff
|
|
cx16.r14 ^= $ffff
|
|
}
|
|
|
|
|
|
sub lerp(ubyte v0, ubyte v1, ubyte t) -> ubyte {
|
|
; Linear interpolation (LERP)
|
|
; returns an interpolation between two inputs (v0, v1) for a parameter t in the interval [0, 255]
|
|
; guarantees v = v1 when t = 255
|
|
return v0 + msb(t as uword * (v1 - v0) + 255)
|
|
}
|
|
|
|
sub lerpw(uword v0, uword v1, uword t) -> uword {
|
|
; Linear interpolation (LERP) on word values
|
|
; returns an interpolation between two inputs (v0, v1) for a parameter t in the interval [0, 65535]
|
|
; guarantees v = v1 when t = 65535
|
|
t *= v1-v0
|
|
cx16.r0 = math.mul16_last_upper()
|
|
if t!=0
|
|
cx16.r0++
|
|
return v0 + cx16.r0
|
|
}
|
|
}
|