mirror of
https://github.com/irmen/prog8.git
synced 2024-11-23 07:32:10 +00:00
551 lines
14 KiB
Lua
551 lines
14 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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%asminclude "library:math.asm"
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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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}}
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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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}}
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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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}}
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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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}}
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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 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 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 math.randword.x1
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sty math.randword.c1
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lda cx16.r0L
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sta math.randword.a1
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lda cx16.r0H
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sta 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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}}
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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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%asm {{
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lda multiply_words.result+2
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ldy 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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}}
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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
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}}
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}
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asmsub diff(ubyte v1 @A, ubyte v2 @Y) -> ubyte @A {
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; -- returns the (absolute) difference, or distance, between the two bytes
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%asm {{
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sty P8ZP_SCRATCH_REG
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sec
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sbc P8ZP_SCRATCH_REG
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bcs +
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eor #255
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inc a
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+ rts
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}}
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}
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asmsub diffw(uword w1 @R0, uword w2 @AY) -> uword @AY {
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; -- returns the (absolute) difference, or distance, between the two words
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%asm {{
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sec
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sbc cx16.r0L
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sta cx16.r0L
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tya
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sbc cx16.r0H
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sta cx16.r0H
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bcs +
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eor #255
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sta cx16.r0H
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lda cx16.r0L
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eor #255
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inc a
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sta cx16.r0L
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bne +
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inc cx16.r0H
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+ lda cx16.r0L
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ldy cx16.r0H
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rts
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}}
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}
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sub crc16(uword data, uword length) -> uword {
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; calculates the CRC16 (XMODEM) checksum of the buffer.
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cx16.r1 = data ; make sure pointer is in zp (on cx16)
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cx16.r0 = 0 ; the crc value
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repeat length {
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cx16.r0H ^= @(cx16.r1)
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repeat 8 {
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if cx16.r0H & $80 !=0 {
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cx16.r0 <<= 1
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cx16.r0 ^= $1021
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}
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else
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cx16.r0<<=1
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}
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cx16.r1++
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}
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return cx16.r0
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}
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sub crc32(uword data, uword length) {
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; Calculates the CRC-32 (POSIX) checksum of the buffer.
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; because prog8 doesn't have 32 bits integers, we have to split up the calculation over 2 words.
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; result stored in cx16.r0 (low word) and cx16.r1 (high word)
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cx16.r2 = data ; make sure pointer is in zp (on cx16)
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cx16.r1 = 0
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cx16.r0 = 0
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repeat length {
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cx16.r1H ^= @(cx16.r2)
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repeat 8 {
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if cx16.r1H & $80 !=0 {
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cx16.r0 <<= 1
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rol(cx16.r1)
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cx16.r1 ^= $04c1
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cx16.r0 ^= $1db7
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}
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else {
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cx16.r0 <<= 1
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rol(cx16.r1)
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}
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}
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cx16.r2++
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}
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cx16.r1 ^= $ffff
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cx16.r0 ^= $ffff
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}
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}
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