prog8/prog8lib/mathlib.p8

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; Prog8 integer math library for 6502
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; (floating point math is done via the C-64's BASIC ROM routines)
;
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; some more interesting routines can be found here:
; http://6502org.wikidot.com/software-math
; http://codebase64.org/doku.php?id=base:6502_6510_maths
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;
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; Written by Irmen de Jong (irmen@razorvine.net) - license: GNU GPL 3.0
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;
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; indent format: TABS, size=8
~ math {
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; note: the following ZP scratch registers must be the same as in c64lib
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memory ubyte SCRATCH_ZP1 = $02 ; scratch register #1 in ZP
memory ubyte SCRATCH_ZP2 = $03 ; scratch register #2 in ZP
memory uword SCRATCH_ZPWORD1 = $fb ; scratch word in ZP ($fb/$fc)
memory uword SCRATCH_ZPWORD2 = $fd ; scratch word in ZP ($fd/$fe)
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asmsub multiply_bytes (byte1: ubyte @ X, byte2: ubyte @ Y) -> clobbers(X) -> (ubyte @ A) {
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; ---- multiply 2 bytes, result as byte in A (signed or unsigned)
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%asm {{
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stx SCRATCH_ZP1
sty SCRATCH_ZP2
ldx #8
- asl a
asl SCRATCH_ZP1
bcc +
clc
adc SCRATCH_ZP2
+ dex
bne -
rts
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}}
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}
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asmsub multiply_bytes_16 (byte1: ubyte @ X, byte2: ubyte @ Y) -> clobbers(A) -> (uword @ XY) {
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; ---- multiply 2 bytes, result as word in X/Y (unsigned)
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%asm {{
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lda #0
_m_with_add stx SCRATCH_ZP1
sty SCRATCH_ZP2
ldx #8
lsr SCRATCH_ZP1
- bcc +
clc
adc SCRATCH_ZP2
+ ror a
ror SCRATCH_ZP1
dex
bne -
tay
ldx SCRATCH_ZP1
rts
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}}
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}
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asmsub multiply_bytes_addA_16 (byte1: ubyte @ X, byte2: ubyte @ Y, add: ubyte @ A) -> clobbers(A) -> (uword @ XY) {
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; ---- multiply 2 bytes and add A, result as word in X/Y (unsigned)
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%asm {{
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jmp multiply_bytes_16._m_with_add
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}}
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}
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word[2] multiply_words_product = 0
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asmsub multiply_words (number: uword @ XY) -> clobbers(A,X) -> () {
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; ---- multiply two 16-bit words into a 32-bit result
; input: X/Y = first 16-bit number, SCRATCH_ZPWORD1 in ZP = second 16-bit number
; output: multiply_words_product 32-bits product, LSB order (low-to-high)
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%asm {{
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stx SCRATCH_ZPWORD2
sty SCRATCH_ZPWORD2+1
mult16 lda #$00
sta multiply_words_product+2 ; clear upper bits of product
sta multiply_words_product+3
ldx #16 ; for all 16 bits...
- lsr SCRATCH_ZPWORD1+1 ; divide multiplier by 2
ror SCRATCH_ZPWORD1
bcc +
lda multiply_words_product+2 ; get upper half of product and add multiplicand
clc
adc SCRATCH_ZPWORD2
sta multiply_words_product+2
lda multiply_words_product+3
adc SCRATCH_ZPWORD2+1
+ ror a ; rotate partial product
sta multiply_words_product+3
ror multiply_words_product+2
ror multiply_words_product+1
ror multiply_words_product
dex
bne -
rts
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}}
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}
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asmsub divmod_bytes (number: ubyte @ X, divisor: ubyte @ Y) -> clobbers() -> (ubyte @ X, ubyte @ A) {
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; ---- divide X by Y, result quotient in X, remainder in A (unsigned)
; division by zero will result in quotient = 255 and remainder = original number
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%asm {{
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stx SCRATCH_ZP1
sty SCRATCH_ZP2
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lda #0
ldx #8
asl SCRATCH_ZP1
- rol a
cmp SCRATCH_ZP2
bcc +
sbc SCRATCH_ZP2
+ rol SCRATCH_ZP1
dex
bne -
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ldx SCRATCH_ZP1
rts
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}}
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}
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asmsub divmod_words (divisor: uword @ XY) -> clobbers(A) -> (uword @ XY) {
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; ---- divide two words (16 bit each) into 16 bit results
; input: SCRATCH_ZPWORD1 in ZP: 16 bit number, X/Y: 16 bit divisor
; output: SCRATCH_ZPWORD1 in ZP: 16 bit result, X/Y: 16 bit remainder
; division by zero will result in quotient = 65535 and remainder = divident
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%asm {{
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remainder = SCRATCH_ZP1
stx SCRATCH_ZPWORD2
sty SCRATCH_ZPWORD2+1
lda #0 ;preset remainder to 0
sta remainder
sta remainder+1
ldx #16 ;repeat for each bit: ...
- asl SCRATCH_ZPWORD1 ;number lb & hb*2, msb -> Carry
rol SCRATCH_ZPWORD1+1
rol remainder ;remainder lb & hb * 2 + msb from carry
rol remainder+1
lda remainder
sec
sbc SCRATCH_ZPWORD2 ;substract divisor to see if it fits in
tay ;lb result -> Y, for we may need it later
lda remainder+1
sbc SCRATCH_ZPWORD2+1
bcc + ;if carry=0 then divisor didn't fit in yet
sta remainder+1 ;else save substraction result as new remainder,
sty remainder
inc SCRATCH_ZPWORD1 ;and INCrement result cause divisor fit in 1 times
+ dex
bne -
lda remainder ; copy remainder to ZPWORD2 result register
sta SCRATCH_ZPWORD2
lda remainder+1
sta SCRATCH_ZPWORD2+1
ldx SCRATCH_ZPWORD1 ; load division result in X/Y
ldy SCRATCH_ZPWORD1+1
rts
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}}
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}
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asmsub randbyte () -> clobbers() -> (ubyte @ A) {
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; ---- 8-bit pseudo random number generator into A
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%asm {{
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lda _seed
beq +
asl a
beq ++ ;if the input was $80, skip the EOR
bcc ++
+ eor _magic ; #$1d ; could be self-modifying code to set new magic
+ sta _seed
rts
_seed .byte $3a
_magic .byte $1d
_magiceors .byte $1d, $2b, $2d, $4d, $5f, $63, $65, $69
.byte $71, $87, $8d, $a9, $c3, $cf, $e7, $f5
;returns - this comment avoids compiler warning
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}}
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}
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asmsub randword () -> clobbers() -> (uword @ XY) {
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; ---- 16 bit pseudo random number generator into XY
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%asm {{
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lda _seed
beq _lowZero ; $0000 and $8000 are special values to test for
; Do a normal shift
asl _seed
lda _seed+1
rol a
bcc _noEor
_doEor ; high byte is in A
eor _magic+1 ; #>magic ; could be self-modifying code to set new magic
sta _seed+1
lda _seed
eor _magic ; #<magic ; could be self-modifying code to set new magic
sta _seed
tax
ldy _seed+1
rts
_lowZero lda _seed+1
beq _doEor ; High byte is also zero, so apply the EOR
; For speed, you could store 'magic' into 'seed' directly
; instead of running the EORs
; wasn't zero, check for $8000
asl a
beq _noEor ; if $00 is left after the shift, then it was $80
bcs _doEor ; else, do the EOR based on the carry bit as usual
_noEor sta _seed+1
tay
ldx _seed
rts
_seed .word $2c9e
_magic .word $3f1d
_magiceors .word $3f1d, $3f81, $3fa5, $3fc5, $4075, $409d, $40cd, $4109
.word $413f, $414b, $4153, $4159, $4193, $4199, $41af, $41bb
;returns - this comment avoids compiler warning
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}}
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}
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}