prog8/prog8lib/mathlib.p8
2018-09-15 16:35:15 +02:00

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; Prog8 integer math library for 6502
; (floating point math is done via the C-64's BASIC ROM routines)
;
; some more interesting routines can be found here:
; http://6502org.wikidot.com/software-math
; http://codebase64.org/doku.php?id=base:6502_6510_maths
;
; Written by Irmen de Jong (irmen@razorvine.net) - license: GNU GPL 3.0
;
; indent format: TABS, size=8
~ math {
; note: the following ZP scratch registers must be the same as in c64lib
memory byte SCRATCH_ZP1 = $02 ; scratch register #1 in ZP
memory byte SCRATCH_ZP2 = $03 ; scratch register #2 in ZP
memory word SCRATCH_ZPWORD1 = $fb ; scratch word in ZP ($fb/$fc)
memory word SCRATCH_ZPWORD2 = $fd ; scratch word in ZP ($fd/$fe)
sub multiply_bytes (byte1: X, byte2: Y) -> (A, X?) {
; ---- multiply 2 bytes, result as byte in A (signed or unsigned)
%asm {{
stx SCRATCH_ZP1
sty SCRATCH_ZP2
ldx #8
- asl a
asl SCRATCH_ZP1
bcc +
clc
adc SCRATCH_ZP2
+ dex
bne -
rts
}}
}
sub multiply_bytes_16 (byte1: X, byte2: Y) -> (A?, XY) {
; ---- multiply 2 bytes, result as word in X/Y (unsigned)
%asm {{
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
}}
}
sub multiply_bytes_addA_16 (byte1: X, byte2: Y, add: A) -> (A?, XY) {
; ---- multiply 2 bytes and add A, result as word in X/Y (unsigned)
%asm {{
jmp multiply_bytes_16._m_with_add
}}
}
word[2] multiply_words_product = 0
sub multiply_words (number: XY) -> (?) {
; ---- 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)
%asm {{
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
}}
}
sub divmod_bytes (number: X, divisor: Y) -> (X, A) {
; ---- divide X by Y, result quotient in X, remainder in A (unsigned)
; division by zero will result in quotient = 255 and remainder = original number
%asm {{
stx SCRATCH_ZP1
sty SCRATCH_ZP2
lda #0
ldx #8
asl SCRATCH_ZP1
- rol a
cmp SCRATCH_ZP2
bcc +
sbc SCRATCH_ZP2
+ rol SCRATCH_ZP1
dex
bne -
ldx SCRATCH_ZP1
rts
}}
}
sub divmod_words (divisor: XY) -> (A?, XY) {
; ---- 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
%asm {{
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
}}
}
sub randbyte () -> (A) {
; ---- 8-bit pseudo random number generator into A
%asm {{
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
}}
}
sub randword () -> (XY) {
; ---- 16 bit pseudo random number generator into XY
%asm {{
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
}}
}
}