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prog8/compiler/res/prog8lib/math.asm
Irmen de Jong 50a85ee6b0 attempt to optimize asm for bitshifts more.
2020-03-23 22:59:29 +01:00

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NASM
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; Prog8 internal Math library routines - always included by the compiler
;
; Written by Irmen de Jong (irmen@razorvine.net) - license: GNU GPL 3.0
;
; indent format: TABS, size=8
; some more interesting routines can be found here:
; http://6502org.wikidot.com/software-math
; http://codebase64.org/doku.php?id=base:6502_6510_maths
;
multiply_bytes .proc
; -- multiply 2 bytes A and Y, result as byte in A (signed or unsigned)
sta c64.SCRATCH_ZPB1 ; num1
sty c64.SCRATCH_ZPREG ; num2
lda #0
beq _enterloop
_doAdd clc
adc c64.SCRATCH_ZPB1
_loop asl c64.SCRATCH_ZPB1
_enterloop lsr c64.SCRATCH_ZPREG
bcs _doAdd
bne _loop
rts
.pend
multiply_bytes_16 .proc
; -- multiply 2 bytes A and Y, result as word in A/Y (unsigned)
sta c64.SCRATCH_ZPB1
sty c64.SCRATCH_ZPREG
stx c64.SCRATCH_ZPREGX
lda #0
ldx #8
lsr c64.SCRATCH_ZPB1
- bcc +
clc
adc c64.SCRATCH_ZPREG
+ ror a
ror c64.SCRATCH_ZPB1
dex
bne -
tay
lda c64.SCRATCH_ZPB1
ldx c64.SCRATCH_ZPREGX
rts
.pend
multiply_words .proc
; -- multiply two 16-bit words into a 32-bit result (signed and unsigned)
; input: A/Y = first 16-bit number, c64.SCRATCH_ZPWORD1 in ZP = second 16-bit number
; output: multiply_words.result 4-bytes/32-bits product, LSB order (low-to-high)
sta c64.SCRATCH_ZPWORD2
sty c64.SCRATCH_ZPWORD2+1
stx c64.SCRATCH_ZPREGX
mult16 lda #$00
sta result+2 ; clear upper bits of product
sta result+3
ldx #16 ; for all 16 bits...
- lsr c64.SCRATCH_ZPWORD1+1 ; divide multiplier by 2
ror c64.SCRATCH_ZPWORD1
bcc +
lda result+2 ; get upper half of product and add multiplicand
clc
adc c64.SCRATCH_ZPWORD2
sta result+2
lda result+3
adc c64.SCRATCH_ZPWORD2+1
+ ror a ; rotate partial product
sta result+3
ror result+2
ror result+1
ror result
dex
bne -
ldx c64.SCRATCH_ZPREGX
rts
result .byte 0,0,0,0
.pend
divmod_ub .proc
; -- divide A by Y, result quotient in Y, remainder in A (unsigned)
; division by zero will result in quotient = 255 and remainder = original number
sty c64.SCRATCH_ZPREG
sta c64.SCRATCH_ZPB1
stx c64.SCRATCH_ZPREGX
lda #0
ldx #8
asl c64.SCRATCH_ZPB1
- rol a
cmp c64.SCRATCH_ZPREG
bcc +
sbc c64.SCRATCH_ZPREG
+ rol c64.SCRATCH_ZPB1
dex
bne -
ldy c64.SCRATCH_ZPB1
ldx c64.SCRATCH_ZPREGX
rts
.pend
divmod_uw_asm .proc
; -- divide two unsigned words (16 bit each) into 16 bit results
; input: c64.SCRATCH_ZPWORD1 in ZP: 16 bit number, A/Y: 16 bit divisor
; output: c64.SCRATCH_ZPWORD2 in ZP: 16 bit remainder, A/Y: 16 bit division result
; division by zero will result in quotient = 65535 and remainder = divident
dividend = c64.SCRATCH_ZPWORD1
remainder = c64.SCRATCH_ZPWORD2
result = dividend ;save memory by reusing divident to store the result
sta _divisor
sty _divisor+1
stx c64.SCRATCH_ZPREGX
lda #0 ;preset remainder to 0
sta remainder
sta remainder+1
ldx #16 ;repeat for each bit: ...
- asl dividend ;dividend lb & hb*2, msb -> Carry
rol dividend+1
rol remainder ;remainder lb & hb * 2 + msb from carry
rol remainder+1
lda remainder
sec
sbc _divisor ;substract divisor to see if it fits in
tay ;lb result -> Y, for we may need it later
lda remainder+1
sbc _divisor+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 result ;and INCrement result cause divisor fit in 1 times
+ dex
bne -
lda result
ldy result+1
ldx c64.SCRATCH_ZPREGX
rts
_divisor .word 0
.pend
randseed .proc
; -- reset the random seeds for the byte and word random generators
; arguments: uword seed in A/Y clobbers A
; (default starting values are: A=$2c Y=$9e)
sta randword._seed
sty randword._seed+1
clc
adc #14
sta randbyte._seed
rts
.pend
randbyte .proc
; -- 8-bit pseudo random number generator into A
lda _seed
beq _eor
asl a
beq _done ; if the input was $80, skip the EOR
bcc _done
_eor eor #$1d ; xor with magic value see below for possible values
_done sta _seed
rts
_seed .byte $3a
; possible 'magic' eor bytes are:
; $1d, $2b, $2d, $4d, $5f, $63, $65, $69
; $71, $87, $8d, $a9, $c3, $cf, $e7, $f5
.pend
randword .proc
; -- 16 bit pseudo random number generator into AY
magic_eor = $3f1d
; possible magic eor words are:
; $3f1d, $3f81, $3fa5, $3fc5, $4075, $409d, $40cd, $4109
; $413f, $414b, $4153, $4159, $4193, $4199, $41af, $41bb
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_eor
sta _seed+1
lda _seed
eor #<magic_eor
sta _seed
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
lda _seed
rts
_seed .word $2c9e
.pend
mul_byte_3 .proc
; X + X*2
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_3 .proc
; W*2 + W
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_5 .proc
; X*4 + X
lda c64.ESTACK_LO+1,x
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_5 .proc
; W*4 + W
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_6 .proc
; (X*2 + X)*2
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_6 .proc
; (W*2 + W)*2
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
asl c64.ESTACK_LO+1,x
rol a
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_7 .proc
; X*8 - X
lda c64.ESTACK_LO+1,x
asl a
asl a
asl a
sec
sbc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_7 .proc
; W*8 - W
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
sec
sbc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
sbc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_9 .proc
; X*8 + X
lda c64.ESTACK_LO+1,x
asl a
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_9 .proc
; W*8 + W
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_10 .proc
; (X*4 + X)*2
lda c64.ESTACK_LO+1,x
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_10 .proc
; (W*4 + W)*2
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
asl c64.ESTACK_LO+1,x
rol a
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_11 .proc
; (X*2 + X)*4 - X
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
sec
sbc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
; mul_word_11 is skipped (too much code)
mul_byte_12 .proc
; (X*2 + X)*4
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_12 .proc
; (W*2 + W)*4
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
asl c64.ESTACK_LO+1,x
rol a
asl c64.ESTACK_LO+1,x
rol a
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_13 .proc
; (X*2 + X)*4 + X
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
; mul_word_13 is skipped (too much code)
mul_byte_14 .proc
; (X*8 - X)*2
lda c64.ESTACK_LO+1,x
asl a
asl a
asl a
sec
sbc c64.ESTACK_LO+1,x
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
; mul_word_14 is skipped (too much code)
mul_byte_15 .proc
; X*16 - X
lda c64.ESTACK_LO+1,x
asl a
asl a
asl a
asl a
sec
sbc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_15 .proc
; W*16 - W
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
sec
sbc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
sbc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_20 .proc
; (X*4 + X)*4
lda c64.ESTACK_LO+1,x
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_20 .proc
; (W*4 + W)*4
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
asl c64.ESTACK_LO+1,x
rol a
asl c64.ESTACK_LO+1,x
rol a
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_25 .proc
; (X*2 + X)*8 + X
lda c64.ESTACK_LO+1,x
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_25 .proc
; W + W*8 + W*16
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPWORD1+1
asl a
rol c64.SCRATCH_ZPWORD1+1
asl a
rol c64.SCRATCH_ZPWORD1+1
sta c64.SCRATCH_ZPWORD1
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPWORD1+1
adc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
lda c64.SCRATCH_ZPWORD1
asl a
rol c64.SCRATCH_ZPWORD1+1
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPWORD1+1
adc c64.ESTACK_HI+1,x
sta c64.ESTACK_HI+1,x
rts
.pend
mul_byte_40 .proc
; (X*4 + X)*8
lda c64.ESTACK_LO+1,x
asl a
asl a
clc
adc c64.ESTACK_LO+1,x
asl a
asl a
asl a
sta c64.ESTACK_LO+1,x
rts
.pend
mul_word_40 .proc
; (W*4 + W)*8
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPREG
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPREG
asl a
rol c64.SCRATCH_ZPREG
clc
adc c64.ESTACK_LO+1,x
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPREG
adc c64.ESTACK_HI+1,x
asl c64.ESTACK_LO+1,x
rol a
asl c64.ESTACK_LO+1,x
rol a
asl c64.ESTACK_LO+1,x
rol a
sta c64.ESTACK_HI+1,x
rts
.pend
sign_b .proc
lda c64.ESTACK_LO+1,x
beq _sign_zero
bmi _sign_neg
_sign_pos lda #1
sta c64.ESTACK_LO+1,x
rts
_sign_neg lda #-1
_sign_zero sta c64.ESTACK_LO+1,x
rts
.pend
sign_ub .proc
lda c64.ESTACK_LO+1,x
beq sign_b._sign_zero
bne sign_b._sign_pos
.pend
sign_w .proc
lda c64.ESTACK_HI+1,x
bmi sign_b._sign_neg
beq sign_ub
bne sign_b._sign_pos
.pend
sign_uw .proc
lda c64.ESTACK_HI+1,x
beq _sign_possibly_zero
_sign_pos lda #1
sta c64.ESTACK_LO+1,x
rts
_sign_possibly_zero lda c64.ESTACK_LO+1,x
bne _sign_pos
sta c64.ESTACK_LO+1,x
rts
.pend
; bit shifts.
; anything below 3 is done inline. anything above 7 is done via other optimizations.
shift_left_w_7 .proc
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_LO+1,x
asl a
rol c64.SCRATCH_ZPB1
_shift6 asl a
rol c64.SCRATCH_ZPB1
_shift5 asl a
rol c64.SCRATCH_ZPB1
_shift4 asl a
rol c64.SCRATCH_ZPB1
_shift3 asl a
rol c64.SCRATCH_ZPB1
asl a
rol c64.SCRATCH_ZPB1
asl a
rol c64.SCRATCH_ZPB1
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPB1
sta c64.ESTACK_HI+1,x
rts
.pend
shift_left_w_6 .proc
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_LO+1,x
jmp shift_left_w_7._shift6
.pend
shift_left_w_5 .proc
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_LO+1,x
jmp shift_left_w_7._shift5
.pend
shift_left_w_4 .proc
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_LO+1,x
jmp shift_left_w_7._shift4
.pend
shift_left_w_3 .proc
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_LO+1,x
jmp shift_left_w_7._shift3
.pend
shift_right_uw_7 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_HI+1,x
lsr a
ror c64.SCRATCH_ZPB1
_shift6 lsr a
ror c64.SCRATCH_ZPB1
_shift5 lsr a
ror c64.SCRATCH_ZPB1
_shift4 lsr a
ror c64.SCRATCH_ZPB1
_shift3 lsr a
ror c64.SCRATCH_ZPB1
lsr a
ror c64.SCRATCH_ZPB1
lsr a
ror c64.SCRATCH_ZPB1
sta c64.ESTACK_HI+1,x
lda c64.SCRATCH_ZPB1
sta c64.ESTACK_LO+1,x
rts
.pend
shift_right_uw_6 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_HI+1,x
jmp shift_right_uw_7._shift6
.pend
shift_right_uw_5 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_HI+1,x
jmp shift_right_uw_7._shift5
.pend
shift_right_uw_4 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_HI+1,x
jmp shift_right_uw_7._shift4
.pend
shift_right_uw_3 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPB1
lda c64.ESTACK_HI+1,x
jmp shift_right_uw_7._shift3
.pend
shift_right_w_7 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPWORD1
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
_shift6 asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
_shift5 asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
_shift4 asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
_shift3 asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1+1
asl a
ror c64.SCRATCH_ZPWORD1+1
ror c64.SCRATCH_ZPWORD1
lda c64.SCRATCH_ZPWORD1
sta c64.ESTACK_LO+1,x
lda c64.SCRATCH_ZPWORD1+1
sta c64.ESTACK_HI+1,x
rts
.pend
shift_right_w_6 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPWORD1
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
jmp shift_right_w_7._shift6
.pend
shift_right_w_5 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPWORD1
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
jmp shift_right_w_7._shift5
.pend
shift_right_w_4 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPWORD1
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
jmp shift_right_w_7._shift4
.pend
shift_right_w_3 .proc
lda c64.ESTACK_LO+1,x
sta c64.SCRATCH_ZPWORD1
lda c64.ESTACK_HI+1,x
sta c64.SCRATCH_ZPWORD1+1
jmp shift_right_w_7._shift3
.pend
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