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Faster imul16 routine

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Improves runtime from 16.24 ms/px to 14.44 ms/px

This uses a routine found on Everything2:
https://everything2.com/title/Fast+6502+multiplication

which uses a lookup table of squares to do 8-bit imuls,
which are then composed into a 16-bit imul
This commit is contained in:
Brooke Vibber 2023-02-11 12:24:48 -08:00 • committed by Brooke Vibber
commit 5637783529
5 changed files with 183 additions and 81 deletions
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176
mandel.s
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@ -25,14 +25,14 @@ z_buffer_active = $b0 ; boolean: 1 if we triggered the lake, 0 if not
z_buffer_start = $b1 ; u8: index into z_buffer
z_buffer_end = $b2 ; u8: index into z_buffer
temp = $b4 ; u16
pixel_ptr = $b6 ; u16
pixel_color = $b8 ; u8
pixel_mask = $b9 ; u8
pixel_shift = $ba ; u8
pixel_offset = $bb ; u8
fill_level = $bc ; u8
palette_offset = $bd ; u8
temp2 = $b6 ; u16
pixel_ptr = $b8 ; u16
pixel_color = $ba ; u8
pixel_mask = $bb ; u8
pixel_shift = $bc ; u8
pixel_offset = $bd ; u8
fill_level = $be ; u8
palette_offset = $bf ; u8
; FP registers in zero page
FR0 = $d4 ; float48
@ -107,6 +107,10 @@ KEY_RIGHT = $87
mantissa .byte 6
.endstruct
.import mul_lobyte256
.import mul_hibyte256
.import mul_hibyte512
.data
strings:
@ -257,6 +261,12 @@ fill_masks:
add 4, dest, arg2, dest
.endmacro
.macro add_carry dest
lda dest
adc #0
sta dest
.endmacro
; 2 + 9 * byte cycles
.macro sub bytes, dest, arg1, arg2
sec ; 2 cyc
@ -334,65 +344,15 @@ fill_masks:
neg 4, arg
.endmacro
; inner loop for imul16
; bitnum < 8: 25 or 41 cycles
; bitnum >= 8: 30 or 46 cycles
.macro bitmul16 arg1, arg2, result, bitnum
.local zero
.local one
.local next
; does 16-bit adds
; arg1 and arg2 are treated as unsigned
; negative signed inputs must be flipped first
; 7 cycles up to the branch
; check if arg1 has 0 or 1 bit in this place
; 5 cycles either way
.if bitnum < 8
lda arg1 ; 3 cyc
and #(1 << (bitnum)) ; 2 cyc
.else
lda arg1 + 1 ; 3 cyc
and #(1 << ((bitnum) - 8)) ; 2 cyc
.endif
bne one ; 2 cyc
zero: ; 18 cyc, 23 cyc
lsr result + 3 ; 5 cyc
jmp next ; 3 cyc
one: ; 32 cyc, 37 cyc
; 16-bit add on the top bits
clc ; 2 cyc
lda result + 2 ; 3 cyc
adc arg2 ; 3 cyc
sta result + 2 ; 3 cyc
lda result + 3 ; 3 cyc
adc arg2 + 1 ; 3 cyc
ror a ; 2 cyc - get a jump on the shift
sta result + 3 ; 3 cyc
next:
ror result + 2 ; 5 cyc
ror result + 1 ; 5 cyc
.if bitnum >= 8
; we can save 5 cycles * 8 bits = 40 cycles total by skipping this byte
; when it's all uninitialized data
ror result ; 5 cyc
.endif
.endmacro
; 5 to 25 cycles
.macro check_sign arg
; Check sign bit and flip argument to postive,
; keeping a count of sign bits in the X register.
; keeping a count of sign bits in the Y register.
.local positive
lda arg + 1 ; 3 cyc
bpl positive ; 2 cyc
neg16 arg ; 18 cyc
inx ; 2 cyc
iny ; 2 cyc
positive:
.endmacro
@ -419,35 +379,93 @@ positive:
copy16 dest, FR2 + 2 ; 12 cyc
.endmacro
; min 470 cycles
; max 780 cycles
; Adapted from https://everything2.com/title/Fast+6502+multiplication
.macro imul8 dest, arg1, arg2
.local under256
.local next
.local small_product
.scope
mul_factor_a = arg1
mul_factor_x = arg2
mul_product_lo = dest
mul_product_hi = dest + 1
lda mul_factor_a ; setup: 6 cycles
;ldx mul_factor_x
clc ; (a + x)^2/2: 23 cycles
adc mul_factor_x
tax
bcc under256
lda mul_hibyte512,x
bcs next
under256:
lda mul_hibyte256,x
sec
next:
sta mul_product_hi
lda mul_lobyte256,x
ldx mul_factor_a ; - a^2/2: 20 cycles
sbc mul_lobyte256,x
sta mul_product_lo
lda mul_product_hi
sbc mul_hibyte256,x
sta mul_product_hi
ldx mul_factor_x ; + x & a & 1: 22 cycles
txa ; (this is a kludge to correct a
and mul_factor_a ; roundoff error that makes odd * odd too low)
and #1
clc
adc mul_product_lo
bcc small_product
inc mul_product_hi
small_product:
sec ; - x^2/2: 25 cycles
sbc mul_lobyte256,x
sta mul_product_lo
lda mul_product_hi
sbc mul_hibyte256,x
sta mul_product_hi
.endscope
.endmacro
.proc imul16_func
arg1 = FR0 ; 16-bit arg (clobbered)
arg2 = FR1 ; 16-bit arg (clobbered)
result = FR2 ; 32-bit result
inter = temp2
ldx #0 ; 2 cyc
; counts the number of sign bits in X
ldy #0 ; 2 cyc
; counts the number of sign bits in Y
check_sign arg1 ; 5 to 25 cyc
check_sign arg2 ; 5 to 25 cyc
; zero out the 32-bit temp's top 16 bits
lda #0 ; 2 cyc
sta result + 2 ; 3 cyc
sta result + 3 ; 3 cyc
; the bottom two bytes will get cleared by the shifts
; unrolled loop for maximum speed, at the cost
; of a larger routine
; 440 to 696 cycles
.repeat 16, bitnum
; bitnum < 8: 25 or 41 cycles
; bitnum >= 8: 30 or 46 cycles
bitmul16 arg1, arg2, result, bitnum
.endrepeat
; h1l1 * h2l2
; (h1*256 + l1) * (h2*256 + l2)
; h1*256*(h2*256 + l2) + l1*(h2*256 + l2)
; h1*h2*256*256 + h1*l2*256 + h2*l1*256 + l1*l2
imul8 result, arg1, arg2
lda #0
sta result + 2
sta result + 3
imul8 inter, arg1 + 1, arg2
add16 result + 1, result + 1, inter
add_carry result + 3
imul8 inter, arg1, arg2 + 1
add16 result + 1, result + 1, inter
add_carry result + 3
imul8 inter, arg1 + 1, arg2 + 1
add16 result + 2, result + 2, inter
; In case of mixed input signs, return a negative result.
cpx #1 ; 2 cyc
cpy #1 ; 2 cyc
bne positive_result ; 2 cyc
neg32 result ; 34 cyc
positive_result: