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prog8/compiler/res/prog8lib/math.asm

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; Internal Math library routines - always included by the compiler
; Generic machine independent 6502 code.
;
; Written by Irmen de Jong (irmen@razorvine.net) - license: GNU GPL 3.0
;
; some more interesting routines can be found here:
; http://6502org.wikidot.com/software-math
; http://codebase64.org/doku.php?id=base:6502_6510_maths
;
math_store_reg .byte 0 ; temporary storage
multiply_bytes .proc
; -- multiply 2 bytes A and Y, result as byte in A (signed or unsigned)
sta P8ZP_SCRATCH_B1 ; num1
sty P8ZP_SCRATCH_REG ; num2
lda #0
beq _enterloop
_doAdd clc
adc P8ZP_SCRATCH_B1
_loop asl P8ZP_SCRATCH_B1
_enterloop lsr P8ZP_SCRATCH_REG
bcs _doAdd
bne _loop
rts
.pend
multiply_bytes_into_word .proc
; -- multiply 2 bytes A and Y, result as word in A/Y (unsigned)
sta P8ZP_SCRATCH_B1
sty P8ZP_SCRATCH_REG
stx math_store_reg
lda #0
ldx #8
lsr P8ZP_SCRATCH_B1
- bcc +
clc
adc P8ZP_SCRATCH_REG
+ ror a
ror P8ZP_SCRATCH_B1
dex
bne -
tay
lda P8ZP_SCRATCH_B1
ldx math_store_reg
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, P8ZP_SCRATCH_W1 in ZP = second 16-bit number
; output: multiply_words.result 4-bytes/32-bits product, LSB order (low-to-high)
; clobbers: A
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
stx P8ZP_SCRATCH_REG
mult16 lda #0
sta result+2 ; clear upper bits of product
sta result+3
ldx #16 ; for all 16 bits...
- lsr P8ZP_SCRATCH_W1+1 ; divide multiplier by 2
ror P8ZP_SCRATCH_W1
bcc +
lda result+2 ; get upper half of product and add multiplicand
clc
adc P8ZP_SCRATCH_W2
sta result+2
lda result+3
adc P8ZP_SCRATCH_W2+1
+ ror a ; rotate partial product
sta result+3
ror result+2
ror result+1
ror result
dex
bne -
ldx P8ZP_SCRATCH_REG
rts
result .byte 0,0,0,0
.pend
divmod_b_asm .proc
; signed byte division: make everything positive and fix sign afterwards
sta P8ZP_SCRATCH_B1
tya
eor P8ZP_SCRATCH_B1
php ; save sign
lda P8ZP_SCRATCH_B1
bpl +
eor #$ff
sec
adc #0 ; make it positive
+ pha
tya
bpl +
eor #$ff
sec
adc #0 ; make it positive
tay
+ pla
jsr divmod_ub_asm
sta _remainder
plp
bpl +
tya
eor #$ff
sec
adc #0 ; negate result
tay
+ rts
_remainder .byte 0
.pend
divmod_ub_asm .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 P8ZP_SCRATCH_REG
sta P8ZP_SCRATCH_B1
stx math_store_reg
lda #0
ldx #8
asl P8ZP_SCRATCH_B1
- rol a
cmp P8ZP_SCRATCH_REG
bcc +
sbc P8ZP_SCRATCH_REG
+ rol P8ZP_SCRATCH_B1
dex
bne -
ldy P8ZP_SCRATCH_B1
ldx math_store_reg
rts
.pend
divmod_w_asm .proc
; signed word division: make everything positive and fix sign afterwards
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
lda P8ZP_SCRATCH_W1+1
eor P8ZP_SCRATCH_W2+1
php ; save sign
lda P8ZP_SCRATCH_W1+1
bpl +
lda #0
sec
sbc P8ZP_SCRATCH_W1
sta P8ZP_SCRATCH_W1
lda #0
sbc P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W1+1
+ lda P8ZP_SCRATCH_W2+1
bpl +
lda #0
sec
sbc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W2
lda #0
sbc P8ZP_SCRATCH_W2+1
sta P8ZP_SCRATCH_W2+1
+ tay
lda P8ZP_SCRATCH_W2
jsr divmod_uw_asm
plp ; restore sign
bpl +
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
lda #0
sec
sbc P8ZP_SCRATCH_W2
pha
lda #0
sbc P8ZP_SCRATCH_W2+1
tay
pla
+ rts
.pend
divmod_uw_asm .proc
; -- divide two unsigned words (16 bit each) into 16 bit results
; input: P8ZP_SCRATCH_W1 in ZP: 16 bit number, A/Y: 16 bit divisor
; output: P8ZP_SCRATCH_W2 in ZP: 16 bit remainder, A/Y: 16 bit division result
; division by zero will result in quotient = 65535 and remainder = divident
dividend = P8ZP_SCRATCH_W1
remainder = P8ZP_SCRATCH_W2
result = dividend ;save memory by reusing divident to store the result
sta _divisor
sty _divisor+1
stx P8ZP_SCRATCH_REG
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 P8ZP_SCRATCH_REG
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 (by just reusing randword)
jmp randword
.pend
randword .proc
; -- 16 bit pseudo random number generator into AY
; rand64k ;Factors of 65535: 3 5 17 257
lda sr1+1
asl a
asl a
eor sr1+1
asl a
eor sr1+1
asl a
asl a
eor sr1+1
asl a
rol sr1 ;shift this left, "random" bit comes from low
rol sr1+1
; rand32k ;Factors of 32767: 7 31 151 are independent and can be combined
lda sr2+1
asl a
eor sr2+1
asl a
asl a
ror sr2 ;shift this right, random bit comes from high - nicer when eor with sr1
rol sr2+1
lda sr1+1 ;can be left out
eor sr2+1 ;if you dont use
tay ;y as suggested
lda sr1 ;mix up lowbytes of SR1
eor sr2 ;and SR2 to combine both
rts
sr1 .word $a55a
sr2 .word $7653
.pend
; ----------- optimized multiplications (stack) : ---------
stack_mul_byte_3 .proc
; X + X*2
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_3 .proc
; W*2 + W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_5 .proc
; X*4 + X
lda P8ESTACK_LO+1,x
asl a
asl a
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_5 .proc
; W*4 + W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_6 .proc
; (X*2 + X)*2
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
asl a
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_6 .proc
; (W*2 + W)*2
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol a
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_7 .proc
; X*8 - X
lda P8ESTACK_LO+1,x
asl a
asl a
asl a
sec
sbc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_7 .proc
; W*8 - W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
sec
sbc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
sbc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_9 .proc
; X*8 + X
lda P8ESTACK_LO+1,x
asl a
asl a
asl a
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_9 .proc
; W*8 + W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_10 .proc
; (X*4 + X)*2
lda P8ESTACK_LO+1,x
asl a
asl a
clc
adc P8ESTACK_LO+1,x
asl a
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_10 .proc
; (W*4 + W)*2
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol a
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_11 .proc
; (X*2 + X)*4 - X
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
asl a
asl a
sec
sbc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
; mul_word_11 is skipped (too much code)
stack_mul_byte_12 .proc
; (X*2 + X)*4
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
asl a
asl a
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_12 .proc
; (W*2 + W)*4
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol a
asl P8ESTACK_LO+1,x
rol a
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_13 .proc
; (X*2 + X)*4 + X
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
asl a
asl a
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
; mul_word_13 is skipped (too much code)
stack_mul_byte_14 .proc
; (X*8 - X)*2
lda P8ESTACK_LO+1,x
asl a
asl a
asl a
sec
sbc P8ESTACK_LO+1,x
asl a
sta P8ESTACK_LO+1,x
rts
.pend
; mul_word_14 is skipped (too much code)
stack_mul_byte_15 .proc
; X*16 - X
lda P8ESTACK_LO+1,x
asl a
asl a
asl a
asl a
sec
sbc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_15 .proc
; W*16 - W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
sec
sbc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
sbc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_20 .proc
; (X*4 + X)*4
lda P8ESTACK_LO+1,x
asl a
asl a
clc
adc P8ESTACK_LO+1,x
asl a
asl a
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_20 .proc
; (W*4 + W)*4
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol a
asl P8ESTACK_LO+1,x
rol a
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_25 .proc
; (X*2 + X)*8 + X
lda P8ESTACK_LO+1,x
asl a
clc
adc P8ESTACK_LO+1,x
asl a
asl a
asl a
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_25 .proc
; W = (W*2 + W) *8 + W
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
lda P8ZP_SCRATCH_W1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_W1+1
adc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_40 .proc
lda P8ESTACK_LO+1,x
and #7
tay
lda mul_byte_40._forties,y
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_40 .proc
; (W*4 + W)*8
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_REG
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
clc
adc P8ESTACK_LO+1,x
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_REG
adc P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol a
asl P8ESTACK_LO+1,x
rol a
asl P8ESTACK_LO+1,x
rol a
sta P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_50 .proc
lda P8ESTACK_LO+1,x
and #7
tay
lda mul_byte_50._fifties, y
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_50 .proc
; W = W * 25 * 2
jsr stack_mul_word_25
asl P8ESTACK_LO+1,x
rol P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_80 .proc
lda P8ESTACK_LO+1,x
and #3
tay
lda mul_byte_80._eighties, y
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_80 .proc
; W = W * 40 * 2
jsr stack_mul_word_40
asl P8ESTACK_LO+1,x
rol P8ESTACK_HI+1,x
rts
.pend
stack_mul_byte_100 .proc
lda P8ESTACK_LO+1,x
and #3
tay
lda mul_byte_100._hundreds, y
sta P8ESTACK_LO+1,x
rts
.pend
stack_mul_word_100 .proc
; W = W * 25 * 4
jsr stack_mul_word_25
asl P8ESTACK_LO+1,x
rol P8ESTACK_HI+1,x
asl P8ESTACK_LO+1,x
rol P8ESTACK_HI+1,x
rts
.pend
stack_mul_word_320 .proc
; stackW = stackLo * 256 + stackLo * 64 (stackHi doesn't matter)
ldy P8ESTACK_LO+1,x
lda #0
sta P8ESTACK_HI+1,x
tya
asl a
rol P8ESTACK_HI+1,x
asl a
rol P8ESTACK_HI+1,x
asl a
rol P8ESTACK_HI+1,x
asl a
rol P8ESTACK_HI+1,x
asl a
rol P8ESTACK_HI+1,x
asl a
rol P8ESTACK_HI+1,x
sta P8ESTACK_LO+1,x
tya
clc
adc P8ESTACK_HI+1,x
sta P8ESTACK_HI+1,x
rts
.pend
; ----------- optimized multiplications (in-place A (byte) and ?? (word)) : ---------
mul_byte_3 .proc
; A = A + A*2
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
rts
.pend
mul_word_3 .proc
; AY = AY*2 + AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_5 .proc
; A = A*4 + A
sta P8ZP_SCRATCH_REG
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
rts
.pend
mul_word_5 .proc
; AY = AY*4 + AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_6 .proc
; A = (A*2 + A)*2
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
rts
.pend
mul_word_6 .proc
; AY = (AY*2 + AY)*2
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
tay
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
sta P8ZP_SCRATCH_W1+1
tya
asl a
rol P8ZP_SCRATCH_W1+1
ldy P8ZP_SCRATCH_W1+1
rts
.pend
mul_byte_7 .proc
; A = A*8 - A
sta P8ZP_SCRATCH_REG
asl a
asl a
asl a
sec
sbc P8ZP_SCRATCH_REG
rts
.pend
mul_word_7 .proc
; AY = AY*8 - AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
sec
sbc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
sbc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_9 .proc
; A = A*8 + A
sta P8ZP_SCRATCH_REG
asl a
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
rts
.pend
mul_word_9 .proc
; AY = AY*8 + AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
rts
.pend
mul_byte_10 .proc
; A=(A*4 + A)*2
sta P8ZP_SCRATCH_REG
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
rts
.pend
mul_word_10 .proc
; AY=(AY*4 + AY)*2
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
sta P8ZP_SCRATCH_W1+1
lda P8ZP_SCRATCH_W1
asl a
rol P8ZP_SCRATCH_W1+1
ldy P8ZP_SCRATCH_W1+1
rts
.pend
mul_byte_11 .proc
; A=(A*2 + A)*4 - A
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
asl a
sec
sbc P8ZP_SCRATCH_REG
rts
.pend
; mul_word_11 is skipped (too much code)
mul_byte_12 .proc
; A=(A*2 + A)*4
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
asl a
rts
.pend
mul_word_12 .proc
; AY=(AY*2 + AY)*4
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
sta P8ZP_SCRATCH_W1+1
lda P8ZP_SCRATCH_W1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
ldy P8ZP_SCRATCH_W1+1
rts
.pend
mul_byte_13 .proc
; A=(A*2 + A)*4 + A
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
rts
.pend
; mul_word_13 is skipped (too much code)
mul_byte_14 .proc
; A=(A*8 - A)*2
sta P8ZP_SCRATCH_REG
asl a
asl a
asl a
sec
sbc P8ZP_SCRATCH_REG
asl a
rts
.pend
; mul_word_14 is skipped (too much code)
mul_byte_15 .proc
; A=A*16 - A
sta P8ZP_SCRATCH_REG
asl a
asl a
asl a
asl a
sec
sbc P8ZP_SCRATCH_REG
rts
.pend
mul_word_15 .proc
; AY = AY * 16 - AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
sec
sbc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
sbc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_20 .proc
; A=(A*4 + A)*4
sta P8ZP_SCRATCH_REG
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
asl a
rts
.pend
mul_word_20 .proc
; AY = AY * 10 * 2
jsr mul_word_10
sty P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
ldy P8ZP_SCRATCH_REG
rts
.pend
mul_byte_25 .proc
; A=(A*2 + A)*8 + A
sta P8ZP_SCRATCH_REG
asl a
clc
adc P8ZP_SCRATCH_REG
asl a
asl a
asl a
clc
adc P8ZP_SCRATCH_REG
rts
.pend
mul_word_25 .proc
; AY = (AY*2 + AY) *8 + AY
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
sta P8ZP_SCRATCH_W1+1
lda P8ZP_SCRATCH_W1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_40 .proc
and #7
tay
lda _forties,y
rts
_forties .byte 0*40, 1*40, 2*40, 3*40, 4*40, 5*40, 6*40, 7*40 & 255
.pend
mul_word_40 .proc
; AY = (AY*4 + AY)*8
sta P8ZP_SCRATCH_W1
sty P8ZP_SCRATCH_W1+1
sta P8ZP_SCRATCH_W2
sty P8ZP_SCRATCH_W2+1
asl a
rol P8ZP_SCRATCH_W1+1
asl a
rol P8ZP_SCRATCH_W1+1
clc
adc P8ZP_SCRATCH_W2
sta P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
adc P8ZP_SCRATCH_W2+1
asl P8ZP_SCRATCH_W1
rol a
asl P8ZP_SCRATCH_W1
rol a
asl P8ZP_SCRATCH_W1
rol a
tay
lda P8ZP_SCRATCH_W1
rts
.pend
mul_byte_50 .proc
and #7
tay
lda _fifties, y
rts
_fifties .byte 0*50, 1*50, 2*50, 3*50, 4*50, 5*50, 6*50 & 255, 7*50 & 255
.pend
mul_word_50 .proc
; AY = AY * 25 * 2
jsr mul_word_25
sty P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
ldy P8ZP_SCRATCH_REG
rts
.pend
mul_byte_80 .proc
and #3
tay
lda _eighties, y
rts
_eighties .byte 0*80, 1*80, 2*80, 3*80
.pend
mul_word_80 .proc
; AY = AY * 40 * 2
jsr mul_word_40
sty P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
ldy P8ZP_SCRATCH_REG
rts
.pend
mul_byte_100 .proc
and #3
tay
lda _hundreds, y
rts
_hundreds .byte 0*100, 1*100, 2*100, 3*100 & 255
.pend
mul_word_100 .proc
; AY = AY * 25 * 4
jsr mul_word_25
sty P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
ldy P8ZP_SCRATCH_REG
rts
.pend
mul_word_320 .proc
; AY = A * 256 + A * 64 (msb in Y doesn't matter)
sta P8ZP_SCRATCH_B1
ldy #0
sty P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
asl a
rol P8ZP_SCRATCH_REG
pha
clc
lda P8ZP_SCRATCH_B1
adc P8ZP_SCRATCH_REG
tay
pla
rts
.pend
; ----------- end optimized multiplications -----------
; bit shifts.
; anything below 3 is done inline. anything above 7 is done via other optimizations.
shift_left_w_7 .proc
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_LO+1,x
asl a
rol P8ZP_SCRATCH_B1
_shift6 asl a
rol P8ZP_SCRATCH_B1
_shift5 asl a
rol P8ZP_SCRATCH_B1
_shift4 asl a
rol P8ZP_SCRATCH_B1
_shift3 asl a
rol P8ZP_SCRATCH_B1
asl a
rol P8ZP_SCRATCH_B1
asl a
rol P8ZP_SCRATCH_B1
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_B1
sta P8ESTACK_HI+1,x
rts
.pend
shift_left_w_6 .proc
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_LO+1,x
jmp shift_left_w_7._shift6
.pend
shift_left_w_5 .proc
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_LO+1,x
jmp shift_left_w_7._shift5
.pend
shift_left_w_4 .proc
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_LO+1,x
jmp shift_left_w_7._shift4
.pend
shift_left_w_3 .proc
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_LO+1,x
jmp shift_left_w_7._shift3
.pend
shift_left_w .proc
; -- variable number of shifts left
inx
ldy P8ESTACK_LO,x
bne _shift
rts
_shift asl P8ESTACK_LO+1,x
rol P8ESTACK_HI+1,x
dey
bne _shift
rts
.pend
shift_right_uw .proc
; -- uword variable number of shifts right
inx
ldy P8ESTACK_LO,x
bne _shift
rts
_shift lsr P8ESTACK_HI+1,x
ror P8ESTACK_LO+1,x
dey
bne _shift
rts
.pend
shift_right_uw_7 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_HI+1,x
lsr a
ror P8ZP_SCRATCH_B1
_shift6 lsr a
ror P8ZP_SCRATCH_B1
_shift5 lsr a
ror P8ZP_SCRATCH_B1
_shift4 lsr a
ror P8ZP_SCRATCH_B1
_shift3 lsr a
ror P8ZP_SCRATCH_B1
lsr a
ror P8ZP_SCRATCH_B1
lsr a
ror P8ZP_SCRATCH_B1
sta P8ESTACK_HI+1,x
lda P8ZP_SCRATCH_B1
sta P8ESTACK_LO+1,x
rts
.pend
shift_right_uw_6 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_HI+1,x
jmp shift_right_uw_7._shift6
.pend
shift_right_uw_5 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_HI+1,x
jmp shift_right_uw_7._shift5
.pend
shift_right_uw_4 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_HI+1,x
jmp shift_right_uw_7._shift4
.pend
shift_right_uw_3 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_B1
lda P8ESTACK_HI+1,x
jmp shift_right_uw_7._shift3
.pend
shift_right_w_7 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
_shift6 asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
_shift5 asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
_shift4 asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
_shift3 asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1+1
asl a
ror P8ZP_SCRATCH_W1+1
ror P8ZP_SCRATCH_W1
lda P8ZP_SCRATCH_W1
sta P8ESTACK_LO+1,x
lda P8ZP_SCRATCH_W1+1
sta P8ESTACK_HI+1,x
rts
.pend
shift_right_w_6 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
jmp shift_right_w_7._shift6
.pend
shift_right_w_5 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
jmp shift_right_w_7._shift5
.pend
shift_right_w_4 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
jmp shift_right_w_7._shift4
.pend
shift_right_w_3 .proc
lda P8ESTACK_LO+1,x
sta P8ZP_SCRATCH_W1
lda P8ESTACK_HI+1,x
sta P8ZP_SCRATCH_W1+1
jmp shift_right_w_7._shift3
.pend
shift_right_w .proc
; -- signed word variable number of shifts right
inx
ldy P8ESTACK_LO,x
bne _shift
rts
_shift lda P8ESTACK_HI+1,x
asl a
ror P8ESTACK_HI+1,x
ror P8ESTACK_LO+1,x
dey
bne _shift
rts
.pend
; support for bit shifting that is too large to be unrolled:
lsr_byte_A .proc
; -- lsr signed byte in A times the value in Y (assume >0)
cmp #0
bmi _negative
- lsr a
dey
bne -
rts
_negative lsr a
ora #$80
dey
bne _negative
rts
.pend
square .proc
; -- calculate square root of signed word in AY, result in AY
; routine by Lee Davsion, source: http://6502.org/source/integers/square.htm
; using this routine is about twice as fast as doing a regular multiplication.
;
; Calculates the 16 bit unsigned integer square of the signed 16 bit integer in
; Numberl/Numberh. The result is always in the range 0 to 65025 and is held in
; Squarel/Squareh
;
; The maximum input range is only +/-255 and no checking is done to ensure that
; this is so.
;
; This routine is useful if you are trying to draw circles as for any circle
;
; x^2+y^2=r^2 where x and y are the co-ordinates of any point on the circle and
; r is the circle radius
numberl = P8ZP_SCRATCH_W1 ; number to square low byte
numberh = P8ZP_SCRATCH_W1+1 ; number to square high byte
squarel = P8ZP_SCRATCH_W2 ; square low byte
squareh = P8ZP_SCRATCH_W2+1 ; square high byte
tempsq = P8ZP_SCRATCH_B1 ; temp byte for intermediate result
sta numberl
sty numberh
stx P8ZP_SCRATCH_REG
lda #$00 ; clear a
sta squarel ; clear square low byte
; (no need to clear the high byte, it gets shifted out)
lda numberl ; get number low byte
ldx numberh ; get number high byte
bpl _nonneg ; if +ve don't negate it
; else do a two's complement
eor #$ff ; invert
sec ; +1
adc #$00 ; and add it
_nonneg:
sta tempsq ; save abs(number)
ldx #$08 ; set bit count
_nextr2bit:
asl squarel ; low byte *2
rol squareh ; high byte *2+carry from low
asl a ; shift number byte
bcc _nosqadd ; don't do add if c = 0
tay ; save a
clc ; clear carry for add
lda tempsq ; get number
adc squarel ; add number^2 low byte
sta squarel ; save number^2 low byte
lda #$00 ; clear a
adc squareh ; add number^2 high byte
sta squareh ; save number^2 high byte
tya ; get a back
_nosqadd:
dex ; decrement bit count
bne _nextr2bit ; go do next bit
lda squarel
ldy squareh
ldx P8ZP_SCRATCH_REG
rts
.pend
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