352 lines
6.7 KiB
ArmAsm
352 lines
6.7 KiB
ArmAsm
; Fast mutiply
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; Note for our purposes we only care about 8.8 x 8.8 fixed point
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; with 8.8 result, which means we only care about the middle two bytes
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; of the 32 bit result. So we disable generation of the high and low byte
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; to save some cycles.
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;
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; The old routine took around 700 cycles for a 16bitx16bit=32bit mutiply
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; This routine, at an expense of 2kB of looku tables, takes around 250
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; If you reuse a term the next time this drops closer to 200
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; This routine was described by Stephen Judd and found
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; in The Fridge and in the C=Hacking magazine
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; http://codebase64.org/doku.php?id=base:seriously_fast_multiplication
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; The key thing to note is that
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; (a+b)^2 (a-b)^2
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; a*b = ------- - --------
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; 4 4
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; So if you have tables of the squares of 0..511 you can lookup and subtract
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; instead of multiplying.
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; Table generation: I:0..511
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; square1_lo = <((I*I)/4)
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; square1_hi = >((I*I)/4)
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; square2_lo = <(((I-255)*(I-255))/4)
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; square2_hi = >(((I-255)*(I-255))/4)
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; Note: DOS3.3 starts at $9600
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.ifndef square1_lo
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square1_lo EQU $8E00
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square1_hi EQU $9000
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square2_lo EQU $9200
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square2_hi EQU $9400
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.endif
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; for(i=0;i<512;i++) {
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; square1_lo[i]=((i*i)/4)&0xff;
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; square1_hi[i]=(((i*i)/4)>>8)&0xff;
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; square2_lo[i]=( ((i-255)*(i-255))/4)&0xff;
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; square2_hi[i]=(( ((i-255)*(i-255))/4)>>8)&0xff;
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; }
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init_multiply_tables:
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; Build the add tables
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ldx #$00
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txa
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.byte $c9 ; CMP #immediate - skip TYA and clear carry flag
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lb1: tya
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adc #$00 ; 0
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ml1: sta square1_hi,x ; square1_hi[0]=0
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tay ; y=0
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cmp #$40 ; subtract 64 and update flags (c=0)
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txa ; a=0
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ror ; rotate
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ml9: adc #$00 ; add 0
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sta ml9+1 ; update add value
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inx ; x=1
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ml0: sta square1_lo,x ; square1_lo[0]=1
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bne lb1 ; if not zero, loop
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inc ml0+2 ; increment values
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inc ml1+2 ; increment values
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clc ; c=0
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iny ; y=1
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bne lb1 ; loop
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; Build the subtract tables based on the existing one
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ldx #$00
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ldy #$ff
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second_table:
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lda square1_hi+1,x
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sta square2_hi+$100,x
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lda square1_hi,x
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sta square2_hi,y
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lda square1_lo+1,x
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sta square2_lo+$100,x
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lda square1_lo,x
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sta square2_lo,y
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dey
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inx
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bne second_table
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rts
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; Fast 16x16 bit unsigned multiplication, 32-bit result
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; Input: NUM1H:NUM1L * NUM2H:NUM2L
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; Result: RESULT3:RESULT2:RESULT1:RESULT0
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;
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; Does self-modifying code to hard-code NUM1H:NUM1L into the code
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; carry=0: re-use previous NUM1H:NUM1L
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; carry=1: reload NUM1H:NUM1L (58 cycles slower)
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;
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; clobbered: RESULT, X, A, C
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; Allocation setup: T1,T2 and RESULT preferably on Zero-page.
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;
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; NUM1H (x_i), NUM1L (x_f)
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; NUM2H (y_i), NUM2L (y_f)
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; NUM1L * NUM2L = AAaa
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; NUM1L * NUM2H = BBbb
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; NUM1H * NUM2L = CCcc
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; NUM1H * NUM2H = DDdd
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;
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; AAaa
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; BBbb
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; CCcc
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; + DDdd
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; ----------
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; RESULT
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;fixed_16x16_mul_unsigned:
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multiply:
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bcc num1_same_as_last_time ; 2nt/3
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;============================
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; Set up self-modifying code
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; this changes the code to be hard-coded to multiply by NUM1H:NUM1L
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;============================
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lda NUM1L ; load the low byte ; 3
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sta sm1a+1 ; 3
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sta sm3a+1 ; 3
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sta sm5a+1 ; 3
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sta sm7a+1 ; 3
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eor #$ff ; invert the bits for subtracting ; 2
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sta sm2a+1 ; 3
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sta sm4a+1 ; 3
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sta sm6a+1 ; 3
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sta sm8a+1 ; 3
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lda NUM1H ; load the high byte ; 3
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sta sm1b+1 ; 3
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sta sm3b+1 ; 3
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sta sm5b+1 ; 3
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; sta sm7b+1 ;
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eor #$ff ; invert the bits for subtractin ; 2
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sta sm2b+1 ; 3
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sta sm4b+1 ; 3
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sta sm6b+1 ; 3
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; sta sm8b+1 ;
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;===========
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; 52
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num1_same_as_last_time:
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;==========================
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; Perform NUM1L * NUM2L = AAaa
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;==========================
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ldx NUM2L ; (low le) ; 3
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sec ; 2
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sm1a:
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lda square1_lo,x ; 4
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sm2a:
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sbc square2_lo,x ; 4
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; a is _aa
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; sta RESULT+0 ;
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sm3a:
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lda square1_hi,x ; 4
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sm4a:
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sbc square2_hi,x ; 4
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; a is _AA
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sta _AA+1 ; 3
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;===========
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; 24
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; Perform NUM1H * NUM2L = CCcc
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sec ; 2
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sm1b:
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lda square1_lo,x ; 4
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sm2b:
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sbc square2_lo,x ; 4
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; a is _cc
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sta _cc+1 ; 3
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sm3b:
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lda square1_hi,x ; 4
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sm4b:
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sbc square2_hi,x ; 4
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; a is _CC
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sta _CC+1 ; 3
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;===========
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; 24
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;==========================
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; Perform NUM1L * NUM2H = BBbb
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;==========================
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ldx NUM2H ; 3
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sec ; 2
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sm5a:
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lda square1_lo,x ; 4
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sm6a:
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sbc square2_lo,x ; 4
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; a is _bb
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sta _bb+1 ; 3
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sm7a:
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lda square1_hi,x ; 4
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sm8a:
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sbc square2_hi,x ; 4
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; a is _BB
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sta _BB+1 ; 3
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;===========
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; 27
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;==========================
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; Perform NUM1H * NUM2H = DDdd
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;==========================
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sec ; 2
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sm5b:
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lda square1_lo,x ; 4
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sm6b:
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sbc square2_lo,x ; 4
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; a is _dd
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sta _dd+1 ; 3
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;sm7b:
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; lda square1_hi,x ;
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;sm8b:
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; sbc square2_hi,x ;
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; a = _DD
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; sta RESULT+3 ;
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;===========
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; 13
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;===========================================
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; Add the separate multiplications together
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;===========================================
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clc ; 2
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_AA:
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lda #0 ; loading _AA ; 2
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_bb:
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adc #0 ; adding in _bb ; 2
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sta RESULT+1 ; 3
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;==========
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; 9
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; product[2]=_BB+_CC+c
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_BB:
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lda #0 ; loading _BB ; 2
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_CC:
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adc #0 ; adding in _CC ; 2
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sta RESULT+2 ; 3
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;===========
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; 7
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; product[3]=_DD+c
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; bcc dd_no_carry1 ;
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; inc RESULT+3 ;
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clc ; 2
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;=============
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; 2
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dd_no_carry1:
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; product[1]=_AA+_bb+_cc
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_cc:
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lda #0 ; load _cc ; 2
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adc RESULT+1 ; 3
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sta RESULT+1 ; 3
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; product[2]=_BB+_CC+_dd+c
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_dd:
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lda #0 ; load _dd ; 2
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adc RESULT+2 ; 3
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sta RESULT+2 ; 3
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;===========
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; 16
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; product[3]=_DD+c
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; bcc dd_no_carry2 ;
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; inc RESULT+3 ;
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;=============
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; 0
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dd_no_carry2:
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; *z_i=product[1];
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; *z_f=product[0];
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; rts ; 6
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;=================
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; Signed multiply
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;=================
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;multiply:
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; jsr fixed_16x16_mul_unsigned ; 6
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lda NUM1H ; x_i ; 3
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;===========
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; 12
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bpl x_positive ;^3/2nt
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sec ; 2
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lda RESULT+2 ; 3
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sbc NUM2L ; 3
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sta RESULT+2 ; 3
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; lda RESULT+3 ;
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; sbc NUM2H ;
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; sta RESULT+3 ;
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;============
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; 10
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x_positive:
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lda NUM2H ; y_i ; 3
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;============
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; ; 6
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bpl y_positive ;^3/2nt
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sec ; 2
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lda RESULT+2 ; 3
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sbc NUM1L ; 3
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sta RESULT+2 ; 3
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; lda RESULT+3 ;
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; sbc NUM1H ;
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; sta RESULT+3 ;
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;===========
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; 10
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y_positive:
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ldx RESULT+2 ; *z_i=product[2]; ; 3
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lda RESULT+1 ; *z_f=product[1]; ; 3
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rts ; 6
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;==========
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; 12
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