base:fastest_multiplication
Fastest 16x16 unsigned multiplication
By Repose
Requires tables or a generator routine such as table_generator_routine_for_fast_8_bit_mul_table
Jack Asser's: 238.1 cycles ref: seriously_fast_multiplication
Chris Jam's: 204.5* ref: http://csdb.dk/forums/?roomid=11&topicid=91766
Mine: 198.6 zp variation: 194.6
Times above need to add 6 for rts
Note: updated 2023; corrected code, typos and timings
*Timing approximate for external code
This is the winner out of 120 published algorithms as independently tested here:
https://github.com/TobyLobster/multiply_test
Note: I have a new version which is 188.1 cycles, excepting the RTS.
;World's fastest 16x16 unsigned mult for 6502 ;you can go faster, but not without more code and/or data ;and being less elegant and harder to follow. ;by Repose 2017 ;table generator by Graham ;addition improvement suggested by JackAsser ;data: 2044 bytes ;zero page ram required: minimum 8 bytes, ideally 14 ;do_add: 30 bytes in zp, if used ;time: 198.6 cycles, option for 194.6 if you use 30 more zp bytes for do_add ;measurement method: average timings over all input combinations ;How to use: ;put numbers in x/y and result is Y reg (z3), A reg (z2), z1, z0 ;tables of squares ;sqr(x)=x^2/4 ;negsqr(x)=(255-x)^2/4 sqrlo=$c100;511 bytes sqrhi=$c300;511 bytes negsqrlo=$c500;511 bytes negsqrhi=$c700;511 bytes ;pointers to square tables above p_sqr_lo=$8b;2 bytes p_sqr_hi=$8d;2 bytes p_invsqr_lo=$8f;2 bytes p_invsqr_hi=$91;2 bytes ;the inputs and outputs x0=$fb;multiplier, 2 bytes x1=$fc y0=$fd;multiplicand, 2 bytes y1=$fe z0=$80;product, 2 bytes z1=$81 z2=$82 ;returned in A reg z3=$83 ;returned in Y reg ;Example showing use *=$c000 lda #$ff sta x0 sta x1 sta y0 sta y1 jsr makesqrtables jsr umult16 sta z2 sty z3 rts ;result should be $fffe0001, e.g. as viewed with a typical m 0080 monitor command: ;0080 01 00 fe ff makesqrtables: ;init zp square tables pointers lda #>sqrlo sta p_sqr_lo+1 lda #>sqrhi sta p_sqr_hi+1 lda #>negsqrlo sta p_invsqr_lo+1 lda #>negsqrhi sta p_invsqr_hi+1 ;generate sqr(x)=x^2/4 ldx #$00 txa !by $c9 ; CMP #immediate - skip TYA and clear carry flag lb1: tya adc #$00 ml1: sta sqrhi,x tay cmp #$40 txa ror ml9: adc #$00 sta ml9+1 inx ml0: sta sqrlo,x bne lb1 inc ml0+2 inc ml1+2 clc iny bne lb1 ;generate negsqr(x)=(255-x)^2/4 ldx #$00 ldy #$ff mt1: lda sqrhi+1,x sta negsqrhi+$100,x lda sqrhi,x sta negsqrhi,y lda sqrlo+1,x sta negsqrlo+$100,x lda sqrlo,x sta negsqrlo,y dey inx bne mt1 rts umult16: ;set multiplier as x0 lda x0 sta p_sqr_lo sta p_sqr_hi eor #$ff sta p_invsqr_lo sta p_invsqr_hi;17 sec ldy y0 lda (p_sqr_lo),y sbc (p_invsqr_lo),y;note these two lines taken as 10.996 total or 10+65280/65536 sta z0;x0*y0l lda (p_sqr_hi),y sbc (p_invsqr_hi),y sta c1a+1;x0*y0h; 2+3+10.996+3+10.996+4=33.992 ;c1a means column 1, row a (partial product to be added later) ldy y1 ;sec ;notice that the high byte of subtraction above is always positive, leaving Carry set lda (p_sqr_lo),y sbc (p_invsqr_lo),y sta c1b+1;x0*y1l lda (p_sqr_hi),y sbc (p_invsqr_hi),y sta c2a+1;x0*y1h; 3+10.996+4+10.996+4=32.992 ;set multiplier as x1 lda x1 sta p_sqr_lo sta p_sqr_hi eor #$ff sta p_invsqr_lo sta p_invsqr_hi;17 ldy y0 ;sec lda (p_sqr_lo),y sbc (p_invsqr_lo),y sta c1c+1;x1*y0l lda (p_sqr_hi),y sbc (p_invsqr_hi),y sta c2b+1;x1*y0h;32.992 ldy y1 ;sec lda (p_sqr_lo),y sbc (p_invsqr_lo),y sta c2c+1;x1*y1l lda (p_sqr_hi),y sbc (p_invsqr_hi),y tay;Y=x1*y1h, 30.992 cycles ;17+34+33+17+33+31=164.97 cycles for main multiply part (minimum=157, maximum=173) ;jmp do_adds; can put do_adds in zp for a slight speed increase do_adds: ;-add the first two numbers of column 1 clc c1a: lda #0 c1b: adc #0 sta z1;9 ;-continue to first two numbers of column 2 c2a: lda #0 c2b: adc #0 tax bcc c1c;9 iny;z3++ clc;(+3) taken 7% of the time, 3*.07=+.21 ;-add last number of column 1 c1c: lda #0 adc z1 sta z1;8 ;-add last number of column 2 txa c2c: adc #0 ;A=z2 bcc fin;7 iny;(+1) taken 42% of the time, 1*.42=.42 ;Y=z3, A=z2 ;add partials part total cycles=33.63 (minimum=33, maximum=37) ;total time=164.97+33.63=198.6 fin: rts;add 6 to include this (204.6) Diagram of the additions y1 y0 x x1 x0 -------- x0y0h x0y0l + x0y1h x0y1l + x1y0h x1y0l +x1y1h x1y1l ------------------------ z3 z2 z1 z0
base/fastest_multiplication.txt · Last modified: 2024-02-13 08:24 by repose