base:seriously_fast_multiplication

By Jackasser

Without further explanation here's the code for really fast multiplications. They require 2k of tables which can be generated using table_generator_routine_for_fast_8_bit_mul_table. The article from C=Hacking 16 which is mentioned in the source is available here.

Here are four routines, signed/unsigned 8/16-bit multiplication with 16/32-bit result:

; Description: Unsigned 8-bit multiplication with unsigned 16-bit result. ; ; Input: 8-bit unsigned value in T1 ; 8-bit unsigned value in T2 ; Carry=0: Re-use T1 from previous multiplication (faster) ; Carry=1: Set T1 (slower) ; ; Output: 16-bit unsigned value in PRODUCT ; ; Clobbered: PRODUCT, X, A, C ; ; Allocation setup: T1,T2 and PRODUCT preferably on Zero-page. ; square1_lo, square1_hi, square2_lo, square2_hi must be ; page aligned. Each table are 512 bytes. Total 2kb. ; ; Table generation: I:0..511 ; square1_lo = <((I*I)/4) ; square1_hi = >((I*I)/4) ; square2_lo = <(((I-255)*(I-255))/4) ; square2_hi = >(((I-255)*(I-255))/4) .proc multiply_8bit_unsigned bcc :+ lda T1 sta sm1+1 sta sm3+1 eor #$ff sta sm2+1 sta sm4+1 : ldx T2 sec sm1: lda square1_lo,x sm2: sbc square2_lo,x sta PRODUCT+0 sm3: lda square1_hi,x sm4: sbc square2_hi,x sta PRODUCT+1 rts .endproc ; Description: Signed 8-bit multiplication with signed 16-bit result. ; ; Input: 8-bit signed value in T1 ; 8-bit signed value in T2 ; Carry=0: Re-use T1 from previous multiplication (faster) ; Carry=1: Set T1 (slower) ; ; Output: 16-bit signed value in PRODUCT ; ; Clobbered: PRODUCT, X, A, C .proc multiply_8bit_signed jsr multiply_8bit_unsigned ; Apply sign (See C=Hacking16 for details). lda T1 bpl :+ sec lda PRODUCT+1 sbc T2 sta PRODUCT+1 : lda T2 bpl :+ sec lda PRODUCT+1 sbc T1 sta PRODUCT+1 : rts .endproc ; Description: Unsigned 16-bit multiplication with unsigned 32-bit result. ; ; Input: 16-bit unsigned value in T1 ; 16-bit unsigned value in T2 ; Carry=0: Re-use T1 from previous multiplication (faster) ; Carry=1: Set T1 (slower) ; ; Output: 32-bit unsigned value in PRODUCT ; ; Clobbered: PRODUCT, X, A, C ; ; Allocation setup: T1,T2 and PRODUCT preferably on Zero-page. ; square1_lo, square1_hi, square2_lo, square2_hi must be ; page aligned. Each table are 512 bytes. Total 2kb. ; ; Table generation: I:0..511 ; square1_lo = <((I*I)/4) ; square1_hi = >((I*I)/4) ; square2_lo = <(((I-255)*(I-255))/4) ; square2_hi = >(((I-255)*(I-255))/4) .proc multiply_16bit_unsigned ; <T1 * <T2 = AAaa ; <T1 * >T2 = BBbb ; >T1 * <T2 = CCcc ; >T1 * >T2 = DDdd ; ; AAaa ; BBbb ; CCcc ; + DDdd ; ---------- ; PRODUCT! ; Setup T1 if changed bcc :+ lda T1+0 sta sm1a+1 sta sm3a+1 sta sm5a+1 sta sm7a+1 eor #$ff sta sm2a+1 sta sm4a+1 sta sm6a+1 sta sm8a+1 lda T1+1 sta sm1b+1 sta sm3b+1 sta sm5b+1 sta sm7b+1 eor #$ff sta sm2b+1 sta sm4b+1 sta sm6b+1 sta sm8b+1 : ; Perform <T1 * <T2 = AAaa ldx T2+0 sec sm1a: lda square1_lo,x sm2a: sbc square2_lo,x sta PRODUCT+0 sm3a: lda square1_hi,x sm4a: sbc square2_hi,x sta _AA+1 ; Perform >T1_hi * <T2 = CCcc sec sm1b: lda square1_lo,x sm2b: sbc square2_lo,x sta _cc+1 sm3b: lda square1_hi,x sm4b: sbc square2_hi,x sta _CC+1 ; Perform <T1 * >T2 = BBbb ldx T2+1 sec sm5a: lda square1_lo,x sm6a: sbc square2_lo,x sta _bb+1 sm7a: lda square1_hi,x sm8a: sbc square2_hi,x sta _BB+1 ; Perform >T1 * >T2 = DDdd sec sm5b: lda square1_lo,x sm6b: sbc square2_lo,x sta _dd+1 sm7b: lda square1_hi,x sm8b: sbc square2_hi,x sta PRODUCT+3 ; Add the separate multiplications together clc _AA: lda #0 _bb: adc #0 sta PRODUCT+1 _BB: lda #0 _CC: adc #0 sta PRODUCT+2 bcc :+ inc PRODUCT+3 clc : _cc: lda #0 adc PRODUCT+1 sta PRODUCT+1 _dd: lda #0 adc PRODUCT+2 sta PRODUCT+2 bcc :+ inc PRODUCT+3 : rts .endproc ; Description: Signed 16-bit multiplication with signed 32-bit result. ; ; Input: 16-bit signed value in T1 ; 16-bit signed value in T2 ; Carry=0: Re-use T1 from previous multiplication (faster) ; Carry=1: Set T1 (slower) ; ; Output: 32-bit signed value in PRODUCT ; ; Clobbered: PRODUCT, X, A, C .proc multiply_16bit_signed jsr multiply_16bit_unsigned ; Apply sign (See C=Hacking16 for details). lda T1+1 bpl :+ sec lda PRODUCT+2 sbc T2+0 sta PRODUCT+2 lda PRODUCT+3 sbc T2+1 sta PRODUCT+3 : lda T2+1 bpl :+ sec lda PRODUCT+2 sbc T1+0 sta PRODUCT+2 lda PRODUCT+3 sbc T1+1 sta PRODUCT+3 : rts .endproc

base/seriously_fast_multiplication.txt · Last modified: 2015-04-17 04:33 (external edit)