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base:fast_floating_point_multiply [2016-02-06 01:34] (current)
malcontent created
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 +====== Fast Floating Point Multiply ======
  
 +This code uses the fast multiplication [[seriously_fast_multiplication|found here]] to quickly multiply the mantissas. Each multiplication is added to the product as you go.
 +
 +In the procedure shown below, the red indicates where the two bytes have been added to the partial product, and the orange is where a carry has propagated.
 +
 +{{:​base:​32bitmul.png|}}
 +
 +<code 6502acme>​
 +;Fast Floating Point Multiplication
 +
 +;ZP
 +
 +RESULT = $26 ;-$2c
 +
 +FACX = $61 ;exponent
 +FAC = $62 ;mantissa - $65
 +;   $66 ;sign, in MSB
 +ARGX = $69 ;exponent
 +ARG = $6a ;mantissa - $6d
 +;   $6e ;sign, in MSB
 +SGNCMP ​ = $6f
 +
 +res8 = $fb ;lobyte of product ​
 +
 +;BASIC Subroutines
 +PRINTFAC = $aabc
 +VARtoFAC = $bba2 ;a/y, lo/hi
 +VARtoARG = $ba8c
 +
 +
 +!macro addresult .num, .carry {
 + pha
 + lda res8
 + clc
 + adc RESULT+.num
 + sta RESULT+.num
 + pla 
 + adc (RESULT-1)+.num
 + sta (RESULT-1)+.num
 + !if .carry != 0 {
 + !set .num = .num - 1
 + bcc +
 + inc (RESULT-1)+.num
 + !do while .carry > 1 {
 + !set .num = .num - 1
 + !set .carry = .carry - 1
 + bne +
 + inc (RESULT-1)+.num
 + }
 + }
 ++
 +}
 +
 +
 +
 + !to "​fastm.prg",​cbm
 +
 + *=$800 ;​10 SYS 10240(3000)
 + !byte $00,​$0E,​$08,​$0A,​$00,​$9E,​$28,​$31,​$32,​$32,​$38,​$38,​$29,​$00,​$00,​$00
 +
 + *=$3000
 +
 + ldx #$00
 + txa
 + !byte $c9 ;cmp #, clears carry, skips tya
 +lb1 tya
 + adc #$00
 +ml1 sta multabhi,x
 + tay
 + cmp #$40
 + txa
 + ror
 +ml9 adc #$00
 + sta ml9+1
 + inx
 +ml0 sta multablo,x
 + bne lb1
 + inc ml0+2
 + inc ml1+2
 + clc
 + iny
 + bne lb1
 + 
 + ldx #$00
 + ldy #$ff
 +- lda multabhi+1,​x
 + sta multab2hi+$100,​x
 + lda multabhi,x
 + sta multab2hi,y
 + lda multablo+1,​x
 + sta multab2lo+$100,​x
 + lda multablo,x
 + sta multab2lo,y
 + dey
 + inx
 + bne -
 +
 + lda #<value
 + ldy #>value
 + jsr VARtoFAC
 + lda #<value
 + ldy #>value
 + jsr VARtoARG
 + jsr mul_FP
 + jsr PRINTFAC
 +
 +here jmp here
 +
 +mul_FP bne +
 + rts ;0 in FAC returns 0
 ++ jsr $bab7 ;add exponents
 + lda #0 ;clear RESULT
 + sta $26
 + sta $27
 + sta $28
 + sta $29
 + sta $2a
 + sta $2b
 + sta $2c
 +
 + lda FAC+3
 + ldx ARG+3
 + jsr mul8x8
 + sta RESULT+6
 + ldx ARG+2
 + jsr mulf
 + +addresult 6,0
 + ldx ARG+1
 + jsr mulf
 + +addresult 5,0
 + ldx ARG
 + jsr mulf
 + +addresult 4,0
 +
 + lda FAC+2
 + ldx ARG+3
 + jsr mul8x8
 + +addresult 6,2
 + ldx ARG+2
 + jsr mulf
 + +addresult 5,2
 + ldx ARG+1
 + jsr mulf
 + +addresult 4,2
 + ldx ARG
 + jsr mulf
 + +addresult 3,2
 +
 + lda FAC+1
 + ldx ARG+3
 + jsr mul8x8
 + +addresult 5,2
 + ldx ARG+2
 + jsr mulf
 + +addresult 4,2
 + ldx ARG+1
 + jsr mulf
 + +addresult 3,2
 + ldx ARG
 + jsr mulf
 + +addresult 2,1
 +
 + lda FAC
 + ldx ARG+3
 + jsr mul8x8
 + +addresult 4,3
 + lda RESULT+4
 + sta $70 ;​rounding byte
 + ldx ARG+2
 + jsr mulf
 + +addresult 3,2
 + ldx ARG+1
 + jsr mulf
 + +addresult 2,1
 + ldx ARG
 + jsr mulf
 + +addresult 1,0
 +
 + jmp $bb8f ;​normal multiply exit.
 + ;copies RESULT to FAC1
 + ;and normalises.
 +
 +mul8x8 sta sm1+1                                             
 + sta sm3+1                                             
 + eor #$ff                                              ​
 + sta sm2+1                                             
 + sta sm4+1
 +mulf sec ​  
 +sm1 lda multablo,x
 +sm2 sbc multab2lo,x
 + sta res8   
 +sm3 lda multabhi,x
 +sm4 sbc multab2hi,x
 + rts
 +
 +value !byte $82,​$49,​$b2,​$6c,​$9c ;3.15151515
 +
 +multablo = $c000
 +multabhi = $c200
 +multab2lo = $c400
 +multab2hi = $c600</​code>​
base/fast_floating_point_multiply.txt ยท Last modified: 2016-02-06 01:34 by malcontent