Difference between revisions of "Z80 Routines:Math:Multiplication"

Revision as of 15:28, 30 September 2019

Introduction

All these routines use the restoring multiplication algorithm, adapted to the z80 architecture to maximize speed. They can easily be unrolled to gain some speed.

Unsigned versions

8*8 multiplication

The following routine multiplies h by e and places the result in hl

mult_h_e
   ld	d, 0	; Combining the overhead and
   sla	h	; optimised first iteration
   sbc	a, a
   and	e
   ld	l, a
   
   ld	b, 7
_loop:
   add	hl, hl          
   jr	nc, $+3
   add	hl, de
   
   djnz	_loop
   
   ret
 

16*8 multiplication

The following routine multiplies de by a and places the result in ahl (which means a is the most significant byte of the product, l the least significant and h the intermediate one...)

mult_a_de
   ld	c, 0
   ld	h, c
   ld	l, h

   add	a, a		; optimised 1st iteration
   jr	nc, $+4
   ld	h,d
   ld	l,e

   ld b, 7
_loop:
   add	hl, hl
   rla
   jr	nc, $+4
   add	hl, de
   adc	a, c            ; yes this is actually adc a, 0 but since c is free we set it to zero and so we can save 1 byte and up to 3 T-states per iteration
   
   djnz	_loop
   
   ret
 

16*16 multiplication

The following routine multiplies bc by de and places the result in dehl.

mult_de_bc
   ld	hl, 0

   sla	e		; optimised 1st iteration
   rl	d
   jr	nc, $+4
   ld	h, b
   ld	l, c

   ld	a, 15
_loop:
   add	hl, hl
   rl	e
   rl	d
   jr	nc, $+6
   add	hl, bc
   jr	nc, $+3
   inc	de
   
   dec	a
   jr	nz, _loop
   
   ret
 

Signed versions

8*8 multiplication

16*8 multiplication

16*16 multiplication

The following routine multiplies bc by de and places the signed result in dehl.

; 16 bit signed multiply by John Metcalf
; 32 bytes, average approx ~1090 cycles

; call with bc, de = 16 bit signed numbers to multiply
; returns   de:hl = 32 bit signed product
; corrupts  a

; de:hl = bc*de

multiply:
  xor a
  ld h,a
  ld l,a
  bit 7,d
  jr z,muldpos
  sbc hl,bc
muldpos:
  ld a,b
  sra a
  and 0C0h
  add a,d
  ld d,a

  ld a,16
mulloop:
  add hl,hl
  rl e
  rl d
  jr nc,mul0bit
  add hl,bc
  jr nc,mul0bit
  inc de
mul0bit:
  dec a
  jr nz,mulloop