Z80 Routines:Math:Multiplication

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	l, 0
   ld	d, l

   sla	h		; optimised 1st iteration
   jr	nc, $+3
   ld	l, e
   
   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
 

24*24 multiplication

The following routine multiplies bcd by ehl and places the result in bcdehl. It uses 2 bytes of ram, but those can be substituted for IX half registers. (By thepenguin77)

multDBCbyEHL:
	
	push	de
	push	hl
	
	ld	ix, $8000
	ld	(ix), l
	xor	a
	ld	h, a
	ld	l, a

	call	do8Bits

	ld	(ix+1), a
	pop	af
	ld	(ix), a		
	push	de
	ld	a, (ix+1)

	call	do8Bits

	ld	(ix+1), a
	pop	af		;least sig number
	ex	de, hl
	ex	(sp), hl	;D and 2nd least sig in for new number
	ld	(ix), l
	pop	hl		;D and 2nd least sig
	push	af		;least sig number
	push	hl		;2nd least sig number
	ex	de, hl
	ld	a, (ix+1)

	call	do8Bits

	ld	b, a
	ld	c, h
	ld	d, l
	pop	hl
	ld	a, l
	pop	hl
	ld	h, a
	ret

;####
;input: DBC = 1 number
;	AHL = running number
;	(ix) = to multiply by
;output: AHLE = output
;	E is done
;	DBC = 1 number

do8Bits:
	ld	(ix+1), 8
loop:
	srl	(ix)
	jr	nc, skip

	add	hl, bc
	adc	a, d
skip:
	rra	
	rr	h
	rr	l
	rr	e
	dec	(ix+1)
	jr	nz, loop
	ret