math32.inc

$NOLIST
;----------------------------------------------------
; math32.asm: Addition, subtraction, multiplication,
; and division of 32-bit integers. Also included are
; binary to bcd and bcd to binary conversion subroutines.
;
; 2011-2013 by Jesus Calvino-Fraga
;
;----------------------------------------------------

CSEG

;----------------------------------------------------
; Converts the 32-bit hex number in 'x' to a 
; 10-digit packed BCD in 'bcd' using the
; double-dabble algorithm.
;---------------------------------------------------
hex2bcd:
	push acc
	push psw
	push AR0
	push AR1
	push AR2
	
	clr a
	mov bcd+0, a ; Initialize BCD to 00-00-00-00-00 
	mov bcd+1, a
	mov bcd+2, a
	mov bcd+3, a
	mov bcd+4, a
	mov r2, #32  ; Loop counter.

hex2bcd_L0:
	; Shift binary left	
	mov a, x+3
	mov c, acc.7 ; This way x remains unchanged!
	mov r1, #4
	mov r0, #(x+0)
hex2bcd_L1:
	mov a, @r0
	rlc a
	mov @r0, a
	inc r0
	djnz r1, hex2bcd_L1
    
	; Perform bcd + bcd + carry using BCD arithmetic
	mov r1, #5
	mov r0, #(bcd+0)
hex2bcd_L2:   
	mov a, @r0
	addc a, @r0
	da a
	mov @r0, a
	inc r0
	djnz r1, hex2bcd_L2

	djnz r2, hex2bcd_L0

	pop AR2
	pop AR1
	pop AR0
	pop psw
	pop acc
	ret


;----------------------------------------------------
; hex2bcd2:
; Converts the 32-bit hex number in 'x' to a 
; 10-digit packed BCD in 'bcd' using the
; double-dabble algorithm.  This is what you would
; have to do in a proccessor without a bcd addition
; instruction.  The 8051 can add bcd number, so
; this function is here for your reference only.  Compare
; to the function above which uses the DA A instruction
; resulting in faster and smaller code. 
;---------------------------------------------------
hex2bcd2:
	push acc
	push psw
	push AR0
	push AR1
	push AR2

	clr a
	mov bcd+0, a ; Initialize BCD to 00-00-00-00-00 
	mov bcd+1, a
	mov bcd+2, a
	mov bcd+3, a
	mov bcd+4, a
	mov r2, #32  ; We need process 32 bits

hex2bcd2_L0:
	; Shift binary left	
	mov a, x+3
	mov c, acc.7 ; This way x remains unchanged!
	mov r1, #4
	mov r0, #(x+0)
hex2bcd2_L1:
	mov a, @r0
	rlc a
	mov @r0, a
	inc r0
	djnz r1, hex2bcd2_L1

	; Shif bcd left	
	mov r1, #5	          ; BCD byte count = 5
	mov r0, #(bcd+0)      ; r0 points to least significant bcd digits
hex2bcd2_L2:
	push psw              ; Save carry
	mov a, @r0
	add a, #33h           ; Pre-correction before shifting left
	jb acc.7, hex2bcd2_L3 ; If the bcd digit was > 4 keep the correction
	add a, #(100h-30h)    ; Remove the correction to the MSD by subtracting 30h
hex2bcd2_L3:
	jb acc.3, hex2bcd2_L4 ; If the bcd digit was > 4 keep the correction
	add a, #(100h-03h)    ; Remove the correction to the LSD by subtracting 03h
hex2bcd2_L4:
	pop psw               ; Restore carry
	rlc a
	mov @r0, a
	inc r0
	djnz r1, hex2bcd2_L2
	
	djnz r2, hex2bcd2_L0

	pop AR2
	pop AR1
	pop AR0
	pop psw
	pop acc

	ret

;------------------------------------------------
; bcd2hex:
; Converts the 10-digit packed BCD in 'bcd' to a 
; 32-bit hex number in 'x'
;------------------------------------------------
bcd2hex:
	push acc
	push psw
	push AR0
	push AR1
	push AR2

	mov r2, #32  ; We need 32 bits

bcd2hex_L0:
	mov r1, #5	           ; BCD byte count = 5
	clr c                  ; clear carry flag
	mov r0, #(bcd+4)       ; r0 points to most significant bcd digits
bcd2hex_L1:
	mov a, @r0             ; transfer bcd to accumulator
	rrc a                  ; rotate right
	push psw               ; save carry flag
	; BCD divide by two correction
	jnb acc.7, bcd2hex_L2  ; test bit 7
	add a, #(100h-30h)     ; bit 7 is set. Perform correction by subtracting 30h.
bcd2hex_L2:
	jnb acc.3, bcd2hex_L3  ; test bit 3            
	add a, #(100h-03h)     ; bit 3 is set. Perform correction by subtracting 03h.
bcd2hex_L3:
	mov @r0, a             ; store the result
	dec r0                 ; point to next pair of bcd digits
	pop psw                ; restore carry flag
	djnz r1, bcd2hex_L1    ; repeat for all bcd pairs

	; rotate binary result right
	mov r1, #4
	mov r0, #(x+3)
bcd2hex_L4:
	mov a, @r0
	rrc a
	mov @r0, a
	dec r0
	djnz r1, bcd2hex_L4
	
	djnz r2, bcd2hex_L0

	pop AR2
	pop AR1
	pop AR0
	pop psw
	pop acc

    ret

;------------------------------------------------
; x = x + y
;------------------------------------------------
add32:
	push acc
	push psw
	mov a, x+0
	add a, y+0
	mov x+0, a
	mov a, x+1
	addc a, y+1
	mov x+1, a
	mov a, x+2
	addc a, y+2
	mov x+2, a
	mov a, x+3
	addc a, y+3
	mov x+3, a
	pop psw
	pop acc
	ret

;------------------------------------------------
; x = x - y
;------------------------------------------------
sub32:
	push acc
	push psw
	clr c
	mov a, x+0
	subb a, y+0
	mov x+0, a
	mov a, x+1
	subb a, y+1
	mov x+1, a
	mov a, x+2
	subb a, y+2
	mov x+2, a
	mov a, x+3
	subb a, y+3
	mov x+3, a
	pop psw
	pop acc
	ret

;------------------------------------------------
; mf=1 if x < y
;------------------------------------------------
x_lt_y:
	push acc
	push psw
	clr c
	mov a, x+0
	subb a, y+0
	mov a, x+1
	subb a, y+1
	mov a, x+2
	subb a, y+2
	mov a, x+3
	subb a, y+3
	mov mf, c
	pop psw
	pop acc
	ret

;------------------------------------------------
; mf=1 if x > y
;------------------------------------------------
x_gt_y:
	push acc
	push psw
	clr c
	mov a, y+0
	subb a, x+0
	mov a, y+1
	subb a, x+1
	mov a, y+2
	subb a, x+2
	mov a, y+3
	subb a, x+3
	mov mf, c
	pop psw
	pop acc
	ret

;------------------------------------------------
; mf=1 if x = y
;------------------------------------------------
x_eq_y:
	push acc
	push psw
	clr mf
	clr c
	mov a, y+0
	subb a, x+0
	jnz x_eq_y_done
	mov a, y+1
	subb a, x+1
	jnz x_eq_y_done
	mov a, y+2
	subb a, x+2
	jnz x_eq_y_done
	mov a, y+3
	subb a, x+3
	jnz x_eq_y_done
	setb mf
x_eq_y_done:
	pop psw
	pop acc
	ret

;------------------------------------------------
; mf=1 if x >= y
;------------------------------------------------
x_gteq_y:
	lcall x_eq_y
	jb mf, x_gteq_y_done
	ljmp x_gt_y
x_gteq_y_done:
	ret

;------------------------------------------------
; mf=1 if x <= y
;------------------------------------------------
x_lteq_y:
	lcall x_eq_y
	jb mf, x_lteq_y_done
	ljmp x_lt_y
x_lteq_y_done:
	ret
	
;------------------------------------------------
; x = x * y
;------------------------------------------------
mul32:

	push acc
	push b
	push psw
	push AR0
	push AR1
	push AR2
	push AR3
		
	; R0 = x+0 * y+0
	; R1 = x+1 * y+0 + x+0 * y+1
	; R2 = x+2 * y+0 + x+1 * y+1 + x+0 * y+2
	; R3 = x+3 * y+0 + x+2 * y+1 + x+1 * y+2 + x+0 * y+3
	
	; Byte 0
	mov	a,x+0
	mov	b,y+0
	mul	ab		; x+0 * y+0
	mov	R0,a
	mov	R1,b
	
	; Byte 1
	mov	a,x+1
	mov	b,y+0
	mul	ab		; x+1 * y+0
	add	a,R1
	mov	R1,a
	clr	a
	addc a,b
	mov	R2,a
	
	mov	a,x+0
	mov	b,y+1
	mul	ab		; x+0 * y+1
	add	a,R1
	mov	R1,a
	mov	a,b
	addc a,R2
	mov	R2,a
	clr	a
	rlc	a
	mov	R3,a
	
	; Byte 2
	mov	a,x+2
	mov	b,y+0
	mul	ab		; x+2 * y+0
	add	a,R2
	mov	R2,a
	mov	a,b
	addc a,R3
	mov	R3,a
	
	mov	a,x+1
	mov	b,y+1
	mul	ab		; x+1 * y+1
	add	a,R2
	mov	R2,a
	mov	a,b
	addc a,R3
	mov	R3,a
	
	mov	a,x+0
	mov	b,y+2
	mul	ab		; x+0 * y+2
	add	a,R2
	mov	R2,a
	mov	a,b
	addc a,R3
	mov	R3,a
	
	; Byte 3
	mov	a,x+3
	mov	b,y+0
	mul	ab		; x+3 * y+0
	add	a,R3
	mov	R3,a
	
	mov	a,x+2
	mov	b,y+1
	mul	ab		; x+2 * y+1
	add	a,R3
	mov	R3,a
	
	mov	a,x+1
	mov	b,y+2
	mul	ab		; x+1 * y+2
	add	a,R3
	mov	R3,a
	
	mov	a,x+0
	mov	b,y+3
	mul	ab		; x+0 * y+3
	add	a,R3
	mov	R3,a
	
	mov	x+3,R3
	mov	x+2,R2
	mov	x+1,R1
	mov	x+0,R0

	pop AR3
	pop AR2
	pop AR1
	pop AR0
	pop psw
	pop b
	pop acc
	
	ret

;------------------------------------------------
; x = x / y
; This subroutine uses the 'paper-and-pencil' 
; method described in page 139 of 'Using the
; MCS-51 microcontroller' by Han-Way Huang.
;------------------------------------------------
div32:
	push acc
	push psw
	push AR0
	push AR1
	push AR2
	push AR3
	push AR4
	
	mov	R4,#32
	clr	a
	mov	R0,a
	mov	R1,a
	mov	R2,a
	mov	R3,a
	
div32_loop:
	; Shift the 64-bit of [[R3..R0], x] left:
	clr c
	; First shift x:
	mov	a,x+0
	rlc a
	mov	x+0,a
	mov	a,x+1
	rlc	a
	mov	x+1,a
	mov	a,x+2
	rlc	a
	mov	x+2,a
	mov	a,x+3
	rlc	a
	mov	x+3,a
	; Then shift [R3..R0]:
	mov	a,R0
	rlc	a 
	mov	R0,a
	mov	a,R1
	rlc	a
	mov	R1,a
	mov	a,R2
	rlc	a
	mov	R2,a
	mov	a,R3
	rlc	a
	mov	R3,a
	
	; [R3..R0] - y
	clr c	     
	mov	a,R0
	subb a,y+0
	mov	a,R1
	subb a,y+1
	mov	a,R2
	subb a,y+2
	mov	a,R3
	subb a,y+3
	
	jc	div32_minus		; temp >= y?
	
	; -> yes;  [R3..R0] -= y;
	; clr c ; carry is always zero here because of the jc above!
	mov	a,R0
	subb a,y+0 
	mov	R0,a
	mov	a,R1
	subb a,y+1
	mov	R1,a
	mov	a,R2
	subb a,y+2
	mov	R2,a
	mov	a,R3
	subb a,y+3
	mov	R3,a
	
	; Set the least significant bit of x to 1
	orl	x+0,#1
	
div32_minus:
	djnz R4, div32_loop	; -> no
	
div32_exit:

	pop AR4
	pop AR3
	pop AR2
	pop AR1
	pop AR0
	pop psw
	pop acc
	
	ret

Load_X MAC
	mov x+0, #low (%0 % 0x10000) 
	mov x+1, #high(%0 % 0x10000) 
	mov x+2, #low (%0 / 0x10000) 
	mov x+3, #high(%0 / 0x10000) 
ENDMAC

Load_y MAC
	mov y+0, #low (%0 % 0x10000) 
	mov y+1, #high(%0 % 0x10000) 
	mov y+2, #low (%0 / 0x10000) 
	mov y+3, #high(%0 / 0x10000) 
ENDMAC
	
$LIST