# PICMicrocontollerMathMethod

## 32 bit Square Root binary restoring method

Andy David says:

Here's my 32 bit routine as written for the 17c43 taken from a mail I sent Scott just after I wrote it, hence the comments about the implementations I used.

Looks a lot like Scott's original 16-bit sqrt. As the root is going to be a 16 bit number the last subtract is awkward, so the 24-bit sqrt method wasn't appropriate. I did actually write this myself rather than automatically converting Scott's code to 32 bit. I DID, however, consciously and unashamedly steal two parts - how to carry out the final 17-bit subtraction and how to count iterations - the extra 'counting' bit in the mask was quite a devious idea. This one took a little longer to write than the 24-bit, probably because it needs to iterate more times...

Standard disclaimer applies

```;=========================================================================
; brSQRT32
;
; Calculates the square root of a thirtytwo bit number using the
; binary restoring method.
;
; Result in ACCaHI:ACCaLO
; Mask in ACCbHI:ACCbLO
; Input in ACCcHI:ACCcLO:ACCdHI:ACCdLO
;
; Takes between 392 and 439 cycles (incl. call and return).
; Uses 58 words ROM, 8 bytes RAM including 4 holding the input.
;
;-------------------------------------------------------------------------

brSQRT32:
movlw 0x40 ; Initial value for Result is...
movwf ACCaHI ; ... 01000000 00000000
clrf ACCaLO,f ;

movlw 0xC0 ; Initial value for mask is...
movwf ACCbHI ; ... 11000000 00000000
clrf ACCbLO,f ; (second '1' is loop counter).

Sub_Cmp:movfp ACCaLO,WREG ; Compare root-so-far with current
subwf ACCcLO,f ; ... remainder.
movfp ACCaHI,WREG ;
subwfb ACCcHI,f ;
btfss ALUSTA,C ;
goto brstr ; (result is -ve, need to restore).

In1:	movfp ACCbLO,WREG ; set the current bit in the result.
iorwf ACCaLO,f ;
movfp ACCbHI,WREG ;
iorwf ACCaHI,f ;

ShftUp:	rlcf ACCdLO,f ;
rlcf ACCdHI,f ;
rlcf ACCcLO,f ;
rlcf ACCcHI,f ;

rrcf ACCbHI,f ; Shift mask right for next bit, whilst
rrcf ACCbLO,f ; ... shifting IN MSB from remainder.
btfsc ACCbHI,7 ; If MSB is set, unconditionally set the
goto USet1 ; ... next bit.

movfp ACCbLO,WREG ; Append '01' to root-so-far
xorwf ACCaLO,f ;
movfp ACCbHI,WREG ;
xorwf ACCaHI,f ;

btfss ALUSTA,C ; If second '1' in mask is shifted out,
goto Sub_Cmp ; ... then that was the last normal iteration.

movfp ACCaLO,WREG 	; Last bit Generation.
subwf ACCcLO,f  	; ... The final subtract is 17-bit (15-bit root
movfp ACCaHI,WREG 	; ... plus '01'). Subtract 16-bits: if result
subwfb ACCcHI,f 	; ... generates a carry, last bit is 0.
btfss ALUSTA,C  	;
return

;Peter Harrison says these next two lines are required to set Z correctly
movfp	ACCcLO,WREG	; Clear zero flag if remainder non zero
xorwf	ACCcHI,WREG	;
;End section added by Peter Harrison.

movlw 1 ; If result is 0 AND msb of is '0', result bit
btfsc ALUSTA,Z ; ... is 0, otherwise '1'.
btfsc ACCdHI,7 ;
xorwf ACCaLO,f ;
return

USet1:	btfsc ALUSTA,C ; If mask has shifted out, leave. final bit
return ; ... has been set by iorwf at in1.
bcf ACCbHI,7 ; clear bit shifted in from input.

movfp ACCbLO,WREG ; Append '01' to root-so-far
xorwf ACCaLO,f ;
movfp ACCbHI,WREG ;
xorwf ACCaHI,f ;

movfp ACCaLO,WREG ; This subtraction is guaranteed not to
subwf ACCcLO,f ; ... cause a borrow, so subtract and
movfp ACCaHI,WREG ; ... jump back to insert a '1' in the
subwfb ACCcHI,f ; ... root.
goto In1 ;

brstr:	movfp ACCaLO,WREG ; A subtract above at Sub_Cmp was -ve, so
addwf ACCcLO,f ; ... restore the remainder by adding.
movfp ACCaHI,WREG ; The current bit of the root is zero.
addwfc ACCcHI,f ;
goto ShftUp ;
```

Comments:

• KILLspampetergharrisonSPAM at KILLspambtinternet.com
32 bit Square Root binary restoring routine.
This routine has an error in the last bit generation routine - basically the Z bit is incorrectly set after the final subtraction.
I have a routine for the PIC18F with this error corrected - two extra lines of code inserted before the decision to set the final bit. It now works correctly on all the numbers tested so far (several thousand!!)
{ed; here is Peters complete PIC18F routine . His corrections have also been added to the routine above. Thank you Peter!}
```;========================================================================================
; SQRT32
;
; Calculates the square root of a thirtytwo bit number using the
; binary restoring method.
;
; Input:	acc2_4:acc2_1
; Mask:		acc3_2:acc3_1
; Result:	acc1_2:acc1_1
;
; Takes between 395 and 457 cycles (incl. call and return).
; Uses 64 words ROM, 8 bytes RAM including 4 holding the input.
;========================================================================================
;
sqrt32	movlw	0x40		; Initial value for Result is...
movwf	acc1_2		; ... 01000000 00000000
clrf	acc1_1		;
;
movlw	0xC0		; Initial value for mask is...
movwf	acc3_2		; ... 11000000 00000000
clrf	acc3_1		; (second '1' is loop counter).
;
compare	movf	acc1_1,w	; Compare root-so-far with current
subwf	acc2_3,f	; ... remainder.
movf	acc1_2,w	;
subwfb	acc2_4,f	;
bc	\$+4		;
goto	restore		; result is -ve, so need to restore
;
setcurr	movf	acc3_1,w	; set the current bit in the result.
iorwf	acc1_1,f	;
movf	acc3_2,w	;
iorwf	acc1_2,f	;
;
shftUp	rlcf	acc2_1,f	;
rlcf	acc2_2,f	;
rlcf	acc2_3,f	;
rlcf	acc2_4,f	;
;
rrcf	acc3_2,f	; Shift mask right for next bit, whilst
rrcf	acc3_1,f	; ... shifting IN MSB from remainder.
btfsc	acc3_2,7	; If MSB is set, unconditionally set the
goto	setnext		; ... next bit.
;
movf	acc3_1,w	; Append '01' to root-so-far.
xorwf	acc1_1,f	;
movf	acc3_2,w	;
xorwf	acc1_2,f	;
;
bc	\$+4		; If second '1' in mask is shifted out,
goto	compare		; ... then that was the last normal iteration.
;
movf	acc1_1,w	; Last bit Generation.
subwf	acc2_3,f	; ... The final subtract is 17-bit (15-bit root
movf	acc1_2,w	; ... plus '01'). Subtract 16-bits: if result
subwfb	acc2_4,f	; ... generates a carry, last bit is 0.
bc	\$+4		;
return
;
movf	acc2_3,w	; Clear zero flag if remainder non zero
xorwf	acc2_4,w	;
;
movlw	1		;
bnz	\$+4		; If result is 0 AND msb of N is '0', result bit
btfsc	acc2_2,7	; ... is 0, otherwise '1'.
xorwf	acc1_1,f	;
return
;
;
setnext	bnc	\$+4		; If mask has shifted out, leave. final bit
return			; ... has been set by iorwf at in1.
bcf	acc3_2,7	; clear bit shifted in from input.
;
movf	acc3_1,w	; Append '01' to root-so-far
xorwf	acc1_1,f	;
movf	acc3_2,w	;
xorwf	acc1_2,f	;
;
movf	acc1_1,w	; This subtraction is guaranteed not to
subwf	acc2_3,f	; ... cause a borrow, so subtract and
movf	acc1_2,w	; ... jump back to insert a '1' in the
subwfb	acc2_4,f	; ... root.
goto	setcurr		;
;
restore	movf	acc1_1,w	; A subtract above at Sub_Cmp was -ve, so
addwf	acc2_3,f	; ... restore the remainder by adding.
movf	acc1_2,w	; The current bit of the root is zero.
addwfc	acc2_4,f	;
goto	shftUp		;
;
;========================================================================================

```

+

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