# SXMicrocontrollerMathMethod

## 32 bit Square Root binary restoring method

Andy David says:

Here's my 32 bit routine as written for the PIC 17c43 [ed: and converted to the Scenix SX] 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 ... and ... cycles (incl. call and return).
; Uses 66 words ROM, 8 bytes RAM including 4 holding the input.
;
;-------------------------------------------------------------------------

brSQRT32:
mov     W, #\$40         ; Initial value for Result is...
mov     ACCaHI, W       ; ... 01000000 00000000
clr     ACCaLO          ;

mov     W, #\$C0         ; Initial value for mask is...
mov     ACCbHI, W       ; ... 11000000 00000000
clr     ACCbLO          ; (second '1' is loop counter).

Sub_Cmp:
mov     W, ACCaLO       ; Compare root-so-far with current
sub     ACCcLO, W       ; ... remainder.
mov     W, ACCaHI       ;
sb      C
movsz   W, ++ACCaHI     ;
sub     ACCcHI, W       ;
sb      C               ;
jmp     brstr           ; (result is negative, need to restore).

In1:    mov     W, ACCbLO       ; set the current bit in the result.
or      ACCaLO, W       ;
mov     W, ACCbHI       ;
or      ACCaHI, W       ;

ShftUp: rl      ACCdLO          ;
rl      ACCdHI          ;
rl      ACCcLO          ;
rl      ACCcHI          ;

rr      ACCbHI          ; Shift mask right for next bit, whilst
rr      ACCbLO          ; ... shifting IN MSB from remainder.
snb     ACCbHI.7        ; If MSB is set, unconditionally set the
jmp     USet1           ; ... next bit.

mov     W, ACCbLO       ; Append '01' to root-so-far
xor     ACCaLO, W       ;
mov     W, ACCbHI       ;
xor     ACCaHI, W       ;

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

mov     W, ACCaLO       ; Last bit Generation.
sub     ACCcLO, W       ; ... The final subtract is 17-bit (15-bit root
mov     W, ACCaHI       ; ... plus '01'). Subtract 16-bits: if result
sb      C
movsz   W, ++ACCaHI
sub     ACCcHI, W       ; ... generates a carry, last bit is 0.
sb      C               ;
ret

mov     W, #1           ; If result is 0 AND msb of is '0', result bit
snb     Z               ; ... is 0, otherwise '1'.
snb     ACCdHI.7        ;
xor     ACCaLO, W       ;
ret

USet1:  snb     C               ; If mask has shifted out, leave. final bit
ret                     ; ... has been set by iorwf at in1.
clrb    ACCbHI.7        ; clear bit shifted in from input.

mov     W, ACCbLO       ; Append '01' to root-so-far
xor     ACCaLO, W       ;
mov     W, ACCbHI       ;
xor     ACCaHI, W       ;

mov     W, ACCaLO       ; This subtraction is guaranteed not to
sub     ACCcLO, W       ; ... cause a borrow, so subtract and
mov     W, ACCaHI       ; ... jump back to insert a '1' in the
sb      C
movsz   W, ++ACCaHI
sub     ACCcHI, W       ; ... root.
jmp     In1     ;

brstr:  mov     W, ACCaLO       ; A subtract above at Sub_Cmp was -ve, so
add     ACCcLO, W       ; ... restore the remainder by adding.
mov     W, ACCaHI       ; The current bit of the root is zero.
snb     C
movsz   W, ++ACCaHI
add     ACCcHI, W       ;
jmp     ShftUp          ;

```

 file: /Techref/scenix/lib/math/sqrt/sqrt32_sx.htm, 5KB, , updated: 2004/6/10 14:40, local time: 2024/7/24 12:22, TOP NEW HELP FIND:  44.192.44.30:LOG IN

 ©2024 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions?Please DO link to this page! Digg it! / MAKE! SX Microcontroller Math Method - 32 bit Square Root binary restoring method

After you find an appropriate page, you are invited to your to this massmind site! (posts will be visible only to you before review) Just type a nice message (short messages are blocked as spam) in the box and press the Post button. (HTML welcomed, but not the <A tag: Instead, use the link box to link to another page. A tutorial is available Members can login to post directly, become page editors, and be credited for their posts.

Link? Put it here:
if you want a response, please enter your email address:
Attn spammers: All posts are reviewed before being made visible to anyone other than the poster.
 Did you find what you needed? "No. I'm looking for: " "No. Take me to the search page." "No. Take me to the top so I can drill down by catagory" "No. I'm willing to pay for help, please refer me to a qualified consultant"

### Welcome to sxlist.com!

Site supported by
& kind contributors
just like you!

(here's why

Copies of the site on CD
are available at minimal cost.

.