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 13:40, local time: 2020/2/27 12:14,
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<A HREF="http://www.sxlist.com/techref/scenix/lib/math/sqrt/sqrt32_sx.htm"> SX Microcontroller Math Method - 32 bit Square Root binary restoring method</A>
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