From: Scott Dattalo
I know at least a few people are interested in this. I finally got around to applying the 18cxxx instruction set to the sqrt algorithm (see: http://www.dattalo.com/technical/software/pic/picsqrt.html and http://www.dattalo.com/technical/theory/sqrt.html ).It takes only 25 instructions and executes between 68 and 108 (excluding the call). I have no idea what the average is. Although, if I made the test code isochronous, it'd be easy to find that out. I still think there's room for optimization too (but after spending 4 hours fixing an elusive bug in gpsim, I'm not up to it [but I see two places that can be tweaked]). BTW, gpsim runs through all 2^16 test cases in just 2 seconds!
Scott
list p=18c242,t=ON,c=132,n=80 radix dec include "p18c242.inc" cblock 0 N_hi,N_lo mask x,y s_hi,s_lo endc ORG 0 ;Reset Vector Main CLRF status CLRF x CLRF s_hi CLRF s_lo INCF x,f ; Here's some test code that goes through all 2^16 cases ; ; psuedo code: : ; int s=0; ; int x=0; ; ; do { ; ; if(x*x == s) ; x++; ; ; n = s; ; w = sqrt(n); ; if(w+1 != x) ; failed(); ; ; s++; ; ; } while (x<256); ; for(i=0; i< 256; i++) xxx MOVF x,W ;W = x*x MULWF x movf prodh,w,0 ;if x*x is equal to the current cpfseq s_hi ;test case, s, then we need to advance bra L1 ;x. Note that x will always be 1 greater movf prodl,w,0 ;than the sqrt(s) cpfseq s_lo bra L1 infsnz x,f here bra here L1: ; N = s movf s_hi,w movwf N_hi movf s_lo,w movwf N_lo ; find the sqrt of N (N_hi:N_lo) RCALL sqrt infsnz s_lo,f ;s++ advance for the next test case incf s_hi,f addlw 1 ;if w (sqrt(N)) is one less than x cpfseq x ; then we've passed bra failed bra xxx failed: bra xxx ;Set a break point here to catch failures ; ;sqrt ; ; The purpose of this routine is take the square root of a 16 bit ;unsigned integer. ;Inputs: N_hi  High byte of the 16 bit number to be square rooted ; N_lo  Low byte " " " ;Outputs: W register returned with the 8 bit result ; ;Memory used: ; mask ; ;Minimum 68 cycles ;Maximum 108 cycles sqrt MOVLW 0xc0 ;Initialize value for mask MOVWF mask MOVLW 0x40 ;Initial value for the root sq1 CPFSLT N_hi BRA sq6 ;Subtract the root developed so far sq3 RLCF N_lo,F ;Shift N left one position RLCF N_hi,F BC sq4 RRCF mask,F ;mov the 2bit mask down 1 XORWF mask,W ;clear the last and set the next bit BNC sq1 ;We are almost done. In the last iteration, we have 7 bits of the root. When ;"01" is appended to it, we will have a 9bit number that must be subtracted ;from N. SUBWF N_hi,F ; SKPC ;If the upper 7 bits cause a borrow, then RETURN ;the appended "01" will as well: We're done. SKPNZ ;If the result of the subtraction is zero BTFSC N_lo,7 ;AND the msb of N_lo is set then the LSB of the ;root is zero. XORLW 1 ;Otherwise, it is one. RETURN ; sq4 BTFSC mask,0 ;Need to unconditionally set the current bit of the root. RETURN ;However, if we're through iterating, then leave. RRNCF mask,F XORWF mask,W ;Append "01" to the root developed so far. sq6 SUBWF N_hi,F IORWF mask,W ;Set the current bit bra sq3 ;Go unconditionally set the current bit. END
(gpsim is a fullfeatured software simulator for Microchip PIC microcontrollers distributed under the GNU General Public License. http://dattalo.com/gnupic/gpsim.html )
Archive:
See also:
file: /Techref/microchip/math/sqrt/16bint18csd.htm, 5KB, , updated: 2003/12/10 16:05, local time: 2019/11/22 08:44,
owner: DAVMPE62a,

©2019 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? <A HREF="http://techref.massmind.org/techref/microchip/math/sqrt/16bint18csd.htm"> 16 bit integer square root (16bint18csd.htm)</A> 
Did you find what you needed? 
Welcome to massmind.org! 
Welcome to techref.massmind.org! 
.