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C, pasted on Jun 7:
/*
 * qsqrt.c
 *
 *  Created on: Jun 6, 2012
 *      Author: Lee
 */

#include <stdio.h>
#include <math.h>

#define SQRT2 1.4142135623730951

float qsqrt(float x){
	// x = [0 eeeeeeeeeee mmmmmmmmmmmmmmmmmmmmmmm]
	int i = *(int*)&x;
	int j = (((i/2-0x1fc00000)+0x3f800000)&0x3ff800000)+((i&0x7fffff)/5*2);

	float y = (*(float*)&j) * ((i-0x3f800000)&(0x800000) ? SQRT2 : 1); // 2-3 sig figs of significance

	// two iterations of newton: y = y - (y^2 - x)/2y yields 2^-18 points of precision
	y = (y + x/y)/2; // this yields 2^-8 points of precision
	return (y + x/y)/2;
}

int main(){
	int i = 1;
	for (; i < 1000; i++){
		float f = (qsqrt(i)-sqrt(i))/(sqrt(i));
		printf("%3d %10f %10f \t rel err: %10f\n",i,qsqrt(i),sqrt(i),f);
	}
	return 0;
}


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939  30.643107  30.643107 	 rel err:   0.000000
940  30.659420  30.659419 	 rel err:   0.000000
941  30.675724  30.675723 	 rel err:   0.000000
942  30.692019  30.692019 	 rel err:   0.000000
943  30.708305  30.708305 	 rel err:   0.000000
944  30.724583  30.724583 	 rel err:   0.000000
945  30.740852  30.740852 	 rel err:   0.000000
946  30.757113  30.757113 	 rel err:   0.000000
947  30.773365  30.773365 	 rel err:   0.000000
948  30.789609  30.789609 	 rel err:   0.000000
949  30.805844  30.805844 	 rel err:   0.000000
950  30.822070  30.822070 	 rel err:   0.000000
951  30.838288  30.838288 	 rel err:   0.000000
952  30.854497  30.854497 	 rel err:   0.000000
953  30.870698  30.870698 	 rel err:   0.000000
954  30.886891  30.886890 	 rel err:   0.000000
955  30.903074  30.903074 	 rel err:   0.000000
956  30.919250  30.919250 	 rel err:   0.000000
957  30.935417  30.935417 	 rel err:   0.000000
958  30.951575  30.951575 	 rel err:   0.000000
959  30.967725  30.967725 	 rel err:   0.000000
960  30.983867  30.983867 	 rel err:   0.000000
961  31.000000  31.000000 	 rel err:   0.000000
962  31.016125  31.016125 	 rel err:   0.000000
963  31.032241  31.032241 	 rel err:   0.000000
964  31.048350  31.048349 	 rel err:   0.000000
965  31.064449  31.064449 	 rel err:   0.000000
966  31.080541  31.080541 	 rel err:   0.000000
967  31.096624  31.096624 	 rel err:   0.000000
968  31.112699  31.112698 	 rel err:   0.000000
969  31.128765  31.128765 	 rel err:   0.000000
970  31.144823  31.144823 	 rel err:   0.000000
971  31.160873  31.160873 	 rel err:   0.000000
972  31.176915  31.176915 	 rel err:   0.000000
973  31.192948  31.192948 	 rel err:   0.000000
974  31.208973  31.208973 	 rel err:   0.000000
975  31.224990  31.224990 	 rel err:   0.000000
976  31.240999  31.240999 	 rel err:   0.000000
977  31.256999  31.256999 	 rel err:   0.000000
978  31.272992  31.272992 	 rel err:   0.000000
979  31.288976  31.288976 	 rel err:   0.000000
980  31.304952  31.304952 	 rel err:   0.000000
981  31.320920  31.320920 	 rel err:   0.000000
982  31.336879  31.336879 	 rel err:   0.000000
983  31.352831  31.352831 	 rel err:   0.000000
984  31.368774  31.368774 	 rel err:   0.000000
985  31.384710  31.384710 	 rel err:   0.000000
986  31.400637  31.400637 	 rel err:   0.000000
987  31.416556  31.416556 	 rel err:   0.000000
988  31.432467  31.432467 	 rel err:   0.000000
989  31.448370  31.448370 	 rel err:   0.000000
990  31.464266  31.464265 	 rel err:   0.000000
991  31.480153  31.480152 	 rel err:   0.000000
992  31.496032  31.496031 	 rel err:   0.000000
993  31.511903  31.511903 	 rel err:   0.000000
994  31.527766  31.527766 	 rel err:   0.000000
995  31.543621  31.543621 	 rel err:   0.000000
996  31.559468  31.559468 	 rel err:   0.000000
997  31.575307  31.575307 	 rel err:   0.000000
998  31.591138  31.591138 	 rel err:   0.000000
999  31.606961  31.606961 	 rel err:   0.000000


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