1 /* @(#)e_hypot.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #ifndef lint 14 static char rcsid[] = "$Id: e_hypot.c,v 1.4 1994/03/03 17:04:12 jtc Exp $"; 15 #endif 16 17 /* __ieee754_hypot(x,y) 18 * 19 * Method : 20 * If (assume round-to-nearest) z=x*x+y*y 21 * has error less than sqrt(2)/2 ulp, than 22 * sqrt(z) has error less than 1 ulp (exercise). 23 * 24 * So, compute sqrt(x*x+y*y) with some care as 25 * follows to get the error below 1 ulp: 26 * 27 * Assume x>y>0; 28 * (if possible, set rounding to round-to-nearest) 29 * 1. if x > 2y use 30 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 31 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 32 * 2. if x <= 2y use 33 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 34 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 35 * y1= y with lower 32 bits chopped, y2 = y-y1. 36 * 37 * NOTE: scaling may be necessary if some argument is too 38 * large or too tiny 39 * 40 * Special cases: 41 * hypot(x,y) is INF if x or y is +INF or -INF; else 42 * hypot(x,y) is NAN if x or y is NAN. 43 * 44 * Accuracy: 45 * hypot(x,y) returns sqrt(x^2+y^2) with error less 46 * than 1 ulps (units in the last place) 47 */ 48 49 #include <math.h> 50 #include <machine/endian.h> 51 52 #if BYTE_ORDER == LITTLE_ENDIAN 53 #define n0 1 54 #else 55 #define n0 0 56 #endif 57 58 #ifdef __STDC__ 59 double __ieee754_hypot(double x, double y) 60 #else 61 double __ieee754_hypot(x,y) 62 double x, y; 63 #endif 64 { 65 double a=x,b=y,t1,t2,y1,y2,w; 66 int j,k,ha,hb; 67 68 ha = *(n0+(int*)&x)&0x7fffffff; /* high word of x */ 69 hb = *(n0+(int*)&y)&0x7fffffff; /* high word of y */ 70 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 71 *(n0+(int*)&a) = ha; /* a <- |a| */ 72 *(n0+(int*)&b) = hb; /* b <- |b| */ 73 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 74 k=0; 75 if(ha > 0x5f300000) { /* a>2**500 */ 76 if(ha >= 0x7ff00000) { /* Inf or NaN */ 77 w = a+b; /* for sNaN */ 78 if(((ha&0xfffff)|*(1-n0+(int*)&a))==0) w = a; 79 if(((hb^0x7ff00000)|*(1-n0+(int*)&b))==0) w = b; 80 return w; 81 } 82 /* scale a and b by 2**-600 */ 83 ha -= 0x25800000; hb -= 0x25800000; k += 600; 84 *(n0+(int*)&a) = ha; 85 *(n0+(int*)&b) = hb; 86 } 87 if(hb < 0x20b00000) { /* b < 2**-500 */ 88 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 89 if((hb|(*(1-n0+(int*)&b)))==0) return a; 90 t1=0; 91 *(n0+(int*)&t1) = 0x7fd00000; /* t1=2^1022 */ 92 b *= t1; 93 a *= t1; 94 k -= 1022; 95 } else { /* scale a and b by 2^600 */ 96 ha += 0x25800000; /* a *= 2^600 */ 97 hb += 0x25800000; /* b *= 2^600 */ 98 k -= 600; 99 *(n0+(int*)&a) = ha; 100 *(n0+(int*)&b) = hb; 101 } 102 } 103 /* medium size a and b */ 104 w = a-b; 105 if (w>b) { 106 t1 = 0; 107 *(n0+(int*)&t1) = ha; 108 t2 = a-t1; 109 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 110 } else { 111 a = a+a; 112 y1 = 0; 113 *(n0+(int*)&y1) = hb; 114 y2 = b - y1; 115 t1 = 0; 116 *(n0+(int*)&t1) = ha+0x00100000; 117 t2 = a - t1; 118 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 119 } 120 if(k!=0) { 121 t1 = 1.0; 122 *(n0+(int*)&t1) += (k<<20); 123 return t1*w; 124 } else return w; 125 } 126