1 2 /* @(#)e_hypot.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* __ieee754_hypot(x,y) 15 * 16 * Method : 17 * If (assume round-to-nearest) z=x*x+y*y 18 * has error less than ieee_sqrt(2)/2 ulp, than 19 * sqrt(z) has error less than 1 ulp (exercise). 20 * 21 * So, compute ieee_sqrt(x*x+y*y) with some care as 22 * follows to get the error below 1 ulp: 23 * 24 * Assume x>y>0; 25 * (if possible, set rounding to round-to-nearest) 26 * 1. if x > 2y use 27 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 28 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 29 * 2. if x <= 2y use 30 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 31 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 32 * y1= y with lower 32 bits chopped, y2 = y-y1. 33 * 34 * NOTE: scaling may be necessary if some argument is too 35 * large or too tiny 36 * 37 * Special cases: 38 * hypot(x,y) is INF if x or y is +INF or -INF; else 39 * hypot(x,y) is NAN if x or y is NAN. 40 * 41 * Accuracy: 42 * hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less 43 * than 1 ulps (units in the last place) 44 */ 45 46 #include "fdlibm.h" 47 48 #ifdef __STDC__ __ieee754_hypot(double x,double y)49 double __ieee754_hypot(double x, double y) 50 #else 51 double __ieee754_hypot(x,y) 52 double x, y; 53 #endif 54 { 55 double a=x,b=y,t1,t2,y1,y2,w; 56 int j,k,ha,hb; 57 58 ha = __HI(x)&0x7fffffff; /* high word of x */ 59 hb = __HI(y)&0x7fffffff; /* high word of y */ 60 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 61 __HI(a) = ha; /* a <- |a| */ 62 __HI(b) = hb; /* b <- |b| */ 63 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 64 k=0; 65 if(ha > 0x5f300000) { /* a>2**500 */ 66 if(ha >= 0x7ff00000) { /* Inf or NaN */ 67 w = a+b; /* for sNaN */ 68 if(((ha&0xfffff)|__LO(a))==0) w = a; 69 if(((hb^0x7ff00000)|__LO(b))==0) w = b; 70 return w; 71 } 72 /* scale a and b by 2**-600 */ 73 ha -= 0x25800000; hb -= 0x25800000; k += 600; 74 __HI(a) = ha; 75 __HI(b) = hb; 76 } 77 if(hb < 0x20b00000) { /* b < 2**-500 */ 78 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 79 if((hb|(__LO(b)))==0) return a; 80 t1=0; 81 __HI(t1) = 0x7fd00000; /* t1=2^1022 */ 82 b *= t1; 83 a *= t1; 84 k -= 1022; 85 } else { /* scale a and b by 2^600 */ 86 ha += 0x25800000; /* a *= 2^600 */ 87 hb += 0x25800000; /* b *= 2^600 */ 88 k -= 600; 89 __HI(a) = ha; 90 __HI(b) = hb; 91 } 92 } 93 /* medium size a and b */ 94 w = a-b; 95 if (w>b) { 96 t1 = 0; 97 __HI(t1) = ha; 98 t2 = a-t1; 99 w = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 100 } else { 101 a = a+a; 102 y1 = 0; 103 __HI(y1) = hb; 104 y2 = b - y1; 105 t1 = 0; 106 __HI(t1) = ha+0x00100000; 107 t2 = a - t1; 108 w = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 109 } 110 if(k!=0) { 111 t1 = 1.0; 112 __HI(t1) += (k<<20); 113 return t1*w; 114 } else return w; 115 } 116