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