1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)e_hypot.c 1.3 95/01/18 */ 3b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* 4b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 5b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 7b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 8b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Permission to use, copy, modify, and distribute this 9b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * software is freely granted, provided that this notice 10b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is preserved. 11b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 12b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 13b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 14b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* __ieee754_hypot(x,y) 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method : 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * If (assume round-to-nearest) z=x*x+y*y 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * has error less than ieee_sqrt(2)/2 ulp, than 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * sqrt(z) has error less than 1 ulp (exercise). 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * So, compute ieee_sqrt(x*x+y*y) with some care as 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * follows to get the error below 1 ulp: 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Assume x>y>0; 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (if possible, set rounding to round-to-nearest) 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. if x > 2y use 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. if x <= 2y use 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1= y with lower 32 bits chopped, y2 = y-y1. 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * NOTE: scaling may be necessary if some argument is too 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * large or too tiny 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Special cases: 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * hypot(x,y) is INF if x or y is +INF or -INF; else 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * hypot(x,y) is NAN if x or y is NAN. 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Accuracy: 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * than 1 ulps (units in the last place) 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_hypot(double x, double y) 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_hypot(x,y) 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x, y; 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double a=x,b=y,t1,t2,y1,y2,w; 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int j,k,ha,hb; 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ha = __HI(x)&0x7fffffff; /* high word of x */ 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hb = __HI(y)&0x7fffffff; /* high word of y */ 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(a) = ha; /* a <- |a| */ 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(b) = hb; /* b <- |b| */ 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project k=0; 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ha > 0x5f300000) { /* a>2**500 */ 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ha >= 0x7ff00000) { /* Inf or NaN */ 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = a+b; /* for sNaN */ 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(((ha&0xfffff)|__LO(a))==0) w = a; 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(((hb^0x7ff00000)|__LO(b))==0) w = b; 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return w; 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* scale a and b by 2**-600 */ 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ha -= 0x25800000; hb -= 0x25800000; k += 600; 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(a) = ha; 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(b) = hb; 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hb < 0x20b00000) { /* b < 2**-500 */ 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hb <= 0x000fffff) { /* subnormal b or 0 */ 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((hb|(__LO(b)))==0) return a; 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t1=0; 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t1) = 0x7fd00000; /* t1=2^1022 */ 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b *= t1; 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a *= t1; 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project k -= 1022; 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { /* scale a and b by 2^600 */ 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ha += 0x25800000; /* a *= 2^600 */ 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hb += 0x25800000; /* b *= 2^600 */ 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project k -= 600; 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(a) = ha; 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(b) = hb; 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* medium size a and b */ 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = a-b; 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if (w>b) { 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t1 = 0; 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t1) = ha; 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t2 = a-t1; 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = a+a; 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y1 = 0; 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(y1) = hb; 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y2 = b - y1; 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t1 = 0; 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t1) = ha+0x00100000; 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t2 = a - t1; 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(k!=0) { 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t1 = 1.0; 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(t1) += (k<<20); 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return t1*w; 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else return w; 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 116