1141296Sdas 2141296Sdas/* @(#)e_hypot.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 122116Sjkh */ 132116Sjkh 14176277Sbde#include <sys/cdefs.h> 15176277Sbde__FBSDID("$FreeBSD$"); 162116Sjkh 172116Sjkh/* __ieee754_hypot(x,y) 182116Sjkh * 19141296Sdas * Method : 20141296Sdas * If (assume round-to-nearest) z=x*x+y*y 21141296Sdas * has error less than sqrt(2)/2 ulp, than 222116Sjkh * sqrt(z) has error less than 1 ulp (exercise). 232116Sjkh * 24141296Sdas * So, compute sqrt(x*x+y*y) with some care as 252116Sjkh * follows to get the error below 1 ulp: 262116Sjkh * 272116Sjkh * Assume x>y>0; 282116Sjkh * (if possible, set rounding to round-to-nearest) 292116Sjkh * 1. if x > 2y use 302116Sjkh * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 312116Sjkh * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 322116Sjkh * 2. if x <= 2y use 332116Sjkh * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 34141296Sdas * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 352116Sjkh * y1= y with lower 32 bits chopped, y2 = y-y1. 36141296Sdas * 37141296Sdas * NOTE: scaling may be necessary if some argument is too 382116Sjkh * large or too tiny 392116Sjkh * 402116Sjkh * Special cases: 412116Sjkh * hypot(x,y) is INF if x or y is +INF or -INF; else 422116Sjkh * hypot(x,y) is NAN if x or y is NAN. 432116Sjkh * 442116Sjkh * Accuracy: 45141296Sdas * hypot(x,y) returns sqrt(x^2+y^2) with error less 46141296Sdas * than 1 ulps (units in the last place) 472116Sjkh */ 482116Sjkh 49177758Sdas#include <float.h> 50177758Sdas 512116Sjkh#include "math.h" 522116Sjkh#include "math_private.h" 532116Sjkh 5497413Salfreddouble 5597413Salfred__ieee754_hypot(double x, double y) 562116Sjkh{ 57226380Sdas double a,b,t1,t2,y1,y2,w; 582116Sjkh int32_t j,k,ha,hb; 592116Sjkh 602116Sjkh GET_HIGH_WORD(ha,x); 612116Sjkh ha &= 0x7fffffff; 622116Sjkh GET_HIGH_WORD(hb,y); 632116Sjkh hb &= 0x7fffffff; 642116Sjkh if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 65177751Sbde a = fabs(a); 66177751Sbde b = fabs(b); 672116Sjkh if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 682116Sjkh k=0; 692116Sjkh if(ha > 0x5f300000) { /* a>2**500 */ 702116Sjkh if(ha >= 0x7ff00000) { /* Inf or NaN */ 712116Sjkh u_int32_t low; 72176277Sbde /* Use original arg order iff result is NaN; quieten sNaNs. */ 73177749Sbde w = fabs(x+0.0)-fabs(y+0.0); 742116Sjkh GET_LOW_WORD(low,a); 752116Sjkh if(((ha&0xfffff)|low)==0) w = a; 762116Sjkh GET_LOW_WORD(low,b); 772116Sjkh if(((hb^0x7ff00000)|low)==0) w = b; 782116Sjkh return w; 792116Sjkh } 802116Sjkh /* scale a and b by 2**-600 */ 812116Sjkh ha -= 0x25800000; hb -= 0x25800000; k += 600; 822116Sjkh SET_HIGH_WORD(a,ha); 832116Sjkh SET_HIGH_WORD(b,hb); 842116Sjkh } 852116Sjkh if(hb < 0x20b00000) { /* b < 2**-500 */ 868870Srgrimes if(hb <= 0x000fffff) { /* subnormal b or 0 */ 872116Sjkh u_int32_t low; 882116Sjkh GET_LOW_WORD(low,b); 892116Sjkh if((hb|low)==0) return a; 902116Sjkh t1=0; 912116Sjkh SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 922116Sjkh b *= t1; 932116Sjkh a *= t1; 942116Sjkh k -= 1022; 952116Sjkh } else { /* scale a and b by 2^600 */ 962116Sjkh ha += 0x25800000; /* a *= 2^600 */ 972116Sjkh hb += 0x25800000; /* b *= 2^600 */ 982116Sjkh k -= 600; 992116Sjkh SET_HIGH_WORD(a,ha); 1002116Sjkh SET_HIGH_WORD(b,hb); 1012116Sjkh } 1022116Sjkh } 1032116Sjkh /* medium size a and b */ 1042116Sjkh w = a-b; 1052116Sjkh if (w>b) { 1062116Sjkh t1 = 0; 1072116Sjkh SET_HIGH_WORD(t1,ha); 1082116Sjkh t2 = a-t1; 109141296Sdas w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 1102116Sjkh } else { 1112116Sjkh a = a+a; 1122116Sjkh y1 = 0; 1132116Sjkh SET_HIGH_WORD(y1,hb); 1142116Sjkh y2 = b - y1; 1152116Sjkh t1 = 0; 1162116Sjkh SET_HIGH_WORD(t1,ha+0x00100000); 1172116Sjkh t2 = a - t1; 118141296Sdas w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 1192116Sjkh } 1202116Sjkh if(k!=0) { 1212116Sjkh u_int32_t high; 1222116Sjkh t1 = 1.0; 1232116Sjkh GET_HIGH_WORD(high,t1); 1242116Sjkh SET_HIGH_WORD(t1,high+(k<<20)); 1252116Sjkh return t1*w; 1262116Sjkh } else return w; 1272116Sjkh} 128177758Sdas 129177758Sdas#if LDBL_MANT_DIG == 53 130177758Sdas__weak_reference(hypot, hypotl); 131177758Sdas#endif 132