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Viewing changes to android/bionic/libm/src/e_hypot.c

  • Committer: Package Import Robot
  • Author(s): Dmitrijs Ledkovs
  • Date: 2013-07-05 10:12:24 UTC
  • Revision ID: package-import@ubuntu.com-20130705101224-6qo3e8jbz8p31aa1
Tags: upstream-0.20130705.1
Import upstream version 0.20130705.1

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android/bionic/libm/src/e_hypot.c
 
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/* @(#)e_hypot.c 1.3 95/01/18 */
 
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/*
 
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 * ====================================================
 
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 
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 *
 
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 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 
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 * Permission to use, copy, modify, and distribute this
 
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 * software is freely granted, provided that this notice 
 
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 * is preserved.
 
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 * ====================================================
 
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 */
 
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#ifndef lint
 
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static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_hypot.c,v 1.9 2005/02/04 18:26:05 das Exp $";
 
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#endif
 
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/* __ieee754_hypot(x,y)
 
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 *
 
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 * Method :                  
 
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 *      If (assume round-to-nearest) z=x*x+y*y 
 
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 *      has error less than sqrt(2)/2 ulp, than 
 
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 *      sqrt(z) has error less than 1 ulp (exercise).
 
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 *
 
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 *      So, compute sqrt(x*x+y*y) with some care as 
 
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 *      follows to get the error below 1 ulp:
 
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 *
 
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 *      Assume x>y>0;
 
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 *      (if possible, set rounding to round-to-nearest)
 
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 *      1. if x > 2y  use
 
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 *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 
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 *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 
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 *      2. if x <= 2y use
 
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 *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
 
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 *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
 
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 *      y1= y with lower 32 bits chopped, y2 = y-y1.
 
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 *              
 
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 *      NOTE: scaling may be necessary if some argument is too 
 
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 *            large or too tiny
 
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 *
 
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 * Special cases:
 
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 *      hypot(x,y) is INF if x or y is +INF or -INF; else
 
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 *      hypot(x,y) is NAN if x or y is NAN.
 
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 *
 
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 * Accuracy:
 
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 *      hypot(x,y) returns sqrt(x^2+y^2) with error less 
 
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 *      than 1 ulps (units in the last place) 
 
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 */
 
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#include "math.h"
 
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#include "math_private.h"
 
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double
 
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__ieee754_hypot(double x, double y)
 
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{
 
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        double a=x,b=y,t1,t2,y1,y2,w;
 
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        int32_t j,k,ha,hb;
 
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        GET_HIGH_WORD(ha,x);
 
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        ha &= 0x7fffffff;
 
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        GET_HIGH_WORD(hb,y);
 
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        hb &= 0x7fffffff;
 
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        if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
 
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        SET_HIGH_WORD(a,ha);    /* a <- |a| */
 
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        SET_HIGH_WORD(b,hb);    /* b <- |b| */
 
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        if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
 
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        k=0;
 
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        if(ha > 0x5f300000) {   /* a>2**500 */
 
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           if(ha >= 0x7ff00000) {       /* Inf or NaN */
 
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               u_int32_t low;
 
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               w = a+b;                 /* for sNaN */
 
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               GET_LOW_WORD(low,a);
 
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               if(((ha&0xfffff)|low)==0) w = a;
 
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               GET_LOW_WORD(low,b);
 
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               if(((hb^0x7ff00000)|low)==0) w = b;
 
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               return w;
 
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           }
 
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           /* scale a and b by 2**-600 */
 
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           ha -= 0x25800000; hb -= 0x25800000;  k += 600;
 
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           SET_HIGH_WORD(a,ha);
 
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           SET_HIGH_WORD(b,hb);
 
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        }
 
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        if(hb < 0x20b00000) {   /* b < 2**-500 */
 
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            if(hb <= 0x000fffff) {      /* subnormal b or 0 */
 
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                u_int32_t low;
 
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                GET_LOW_WORD(low,b);
 
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                if((hb|low)==0) return a;
 
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                t1=0;
 
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                SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
 
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                b *= t1;
 
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                a *= t1;
 
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                k -= 1022;
 
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            } else {            /* scale a and b by 2^600 */
 
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                ha += 0x25800000;       /* a *= 2^600 */
 
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                hb += 0x25800000;       /* b *= 2^600 */
 
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                k -= 600;
 
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                SET_HIGH_WORD(a,ha);
 
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                SET_HIGH_WORD(b,hb);
 
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            }
 
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        }
 
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    /* medium size a and b */
 
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        w = a-b;
 
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        if (w>b) {
 
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            t1 = 0;
 
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            SET_HIGH_WORD(t1,ha);
 
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            t2 = a-t1;
 
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            w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 
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        } else {
 
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            a  = a+a;
 
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            y1 = 0;
 
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            SET_HIGH_WORD(y1,hb);
 
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            y2 = b - y1;
 
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            t1 = 0;
 
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            SET_HIGH_WORD(t1,ha+0x00100000);
 
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            t2 = a - t1;
 
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            w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 
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        }
 
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        if(k!=0) {
 
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            u_int32_t high;
 
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            t1 = 1.0;
 
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            GET_HIGH_WORD(high,t1);
 
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            SET_HIGH_WORD(t1,high+(k<<20));
 
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            return t1*w;
 
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        } else return w;
 
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}