e_hypot.c

来自「This is a resource based on j2me embedde」· C语言 代码 · 共 130 行

/*
 * @(#)e_hypot.c	1.9 06/10/10
 *
 * Copyright  1990-2008 Sun Microsystems, Inc. All Rights Reserved.  
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER  
 *   
 * This program is free software; you can redistribute it and/or  
 * modify it under the terms of the GNU General Public License version  
 * 2 only, as published by the Free Software Foundation.   
 *   
 * This program is distributed in the hope that it will be useful, but  
 * WITHOUT ANY WARRANTY; without even the implied warranty of  
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU  
 * General Public License version 2 for more details (a copy is  
 * included at /legal/license.txt).   
 *   
 * You should have received a copy of the GNU General Public License  
 * version 2 along with this work; if not, write to the Free Software  
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  
 * 02110-1301 USA   
 *   
 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa  
 * Clara, CA 95054 or visit www.sun.com if you need additional  
 * information or have any questions. 
 *
 */

/* __ieee754_hypot(x,y)
 *
 * Method :
 *	If (assume round-to-nearest) z=x*x+y*y
 *	has error less than sqrt(2)/2 ulp, than
 *	sqrt(z) has error less than 1 ulp (exercise).
 *
 *	So, compute sqrt(x*x+y*y) with some care as
 *	follows to get the error below 1 ulp:
 *
 *	Assume x>y>0;
 *	(if possible, set rounding to round-to-nearest)
 *	1. if x > 2y  use
 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 *	2. if x <= 2y use
 *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
 *	y1= y with lower 32 bits chopped, y2 = y-y1.
 *
 *	NOTE: scaling may be necessary if some argument is too
 *	      large or too tiny
 *
 * Special cases:
 *	hypot(x,y) is INF if x or y is +INF or -INF; else
 *	hypot(x,y) is NAN if x or y is NAN.
 *
 * Accuracy:
 * 	hypot(x,y) returns sqrt(x^2+y^2) with error less
 * 	than 1 ulps (units in the last place)
 */

#include "fdlibm.h"

#ifdef __STDC__
	double __ieee754_hypot(double x, double y)
#else
	double __ieee754_hypot(x,y)
	double x, y;
#endif
{
	double a=x,b=y,t1,t2,y1,y2,w;
	int j,k,ha,hb;

	ha = __HI(x)&0x7fffffff;	/* high word of  x */
	hb = __HI(y)&0x7fffffff;	/* high word of  y */
	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
	__HI(a) = ha;	/* a <- |a| */
	__HI(b) = hb;	/* b <- |b| */
	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
	k=0;
	if(ha > 0x5f300000) {	/* a>2**500 */
	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
	       w = a+b;			/* for sNaN */
	       if(((ha&0xfffff)|__LO(a))==0) w = a;
	       if(((hb^0x7ff00000)|__LO(b))==0) w = b;
	       return w;
	   }
	   /* scale a and b by 2**-600 */
	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
	   __HI(a) = ha;
	   __HI(b) = hb;
	}
	if(hb < 0x20b00000) {	/* b < 2**-500 */
	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
		if((hb|(__LO(b)))==0) return a;
		t1=0;
		__HI(t1) = 0x7fd00000;	/* t1=2^1022 */
		b *= t1;
		a *= t1;
		k -= 1022;
	    } else {		/* scale a and b by 2^600 */
	        ha += 0x25800000; 	/* a *= 2^600 */
		hb += 0x25800000;	/* b *= 2^600 */
		k -= 600;
	   	__HI(a) = ha;
	   	__HI(b) = hb;
	    }
	}
    /* medium size a and b */
	w = a-b;
	if (w>b) {
	    t1 = 0;
	    __HI(t1) = ha;
	    t2 = a-t1;
	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
	} else {
	    a  = a+a;
	    y1 = 0;
	    __HI(y1) = hb;
	    y2 = b - y1;
	    t1 = 0;
	    __HI(t1) = ha+0x00100000;
	    t2 = a - t1;
	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
	}
	if(k!=0) {
	    t1 = 1.0;
	    __HI(t1) += (k<<20);
	    return t1*w;
	} else return w;
}