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Revision 1.13, Fri Apr 25 22:21:53 2008 UTC (15 years, 11 months ago) by christos
Branch: MAIN
CVS Tags: yamt-pf42-base4, yamt-pf42-base3, yamt-pf42-base2, yamt-pagecache-tag8, yamt-pagecache-base9, yamt-pagecache-base8, yamt-pagecache-base7, yamt-pagecache-base6, yamt-pagecache-base5, yamt-pagecache-base4, yamt-pagecache-base3, yamt-pagecache-base2, yamt-pagecache-base, yamt-pagecache, wrstuden-revivesa-base-3, wrstuden-revivesa-base-2, wrstuden-revivesa-base-1, wrstuden-revivesa-base, wrstuden-revivesa, tls-maxphys-base, tls-maxphys, tls-earlyentropy-base, tls-earlyentropy, riastradh-xf86-video-intel-2-7-1-pre-2-21-15, riastradh-drm2-base3, riastradh-drm2-base2, riastradh-drm2-base1, riastradh-drm2-base, riastradh-drm2, prg-localcount2-base3, prg-localcount2-base2, prg-localcount2-base1, prg-localcount2-base, prg-localcount2, phil-wifi-base, phil-wifi-20200421, phil-wifi-20200411, phil-wifi-20200406, phil-wifi-20191119, phil-wifi-20190609, phil-wifi, pgoyette-localcount-base, pgoyette-localcount-20170426, pgoyette-localcount-20170320, pgoyette-localcount-20170107, pgoyette-localcount-20161104, pgoyette-localcount-20160806, pgoyette-localcount-20160726, pgoyette-localcount, pgoyette-compat-merge-20190127, pgoyette-compat-base, pgoyette-compat-20190127, pgoyette-compat-20190118, pgoyette-compat-1226, pgoyette-compat-1126, pgoyette-compat-1020, pgoyette-compat-0930, pgoyette-compat-0906, pgoyette-compat-0728, pgoyette-compat-0625, pgoyette-compat-0521, pgoyette-compat-0502, pgoyette-compat-0422, pgoyette-compat-0415, pgoyette-compat-0407, pgoyette-compat-0330, pgoyette-compat-0322, pgoyette-compat-0315, pgoyette-compat, perseant-stdc-iso10646-base, perseant-stdc-iso10646, netbsd-9-base, netbsd-9-3-RELEASE, netbsd-9-2-RELEASE, netbsd-9-1-RELEASE, netbsd-9-0-RELEASE, netbsd-9-0-RC2, netbsd-9-0-RC1, netbsd-9, netbsd-8-base, netbsd-8-2-RELEASE, netbsd-8-1-RELEASE, netbsd-8-1-RC1, netbsd-8-0-RELEASE, netbsd-8-0-RC2, netbsd-8-0-RC1, netbsd-8, netbsd-7-nhusb-base-20170116, netbsd-7-nhusb-base, netbsd-7-nhusb, netbsd-7-base, netbsd-7-2-RELEASE, netbsd-7-1-RELEASE, netbsd-7-1-RC2, netbsd-7-1-RC1, netbsd-7-1-2-RELEASE, netbsd-7-1-1-RELEASE, netbsd-7-1, netbsd-7-0-RELEASE, netbsd-7-0-RC3, netbsd-7-0-RC2, netbsd-7-0-RC1, netbsd-7-0-2-RELEASE, netbsd-7-0-1-RELEASE, netbsd-7-0, netbsd-7, netbsd-6-base, netbsd-6-1-RELEASE, netbsd-6-1-RC4, netbsd-6-1-RC3, netbsd-6-1-RC2, netbsd-6-1-RC1, netbsd-6-1-5-RELEASE, netbsd-6-1-4-RELEASE, netbsd-6-1-3-RELEASE, netbsd-6-1-2-RELEASE, netbsd-6-1-1-RELEASE, netbsd-6-1, netbsd-6-0-RELEASE, netbsd-6-0-RC2, netbsd-6-0-RC1, netbsd-6-0-6-RELEASE, netbsd-6-0-5-RELEASE, netbsd-6-0-4-RELEASE, netbsd-6-0-3-RELEASE, netbsd-6-0-2-RELEASE, netbsd-6-0-1-RELEASE, netbsd-6-0, netbsd-6, netbsd-5-base, netbsd-5-2-RELEASE, netbsd-5-2-RC1, netbsd-5-2-3-RELEASE, netbsd-5-2-2-RELEASE, netbsd-5-2-1-RELEASE, netbsd-5-2, netbsd-5-1-RELEASE, netbsd-5-1-RC4, netbsd-5-1-RC3, netbsd-5-1-RC2, netbsd-5-1-RC1, netbsd-5-1-5-RELEASE, netbsd-5-1-4-RELEASE, netbsd-5-1-3-RELEASE, netbsd-5-1-2-RELEASE, netbsd-5-1-1-RELEASE, netbsd-5-1, netbsd-5-0-RELEASE, netbsd-5-0-RC4, netbsd-5-0-RC3, netbsd-5-0-RC2, netbsd-5-0-RC1, netbsd-5-0-2-RELEASE, netbsd-5-0-1-RELEASE, netbsd-5-0, netbsd-5, netbsd-10-base, netbsd-10-0-RELEASE, netbsd-10-0-RC6, netbsd-10-0-RC5, netbsd-10-0-RC4, netbsd-10-0-RC3, netbsd-10-0-RC2, netbsd-10-0-RC1, netbsd-10, matt-premerge-20091211, matt-nb8-mediatek-base, matt-nb8-mediatek, matt-nb6-plus-nbase, matt-nb6-plus-base, matt-nb6-plus, matt-nb5-pq3-base, matt-nb5-pq3, matt-nb5-mips64-u2-k2-k4-k7-k8-k9, matt-nb5-mips64-u1-k1-k5, matt-nb5-mips64-premerge-20101231, matt-nb5-mips64-premerge-20091211, matt-nb5-mips64-k15, matt-nb5-mips64, matt-nb4-mips64-k7-u2a-k9b, matt-mips64-premerge-20101231, matt-mips64-base2, localcount-20160914, jym-xensuspend-nbase, jym-xensuspend-base, jym-xensuspend, is-mlppp-base, is-mlppp, hpcarm-cleanup-nbase, cjep_sun2x-base1, cjep_sun2x-base, cjep_sun2x, cjep_staticlib_x-base1, cjep_staticlib_x-base, cjep_staticlib_x, cherry-xenmp-base, cherry-xenmp, bouyer-socketcan-base1, bouyer-socketcan-base, bouyer-socketcan, bouyer-quota2-nbase, bouyer-quota2-base, bouyer-quota2, agc-symver-base, agc-symver, HEAD
Changes since 1.12: +8 -8 lines 

avoid shadow variables, and enable lint.

/* @(#)e_hypot.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos Exp $");
#endif

/* __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*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
 *	yy1= y with lower 32 bits chopped, y2 = y-yy1.
 *
 *	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 "math.h"
#include "math_private.h"

double
__ieee754_hypot(double x, double y)
{
	double a=x,b=y,t1,t2,yy1,y2,w;
	int32_t j,k,ha,hb;

	GET_HIGH_WORD(ha,x);
	ha &= 0x7fffffff;
	GET_HIGH_WORD(hb,y);
	hb &= 0x7fffffff;
	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
	SET_HIGH_WORD(a,ha);	/* a <- |a| */
	SET_HIGH_WORD(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 */
	       u_int32_t low;
	       w = a+b;			/* for sNaN */
	       GET_LOW_WORD(low,a);
	       if(((ha&0xfffff)|low)==0) w = a;
	       GET_LOW_WORD(low,b);
	       if(((hb^0x7ff00000)|low)==0) w = b;
	       return w;
	   }
	   /* scale a and b by 2**-600 */
	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
	   SET_HIGH_WORD(a,ha);
	   SET_HIGH_WORD(b,hb);
	}
	if(hb < 0x20b00000) {	/* b < 2**-500 */
	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
	        u_int32_t low;
		GET_LOW_WORD(low,b);
		if((hb|low)==0) return a;
		t1=0;
		SET_HIGH_WORD(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;
		SET_HIGH_WORD(a,ha);
		SET_HIGH_WORD(b,hb);
	    }
	}
    /* medium size a and b */
	w = a-b;
	if (w>b) {
	    t1 = 0;
	    SET_HIGH_WORD(t1,ha);
	    t2 = a-t1;
	    w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
	} else {
	    a  = a+a;
	    yy1 = 0;
	    SET_HIGH_WORD(yy1,hb);
	    y2 = b - yy1;
	    t1 = 0;
	    SET_HIGH_WORD(t1,ha+0x00100000);
	    t2 = a - t1;
	    w  = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
	}
	if(k!=0) {
	    u_int32_t high;
	    t1 = 1.0;
	    GET_HIGH_WORD(high,t1);
	    SET_HIGH_WORD(t1,high+(k<<20));
	    return t1*w;
	} else return w;
}