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-/*
- * Copyright (c) 1985 Regents of the University of California.
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- *    notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- *    notice, this list of conditions and the following disclaimer in the
- *    documentation and/or other materials provided with the distribution.
- * 3. All advertising materials mentioning features or use of this software
- *    must display the following acknowledgement:
- *	This product includes software developed by the University of
- *	California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- *    may be used to endorse or promote products derived from this software
- *    without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)cabs.c	5.6 (Berkeley) 10/9/90";
-#endif /* not lint */
-
-/* HYPOT(X,Y)
- * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
- * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 11/28/84; 
- * REVISED BY K.C. NG, 7/12/85.
- *
- * Required system supported functions :
- *	copysign(x,y)
- *	finite(x)
- *	scalb(x,N)
- *	sqrt(x)
- *
- * Method :
- *	1. replace x by |x| and y by |y|, and swap x and
- *	   y if y > x (hence x is never smaller than y).
- *	2. Hypot(x,y) is computed by:
- *	   Case I, x/y > 2
- *		
- *				       y
- *		hypot = x + -----------------------------
- *			 		    2
- *			    sqrt ( 1 + [x/y]  )  +  x/y
- *
- *	   Case II, x/y <= 2 
- *				                   y
- *		hypot = x + --------------------------------------------------
- *				          		     2 
- *				     			[x/y]   -  2
- *			   (sqrt(2)+1) + (x-y)/y + -----------------------------
- *			 		    			  2
- *			    			  sqrt ( 1 + [x/y]  )  + sqrt(2)
- *
- *
- *
- * 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 the sqrt(x^2+y^2) with error less than 1 ulps (units
- *	in the last place). See Kahan's "Interval Arithmetic Options in the
- *	Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
- *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
- *	code follows in	comments.) In a test run with 500,000 random arguments
- *	on a VAX, the maximum observed error was .959 ulps.
- *
- * Constants:
- * The hexadecimal values are the intended ones for the following constants.
- * The decimal values may be used, provided that the compiler will convert
- * from decimal to binary accurately enough to produce the hexadecimal values
- * shown.
- */
-#include "mathimpl.h"
-
-#if 0 /* Moved to separate file.  */
-
-vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
-vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
-vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
-
-ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
-ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
-ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)
-
-#ifdef vccast
-#define	r2p1hi	vccast(r2p1hi)
-#define	r2p1lo	vccast(r2p1lo)
-#define	sqrt2	vccast(sqrt2)
-#endif
-
-double
-hypot(x,y)
-double x, y;
-{
-	static const double zero=0, one=1, 
-		      small=1.0E-18;	/* fl(1+small)==1 */
-	static const ibig=30;	/* fl(1+2**(2*ibig))==1 */
-	double t,r;
-	int exp;
-
-	if(finite(x))
-	    if(finite(y))
-	    {	
-		x=copysign(x,one);
-		y=copysign(y,one);
-		if(y > x) 
-		    { t=x; x=y; y=t; }
-		if(x == zero) return(zero);
-		if(y == zero) return(x);
-		exp= logb(x);
-		if(exp-(int)logb(y) > ibig ) 	
-			/* raise inexact flag and return |x| */
-		   { one+small; return(x); }
-
-	    /* start computing sqrt(x^2 + y^2) */
-		r=x-y;
-		if(r>y) { 	/* x/y > 2 */
-		    r=x/y;
-		    r=r+sqrt(one+r*r); }
-		else {		/* 1 <= x/y <= 2 */
-		    r/=y; t=r*(r+2.0);
-		    r+=t/(sqrt2+sqrt(2.0+t));
-		    r+=r2p1lo; r+=r2p1hi; }
-
-		r=y/r;
-		return(x+r);
-
-	    }
-
-	    else if(y==y)   	   /* y is +-INF */
-		     return(copysign(y,one));
-	    else 
-		     return(y);	   /* y is NaN and x is finite */
-
-	else if(x==x) 		   /* x is +-INF */
-	         return (copysign(x,one));
-	else if(finite(y))
-	         return(x);		   /* x is NaN, y is finite */
-#if !defined(vax)&&!defined(tahoe)
-	else if(y!=y) return(y);  /* x and y is NaN */
-#endif	/* !defined(vax)&&!defined(tahoe) */
-	else return(copysign(y,one));   /* y is INF */
-}
-
-#endif /* 0 */
-
-/* CABS(Z)
- * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
- * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 11/28/84.
- * REVISED BY K.C. NG, 7/12/85.
- *
- * Required kernel function :
- *	hypot(x,y)
- *
- * Method :
- *	cabs(z) = hypot(x,y) .
- */
-
-double
-cabs(z)
-struct __cabs_complex z;
-{
-	return hypot(z.__x,z.__y);
-}
-
-double
-z_abs(z)
-struct __cabs_complex *z;
-{
-	return hypot(z->__x,z->__y);
-}
-
-/* A faster but less accurate version of cabs(x,y) */
-#if 0
-double hypot(x,y)
-double x, y;
-{
-	static const double zero=0, one=1;
-		      small=1.0E-18;	/* fl(1+small)==1 */
-	static const ibig=30;	/* fl(1+2**(2*ibig))==1 */
-	double temp;
-	int exp;
-
-	if(finite(x))
-	    if(finite(y))
-	    {	
-		x=copysign(x,one);
-		y=copysign(y,one);
-		if(y > x) 
-		    { temp=x; x=y; y=temp; }
-		if(x == zero) return(zero);
-		if(y == zero) return(x);
-		exp= logb(x);
-		x=scalb(x,-exp);
-		if(exp-(int)logb(y) > ibig ) 
-			/* raise inexact flag and return |x| */
-		   { one+small; return(scalb(x,exp)); }
-		else y=scalb(y,-exp);
-		return(scalb(sqrt(x*x+y*y),exp));
-	    }
-
-	    else if(y==y)   	   /* y is +-INF */
-		     return(copysign(y,one));
-	    else 
-		     return(y);	   /* y is NaN and x is finite */
-
-	else if(x==x) 		   /* x is +-INF */
-	         return (copysign(x,one));
-	else if(finite(y))
-	         return(x);		   /* x is NaN, y is finite */
-	else if(y!=y) return(y);  	/* x and y is NaN */
-	else return(copysign(y,one));   /* y is INF */
-}
-#endif
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