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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.
- */
-
-/* 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"
-
-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 */
-}
-
-/* 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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