231 lines
6.8 KiB
C
231 lines
6.8 KiB
C
/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)cabs.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* HYPOT(X,Y)
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* RETURN THE SQUARE ROOT OF X^2 + Y^2 WHERE Z=X+iY
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 11/28/84;
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* REVISED BY K.C. NG, 7/12/85.
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*
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* Required system supported functions :
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* copysign(x,y)
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* finite(x)
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* scalb(x,N)
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* sqrt(x)
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*
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* Method :
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* 1. replace x by |x| and y by |y|, and swap x and
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* y if y > x (hence x is never smaller than y).
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* 2. Hypot(x,y) is computed by:
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* Case I, x/y > 2
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*
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* y
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* hypot = x + -----------------------------
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* 2
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* sqrt ( 1 + [x/y] ) + x/y
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*
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* Case II, x/y <= 2
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* y
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* hypot = x + --------------------------------------------------
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* 2
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* [x/y] - 2
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* (sqrt(2)+1) + (x-y)/y + -----------------------------
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* 2
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* sqrt ( 1 + [x/y] ) + sqrt(2)
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*
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*
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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 the sqrt(x^2+y^2) with error less than 1 ulps (units
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* in the last place). See Kahan's "Interval Arithmetic Options in the
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* Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
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* 1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
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* code follows in comments.) In a test run with 500,000 random arguments
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* on a VAX, the maximum observed error was .959 ulps.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#include "mathimpl.h"
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vc(r2p1hi, 2.4142135623730950345E0 ,8279,411a,ef32,99fc, 2, .9A827999FCEF32)
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vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
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vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65)
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ic(r2p1hi, 2.4142135623730949234E0 , 1, 1.3504F333F9DE6)
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ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
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ic(sqrt2, 1.4142135623730951455E0 , 0, 1.6A09E667F3BCD)
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#ifdef vccast
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#define r2p1hi vccast(r2p1hi)
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#define r2p1lo vccast(r2p1lo)
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#define sqrt2 vccast(sqrt2)
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#endif
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double
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hypot(x,y)
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double x, y;
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{
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static const double zero=0, one=1,
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small=1.0E-18; /* fl(1+small)==1 */
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static const ibig=30; /* fl(1+2**(2*ibig))==1 */
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double t,r;
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int exp;
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if(finite(x))
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if(finite(y))
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{
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x=copysign(x,one);
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y=copysign(y,one);
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if(y > x)
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{ t=x; x=y; y=t; }
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if(x == zero) return(zero);
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if(y == zero) return(x);
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exp= logb(x);
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if(exp-(int)logb(y) > ibig )
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/* raise inexact flag and return |x| */
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{ one+small; return(x); }
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/* start computing sqrt(x^2 + y^2) */
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r=x-y;
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if(r>y) { /* x/y > 2 */
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r=x/y;
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r=r+sqrt(one+r*r); }
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else { /* 1 <= x/y <= 2 */
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r/=y; t=r*(r+2.0);
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r+=t/(sqrt2+sqrt(2.0+t));
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r+=r2p1lo; r+=r2p1hi; }
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r=y/r;
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return(x+r);
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}
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else if(y==y) /* y is +-INF */
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return(copysign(y,one));
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else
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return(y); /* y is NaN and x is finite */
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else if(x==x) /* x is +-INF */
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return (copysign(x,one));
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else if(finite(y))
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return(x); /* x is NaN, y is finite */
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#if !defined(vax)&&!defined(tahoe)
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else if(y!=y) return(y); /* x and y is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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else return(copysign(y,one)); /* y is INF */
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}
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/* CABS(Z)
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* RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER Z = X + iY
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 11/28/84.
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* REVISED BY K.C. NG, 7/12/85.
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*
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* Required kernel function :
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* hypot(x,y)
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*
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* Method :
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* cabs(z) = hypot(x,y) .
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*/
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struct complex { double x, y; };
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double
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cabs(z)
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struct complex z;
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{
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return hypot(z.x,z.y);
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}
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double
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z_abs(z)
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struct complex *z;
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{
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return hypot(z->x,z->y);
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}
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/* A faster but less accurate version of cabs(x,y) */
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#if 0
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double hypot(x,y)
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double x, y;
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{
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static const double zero=0, one=1;
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small=1.0E-18; /* fl(1+small)==1 */
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static const ibig=30; /* fl(1+2**(2*ibig))==1 */
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double temp;
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int exp;
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if(finite(x))
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if(finite(y))
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{
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x=copysign(x,one);
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y=copysign(y,one);
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if(y > x)
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{ temp=x; x=y; y=temp; }
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if(x == zero) return(zero);
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if(y == zero) return(x);
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exp= logb(x);
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x=scalb(x,-exp);
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if(exp-(int)logb(y) > ibig )
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/* raise inexact flag and return |x| */
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{ one+small; return(scalb(x,exp)); }
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else y=scalb(y,-exp);
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return(scalb(sqrt(x*x+y*y),exp));
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}
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else if(y==y) /* y is +-INF */
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return(copysign(y,one));
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else
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return(y); /* y is NaN and x is finite */
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else if(x==x) /* x is +-INF */
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return (copysign(x,one));
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else if(finite(y))
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return(x); /* x is NaN, y is finite */
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else if(y!=y) return(y); /* x and y is NaN */
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else return(copysign(y,one)); /* y is INF */
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}
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#endif
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