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/* @(#)e_hypot.c 5.1 93/09/24 */
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/* @(#)e_hypot.c 5.1 93/09/24 */
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/*
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/*
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* ====================================================
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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/*
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/*
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FUNCTION
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FUNCTION
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<<hypot>>, <<hypotf>>---distance from origin
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<<hypot>>, <<hypotf>>---distance from origin
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INDEX
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INDEX
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hypot
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hypot
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INDEX
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INDEX
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hypotf
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hypotf
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ANSI_SYNOPSIS
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ANSI_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double hypot(double <[x]>, double <[y]>);
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double hypot(double <[x]>, double <[y]>);
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float hypotf(float <[x]>, float <[y]>);
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float hypotf(float <[x]>, float <[y]>);
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TRAD_SYNOPSIS
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TRAD_SYNOPSIS
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double hypot(<[x]>, <[y]>)
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double hypot(<[x]>, <[y]>)
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double <[x]>, <[y]>;
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double <[x]>, <[y]>;
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float hypotf(<[x]>, <[y]>)
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float hypotf(<[x]>, <[y]>)
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float <[x]>, <[y]>;
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float <[x]>, <[y]>;
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DESCRIPTION
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DESCRIPTION
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<<hypot>> calculates the Euclidean distance
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<<hypot>> calculates the Euclidean distance
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@tex
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@tex
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$\sqrt{x^2+y^2}$
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$\sqrt{x^2+y^2}$
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@end tex
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@end tex
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@ifnottex
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@ifnottex
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<<sqrt(<[x]>*<[x]> + <[y]>*<[y]>)>>
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<<sqrt(<[x]>*<[x]> + <[y]>*<[y]>)>>
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@end ifnottex
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@end ifnottex
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between the origin (0,0) and a point represented by the
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between the origin (0,0) and a point represented by the
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Cartesian coordinates (<[x]>,<[y]>). <<hypotf>> differs only
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Cartesian coordinates (<[x]>,<[y]>). <<hypotf>> differs only
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in the type of its arguments and result.
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in the type of its arguments and result.
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RETURNS
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RETURNS
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Normally, the distance value is returned. On overflow,
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Normally, the distance value is returned. On overflow,
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<<hypot>> returns <<HUGE_VAL>> and sets <<errno>> to
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<<hypot>> returns <<HUGE_VAL>> and sets <<errno>> to
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<<ERANGE>>.
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<<ERANGE>>.
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You can change the error treatment with <<matherr>>.
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You can change the error treatment with <<matherr>>.
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PORTABILITY
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PORTABILITY
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<<hypot>> and <<hypotf>> are not ANSI C. */
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<<hypot>> and <<hypotf>> are not ANSI C. */
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/* hypot(x,y)
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/* hypot(x,y)
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*
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*
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* Method :
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* Method :
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* If (assume round-to-nearest) z=x*x+y*y
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* If (assume round-to-nearest) z=x*x+y*y
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* has error less than sqrt(2)/2 ulp, than
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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*
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* So, compute sqrt(x*x+y*y) with some care as
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* So, compute sqrt(x*x+y*y) with some care as
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* follows to get the error below 1 ulp:
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* follows to get the error below 1 ulp:
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*
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*
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* Assume x>y>0;
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* Assume x>y>0;
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* (if possible, set rounding to round-to-nearest)
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* 1. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* 2. if x <= 2y use
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* 2. if x <= 2y use
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* y1= y with lower 32 bits chopped, y2 = y-y1.
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* y1= y with lower 32 bits chopped, y2 = y-y1.
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*
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*
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* NOTE: scaling may be necessary if some argument is too
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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* large or too tiny
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*
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*
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* Special cases:
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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 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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* hypot(x,y) is NAN if x or y is NAN.
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*
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*
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* Accuracy:
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2+y^2) with error less
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* hypot(x,y) returns sqrt(x^2+y^2) with error less
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* than 1 ulps (units in the last place)
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* than 1 ulps (units in the last place)
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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double hypot(double x, double y)
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double hypot(double x, double y)
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#else
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#else
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double hypot(x,y)
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double hypot(x,y)
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double x, y;
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double x, y;
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#endif
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#endif
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{
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{
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double a=x,b=y,t1,t2,y1,y2,w;
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double a=x,b=y,t1,t2,y1,y2,w;
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__int32_t j,k,ha,hb;
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__int32_t j,k,ha,hb;
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GET_HIGH_WORD(ha,x);
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GET_HIGH_WORD(ha,x);
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ha &= 0x7fffffff;
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ha &= 0x7fffffff;
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GET_HIGH_WORD(hb,y);
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GET_HIGH_WORD(hb,y);
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hb &= 0x7fffffff;
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hb &= 0x7fffffff;
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if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
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if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
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SET_HIGH_WORD(a,ha); /* a <- |a| */
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SET_HIGH_WORD(a,ha); /* a <- |a| */
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SET_HIGH_WORD(b,hb); /* b <- |b| */
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SET_HIGH_WORD(b,hb); /* b <- |b| */
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if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
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if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
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k=0;
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k=0;
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if(ha > 0x5f300000) { /* a>2**500 */
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if(ha > 0x5f300000) { /* a>2**500 */
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if(ha >= 0x7ff00000) { /* Inf or NaN */
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if(ha >= 0x7ff00000) { /* Inf or NaN */
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__uint32_t low;
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__uint32_t low;
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w = a+b; /* for sNaN */
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w = a+b; /* for sNaN */
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GET_LOW_WORD(low,a);
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GET_LOW_WORD(low,a);
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if(((ha&0xfffff)|low)==0) w = a;
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if(((ha&0xfffff)|low)==0) w = a;
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GET_LOW_WORD(low,b);
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GET_LOW_WORD(low,b);
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if(((hb^0x7ff00000)|low)==0) w = b;
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if(((hb^0x7ff00000)|low)==0) w = b;
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return w;
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return w;
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}
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}
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/* scale a and b by 2**-600 */
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/* scale a and b by 2**-600 */
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ha -= 0x25800000; hb -= 0x25800000; k += 600;
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ha -= 0x25800000; hb -= 0x25800000; k += 600;
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(b,hb);
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SET_HIGH_WORD(b,hb);
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}
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}
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if(hb < 0x20b00000) { /* b < 2**-500 */
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if(hb < 0x20b00000) { /* b < 2**-500 */
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if(hb <= 0x000fffff) { /* subnormal b or 0 */
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if(hb <= 0x000fffff) { /* subnormal b or 0 */
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__uint32_t low;
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__uint32_t low;
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GET_LOW_WORD(low,b);
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GET_LOW_WORD(low,b);
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if((hb|low)==0) return a;
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if((hb|low)==0) return a;
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t1=0;
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t1=0;
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SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
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SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
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b *= t1;
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b *= t1;
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a *= t1;
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a *= t1;
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k -= 1022;
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k -= 1022;
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} else { /* scale a and b by 2^600 */
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} else { /* scale a and b by 2^600 */
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ha += 0x25800000; /* a *= 2^600 */
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ha += 0x25800000; /* a *= 2^600 */
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hb += 0x25800000; /* b *= 2^600 */
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hb += 0x25800000; /* b *= 2^600 */
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k -= 600;
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k -= 600;
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(a,ha);
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SET_HIGH_WORD(b,hb);
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SET_HIGH_WORD(b,hb);
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}
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}
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}
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}
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/* medium size a and b */
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/* medium size a and b */
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w = a-b;
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w = a-b;
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if (w>b) {
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if (w>b) {
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t1 = 0;
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t1 = 0;
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SET_HIGH_WORD(t1,ha);
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SET_HIGH_WORD(t1,ha);
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t2 = a-t1;
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t2 = a-t1;
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w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
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w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
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} else {
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} else {
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a = a+a;
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a = a+a;
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y1 = 0;
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y1 = 0;
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SET_HIGH_WORD(y1,hb);
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SET_HIGH_WORD(y1,hb);
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y2 = b - y1;
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y2 = b - y1;
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t1 = 0;
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t1 = 0;
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SET_HIGH_WORD(t1,ha+0x00100000);
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SET_HIGH_WORD(t1,ha+0x00100000);
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t2 = a - t1;
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t2 = a - t1;
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w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
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w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
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}
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}
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if(k!=0) {
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if(k!=0) {
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__uint32_t high;
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__uint32_t high;
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t1 = 1.0;
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t1 = 1.0;
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GET_HIGH_WORD(high,t1);
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GET_HIGH_WORD(high,t1);
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SET_HIGH_WORD(t1,high+(k<<20));
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SET_HIGH_WORD(t1,high+(k<<20));
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return t1*w;
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return t1*w;
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} else return w;
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} else return w;
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}
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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#endif /* defined(_DOUBLE_IS_32BITS) */
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