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/* @(#)s_asinh.c 5.1 93/09/24 */
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/* @(#)s_asinh.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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<<asinh>>, <<asinhf>>---inverse hyperbolic sine
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<<asinh>>, <<asinhf>>---inverse hyperbolic sine
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INDEX
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INDEX
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asinh
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asinh
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INDEX
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INDEX
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asinhf
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asinhf
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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 asinh(double <[x]>);
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double asinh(double <[x]>);
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float asinhf(float <[x]>);
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float asinhf(float <[x]>);
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TRAD_SYNOPSIS
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TRAD_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double asinh(<[x]>)
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double asinh(<[x]>)
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double <[x]>;
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double <[x]>;
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float asinhf(<[x]>)
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float asinhf(<[x]>)
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float <[x]>;
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float <[x]>;
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DESCRIPTION
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DESCRIPTION
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<<asinh>> calculates the inverse hyperbolic sine of <[x]>.
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<<asinh>> calculates the inverse hyperbolic sine of <[x]>.
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<<asinh>> is defined as
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<<asinh>> is defined as
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@ifnottex
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@ifnottex
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. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
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. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
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@end ifnottex
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@end ifnottex
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@tex
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@tex
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$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
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$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
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@end tex
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@end tex
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<<asinhf>> is identical, other than taking and returning floats.
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<<asinhf>> is identical, other than taking and returning floats.
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RETURNS
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RETURNS
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<<asinh>> and <<asinhf>> return the calculated value.
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<<asinh>> and <<asinhf>> return the calculated value.
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PORTABILITY
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PORTABILITY
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Neither <<asinh>> nor <<asinhf>> are ANSI C.
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Neither <<asinh>> nor <<asinhf>> are ANSI C.
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*/
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*/
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/* asinh(x)
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/* asinh(x)
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* Method :
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* Method :
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* Based on
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* we have
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* we have
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* asinh(x) := x if 1+x*x=1,
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(log(x)+ln2)) for large |x|, else
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* := sign(x)*(log(x)+ln2)) for large |x|, else
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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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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static const double
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static const double
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#else
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#else
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static double
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static double
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#endif
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#endif
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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huge= 1.00000000000000000000e+300;
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huge= 1.00000000000000000000e+300;
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#ifdef __STDC__
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#ifdef __STDC__
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double asinh(double x)
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double asinh(double x)
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#else
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#else
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double asinh(x)
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double asinh(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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double t,w;
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double t,w;
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__int32_t hx,ix;
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__int32_t hx,ix;
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GET_HIGH_WORD(hx,x);
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GET_HIGH_WORD(hx,x);
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ix = hx&0x7fffffff;
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ix = hx&0x7fffffff;
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if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
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if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
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if(ix< 0x3e300000) { /* |x|<2**-28 */
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if(ix< 0x3e300000) { /* |x|<2**-28 */
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if(huge+x>one) return x; /* return x inexact except 0 */
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if(huge+x>one) return x; /* return x inexact except 0 */
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}
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}
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if(ix>0x41b00000) { /* |x| > 2**28 */
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if(ix>0x41b00000) { /* |x| > 2**28 */
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w = __ieee754_log(fabs(x))+ln2;
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w = __ieee754_log(fabs(x))+ln2;
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} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
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} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
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t = fabs(x);
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t = fabs(x);
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w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
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w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
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} else { /* 2.0 > |x| > 2**-28 */
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} else { /* 2.0 > |x| > 2**-28 */
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t = x*x;
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t = x*x;
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w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
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w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
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}
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}
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if(hx>0) return w; else return -w;
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if(hx>0) return w; else return -w;
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}
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}
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#endif /* _DOUBLE_IS_32BITS */
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#endif /* _DOUBLE_IS_32BITS */
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