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/* @(#)s_asinh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* asinh(x)
* Method :
* Based on
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(log(x)+ln2)) for large |x|, else
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-double.h>
static const double
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge = 1.00000000000000000000e+300;
double
__asinh (double x)
{
double w;
int32_t hx, ix;
GET_HIGH_WORD (hx, x);
ix = hx & 0x7fffffff;
if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */
{
math_check_force_underflow (x);
if (huge + x > one)
return x; /* return x inexact except 0 */
}
if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */
{
if (ix >= 0x7ff00000)
return x + x; /* x is inf or NaN */
w = __ieee754_log (fabs (x)) + ln2;
}
else
{
double xa = fabs (x);
if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */
{
w = __ieee754_log (2.0 * xa + one / (sqrt (xa * xa + one) +
xa));
}
else /* 2.0 > |x| > 2**-28 */
{
double t = xa * xa;
w = __log1p (xa + t / (one + sqrt (one + t)));
}
}
return __copysign (w, x);
}
libm_alias_double (__asinh, asinh)
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