71 lines
1.9 KiB
C
71 lines
1.9 KiB
C
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/* @(#)s_asinh.c 5.1 93/09/24 */
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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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*
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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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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* asinh(x)
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* Method :
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* we have
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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(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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*/
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#include <float.h>
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#include <math.h>
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#include <math_private.h>
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#include <math-underflow.h>
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#include <libm-alias-double.h>
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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huge = 1.00000000000000000000e+300;
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double
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__asinh (double x)
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{
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double w;
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int32_t hx, ix;
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GET_HIGH_WORD (hx, x);
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ix = hx & 0x7fffffff;
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if (__glibc_unlikely (ix < 0x3e300000)) /* |x|<2**-28 */
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{
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math_check_force_underflow (x);
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if (huge + x > one)
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return x; /* return x inexact except 0 */
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}
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if (__glibc_unlikely (ix > 0x41b00000)) /* |x| > 2**28 */
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{
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if (ix >= 0x7ff00000)
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return x + x; /* x is inf or NaN */
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w = __ieee754_log (fabs (x)) + ln2;
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}
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else
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{
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double xa = fabs (x);
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if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */
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{
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w = __ieee754_log (2.0 * xa + one / (sqrt (xa * xa + one) +
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xa));
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}
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else /* 2.0 > |x| > 2**-28 */
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{
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double t = xa * xa;
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w = __log1p (xa + t / (one + sqrt (one + t)));
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}
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}
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return copysign (w, x);
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}
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libm_alias_double (__asinh, asinh)
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