libm: Sync with FreeBSD (gains 6 long double functions)
[dragonfly.git] / lib / libm / src / s_tanh.c
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1/* @(#)s_tanh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
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11 */
12
2fedfd5c 13
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14/* Tanh(x)
15 * Return the Hyperbolic Tangent of x
16 *
17 * Method :
18 * x -x
19 * e - e
20 * 0. tanh(x) is defined to be -----------
21 * x -x
22 * e + e
23 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
6ff43c94 24 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
b34b60bc 25 * -t
6ff43c94 26 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
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27 * t + 2
28 * 2
6ff43c94 29 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
b34b60bc 30 * t + 2
6ff43c94 31 * 22 <= x <= INF : tanh(x) := 1.
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32 *
33 * Special cases:
34 * tanh(NaN) is NaN;
35 * only tanh(0)=0 is exact for finite argument.
36 */
37
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38#include <float.h>
39
6ff43c94 40#include "math.h"
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41#include "math_private.h"
42
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43static const volatile double tiny = 1.0e-300;
44static const double one = 1.0, two = 2.0, huge = 1.0e300;
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45
46double
47tanh(double x)
48{
49 double t,z;
50 int32_t jx,ix;
51
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52 GET_HIGH_WORD(jx,x);
53 ix = jx&0x7fffffff;
54
55 /* x is INF or NaN */
56 if(ix>=0x7ff00000) {
57 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
58 else return one/x-one; /* tanh(NaN) = NaN */
59 }
60
61 /* |x| < 22 */
62 if (ix < 0x40360000) { /* |x|<22 */
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63 if (ix<0x3e300000) { /* |x|<2**-28 */
64 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
65 }
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66 if (ix>=0x3ff00000) { /* |x|>=1 */
67 t = expm1(two*fabs(x));
68 z = one - two/(t+two);
69 } else {
70 t = expm1(-two*fabs(x));
71 z= -t/(t+two);
72 }
6ff43c94 73 /* |x| >= 22, return +-1 */
b34b60bc 74 } else {
6ff43c94 75 z = one - tiny; /* raise inexact flag */
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76 }
77 return (jx>=0)? z: -z;
78}
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79
80#if (LDBL_MANT_DIG == 53)
81__weak_reference(tanh, tanhl);
82#endif