| 1 | /* s_tanhl.c -- long double version of s_tanh.c. |
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| 2 | */ |
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| 3 | |
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| 4 | /* |
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| 5 | * ==================================================== |
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| 6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 7 | * |
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| 8 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 9 | * Permission to use, copy, modify, and distribute this |
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| 10 | * software is freely granted, provided that this notice |
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| 11 | * is preserved. |
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| 12 | * ==================================================== |
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| 13 | */ |
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| 14 | |
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| 15 | /* tanhl(x) |
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| 16 | * Return the Hyperbolic Tangent of x |
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| 17 | * |
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| 18 | * Method : |
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| 19 | * x -x |
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| 20 | * e - e |
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| 21 | * 0. tanhl(x) is defined to be ----------- |
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| 22 | * x -x |
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| 23 | * e + e |
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| 24 | * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). |
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| 25 | * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) |
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| 26 | * -t |
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| 27 | * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) |
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| 28 | * t + 2 |
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| 29 | * 2 |
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| 30 | * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) |
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| 31 | * t + 2 |
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| 32 | * 40.0 < x <= INF : tanhl(x) := 1. |
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| 33 | * |
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| 34 | * Special cases: |
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| 35 | * tanhl(NaN) is NaN; |
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| 36 | * only tanhl(0)=0 is exact for finite argument. |
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| 37 | */ |
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| 38 | |
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| 39 | #include <float.h> |
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| 40 | #include <math.h> |
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| 41 | #include <math_private.h> |
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| 42 | #include <math-underflow.h> |
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| 43 | #include <libm-alias-ldouble.h> |
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| 44 | |
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| 45 | static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900); |
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| 46 | |
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| 47 | _Float128 |
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| 48 | __tanhl (_Float128 x) |
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| 49 | { |
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| 50 | _Float128 t, z; |
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| 51 | uint32_t jx, ix; |
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| 52 | ieee854_long_double_shape_type u; |
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| 53 | |
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| 54 | /* Words of |x|. */ |
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| 55 | u.value = x; |
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| 56 | jx = u.parts32.w0; |
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| 57 | ix = jx & 0x7fffffff; |
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| 58 | /* x is INF or NaN */ |
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| 59 | if (ix >= 0x7fff0000) |
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| 60 | { |
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| 61 | /* for NaN it's not important which branch: tanhl(NaN) = NaN */ |
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| 62 | if (jx & 0x80000000) |
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| 63 | return one / x - one; /* tanhl(-inf)= -1; */ |
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| 64 | else |
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| 65 | return one / x + one; /* tanhl(+inf)=+1 */ |
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| 66 | } |
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| 67 | |
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| 68 | /* |x| < 40 */ |
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| 69 | if (ix < 0x40044000) |
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| 70 | { |
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| 71 | if (u.value == 0) |
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| 72 | return x; /* x == +- 0 */ |
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| 73 | if (ix < 0x3fc60000) /* |x| < 2^-57 */ |
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| 74 | { |
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| 75 | math_check_force_underflow (x); |
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| 76 | return x * (one + tiny); /* tanh(small) = small */ |
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| 77 | } |
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| 78 | u.parts32.w0 = ix; /* Absolute value of x. */ |
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| 79 | if (ix >= 0x3fff0000) |
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| 80 | { /* |x| >= 1 */ |
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| 81 | t = __expm1l (two * u.value); |
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| 82 | z = one - two / (t + two); |
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| 83 | } |
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| 84 | else |
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| 85 | { |
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| 86 | t = __expm1l (-two * u.value); |
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| 87 | z = -t / (t + two); |
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| 88 | } |
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| 89 | /* |x| > 40, return +-1 */ |
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| 90 | } |
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| 91 | else |
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| 92 | { |
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| 93 | z = one - tiny; /* raised inexact flag */ |
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| 94 | } |
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| 95 | return (jx & 0x80000000) ? -z : z; |
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| 96 | } |
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| 97 | libm_alias_ldouble (__tanh, tanh) |
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| 98 | |
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