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| 1906 | serge | 1 | /* tanhl.c |
| 2 | * |
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| 3 | * Hyperbolic tangent, long double precision |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * long double x, y, tanhl(); |
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| 10 | * |
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| 11 | * y = tanhl( x ); |
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| 12 | * |
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| 13 | * |
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| 14 | * |
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| 15 | * DESCRIPTION: |
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| 16 | * |
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| 17 | * Returns hyperbolic tangent of argument in the range MINLOGL to |
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| 18 | * MAXLOGL. |
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| 19 | * |
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| 20 | * A rational function is used for |x| < 0.625. The form |
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| 21 | * x + x**3 P(x)/Q(x) of Cody _& Waite is employed. |
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| 22 | * Otherwise, |
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| 23 | * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1). |
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| 24 | * |
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| 25 | * |
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| 26 | * |
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| 27 | * ACCURACY: |
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| 28 | * |
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| 29 | * Relative error: |
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| 30 | * arithmetic domain # trials peak rms |
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| 31 | * IEEE -2,2 30000 1.3e-19 2.4e-20 |
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| 32 | * |
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| 33 | */ |
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| 34 | |||
| 35 | /* |
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| 36 | Cephes Math Library Release 2.7: May, 1998 |
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| 37 | Copyright 1984, 1987, 1989, 1998 by Stephen L. Moshier |
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| 38 | */ |
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| 39 | |||
| 40 | /* |
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| 41 | Modified for mingw |
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| 42 | 2002-07-22 Danny Smith |
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| 43 | */ |
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| 44 | |||
| 45 | #ifdef __MINGW32__ |
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| 46 | #include "cephes_mconf.h" |
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| 47 | #else |
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| 48 | #include "mconf.h" |
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| 49 | #endif |
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| 50 | |||
| 51 | #ifndef _SET_ERRNO |
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| 52 | #define _SET_ERRNO(x) |
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| 53 | #endif |
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| 54 | |||
| 55 | #ifdef UNK |
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| 56 | static long double P[] = { |
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| 57 | -6.8473739392677100872869E-5L, |
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| 58 | -9.5658283111794641589011E-1L, |
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| 59 | -8.4053568599672284488465E1L, |
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| 60 | -1.3080425704712825945553E3L, |
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| 61 | }; |
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| 62 | static long double Q[] = { |
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| 63 | /* 1.0000000000000000000000E0L,*/ |
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| 64 | 9.6259501838840336946872E1L, |
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| 65 | 1.8218117903645559060232E3L, |
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| 66 | 3.9241277114138477845780E3L, |
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| 67 | }; |
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| 68 | #endif |
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| 69 | |||
| 70 | #ifdef IBMPC |
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| 71 | static unsigned short P[] = { |
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| 72 | 0xd2a4,0x1b0c,0x8f15,0x8f99,0xbff1, XPD |
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| 73 | 0x5959,0x9111,0x9cc7,0xf4e2,0xbffe, XPD |
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| 74 | 0xb576,0xef5e,0x6d57,0xa81b,0xc005, XPD |
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| 75 | 0xe3be,0xbfbd,0x5cbc,0xa381,0xc009, XPD |
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| 76 | }; |
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| 77 | static unsigned short Q[] = { |
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| 78 | /*0x0000,0x0000,0x0000,0x8000,0x3fff,*/ |
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| 79 | 0x687f,0xce24,0xdd6c,0xc084,0x4005, XPD |
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| 80 | 0x3793,0xc95f,0xfa2f,0xe3b9,0x4009, XPD |
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| 81 | 0xd5a2,0x1f9c,0x0b1b,0xf542,0x400a, XPD |
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| 82 | }; |
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| 83 | #endif |
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| 84 | |||
| 85 | #ifdef MIEEE |
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| 86 | static long P[] = { |
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| 87 | 0xbff10000,0x8f998f15,0x1b0cd2a4, |
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| 88 | 0xbffe0000,0xf4e29cc7,0x91115959, |
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| 89 | 0xc0050000,0xa81b6d57,0xef5eb576, |
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| 90 | 0xc0090000,0xa3815cbc,0xbfbde3be, |
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| 91 | }; |
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| 92 | static long Q[] = { |
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| 93 | /*0x3fff0000,0x80000000,0x00000000,*/ |
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| 94 | 0x40050000,0xc084dd6c,0xce24687f, |
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| 95 | 0x40090000,0xe3b9fa2f,0xc95f3793, |
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| 96 | 0x400a0000,0xf5420b1b,0x1f9cd5a2, |
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| 97 | }; |
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| 98 | #endif |
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| 99 | |||
| 100 | #ifndef __MINGW32__ |
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| 101 | extern long double MAXLOGL; |
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| 102 | #ifdef ANSIPROT |
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| 103 | extern long double fabsl ( long double ); |
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| 104 | extern long double expl ( long double ); |
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| 105 | extern long double polevll ( long double, void *, int ); |
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| 106 | extern long double p1evll ( long double, void *, int ); |
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| 107 | #else |
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| 108 | long double fabsl(), expl(), polevll(), p1evll(); |
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| 109 | #endif |
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| 110 | #endif /* __MINGW32__ */ |
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| 111 | |||
| 112 | long double tanhl(x) |
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| 113 | long double x; |
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| 114 | { |
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| 115 | long double s, z; |
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| 116 | |||
| 117 | #ifdef MINUSZERO |
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| 118 | if( x == 0.0L ) |
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| 119 | return(x); |
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| 120 | #endif |
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| 121 | if (isnanl(x)) |
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| 122 | { |
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| 123 | _SET_ERRNO (EDOM); |
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| 124 | return x; |
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| 125 | } |
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| 126 | |||
| 127 | z = fabsl(x); |
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| 128 | if( z > 0.5L * MAXLOGL ) |
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| 129 | { |
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| 130 | _SET_ERRNO (ERANGE); |
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| 131 | if( x > 0 ) |
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| 132 | return( 1.0L ); |
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| 133 | else |
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| 134 | return( -1.0L ); |
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| 135 | } |
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| 136 | if( z >= 0.625L ) |
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| 137 | { |
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| 138 | s = expl(2.0*z); |
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| 139 | z = 1.0L - 2.0/(s + 1.0L); |
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| 140 | if( x < 0 ) |
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| 141 | z = -z; |
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| 142 | } |
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| 143 | else |
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| 144 | { |
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| 145 | s = x * x; |
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| 146 | z = polevll( s, P, 3 )/p1evll(s, Q, 3); |
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| 147 | z = x * s * z; |
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| 148 | z = x + z; |
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| 149 | } |
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| 150 | return( z ); |
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| 151 | } |