1 2 /******************************************************************************* 3 MIT License 4 ----------- 5 6 Copyright (c) 2002-2019 Advanced Micro Devices, Inc. 7 8 Permission is hereby granted, free of charge, to any person obtaining a copy 9 of this Software and associated documentaon files (the "Software"), to deal 10 in the Software without restriction, including without limitation the rights 11 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 12 copies of the Software, and to permit persons to whom the Software is 13 furnished to do so, subject to the following conditions: 14 15 The above copyright notice and this permission notice shall be included in 16 all copies or substantial portions of the Software. 17 18 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 19 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 20 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 21 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 22 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 23 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 24 THE SOFTWARE. 25 *******************************************************************************/ 26 27 #include "libm.h" 28 #include "libm_util.h" 29 30 #define USE_HANDLE_ERROR 31 #define USE_SPLITEXP 32 #define USE_SCALEDOUBLE_2 33 #define USE_VAL_WITH_FLAGS 34 #include "libm_inlines.h" 35 #undef USE_SPLITEXP 36 #undef USE_SCALEDOUBLE_2 37 #undef USE_VAL_WITH_FLAGS 38 #undef USE_HANDLE_ERROR 39 40 #include "libm_errno.h" 41 42 #ifdef _MSC_VER 43 #pragma function(tanh) 44 #endif 45 46 double tanh(double x) 47 { 48 /* 49 The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent 50 to the following three formulae: 51 1. (exp(x) - exp(-x))/(exp(x) + exp(-x)) 52 2. (1 - (2/(exp(2*x) + 1 ))) 53 3. (exp(2*x) - 1)/(exp(2*x) + 1) 54 but computationally, some formulae are better on some ranges. 55 */ 56 static const double 57 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */ 58 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */ 59 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */ 60 large_threshold = 20.0; /* 0x4034000000000000 */ 61 62 unsigned long long ux, aux, xneg; 63 double y, z, p, z1, z2; 64 int m; 65 66 /* Special cases */ 67 68 GET_BITS_DP64(x, ux); 69 aux = ux & ~SIGNBIT_DP64; 70 if (aux < 0x3e30000000000000) /* |x| small enough that tanh(x) = x */ 71 { 72 if (aux == 0) 73 return x; /* with no inexact */ 74 else 75 return val_with_flags(x, AMD_F_INEXACT); 76 } 77 else if (aux > 0x7ff0000000000000) /* |x| is NaN */ 78 return _handle_error("tanh", OP_TANH, ux|0x0008000000000000, _DOMAIN, 79 0, EDOM, x, 0.0, 1); 80 // return x + x; 81 82 xneg = (aux != ux); 83 84 y = x; 85 if (xneg) y = -x; 86 87 if (y > large_threshold) 88 { 89 /* If x is large then exp(-x) is negligible and 90 formula 1 reduces to plus or minus 1.0 */ 91 z = 1.0; 92 } 93 else if (y <= 1.0) 94 { 95 double y2; 96 y2 = y*y; 97 if (y < 0.9) 98 { 99 /* Use a [3,3] Remez approximation on [0,0.9]. */ 100 z = y + y*y2* 101 (-0.274030424656179760118928e0 + 102 (-0.176016349003044679402273e-1 + 103 (-0.200047621071909498730453e-3 - 104 0.142077926378834722618091e-7*y2)*y2)*y2)/ 105 (0.822091273968539282568011e0 + 106 (0.381641414288328849317962e0 + 107 (0.201562166026937652780575e-1 + 108 0.2091140262529164482568557e-3*y2)*y2)*y2); 109 } 110 else 111 { 112 /* Use a [3,3] Remez approximation on [0.9,1]. */ 113 z = y + y*y2* 114 (-0.227793870659088295252442e0 + 115 (-0.146173047288731678404066e-1 + 116 (-0.165597043903549960486816e-3 - 117 0.115475878996143396378318e-7*y2)*y2)*y2)/ 118 (0.683381611977295894959554e0 + 119 (0.317204558977294374244770e0 + 120 (0.167358775461896562588695e-1 + 121 0.173076050126225961768710e-3*y2)*y2)*y2); 122 } 123 } 124 else 125 { 126 /* Compute p = exp(2*y) + 1. The code is basically inlined 127 from exp_amd. */ 128 129 splitexp(2*y, 1.0, thirtytwo_by_log2, log2_by_32_lead, 130 log2_by_32_tail, &m, &z1, &z2); 131 p = scaleDouble_2(z1 + z2, m) + 1.0; 132 133 /* Now reconstruct tanh from p. */ 134 z = (1.0 - 2.0/p); 135 } 136 137 if (xneg) z = - z; 138 return z; 139 } 140