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_ERRORF 31 #define USE_SPLITEXPF 32 #define USE_SCALEFLOAT_2 33 #define USE_VALF_WITH_FLAGS 34 #include "libm_inlines.h" 35 #undef USE_SPLITEXPF 36 #undef USE_SCALEFLOAT_2 37 #undef USE_VALF_WITH_FLAGS 38 #undef USE_HANDLE_ERRORF 39 40 #include "libm_errno.h" 41 42 #ifdef _MSC_VER 43 // Disable "C4163: not available as intrinsic function" warning that older 44 // compilers may issue here. 45 #pragma warning(disable:4163) 46 #pragma function(tanhf) 47 #endif 48 49 float tanhf(float x) 50 { 51 /* 52 The definition of tanh(x) is sinh(x)/cosh(x), which is also equivalent 53 to the following three formulae: 54 1. (exp(x) - exp(-x))/(exp(x) + exp(-x)) 55 2. (1 - (2/(exp(2*x) + 1 ))) 56 3. (exp(2*x) - 1)/(exp(2*x) + 1) 57 but computationally, some formulae are better on some ranges. 58 */ 59 static const float 60 thirtytwo_by_log2 = 4.6166240692e+01F, /* 0x4238aa3b */ 61 log2_by_32_lead = 2.1659851074e-02F, /* 0x3cb17000 */ 62 log2_by_32_tail = 9.9831822808e-07F, /* 0x3585fdf4 */ 63 large_threshold = 10.0F; /* 0x41200000 */ 64 65 unsigned int ux, aux; 66 float y, z, p, z1, z2, xneg; 67 int m; 68 69 /* Special cases */ 70 71 GET_BITS_SP32(x, ux); 72 aux = ux & ~SIGNBIT_SP32; 73 if (aux < 0x39000000) /* |x| small enough that tanh(x) = x */ 74 { 75 if (aux == 0) 76 return x; /* with no inexact */ 77 else 78 return valf_with_flags(x, AMD_F_INEXACT); 79 } 80 else if (aux > 0x7f800000) /* |x| is NaN */ 81 { 82 unsigned int ufx; 83 GET_BITS_SP32(x, ufx); 84 return _handle_errorf("tanhf", OP_TANH, ufx|0x00400000, _DOMAIN, 0, 85 EDOM, x, 0.0F, 1); 86 } 87 // return x + x; 88 89 xneg = 1.0F - 2.0F * (aux != ux); 90 91 y = xneg * x; 92 93 if (y > large_threshold) 94 { 95 /* If x is large then exp(-x) is negligible and 96 formula 1 reduces to plus or minus 1.0 */ 97 z = 1.0F; 98 } 99 else if (y <= 1.0F) 100 { 101 float y2; 102 y2 = y*y; 103 104 if (y < 0.9F) 105 { 106 /* Use a [2,1] Remez approximation on [0,0.9]. */ 107 z = y + y*y2* 108 (-0.28192806108402678e0F + 109 (-0.14628356048797849e-2F + 110 0.4891631088530669873e-4F*y2)*y2)/ 111 (0.845784192581041099e0F + 112 0.3427017942262751343e0F*y2); 113 } 114 else 115 { 116 /* Use a [2,1] Remez approximation on [0.9,1]. */ 117 z = y + y*y2* 118 (-0.24069858695196524e0F + 119 (-0.12325644183611929e-2F + 120 0.3827534993599483396e-4F*y2)*y2)/ 121 (0.72209738473684982e0F + 122 0.292529068698052819e0F*y2); 123 } 124 } 125 else 126 { 127 /* Compute p = exp(2*y) + 1. The code is basically inlined 128 from exp_amd. */ 129 130 splitexpf(2*y, 1.0F, thirtytwo_by_log2, log2_by_32_lead, 131 log2_by_32_tail, &m, &z1, &z2); 132 p = scaleFloat_2(z1 + z2, m) + 1.0F; 133 /* Now reconstruct tanh from p. */ 134 z = (1.0F - 2.0F/p); 135 } 136 137 return xneg * z; 138 } 139