MathFunctions.h (8024B)
1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2007 Julien Pommier 5 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> 6 // Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org> 7 // 8 // This Source Code Form is subject to the terms of the Mozilla 9 // Public License v. 2.0. If a copy of the MPL was not distributed 10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 11 12 /* The sin, cos, exp, and log functions of this file come from 13 * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ 14 */ 15 16 #ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H 17 #define EIGEN_MATH_FUNCTIONS_ALTIVEC_H 18 19 namespace Eigen { 20 21 namespace internal { 22 23 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12) 24 static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); 25 static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); 26 static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); 27 static _EIGEN_DECLARE_CONST_Packet4i(23, 23); 28 29 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000); 30 31 /* the smallest non denormalized float number */ 32 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000); 33 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f 34 static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff); 35 36 /* natural logarithm computed for 4 simultaneous float 37 return NaN for x <= 0 38 */ 39 static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); 40 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f); 41 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f); 42 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f); 43 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f); 44 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f); 45 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f); 46 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f); 47 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f); 48 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f); 49 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); 50 static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); 51 52 static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f); 53 static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f); 54 55 static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); 56 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); 57 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); 58 59 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f); 60 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f); 61 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f); 62 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f); 63 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f); 64 static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f); 65 #endif 66 67 static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0); 68 static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0); 69 static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); 70 71 static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437); 72 static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303); 73 74 static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); 75 76 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); 77 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); 78 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); 79 80 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); 81 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); 82 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); 83 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); 84 85 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); 86 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); 87 88 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 89 Packet2d pexp<Packet2d>(const Packet2d& _x) 90 { 91 Packet2d x = _x; 92 93 Packet2d tmp, fx; 94 Packet2l emm0; 95 96 // clamp x 97 x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo); 98 /* express exp(x) as exp(g + n*log(2)) */ 99 fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half); 100 101 fx = vec_floor(fx); 102 103 tmp = pmul(fx, p2d_cephes_exp_C1); 104 Packet2d z = pmul(fx, p2d_cephes_exp_C2); 105 x = psub(x, tmp); 106 x = psub(x, z); 107 108 Packet2d x2 = pmul(x,x); 109 110 Packet2d px = p2d_cephes_exp_p0; 111 px = pmadd(px, x2, p2d_cephes_exp_p1); 112 px = pmadd(px, x2, p2d_cephes_exp_p2); 113 px = pmul (px, x); 114 115 Packet2d qx = p2d_cephes_exp_q0; 116 qx = pmadd(qx, x2, p2d_cephes_exp_q1); 117 qx = pmadd(qx, x2, p2d_cephes_exp_q2); 118 qx = pmadd(qx, x2, p2d_cephes_exp_q3); 119 120 x = pdiv(px,psub(qx,px)); 121 x = pmadd(p2d_2,x,p2d_1); 122 123 // build 2^n 124 emm0 = vec_ctsl(fx, 0); 125 126 static const Packet2l p2l_1023 = { 1023, 1023 }; 127 static const Packet2ul p2ul_52 = { 52, 52 }; 128 129 emm0 = emm0 + p2l_1023; 130 emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52); 131 132 // Altivec's max & min operators just drop silent NaNs. Check NaNs in 133 // inputs and return them unmodified. 134 Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x)); 135 return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), 136 isnumber_mask); 137 } 138 139 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 140 Packet4f pexp<Packet4f>(const Packet4f& _x) 141 { 142 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12) 143 Packet4f x = _x; 144 145 Packet4f tmp, fx; 146 Packet4i emm0; 147 148 // clamp x 149 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo); 150 151 // express exp(x) as exp(g + n*log(2)) 152 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half); 153 154 fx = pfloor(fx); 155 156 tmp = pmul(fx, p4f_cephes_exp_C1); 157 Packet4f z = pmul(fx, p4f_cephes_exp_C2); 158 x = psub(x, tmp); 159 x = psub(x, z); 160 161 z = pmul(x,x); 162 163 Packet4f y = p4f_cephes_exp_p0; 164 y = pmadd(y, x, p4f_cephes_exp_p1); 165 y = pmadd(y, x, p4f_cephes_exp_p2); 166 y = pmadd(y, x, p4f_cephes_exp_p3); 167 y = pmadd(y, x, p4f_cephes_exp_p4); 168 y = pmadd(y, x, p4f_cephes_exp_p5); 169 y = pmadd(y, z, x); 170 y = padd(y, p4f_1); 171 172 // build 2^n 173 emm0 = (Packet4i){ (int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3] }; 174 emm0 = emm0 + p4i_0x7f; 175 emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23); 176 177 return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x); 178 #else 179 Packet4f res; 180 res.v4f[0] = pexp<Packet2d>(_x.v4f[0]); 181 res.v4f[1] = pexp<Packet2d>(_x.v4f[1]); 182 return res; 183 #endif 184 } 185 186 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 187 Packet2d psqrt<Packet2d>(const Packet2d& x) 188 { 189 return vec_sqrt(x); 190 } 191 192 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 193 Packet4f psqrt<Packet4f>(const Packet4f& x) 194 { 195 Packet4f res; 196 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12) 197 res = vec_sqrt(x); 198 #else 199 res.v4f[0] = psqrt<Packet2d>(x.v4f[0]); 200 res.v4f[1] = psqrt<Packet2d>(x.v4f[1]); 201 #endif 202 return res; 203 } 204 205 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 206 Packet2d prsqrt<Packet2d>(const Packet2d& x) { 207 return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x); 208 } 209 210 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 211 Packet4f prsqrt<Packet4f>(const Packet4f& x) { 212 Packet4f res; 213 #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12) 214 res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x); 215 #else 216 res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]); 217 res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]); 218 #endif 219 return res; 220 } 221 222 // Hyperbolic Tangent function. 223 template <> 224 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f 225 ptanh<Packet4f>(const Packet4f& x) { 226 return internal::generic_fast_tanh_float(x); 227 } 228 229 } // end namespace internal 230 231 } // end namespace Eigen 232 233 #endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H