Eigen  3.3.3
MathFunctions.h
00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2007 Julien Pommier
00005 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00006 // Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
00007 //
00008 // This Source Code Form is subject to the terms of the Mozilla
00009 // Public License v. 2.0. If a copy of the MPL was not distributed
00010 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00011 
00012 /* The sin, cos, exp, and log functions of this file come from
00013  * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
00014  */
00015 
00016 #ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H
00017 #define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
00018 
00019 namespace Eigen {
00020 
00021 namespace internal {
00022 
00023 static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
00024 static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
00025 static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
00026 
00027 static _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);
00028 static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
00029 
00030 static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
00031 
00032 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
00033 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
00034 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
00035 
00036 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
00037 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
00038 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
00039 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
00040 
00041 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
00042 static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
00043 
00044 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00045 Packet2d pexp<Packet2d>(const Packet2d& _x)
00046 {
00047   Packet2d x = _x;
00048 
00049   Packet2d tmp, fx;
00050   Packet2l emm0;
00051 
00052   // clamp x
00053   x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
00054   /* express exp(x) as exp(g + n*log(2)) */
00055   fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
00056 
00057   fx = vec_floor(fx);
00058 
00059   tmp = pmul(fx, p2d_cephes_exp_C1);
00060   Packet2d z = pmul(fx, p2d_cephes_exp_C2);
00061   x = psub(x, tmp);
00062   x = psub(x, z);
00063 
00064   Packet2d x2 = pmul(x,x);
00065 
00066   Packet2d px = p2d_cephes_exp_p0;
00067   px = pmadd(px, x2, p2d_cephes_exp_p1);
00068   px = pmadd(px, x2, p2d_cephes_exp_p2);
00069   px = pmul (px, x);
00070 
00071   Packet2d qx = p2d_cephes_exp_q0;
00072   qx = pmadd(qx, x2, p2d_cephes_exp_q1);
00073   qx = pmadd(qx, x2, p2d_cephes_exp_q2);
00074   qx = pmadd(qx, x2, p2d_cephes_exp_q3);
00075 
00076   x = pdiv(px,psub(qx,px));
00077   x = pmadd(p2d_2,x,p2d_1);
00078 
00079   // build 2^n
00080   emm0 = vec_ctsl(fx, 0);
00081 
00082   static const Packet2l p2l_1023 = { 1023, 1023 };
00083   static const Packet2ul p2ul_52 = { 52, 52 };
00084 
00085   emm0 = emm0 + p2l_1023;
00086   emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
00087 
00088   // Altivec's max & min operators just drop silent NaNs. Check NaNs in 
00089   // inputs and return them unmodified.
00090   Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
00091   return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
00092                  isnumber_mask);
00093 }
00094 
00095 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00096 Packet4f pexp<Packet4f>(const Packet4f& x)
00097 {
00098   Packet4f res;
00099   res.v4f[0] = pexp<Packet2d>(x.v4f[0]);
00100   res.v4f[1] = pexp<Packet2d>(x.v4f[1]);
00101   return res;
00102 }
00103 
00104 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00105 Packet2d psqrt<Packet2d>(const Packet2d& x)
00106 {
00107   return  __builtin_s390_vfsqdb(x);
00108 }
00109 
00110 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00111 Packet4f psqrt<Packet4f>(const Packet4f& x)
00112 {
00113   Packet4f res;
00114   res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
00115   res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
00116   return res;
00117 }
00118 
00119 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00120 Packet2d prsqrt<Packet2d>(const Packet2d& x) {
00121   // Unfortunately we can't use the much faster mm_rqsrt_pd since it only provides an approximation.
00122   return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
00123 }
00124 
00125 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00126 Packet4f prsqrt<Packet4f>(const Packet4f& x) {
00127   Packet4f res;
00128   res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
00129   res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
00130   return res;
00131 }
00132 
00133 }  // end namespace internal
00134 
00135 }  // end namespace Eigen
00136 
00137 #endif  // EIGEN_MATH_FUNCTIONS_ALTIVEC_H
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