| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2007 Julien Pommier |
| // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| |
| /* The sin, cos, exp, and log functions of this file come from |
| * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ |
| */ |
| |
| #ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H |
| #define EIGEN_MATH_FUNCTIONS_ALTIVEC_H |
| |
| #include <iostream> |
| using ::std::cout; |
| using ::std::cin; |
| using ::std::cerr; |
| using ::std::ios; |
| using ::std::endl; |
| using ::std::iostream; |
| using ::std::ios_base; |
| using ::std::ostream; |
| using ::std::istream; |
| |
| #define DUMP(v) do { std::cout << #v " = " << (v) << std::endl; } while(0) |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet4f plog<Packet4f>(const Packet4f& _x) |
| { |
| Packet4f x = _x; |
| _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); |
| _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); |
| _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); |
| _EIGEN_DECLARE_CONST_Packet4i(23, 23); |
| |
| _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000); |
| |
| /* the smallest non denormalized float number */ |
| _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000); |
| _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f |
| _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff); |
| |
| /* natural logarithm computed for 4 simultaneous float |
| return NaN for x <= 0 |
| */ |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); |
| |
| |
| Packet4i emm0; |
| |
| /* isvalid_mask is 0 if x < 0 or x is NaN. */ |
| Packet4ui isvalid_mask = reinterpret_cast<Packet4ui>(vec_cmpge(x, p4f_ZERO)); |
| Packet4ui iszero_mask = reinterpret_cast<Packet4ui>(vec_cmpeq(x, p4f_ZERO)); |
| |
| x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */ |
| emm0 = vec_sr(reinterpret_cast<Packet4i>(x), |
| reinterpret_cast<Packet4ui>(p4i_23)); |
| |
| /* keep only the fractional part */ |
| x = pand(x, p4f_inv_mant_mask); |
| x = por(x, p4f_half); |
| |
| emm0 = psub(emm0, p4i_0x7f); |
| Packet4f e = padd(vec_ctf(emm0, 0), p4f_1); |
| |
| /* part2: |
| if( x < SQRTHF ) { |
| e -= 1; |
| x = x + x - 1.0; |
| } else { x = x - 1.0; } |
| */ |
| Packet4f mask = reinterpret_cast<Packet4f>(vec_cmplt(x, p4f_cephes_SQRTHF)); |
| Packet4f tmp = pand(x, mask); |
| x = psub(x, p4f_1); |
| e = psub(e, pand(p4f_1, mask)); |
| x = padd(x, tmp); |
| |
| Packet4f x2 = pmul(x,x); |
| Packet4f x3 = pmul(x2,x); |
| |
| Packet4f y, y1, y2; |
| y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1); |
| y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4); |
| y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7); |
| y = pmadd(y , x, p4f_cephes_log_p2); |
| y1 = pmadd(y1, x, p4f_cephes_log_p5); |
| y2 = pmadd(y2, x, p4f_cephes_log_p8); |
| y = pmadd(y, x3, y1); |
| y = pmadd(y, x3, y2); |
| y = pmul(y, x3); |
| |
| y1 = pmul(e, p4f_cephes_log_q1); |
| tmp = pmul(x2, p4f_half); |
| y = padd(y, y1); |
| x = psub(x, tmp); |
| y2 = pmul(e, p4f_cephes_log_q2); |
| x = padd(x, y); |
| x = padd(x, y2); |
| // negative arg will be NAN, 0 will be -INF |
| x = vec_sel(x, p4f_minus_inf, iszero_mask); |
| x = vec_sel(p4f_minus_nan, x, isvalid_mask); |
| return x; |
| } |
| |
| template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet4f pexp<Packet4f>(const Packet4f& _x) |
| { |
| Packet4f x = _x; |
| _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); |
| _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); |
| _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); |
| _EIGEN_DECLARE_CONST_Packet4i(23, 23); |
| |
| |
| _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f); |
| _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f); |
| |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); |
| |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f); |
| _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f); |
| |
| Packet4f tmp, fx; |
| Packet4i emm0; |
| |
| // clamp x |
| x = vec_max(vec_min(x, p4f_exp_hi), p4f_exp_lo); |
| |
| /* express exp(x) as exp(g + n*log(2)) */ |
| fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half); |
| |
| fx = vec_floor(fx); |
| |
| tmp = pmul(fx, p4f_cephes_exp_C1); |
| Packet4f z = pmul(fx, p4f_cephes_exp_C2); |
| x = psub(x, tmp); |
| x = psub(x, z); |
| |
| z = pmul(x,x); |
| |
| Packet4f y = p4f_cephes_exp_p0; |
| y = pmadd(y, x, p4f_cephes_exp_p1); |
| y = pmadd(y, x, p4f_cephes_exp_p2); |
| y = pmadd(y, x, p4f_cephes_exp_p3); |
| y = pmadd(y, x, p4f_cephes_exp_p4); |
| y = pmadd(y, x, p4f_cephes_exp_p5); |
| y = pmadd(y, z, x); |
| y = padd(y, p4f_1); |
| |
| // build 2^n |
| emm0 = vec_cts(fx, 0); |
| emm0 = vec_add(emm0, p4i_0x7f); |
| emm0 = vec_sl(emm0, reinterpret_cast<Packet4ui>(p4i_23)); |
| |
| // Altivec's max & min operators just drop silent NaNs. Check NaNs in |
| // inputs and return them unmodified. |
| Packet4ui isnumber_mask = reinterpret_cast<Packet4ui>(vec_cmpeq(_x, _x)); |
| return vec_sel(_x, pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x), |
| isnumber_mask); |
| } |
| |
| #ifdef __VSX__ |
| |
| #undef GCC_VERSION |
| #define GCC_VERSION (__GNUC__ * 10000 \ |
| + __GNUC_MINOR__ * 100 \ |
| + __GNUC_PATCHLEVEL__) |
| |
| // VSX support varies between different compilers and even different |
| // versions of the same compiler. For gcc version >= 4.9.3, we can use |
| // vec_cts to efficiently convert Packet2d to Packet2l. Otherwise, use |
| // a slow version that works with older compilers. |
| static inline Packet2l ConvertToPacket2l(const Packet2d& x) { |
| #if GCC_VERSION >= 40903 || defined(__clang__) |
| return vec_cts(x, 0); |
| #else |
| double tmp[2]; |
| memcpy(tmp, &x, sizeof(tmp)); |
| Packet2l l = { static_cast<long long>(tmp[0]), |
| static_cast<long long>(tmp[1]) }; |
| return l; |
| #endif |
| } |
| |
| template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet2d pexp<Packet2d>(const Packet2d& _x) |
| { |
| Packet2d x = _x; |
| |
| _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0); |
| _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0); |
| _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); |
| |
| _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437); |
| _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303); |
| |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); |
| |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); |
| |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); |
| |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); |
| _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); |
| |
| Packet2d tmp, fx; |
| Packet2l emm0; |
| |
| // clamp x |
| x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo); |
| /* express exp(x) as exp(g + n*log(2)) */ |
| fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half); |
| |
| fx = vec_floor(fx); |
| |
| tmp = pmul(fx, p2d_cephes_exp_C1); |
| Packet2d z = pmul(fx, p2d_cephes_exp_C2); |
| x = psub(x, tmp); |
| x = psub(x, z); |
| |
| Packet2d x2 = pmul(x,x); |
| |
| Packet2d px = p2d_cephes_exp_p0; |
| px = pmadd(px, x2, p2d_cephes_exp_p1); |
| px = pmadd(px, x2, p2d_cephes_exp_p2); |
| px = pmul (px, x); |
| |
| Packet2d qx = p2d_cephes_exp_q0; |
| qx = pmadd(qx, x2, p2d_cephes_exp_q1); |
| qx = pmadd(qx, x2, p2d_cephes_exp_q2); |
| qx = pmadd(qx, x2, p2d_cephes_exp_q3); |
| |
| x = pdiv(px,psub(qx,px)); |
| x = pmadd(p2d_2,x,p2d_1); |
| |
| // build 2^n |
| emm0 = ConvertToPacket2l(fx); |
| |
| #ifdef __POWER8_VECTOR__ |
| static const Packet2l p2l_1023 = { 1023, 1023 }; |
| static const Packet2ul p2ul_52 = { 52, 52 }; |
| |
| emm0 = vec_add(emm0, p2l_1023); |
| emm0 = vec_sl(emm0, p2ul_52); |
| #else |
| // Code is a bit complex for POWER7. There is actually a |
| // vec_xxsldi intrinsic but it is not supported by some gcc versions. |
| // So we shift (52-32) bits and do a word swap with zeros. |
| _EIGEN_DECLARE_CONST_Packet4i(1023, 1023); |
| _EIGEN_DECLARE_CONST_Packet4i(20, 20); // 52 - 32 |
| |
| Packet4i emm04i = reinterpret_cast<Packet4i>(emm0); |
| emm04i = vec_add(emm04i, p4i_1023); |
| emm04i = vec_sl(emm04i, reinterpret_cast<Packet4ui>(p4i_20)); |
| static const Packet16uc perm = { |
| 0x14, 0x15, 0x16, 0x17, 0x00, 0x01, 0x02, 0x03, |
| 0x1c, 0x1d, 0x1e, 0x1f, 0x08, 0x09, 0x0a, 0x0b }; |
| #ifdef _BIG_ENDIAN |
| emm0 = reinterpret_cast<Packet2l>(vec_perm(p4i_ZERO, emm04i, perm)); |
| #else |
| emm0 = reinterpret_cast<Packet2l>(vec_perm(emm04i, p4i_ZERO, perm)); |
| #endif |
| |
| #endif |
| |
| // Altivec's max & min operators just drop silent NaNs. Check NaNs in |
| // inputs and return them unmodified. |
| Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x)); |
| return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), |
| isnumber_mask); |
| } |
| #endif |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H |