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17860e578c
Pommier. They are for float only, and they return exactly the same result as the standard versions in about 90% of the cases. Otherwise the max error is below 1e-7. However, for very large values (>1e3) the accuracy of sin and cos slighlty decrease. They are about 3 or 4 times faster than 4 calls to their respective standard versions. So, is it ok to enable them by default in their respective functors ?
434 lines
14 KiB
C++
434 lines
14 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Konstantinos Margaritis <markos@codex.gr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
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#define EIGEN_PACKET_MATH_ALTIVEC_H
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#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
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#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
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#endif
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typedef __vector float v4f;
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typedef __vector int v4i;
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typedef __vector unsigned int v4ui;
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typedef __vector __bool int v4bi;
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// We don't want to write the same code all the time, but we need to reuse the constants
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// and it doesn't really work to declare them global, so we define macros instead
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#define USE_CONST_v0i const v4i v0i = vec_splat_s32(0)
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#define USE_CONST_v1i const v4i v1i = vec_splat_s32(1)
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#define USE_CONST_v16i_ const v4i v16i_ = vec_splat_s32(-16)
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#define USE_CONST_v0f USE_CONST_v0i; const v4f v0f = (v4f) v0i
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#define USE_CONST_v1f USE_CONST_v1i; const v4f v1f = vec_ctf(v1i, 0)
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#define USE_CONST_v1i_ const v4ui v1i_ = vec_splat_u32(-1)
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#define USE_CONST_v0f_ USE_CONST_v1i_; const v4f v0f_ = (v4f) vec_sl(v1i_, v1i_)
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template<> struct ei_packet_traits<float> : ei_default_packet_traits
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{ typedef v4f type; enum {size=4}; };
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template<> struct ei_packet_traits<int> : ei_default_packet_traits
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{ typedef v4i type; enum {size=4}; };
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template<> struct ei_unpacket_traits<v4f> { typedef float type; enum {size=4}; };
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template<> struct ei_unpacket_traits<v4i> { typedef int type; enum {size=4}; };
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inline std::ostream & operator <<(std::ostream & s, const v4f & v)
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{
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union {
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v4f v;
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float n[4];
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} vt;
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vt.v = v;
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s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
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return s;
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}
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inline std::ostream & operator <<(std::ostream & s, const v4i & v)
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{
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union {
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v4i v;
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int n[4];
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} vt;
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vt.v = v;
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s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
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return s;
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}
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inline std::ostream & operator <<(std::ostream & s, const v4ui & v)
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{
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union {
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v4ui v;
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unsigned int n[4];
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} vt;
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vt.v = v;
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s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
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return s;
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}
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inline std::ostream & operator <<(std::ostream & s, const v4bi & v)
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{
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union {
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__vector __bool int v;
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unsigned int n[4];
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} vt;
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vt.v = v;
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s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
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return s;
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}
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template<> inline v4f ei_padd(const v4f& a, const v4f& b) { return vec_add(a,b); }
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template<> inline v4i ei_padd(const v4i& a, const v4i& b) { return vec_add(a,b); }
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template<> inline v4f ei_psub(const v4f& a, const v4f& b) { return vec_sub(a,b); }
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template<> inline v4i ei_psub(const v4i& a, const v4i& b) { return vec_sub(a,b); }
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template<> EIGEN_STRONG_INLINE v4f ei_pnegate(const v4f& a)
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{
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v4i mask = {0x80000000, 0x80000000, 0x80000000, 0x80000000};
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return vec_xor(a,(v4f) mask);
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}
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template<> EIGEN_STRONG_INLINE v4i ei_pnegate(const v4i& a)
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{
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USE_CONST_v0i;
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return ei_psub(v0i, a);
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}
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template<> inline v4f ei_pmul(const v4f& a, const v4f& b) { USE_CONST_v0f; return vec_madd(a,b, v0f); }
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template<> inline v4i ei_pmul(const v4i& a, const v4i& b)
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{
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// Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
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//Set up constants, variables
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v4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
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USE_CONST_v0i;
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USE_CONST_v1i;
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USE_CONST_v16i_;
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// Get the absolute values
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a1 = vec_abs(a);
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b1 = vec_abs(b);
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// Get the signs using xor
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v4bi sgn = (v4bi) vec_cmplt(vec_xor(a, b), v0i);
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// Do the multiplication for the asbolute values.
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bswap = (v4i) vec_rl((v4ui) b1, (v4ui) v16i_ );
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low_prod = vec_mulo((__vector short)a1, (__vector short)b1);
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high_prod = vec_msum((__vector short)a1, (__vector short)bswap, v0i);
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high_prod = (v4i) vec_sl((v4ui) high_prod, (v4ui) v16i_);
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prod = vec_add( low_prod, high_prod );
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// NOR the product and select only the negative elements according to the sign mask
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prod_ = vec_nor(prod, prod);
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prod_ = vec_sel(v0i, prod_, sgn);
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// Add 1 to the result to get the negative numbers
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v1sel = vec_sel(v0i, v1i, sgn);
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prod_ = vec_add(prod_, v1sel);
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// Merge the results back to the final vector.
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prod = vec_sel(prod, prod_, sgn);
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return prod;
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}
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template<> inline v4f ei_pdiv(const v4f& a, const v4f& b) {
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v4f t, y_0, y_1, res;
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USE_CONST_v0f;
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USE_CONST_v1f;
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// Altivec does not offer a divide instruction, we have to do a reciprocal approximation
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y_0 = vec_re(b);
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// Do one Newton-Raphson iteration to get the needed accuracy
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t = vec_nmsub(y_0, b, v1f);
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y_1 = vec_madd(y_0, t, y_0);
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res = vec_madd(a, y_1, v0f);
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return res;
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}
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template<> inline v4f ei_pmadd(const v4f& a, const v4f& b, const v4f& c) { return vec_madd(a, b, c); }
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template<> inline v4f ei_pmin(const v4f& a, const v4f& b) { return vec_min(a,b); }
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template<> inline v4i ei_pmin(const v4i& a, const v4i& b) { return vec_min(a,b); }
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template<> inline v4f ei_pmax(const v4f& a, const v4f& b) { return vec_max(a,b); }
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template<> inline v4i ei_pmax(const v4i& a, const v4i& b) { return vec_max(a,b); }
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template<> EIGEN_STRONG_INLINE v4f ei_pabs(const v4f& a) { return vec_abs(a); }
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template<> EIGEN_STRONG_INLINE v4i ei_pabs(const v4i& a) { return vec_abs(a); }
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template<> inline v4f ei_pload(const float* from) { return vec_ld(0, from); }
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template<> inline v4i ei_pload(const int* from) { return vec_ld(0, from); }
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template<> inline v4f ei_ploadu(const float* from)
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{
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// Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
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__vector unsigned char MSQ, LSQ;
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__vector unsigned char mask;
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MSQ = vec_ld(0, (unsigned char *)from); // most significant quadword
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LSQ = vec_ld(15, (unsigned char *)from); // least significant quadword
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mask = vec_lvsl(0, from); // create the permute mask
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return (v4f) vec_perm(MSQ, LSQ, mask); // align the data
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}
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template<> inline v4i ei_ploadu(const int* from)
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{
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// Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
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__vector unsigned char MSQ, LSQ;
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__vector unsigned char mask;
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MSQ = vec_ld(0, (unsigned char *)from); // most significant quadword
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LSQ = vec_ld(15, (unsigned char *)from); // least significant quadword
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mask = vec_lvsl(0, from); // create the permute mask
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return (v4i) vec_perm(MSQ, LSQ, mask); // align the data
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}
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template<> inline v4f ei_pset1(const float& from)
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{
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// Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
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float __attribute__(aligned(16)) af[4];
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af[0] = from;
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v4f vc = vec_ld(0, af);
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vc = vec_splat(vc, 0);
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return vc;
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}
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template<> inline v4i ei_pset1(const int& from)
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{
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int __attribute__(aligned(16)) ai[4];
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ai[0] = from;
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v4i vc = vec_ld(0, ai);
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vc = vec_splat(vc, 0);
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return vc;
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}
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template<> inline void ei_pstore(float* to, const v4f& from) { vec_st(from, 0, to); }
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template<> inline void ei_pstore(int* to, const v4i& from) { vec_st(from, 0, to); }
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template<> inline void ei_pstoreu(float* to, const v4f& from)
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{
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// Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
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// Warning: not thread safe!
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__vector unsigned char MSQ, LSQ, edges;
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__vector unsigned char edgeAlign, align;
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MSQ = vec_ld(0, (unsigned char *)to); // most significant quadword
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LSQ = vec_ld(15, (unsigned char *)to); // least significant quadword
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edgeAlign = vec_lvsl(0, to); // permute map to extract edges
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edges=vec_perm(LSQ,MSQ,edgeAlign); // extract the edges
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align = vec_lvsr( 0, to ); // permute map to misalign data
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MSQ = vec_perm(edges,(__vector unsigned char)from,align); // misalign the data (MSQ)
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LSQ = vec_perm((__vector unsigned char)from,edges,align); // misalign the data (LSQ)
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vec_st( LSQ, 15, (unsigned char *)to ); // Store the LSQ part first
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vec_st( MSQ, 0, (unsigned char *)to ); // Store the MSQ part
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}
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template<> inline void ei_pstoreu(int* to , const v4i& from )
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{
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// Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
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// Warning: not thread safe!
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__vector unsigned char MSQ, LSQ, edges;
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__vector unsigned char edgeAlign, align;
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MSQ = vec_ld(0, (unsigned char *)to); // most significant quadword
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LSQ = vec_ld(15, (unsigned char *)to); // least significant quadword
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edgeAlign = vec_lvsl(0, to); // permute map to extract edges
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edges=vec_perm(LSQ,MSQ,edgeAlign); // extract the edges
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align = vec_lvsr( 0, to ); // permute map to misalign data
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MSQ = vec_perm(edges,(__vector unsigned char)from,align); // misalign the data (MSQ)
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LSQ = vec_perm((__vector unsigned char)from,edges,align); // misalign the data (LSQ)
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vec_st( LSQ, 15, (unsigned char *)to ); // Store the LSQ part first
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vec_st( MSQ, 0, (unsigned char *)to ); // Store the MSQ part
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}
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template<> inline float ei_pfirst(const v4f& a)
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{
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float EIGEN_ALIGN_128 af[4];
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vec_st(a, 0, af);
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return af[0];
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}
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template<> inline int ei_pfirst(const v4i& a)
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{
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int EIGEN_ALIGN_128 ai[4];
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vec_st(a, 0, ai);
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return ai[0];
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}
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template<> EIGEN_STRONG_INLINE v4f ei_preverse(const v4f& a)
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{
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static const __vector unsigned char reverse_mask =
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{12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
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return (v4f)vec_perm((__vector unsigned char)a,(__vector unsigned char)a,reverse_mask);
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}
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template<> EIGEN_STRONG_INLINE v4i ei_preverse(const v4i& a)
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{
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static const __vector unsigned char __attribute__(aligned(16)) reverse_mask =
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{12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
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return (v4i)vec_perm((__vector unsigned char)a,(__vector unsigned char)a,reverse_mask);
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}
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inline v4f ei_preduxp(const v4f* vecs)
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{
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v4f v[4], sum[4];
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// It's easier and faster to transpose then add as columns
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// Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
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// Do the transpose, first set of moves
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v[0] = vec_mergeh(vecs[0], vecs[2]);
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v[1] = vec_mergel(vecs[0], vecs[2]);
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v[2] = vec_mergeh(vecs[1], vecs[3]);
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v[3] = vec_mergel(vecs[1], vecs[3]);
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// Get the resulting vectors
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sum[0] = vec_mergeh(v[0], v[2]);
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sum[1] = vec_mergel(v[0], v[2]);
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sum[2] = vec_mergeh(v[1], v[3]);
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sum[3] = vec_mergel(v[1], v[3]);
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// Now do the summation:
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// Lines 0+1
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sum[0] = vec_add(sum[0], sum[1]);
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// Lines 2+3
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sum[1] = vec_add(sum[2], sum[3]);
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// Add the results
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sum[0] = vec_add(sum[0], sum[1]);
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return sum[0];
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}
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inline v4i ei_preduxp(const v4i* vecs)
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{
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v4i v[4], sum[4];
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// It's easier and faster to transpose then add as columns
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// Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
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// Do the transpose, first set of moves
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v[0] = vec_mergeh(vecs[0], vecs[2]);
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v[1] = vec_mergel(vecs[0], vecs[2]);
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v[2] = vec_mergeh(vecs[1], vecs[3]);
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v[3] = vec_mergel(vecs[1], vecs[3]);
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// Get the resulting vectors
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sum[0] = vec_mergeh(v[0], v[2]);
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sum[1] = vec_mergel(v[0], v[2]);
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sum[2] = vec_mergeh(v[1], v[3]);
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sum[3] = vec_mergel(v[1], v[3]);
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// Now do the summation:
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// Lines 0+1
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sum[0] = vec_add(sum[0], sum[1]);
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// Lines 2+3
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sum[1] = vec_add(sum[2], sum[3]);
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// Add the results
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sum[0] = vec_add(sum[0], sum[1]);
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return sum[0];
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}
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inline float ei_predux(const v4f& a)
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{
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v4f b, sum;
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b = (v4f)vec_sld(a, a, 8);
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sum = vec_add(a, b);
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b = (v4f)vec_sld(sum, sum, 4);
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sum = vec_add(sum, b);
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return ei_pfirst(sum);
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}
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inline int ei_predux(const v4i& a)
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{
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USE_CONST_v0i;
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v4i sum;
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sum = vec_sums(a, v0i);
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sum = vec_sld(sum, v0i, 12);
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return ei_pfirst(sum);
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}
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// implement other reductions operators
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inline float ei_predux_mul(const v4f& a)
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{
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v4f prod;
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prod = ei_pmul(a, (v4f)vec_sld(a, a, 8));
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return ei_pfirst(ei_pmul(prod, (v4f)vec_sld(prod, prod, 4)));
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}
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inline int ei_predux_mul(const v4i& a)
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{
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EIGEN_ALIGN_128 int aux[4];
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ei_pstore(aux, a);
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return aux[0] * aux[1] * aux[2] * aux[3];
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}
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inline float ei_predux_min(const v4f& a)
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{
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v4f b, res;
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b = vec_min(a, vec_sld(a, a, 8));
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res = vec_min(b, vec_sld(b, b, 4));
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return ei_pfirst(res);
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}
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inline int ei_predux_min(const v4i& a)
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{
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v4i b, res;
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b = vec_min(a, vec_sld(a, a, 8));
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res = vec_min(b, vec_sld(b, b, 4));
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return ei_pfirst(res);
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}
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inline float ei_predux_max(const v4f& a)
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{
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v4f b, res;
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b = vec_max(a, vec_sld(a, a, 8));
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res = vec_max(b, vec_sld(b, b, 4));
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return ei_pfirst(res);
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}
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inline int ei_predux_max(const v4i& a)
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{
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v4i b, res;
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b = vec_max(a, vec_sld(a, a, 8));
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res = vec_max(b, vec_sld(b, b, 4));
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return ei_pfirst(res);
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}
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template<int Offset>
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struct ei_palign_impl<Offset, v4f>
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|
{
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inline static void run(v4f& first, const v4f& second)
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|
{
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first = vec_sld(first, second, Offset*4);
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}
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};
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template<int Offset>
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struct ei_palign_impl<Offset, v4i>
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|
{
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inline static void run(v4i& first, const v4i& second)
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|
{
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|
first = vec_sld(first, second, Offset*4);
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|
}
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|
};
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|
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#endif // EIGEN_PACKET_MATH_ALTIVEC_H
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