AVX gradients (#2878)
* AVX gradients * Add google test for AVX * Create fallback implementation, remove fma instruction * Improved accuracy of AVX exp function
This commit is contained in:
Rory Mitchell
GitHub
287
src/common/avx_helpers.h
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287
src/common/avx_helpers.h
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/*!
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* Copyright 2017 by Contributors
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* \author Rory Mitchell
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*/
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#pragma once
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#include <algorithm>
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#include "xgboost/base.h"
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#ifdef XGBOOST_USE_AVX
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namespace avx {
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/**
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* \struct Float8
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*
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* \brief Helper class for processing a vector of eight floats using AVX
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* instructions. Implements basic math operators.
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*/
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struct Float8 {
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__m256 x;
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explicit Float8(const __m256& x) : x(x) {}
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explicit Float8(const float& val) : x(_mm256_broadcast_ss(&val)) {}
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explicit Float8(const float* vec) : x(_mm256_loadu_ps(vec)) {}
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Float8() : x() {}
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Float8& operator+=(const Float8& rhs) {
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x = _mm256_add_ps(x, rhs.x);
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return *this;
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}
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Float8& operator-=(const Float8& rhs) {
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x = _mm256_sub_ps(x, rhs.x);
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return *this;
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}
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Float8& operator*=(const Float8& rhs) {
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x = _mm256_mul_ps(x, rhs.x);
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return *this;
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}
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Float8& operator/=(const Float8& rhs) {
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x = _mm256_div_ps(x, rhs.x);
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return *this;
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}
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void Print() {
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float* f = reinterpret_cast<float*>(&x);
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printf("%f %f %f %f %f %f %f %f\n", f[0], f[1], f[2], f[3], f[4], f[5],
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f[6], f[7]);
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}
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};
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inline Float8 operator+(Float8 lhs, const Float8& rhs) {
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lhs += rhs;
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return lhs;
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}
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inline Float8 operator-(Float8 lhs, const Float8& rhs) {
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lhs -= rhs;
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return lhs;
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}
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inline Float8 operator*(Float8 lhs, const Float8& rhs) {
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lhs *= rhs;
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return lhs;
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}
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inline Float8 operator/(Float8 lhs, const Float8& rhs) {
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lhs /= rhs;
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return lhs;
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}
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inline Float8 round(const Float8& x) {
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return Float8(_mm256_round_ps(x.x, _MM_FROUND_TO_NEAREST_INT));
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}
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} // namespace avx
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// Overload std::max/min
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namespace std {
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inline avx::Float8 max(const avx::Float8& a, const avx::Float8& b) {
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return avx::Float8(_mm256_max_ps(a.x, b.x));
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}
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inline avx::Float8 min(const avx::Float8& a, const avx::Float8& b) {
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return avx::Float8(_mm256_min_ps(a.x, b.x));
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}
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} // namespace std
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namespace avx {
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// https://codingforspeed.com/using-faster-exponential-approximation/
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inline Float8 Exp4096(Float8 x) {
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x *= Float8(1.0f / 4096.0f);
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x += Float8(1.0f);
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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x *= x;
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return x;
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}
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inline Float8 pow2n(Float8 const& n) {
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const float pow2_23 = 8388608.0; // 2^23
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const float bias = 127.0; // bias in exponent
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Float8 a =
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n + Float8(bias + pow2_23); // put n + bias in least significant bits
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__m256i b = _mm256_castps_si256(a.x);
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// Do bit shift in SSE so we don't have to use AVX2 instructions
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__m128i c1 = _mm256_castsi256_si128(b);
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b = _mm256_permute2f128_si256(b, b, 1);
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__m128i c2 = _mm256_castsi256_si128(b);
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c1 = _mm_slli_epi32(c1, 23);
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c2 = _mm_slli_epi32(c2, 23);
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__m256i c = _mm256_insertf128_si256(_mm256_castsi128_si256(c1), (c2), 0x1);
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return Float8(_mm256_castsi256_ps(c));
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}
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inline Float8 polynomial_5(Float8 const& x, const float c0, const float c1,
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const float c2, const float c3, const float c4,
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const float c5) {
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// calculates polynomial c5*x^5 + c4*x^4 + c3*x^3 + c2*x^2 + c1*x + c0
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Float8 x2 = x * x;
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Float8 x4 = x2 * x2;
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return (Float8(c2) + Float8(c3) * x) * x2 +
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((Float8(c4) + Float8(c5) * x) * x4 + (Float8(c0) + Float8(c1) * x));
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}
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// AVX exp Function based off Agner Fog's vector library
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// https://github.com/darealshinji/vectorclass/blob/master/vectormath_exp.h
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// Modified so it doesn't require AVX2 instructions
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// Clamps input values to the range -87.3f, +87.3f
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inline Float8 ExpAgner(Float8 x) {
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// Clamp input values
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float max_x = 87.3f;
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x = std::min(x, Float8(max_x));
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x = std::max(x, Float8(-max_x));
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// 1/log(2)
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const float log2e = 1.44269504088896340736f;
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// Taylor coefficients
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const float P0expf = 1.f / 2.f;
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const float P1expf = 1.f / 6.f;
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const float P2expf = 1.f / 24.f;
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const float P3expf = 1.f / 120.f;
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const float P4expf = 1.f / 720.f;
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const float P5expf = 1.f / 5040.f;
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const float ln2f_hi = 0.693359375f;
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const float ln2f_lo = -2.12194440e-4f;
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Float8 r = round(x * Float8(log2e));
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x -= r * Float8(ln2f_hi);
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x -= r * Float8(ln2f_lo);
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Float8 x2 = x * x;
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Float8 z = polynomial_5(x, P0expf, P1expf, P2expf, P3expf, P4expf, P5expf);
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z *= x2;
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z += x;
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// multiply by power of 2
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Float8 n2 = pow2n(r);
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z = (z + Float8(1.0f)) * n2;
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return z;
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}
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inline Float8 Sigmoid(Float8 x) {
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Float8 exp = ExpAgner(x * Float8(-1.0f));
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x = Float8(1.0f) + exp;
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return Float8(_mm256_rcp_ps(x.x));
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}
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// Store 8 gradient pairs given vectors containing gradient and Hessian
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inline void StoreGpair(xgboost::bst_gpair* dst, const Float8& grad,
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const Float8& hess) {
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float* ptr = reinterpret_cast<float*>(dst);
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__m256 gpair_low = _mm256_unpacklo_ps(grad.x, hess.x);
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__m256 gpair_high = _mm256_unpackhi_ps(grad.x, hess.x);
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_mm256_storeu_ps(ptr, _mm256_permute2f128_ps(gpair_low, gpair_high, 0x20));
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_mm256_storeu_ps(ptr + 8,
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_mm256_permute2f128_ps(gpair_low, gpair_high, 0x31));
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}
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} // namespace avx
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#else
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namespace avx {
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/**
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* \struct Float8
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*
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* \brief Fallback implementation not using AVX.
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*/
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struct Float8 {
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float x[8];
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explicit Float8(const float& val) {
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for (int i = 0; i < 8; i++) {
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x[i] = val;
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}
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}
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explicit Float8(const float* vec) {
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for (int i = 0; i < 8; i++) {
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x[i] = vec[i];
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}
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}
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Float8() {}
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Float8& operator+=(const Float8& rhs) {
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for (int i = 0; i < 8; i++) {
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x[i] += rhs.x[i];
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}
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return *this;
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}
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Float8& operator-=(const Float8& rhs) {
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for (int i = 0; i < 8; i++) {
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x[i] -= rhs.x[i];
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}
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return *this;
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}
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Float8& operator*=(const Float8& rhs) {
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for (int i = 0; i < 8; i++) {
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x[i] *= rhs.x[i];
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}
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return *this;
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}
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Float8& operator/=(const Float8& rhs) {
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for (int i = 0; i < 8; i++) {
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x[i] /= rhs.x[i];
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}
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return *this;
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}
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void Print() {
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float* f = reinterpret_cast<float*>(&x);
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printf("%f %f %f %f %f %f %f %f\n", f[0], f[1], f[2], f[3], f[4], f[5],
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f[6], f[7]);
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}
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};
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inline Float8 operator+(Float8 lhs, const Float8& rhs) {
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lhs += rhs;
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return lhs;
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}
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inline Float8 operator-(Float8 lhs, const Float8& rhs) {
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lhs -= rhs;
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return lhs;
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}
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inline Float8 operator*(Float8 lhs, const Float8& rhs) {
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lhs *= rhs;
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return lhs;
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}
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inline Float8 operator/(Float8 lhs, const Float8& rhs) {
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lhs /= rhs;
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return lhs;
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}
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// Store 8 gradient pairs given vectors containing gradient and Hessian
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inline void StoreGpair(xgboost::bst_gpair* dst, const Float8& grad,
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const Float8& hess) {
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for (int i = 0; i < 8; i++) {
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dst[i] = xgboost::bst_gpair(grad.x[i], hess.x[i]);
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}
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}
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inline Float8 Sigmoid(Float8 x) {
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Float8 sig;
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for (int i = 0; i < 8; i++) {
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sig.x[i] = 1.0f / (1.0f + std::exp(-x.x[i]));
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}
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return sig;
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}
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} // namespace avx
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namespace std {
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inline avx::Float8 max(const avx::Float8& a, const avx::Float8& b) {
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avx::Float8 max;
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for (int i = 0; i < 8; i++) {
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max.x[i] = std::max(a.x[i], b.x[i]);
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}
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return max;
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}
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inline avx::Float8 min(const avx::Float8& a, const avx::Float8& b) {
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avx::Float8 min;
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for (int i = 0; i < 8; i++) {
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min.x[i] = std::min(a.x[i], b.x[i]);
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}
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return min;
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}
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} // namespace std
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#endif
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@@ -11,6 +11,7 @@
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#include <vector>
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#include <cmath>
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#include <algorithm>
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#include "avx_helpers.h"
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namespace xgboost {
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namespace common {
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@@ -23,6 +24,10 @@ inline float Sigmoid(float x) {
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return 1.0f / (1.0f + std::exp(-x));
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}
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inline avx::Float8 Sigmoid(avx::Float8 x) {
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return avx::Sigmoid(x);
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}
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/*!
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* \brief do inplace softmax transformaton on p_rec
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* \param p_rec the input/output vector of the values.
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