/* Copyright (c) 2018 Mozilla 2012-2017 Jean-Marc Valin */ /* Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. - Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* AVX implementation of vector operations, compile with -mavx AVX2/FMA implementation of vector operations, compile with -mavx2 -mfma */ #ifndef VEC_AVX_H #define VEC_AVX_H #include #ifndef DISABLE_DOT_PROD #define DOT_PROD #define USE_SU_BIAS #endif #ifndef __FMA__ #define _mm256_fmadd_ps(a,b,c) _mm256_add_ps(_mm256_mul_ps(a, b), c) #define _mm_fmadd_ps(a,b,c) _mm_add_ps(_mm_mul_ps(a, b), c) #endif #ifdef __AVX2__ static inline __m256 exp8_approx(__m256 X) { const __m256 K0 = _mm256_set1_ps(0.99992522f); const __m256 K1 = _mm256_set1_ps(0.69583354f); const __m256 K2 = _mm256_set1_ps(0.22606716f); const __m256 K3 = _mm256_set1_ps(0.078024523f); const __m256 log2_E = _mm256_set1_ps(1.44269504); const __m256 max_in = _mm256_set1_ps(50.f); const __m256 min_in = _mm256_set1_ps(-50.f); __m256 XF, Y; __m256i I; X = _mm256_mul_ps(X, log2_E); X = _mm256_max_ps(min_in, _mm256_min_ps(max_in, X)); XF = _mm256_floor_ps(X); I = _mm256_cvtps_epi32(XF); X = _mm256_sub_ps(X, XF); Y = _mm256_fmadd_ps(_mm256_fmadd_ps(_mm256_fmadd_ps(K3, X, K2), X, K1), X, K0); I = _mm256_slli_epi32(I, 23); Y = _mm256_castsi256_ps(_mm256_add_epi32(I, _mm256_castps_si256(Y))); return Y; } /* Approximating tanh() using a Padé-like rational function: tanh(x) ~= x * (N0 + N1*x^2 + N2*x^4)/(D0 + D1*x^2 + D2*x^4) subject to the +/- 1 bounds. The coefficients were determined by gradient descent trying to minimize the maximum deviation over the whole range (this is only possible because of the bounds). The max error is around 3e-4 and is dominated by the reciprocal approximation (the max error of the rational function is around 6e-5). */ static inline __m256 tanh8_approx(__m256 X) { const __m256 N0 = _mm256_set1_ps(952.52801514f); const __m256 N1 = _mm256_set1_ps(96.39235687f); const __m256 N2 = _mm256_set1_ps(0.60863042f); const __m256 D0 = _mm256_set1_ps(952.72399902f); const __m256 D1 = _mm256_set1_ps(413.36801147f); const __m256 D2 = _mm256_set1_ps(11.88600922f); const __m256 max_out = _mm256_set1_ps(1.f); const __m256 min_out = _mm256_set1_ps(-1.f); __m256 X2, num, den; X2 = _mm256_mul_ps(X, X); num = _mm256_fmadd_ps(_mm256_fmadd_ps(N2, X2, N1), X2, N0); den = _mm256_fmadd_ps(_mm256_fmadd_ps(D2, X2, D1), X2, D0); num = _mm256_mul_ps(num, X); den = _mm256_rcp_ps(den); num = _mm256_mul_ps(num, den); return _mm256_max_ps(min_out, _mm256_min_ps(max_out, num)); } /* Sigmoid approximation using a Padé-like rational function: 1/(1+exp(-x)) ~= 0.5 + x * (N0 + N1*x^2 + N2*x^4)/(D0 + D1*x^2 + D2*x^4) subject to the [0, 1] bounds. The coefficients are directly derived by dividing the tanh() coefficients by powers of two to get the correct scaling. The max error is around 1.5e-4 and is dominated by the reciprocal approximation (the max error of the rational function is around 3e-5). */ static inline __m256 sigmoid8_approx(__m256 X) { const __m256 N0 = _mm256_set1_ps(238.13200378f); const __m256 N1 = _mm256_set1_ps(6.02452230f); const __m256 N2 = _mm256_set1_ps(0.00950985f); const __m256 D0 = _mm256_set1_ps(952.72399902f); const __m256 D1 = _mm256_set1_ps(103.34200287f); const __m256 D2 = _mm256_set1_ps(0.74287558f); const __m256 half = _mm256_set1_ps(0.5); const __m256 max_out = _mm256_set1_ps(1.f); const __m256 min_out = _mm256_set1_ps(0.f); __m256 X2, num, den; X2 = _mm256_mul_ps(X, X); num = _mm256_fmadd_ps(_mm256_fmadd_ps(N2, X2, N1), X2, N0); den = _mm256_fmadd_ps(_mm256_fmadd_ps(D2, X2, D1), X2, D0); num = _mm256_mul_ps(num, X); den = _mm256_rcp_ps(den); num = _mm256_fmadd_ps(num, den, half); return _mm256_max_ps(min_out, _mm256_min_ps(max_out, num)); } #else static inline __m128 exp4_approx(__m128 X) { const __m128 K0 = _mm_set1_ps(0.99992522f); const __m128 K1 = _mm_set1_ps(0.69583354f); const __m128 K2 = _mm_set1_ps(0.22606716f); const __m128 K3 = _mm_set1_ps(0.078024523f); const __m128 log2_E = _mm_set1_ps(1.44269504); const __m128 max_in = _mm_set1_ps(50.f); const __m128 min_in = _mm_set1_ps(-50.f); const __m128i mask = _mm_set1_epi32(0x7fffffff); __m128 XF, Y; __m128i I; X = _mm_mul_ps(X, log2_E); X = _mm_max_ps(min_in, _mm_min_ps(max_in, X)); XF = _mm_floor_ps(X); I = _mm_cvtps_epi32(XF); X = _mm_sub_ps(X, XF); Y = _mm_fmadd_ps(_mm_fmadd_ps(_mm_fmadd_ps(K3, X, K2), X, K1), X, K0); I = _mm_slli_epi32(I, 23); Y = _mm_castsi128_ps(_mm_and_si128(mask, _mm_add_epi32(I, _mm_castps_si128(Y)))); return Y; } static inline __m256 exp8_approx(__m256 X) { __m256 Y; __m128 Xhi, Xlo, Yhi, Ylo; Xhi = _mm256_extractf128_ps(X, 1); Xlo = _mm256_extractf128_ps(X, 0); Yhi = exp4_approx(Xhi); Ylo = exp4_approx(Xlo); Y = _mm256_insertf128_ps(_mm256_setzero_ps(), Yhi, 1); Y = _mm256_insertf128_ps(Y, Ylo, 0); return Y; } static inline __m128 tanh4_approx(__m128 X) { const __m128 N0 = _mm_set1_ps(952.52801514f); const __m128 N1 = _mm_set1_ps(96.39235687f); const __m128 N2 = _mm_set1_ps(0.60863042f); const __m128 D0 = _mm_set1_ps(952.72399902f); const __m128 D1 = _mm_set1_ps(413.36801147f); const __m128 D2 = _mm_set1_ps(11.88600922f); const __m128 max_out = _mm_set1_ps(1.f); const __m128 min_out = _mm_set1_ps(-1.f); __m128 X2, num, den; X2 = _mm_mul_ps(X, X); num = _mm_fmadd_ps(_mm_fmadd_ps(N2, X2, N1), X2, N0); den = _mm_fmadd_ps(_mm_fmadd_ps(D2, X2, D1), X2, D0); num = _mm_mul_ps(num, X); den = _mm_rcp_ps(den); num = _mm_mul_ps(num, den); return _mm_max_ps(min_out, _mm_min_ps(max_out, num)); } static inline __m128 sigmoid4_approx(__m128 X) { const __m128 N0 = _mm_set1_ps(238.13200378f); const __m128 N1 = _mm_set1_ps(6.02452230f); const __m128 N2 = _mm_set1_ps(0.00950985f); const __m128 D0 = _mm_set1_ps(952.72399902f); const __m128 D1 = _mm_set1_ps(103.34200287f); const __m128 D2 = _mm_set1_ps(0.74287558f); const __m128 half = _mm_set1_ps(0.5); const __m128 max_out = _mm_set1_ps(1.f); const __m128 min_out = _mm_set1_ps(0.f); __m128 X2, num, den; X2 = _mm_mul_ps(X, X); num = _mm_fmadd_ps(_mm_fmadd_ps(N2, X2, N1), X2, N0); den = _mm_fmadd_ps(_mm_fmadd_ps(D2, X2, D1), X2, D0); num = _mm_mul_ps(num, X); den = _mm_rcp_ps(den); num = _mm_fmadd_ps(num, den, half); return _mm_max_ps(min_out, _mm_min_ps(max_out, num)); } #endif static inline float celt_exp(float x) { float out[8]; __m256 X, Y; X = _mm256_set1_ps(x); Y = exp8_approx(X); _mm256_storeu_ps(out, Y); return out[0]; } static inline float tanh_approx(float x) { float out[8]; __m256 X, Y; X = _mm256_set1_ps(x); Y = tanh8_approx(X); _mm256_storeu_ps(out, Y); return out[0]; } static inline float sigmoid_approx(float x) { float out[8]; __m256 X, Y; X = _mm256_set1_ps(x); Y = sigmoid8_approx(X); _mm256_storeu_ps(out, Y); return out[0]; } static inline void softmax(float *y, const float *x, int N) { int i; for (i=0;i