// Auto-generated file. Do not edit! // Template: src/f32-vscaleexpminusmax/avx2-p5.c.in // Generator: tools/xngen // // Copyright 2019 Google LLC // // This source code is licensed under the BSD-style license found in the // LICENSE file in the root directory of this source tree. #include #include #include #include static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0}; void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x88( size_t elements, const float* input, float* output, float scale, float max) { assert(elements % sizeof(float) == 0); const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f); // The smallest x for which expf(x) is normalized. const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f); const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f); const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f); const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f); const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f); const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f); const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f); const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f); const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f); const __m256 vscale = _mm256_set1_ps(scale); const __m256 vi_max = _mm256_set1_ps(max); for (; elements >= 88 * sizeof(float); elements -= 88 * sizeof(float)) { // Load 88 (11x8) inputs at a time. const __m256 vi0 = _mm256_loadu_ps(input); const __m256 vi1 = _mm256_loadu_ps(input + 8); const __m256 vi2 = _mm256_loadu_ps(input + 16); const __m256 vi3 = _mm256_loadu_ps(input + 24); const __m256 vi4 = _mm256_loadu_ps(input + 32); const __m256 vi5 = _mm256_loadu_ps(input + 40); const __m256 vi6 = _mm256_loadu_ps(input + 48); const __m256 vi7 = _mm256_loadu_ps(input + 56); const __m256 vi8 = _mm256_loadu_ps(input + 64); const __m256 vi9 = _mm256_loadu_ps(input + 72); const __m256 vi10 = _mm256_loadu_ps(input + 80); input += 88; // Subtract maximum input x := i - i_max. This implies x <= 0. const __m256 vx0 = _mm256_sub_ps(vi0, vi_max); const __m256 vx1 = _mm256_sub_ps(vi1, vi_max); const __m256 vx2 = _mm256_sub_ps(vi2, vi_max); const __m256 vx3 = _mm256_sub_ps(vi3, vi_max); const __m256 vx4 = _mm256_sub_ps(vi4, vi_max); const __m256 vx5 = _mm256_sub_ps(vi5, vi_max); const __m256 vx6 = _mm256_sub_ps(vi6, vi_max); const __m256 vx7 = _mm256_sub_ps(vi7, vi_max); const __m256 vx8 = _mm256_sub_ps(vi8, vi_max); const __m256 vx9 = _mm256_sub_ps(vi9, vi_max); const __m256 vx10 = _mm256_sub_ps(vi10, vi_max); // Compute reduced argument elements := round(x / log(2)). __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias); __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias); __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias); __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias); __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias); __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias); __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias); __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias); __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias); __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias); __m256 vn10 = _mm256_fmadd_ps(vx10, vlog2e, vmagic_bias); // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23)); const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23)); const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23)); const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23)); const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23)); const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23)); const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23)); const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23)); const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23)); const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23)); const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn10), 23)); // Subtract the large number back to get final elements := round(x / log(2)). vn0 = _mm256_sub_ps(vn0, vmagic_bias); vn1 = _mm256_sub_ps(vn1, vmagic_bias); vn2 = _mm256_sub_ps(vn2, vmagic_bias); vn3 = _mm256_sub_ps(vn3, vmagic_bias); vn4 = _mm256_sub_ps(vn4, vmagic_bias); vn5 = _mm256_sub_ps(vn5, vmagic_bias); vn6 = _mm256_sub_ps(vn6, vmagic_bias); vn7 = _mm256_sub_ps(vn7, vmagic_bias); vn8 = _mm256_sub_ps(vn8, vmagic_bias); vn9 = _mm256_sub_ps(vn9, vmagic_bias); vn10 = _mm256_sub_ps(vn10, vmagic_bias); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0); __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1); __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2); __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3); __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4); __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5); __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6); __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7); __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8); __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9); __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10); vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0); vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1); vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2); vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3); vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4); vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5); vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6); vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7); vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8); vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9); vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4); __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4); __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4); __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4); __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4); __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4); __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4); __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4); __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4); __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4); __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4); vp0 = _mm256_fmadd_ps(vp0, vt0, vc3); vp1 = _mm256_fmadd_ps(vp1, vt1, vc3); vp2 = _mm256_fmadd_ps(vp2, vt2, vc3); vp3 = _mm256_fmadd_ps(vp3, vt3, vc3); vp4 = _mm256_fmadd_ps(vp4, vt4, vc3); vp5 = _mm256_fmadd_ps(vp5, vt5, vc3); vp6 = _mm256_fmadd_ps(vp6, vt6, vc3); vp7 = _mm256_fmadd_ps(vp7, vt7, vc3); vp8 = _mm256_fmadd_ps(vp8, vt8, vc3); vp9 = _mm256_fmadd_ps(vp9, vt9, vc3); vp10 = _mm256_fmadd_ps(vp10, vt10, vc3); vp0 = _mm256_fmadd_ps(vp0, vt0, vc2); vp1 = _mm256_fmadd_ps(vp1, vt1, vc2); vp2 = _mm256_fmadd_ps(vp2, vt2, vc2); vp3 = _mm256_fmadd_ps(vp3, vt3, vc2); vp4 = _mm256_fmadd_ps(vp4, vt4, vc2); vp5 = _mm256_fmadd_ps(vp5, vt5, vc2); vp6 = _mm256_fmadd_ps(vp6, vt6, vc2); vp7 = _mm256_fmadd_ps(vp7, vt7, vc2); vp8 = _mm256_fmadd_ps(vp8, vt8, vc2); vp9 = _mm256_fmadd_ps(vp9, vt9, vc2); vp10 = _mm256_fmadd_ps(vp10, vt10, vc2); vp0 = _mm256_fmadd_ps(vp0, vt0, vc1); vp1 = _mm256_fmadd_ps(vp1, vt1, vc1); vp2 = _mm256_fmadd_ps(vp2, vt2, vc1); vp3 = _mm256_fmadd_ps(vp3, vt3, vc1); vp4 = _mm256_fmadd_ps(vp4, vt4, vc1); vp5 = _mm256_fmadd_ps(vp5, vt5, vc1); vp6 = _mm256_fmadd_ps(vp6, vt6, vc1); vp7 = _mm256_fmadd_ps(vp7, vt7, vc1); vp8 = _mm256_fmadd_ps(vp8, vt8, vc1); vp9 = _mm256_fmadd_ps(vp9, vt9, vc1); vp10 = _mm256_fmadd_ps(vp10, vt10, vc1); // Reconstruct the final f value: // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) // = s + (t * s) * p vt0 = _mm256_mul_ps(vt0, vs0); vt1 = _mm256_mul_ps(vt1, vs1); vt2 = _mm256_mul_ps(vt2, vs2); vt3 = _mm256_mul_ps(vt3, vs3); vt4 = _mm256_mul_ps(vt4, vs4); vt5 = _mm256_mul_ps(vt5, vs5); vt6 = _mm256_mul_ps(vt6, vs6); vt7 = _mm256_mul_ps(vt7, vs7); vt8 = _mm256_mul_ps(vt8, vs8); vt9 = _mm256_mul_ps(vt9, vs9); vt10 = _mm256_mul_ps(vt10, vs10); __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0); __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1); __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2); __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3); __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4); __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5); __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6); __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7); __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8); __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9); __m256 vf10 = _mm256_fmadd_ps(vt10, vp10, vs10); // For inputs below zero cutoff, replace output with +0.0f. // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0); vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1); vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2); vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3); vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4); vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5); vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6); vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7); vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8); vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9); vf10 = _mm256_andnot_ps(_mm256_cmp_ps(vx10, vdenorm_cutoff, _CMP_LT_OS), vf10); // Multiply by scale. vf0 = _mm256_mul_ps(vf0, vscale); vf1 = _mm256_mul_ps(vf1, vscale); vf2 = _mm256_mul_ps(vf2, vscale); vf3 = _mm256_mul_ps(vf3, vscale); vf4 = _mm256_mul_ps(vf4, vscale); vf5 = _mm256_mul_ps(vf5, vscale); vf6 = _mm256_mul_ps(vf6, vscale); vf7 = _mm256_mul_ps(vf7, vscale); vf8 = _mm256_mul_ps(vf8, vscale); vf9 = _mm256_mul_ps(vf9, vscale); vf10 = _mm256_mul_ps(vf10, vscale); // Store 88 (11x8) outputs at a time. _mm256_storeu_ps(output, vf0); _mm256_storeu_ps(output + 8, vf1); _mm256_storeu_ps(output + 16, vf2); _mm256_storeu_ps(output + 24, vf3); _mm256_storeu_ps(output + 32, vf4); _mm256_storeu_ps(output + 40, vf5); _mm256_storeu_ps(output + 48, vf6); _mm256_storeu_ps(output + 56, vf7); _mm256_storeu_ps(output + 64, vf8); _mm256_storeu_ps(output + 72, vf9); _mm256_storeu_ps(output + 80, vf10); output += 88; } for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) { // Load 8 inputs at a time. const __m256 vi = _mm256_loadu_ps(input); input += 8; // Subtract maximum input x := i - i_max. This implies x <= 0. const __m256 vx = _mm256_sub_ps(vi, vi_max); // Compute reduced argument elements := round(x / log(2)). __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias); // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); // Subtract the large number back to get final elements := round(x / log(2)). vn = _mm256_sub_ps(vn, vmagic_bias); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx); vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); vp = _mm256_fmadd_ps(vp, vt, vc3); vp = _mm256_fmadd_ps(vp, vt, vc2); vp = _mm256_fmadd_ps(vp, vt, vc1); // Reconstruct the final f value: // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) // = s + (t * s) * p vt = _mm256_mul_ps(vt, vs); __m256 vf = _mm256_fmadd_ps(vt, vp, vs); // For inputs below zero cutoff, replace output with +0.0f. // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf); // Multiply by scale. vf = _mm256_mul_ps(vf, vscale); // Store 64 (8x8) outputs at a time. _mm256_storeu_ps(output, vf); output += 8; } if (elements != 0) { assert(elements >= 1 * sizeof(float)); assert(elements <= 7 * sizeof(float)); const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements)); // Load up to 7 inputs at a time. const __m256 vi = _mm256_maskload_ps(input, vmask); // Subtract maximum input x := i - i_max. This implies x <= 0. const __m256 vx = _mm256_sub_ps(vi, vi_max); // Compute reduced argument elements := round(x / log(2)). __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias); // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); // Subtract the large number back to get final elements := round(x / log(2)). vn = _mm256_sub_ps(vn, vmagic_bias); // Compute reduced argument t := x - elements * log(2). // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx); vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); vp = _mm256_fmadd_ps(vp, vt, vc3); vp = _mm256_fmadd_ps(vp, vt, vc2); vp = _mm256_fmadd_ps(vp, vt, vc1); // Reconstruct the final f value: // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) // = s + (t * s) * p vt = _mm256_mul_ps(vt, vs); __m256 vf = _mm256_fmadd_ps(vt, vp, vs); // For inputs below zero cutoff, replace output with +0.0f. // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf); // Multiply by scale. vf = _mm256_mul_ps(vf, vscale); // Store up to 7 outputs at a time. _mm256_maskstore_ps(output, vmask, vf); } }