Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 1 | // Auto-generated file. Do not edit! |
| 2 | // Template: src/f32-raddstoreexpminusmax/avx2-p5.c.in |
| 3 | // Generator: tools/xngen |
| 4 | // |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 5 | // Copyright 2019 Google LLC |
| 6 | // |
| 7 | // This source code is licensed under the BSD-style license found in the |
| 8 | // LICENSE file in the root directory of this source tree. |
| 9 | |
| 10 | #include <assert.h> |
| 11 | |
| 12 | #include <immintrin.h> |
| 13 | |
| 14 | #include <xnnpack/raddstoreexpminusmax.h> |
| 15 | |
| 16 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 17 | static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0}; |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 18 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 19 | void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x72_acc3( |
| 20 | size_t elements, |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 21 | const float* input, |
| 22 | float* output, |
| 23 | float* sum, |
| 24 | float max) |
| 25 | { |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 26 | assert(elements % sizeof(float) == 0); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 27 | |
| 28 | const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f); |
| 29 | // The smallest x for which expf(x) is normalized. |
| 30 | const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f); |
| 31 | const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f); |
| 32 | const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f); |
| 33 | const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f); |
| 34 | |
| 35 | const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f); |
| 36 | const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f); |
| 37 | const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f); |
| 38 | const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f); |
| 39 | const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f); |
| 40 | |
| 41 | const __m256 vi_max = _mm256_set1_ps(max); |
| 42 | |
| 43 | __m256 vacc0 = _mm256_setzero_ps(); |
| 44 | __m256 vacc1 = _mm256_setzero_ps(); |
| 45 | __m256 vacc2 = _mm256_setzero_ps(); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 46 | for (; elements >= 72 * sizeof(float); elements -= 72 * sizeof(float)) { |
| 47 | // Load 72 (9x8) inputs at a time. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 48 | const __m256 vi0 = _mm256_loadu_ps(input); |
| 49 | const __m256 vi1 = _mm256_loadu_ps(input + 8); |
| 50 | const __m256 vi2 = _mm256_loadu_ps(input + 16); |
| 51 | const __m256 vi3 = _mm256_loadu_ps(input + 24); |
| 52 | const __m256 vi4 = _mm256_loadu_ps(input + 32); |
| 53 | const __m256 vi5 = _mm256_loadu_ps(input + 40); |
| 54 | const __m256 vi6 = _mm256_loadu_ps(input + 48); |
| 55 | const __m256 vi7 = _mm256_loadu_ps(input + 56); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 56 | const __m256 vi8 = _mm256_loadu_ps(input + 64); |
| 57 | input += 72; |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 58 | |
| 59 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 60 | const __m256 vx0 = _mm256_sub_ps(vi0, vi_max); |
| 61 | const __m256 vx1 = _mm256_sub_ps(vi1, vi_max); |
| 62 | const __m256 vx2 = _mm256_sub_ps(vi2, vi_max); |
| 63 | const __m256 vx3 = _mm256_sub_ps(vi3, vi_max); |
| 64 | const __m256 vx4 = _mm256_sub_ps(vi4, vi_max); |
| 65 | const __m256 vx5 = _mm256_sub_ps(vi5, vi_max); |
| 66 | const __m256 vx6 = _mm256_sub_ps(vi6, vi_max); |
| 67 | const __m256 vx7 = _mm256_sub_ps(vi7, vi_max); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 68 | const __m256 vx8 = _mm256_sub_ps(vi8, vi_max); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 69 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 70 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 71 | __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias); |
| 72 | __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias); |
| 73 | __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias); |
| 74 | __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias); |
| 75 | __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias); |
| 76 | __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias); |
| 77 | __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias); |
| 78 | __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 79 | __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 80 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 81 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 82 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 83 | const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23)); |
| 84 | const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23)); |
| 85 | const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23)); |
| 86 | const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23)); |
| 87 | const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23)); |
| 88 | const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23)); |
| 89 | const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23)); |
| 90 | const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23)); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 91 | const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23)); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 92 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 93 | // Subtract the large number back to get final elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 94 | vn0 = _mm256_sub_ps(vn0, vmagic_bias); |
| 95 | vn1 = _mm256_sub_ps(vn1, vmagic_bias); |
| 96 | vn2 = _mm256_sub_ps(vn2, vmagic_bias); |
| 97 | vn3 = _mm256_sub_ps(vn3, vmagic_bias); |
| 98 | vn4 = _mm256_sub_ps(vn4, vmagic_bias); |
| 99 | vn5 = _mm256_sub_ps(vn5, vmagic_bias); |
| 100 | vn6 = _mm256_sub_ps(vn6, vmagic_bias); |
| 101 | vn7 = _mm256_sub_ps(vn7, vmagic_bias); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 102 | vn8 = _mm256_sub_ps(vn8, vmagic_bias); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 103 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 104 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 105 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 106 | __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0); |
| 107 | __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1); |
| 108 | __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2); |
| 109 | __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3); |
| 110 | __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4); |
| 111 | __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5); |
| 112 | __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6); |
| 113 | __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 114 | __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 115 | |
| 116 | vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0); |
| 117 | vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1); |
| 118 | vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2); |
| 119 | vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3); |
| 120 | vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4); |
| 121 | vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5); |
| 122 | vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6); |
| 123 | vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 124 | vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 125 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 126 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 127 | __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4); |
| 128 | __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4); |
| 129 | __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4); |
| 130 | __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4); |
| 131 | __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4); |
| 132 | __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4); |
| 133 | __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4); |
| 134 | __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 135 | __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 136 | |
| 137 | vp0 = _mm256_fmadd_ps(vp0, vt0, vc3); |
| 138 | vp1 = _mm256_fmadd_ps(vp1, vt1, vc3); |
| 139 | vp2 = _mm256_fmadd_ps(vp2, vt2, vc3); |
| 140 | vp3 = _mm256_fmadd_ps(vp3, vt3, vc3); |
| 141 | vp4 = _mm256_fmadd_ps(vp4, vt4, vc3); |
| 142 | vp5 = _mm256_fmadd_ps(vp5, vt5, vc3); |
| 143 | vp6 = _mm256_fmadd_ps(vp6, vt6, vc3); |
| 144 | vp7 = _mm256_fmadd_ps(vp7, vt7, vc3); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 145 | vp8 = _mm256_fmadd_ps(vp8, vt8, vc3); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 146 | |
| 147 | vp0 = _mm256_fmadd_ps(vp0, vt0, vc2); |
| 148 | vp1 = _mm256_fmadd_ps(vp1, vt1, vc2); |
| 149 | vp2 = _mm256_fmadd_ps(vp2, vt2, vc2); |
| 150 | vp3 = _mm256_fmadd_ps(vp3, vt3, vc2); |
| 151 | vp4 = _mm256_fmadd_ps(vp4, vt4, vc2); |
| 152 | vp5 = _mm256_fmadd_ps(vp5, vt5, vc2); |
| 153 | vp6 = _mm256_fmadd_ps(vp6, vt6, vc2); |
| 154 | vp7 = _mm256_fmadd_ps(vp7, vt7, vc2); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 155 | vp8 = _mm256_fmadd_ps(vp8, vt8, vc2); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 156 | |
| 157 | vp0 = _mm256_fmadd_ps(vp0, vt0, vc1); |
| 158 | vp1 = _mm256_fmadd_ps(vp1, vt1, vc1); |
| 159 | vp2 = _mm256_fmadd_ps(vp2, vt2, vc1); |
| 160 | vp3 = _mm256_fmadd_ps(vp3, vt3, vc1); |
| 161 | vp4 = _mm256_fmadd_ps(vp4, vt4, vc1); |
| 162 | vp5 = _mm256_fmadd_ps(vp5, vt5, vc1); |
| 163 | vp6 = _mm256_fmadd_ps(vp6, vt6, vc1); |
| 164 | vp7 = _mm256_fmadd_ps(vp7, vt7, vc1); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 165 | vp8 = _mm256_fmadd_ps(vp8, vt8, vc1); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 166 | |
| 167 | // Reconstruct the final f value: |
| 168 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 169 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 170 | // = s + (t * s) * p |
| 171 | vt0 = _mm256_mul_ps(vt0, vs0); |
| 172 | vt1 = _mm256_mul_ps(vt1, vs1); |
| 173 | vt2 = _mm256_mul_ps(vt2, vs2); |
| 174 | vt3 = _mm256_mul_ps(vt3, vs3); |
| 175 | vt4 = _mm256_mul_ps(vt4, vs4); |
| 176 | vt5 = _mm256_mul_ps(vt5, vs5); |
| 177 | vt6 = _mm256_mul_ps(vt6, vs6); |
| 178 | vt7 = _mm256_mul_ps(vt7, vs7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 179 | vt8 = _mm256_mul_ps(vt8, vs8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 180 | |
| 181 | __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0); |
| 182 | __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1); |
| 183 | __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2); |
| 184 | __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3); |
| 185 | __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4); |
| 186 | __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5); |
| 187 | __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6); |
| 188 | __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 189 | __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 190 | |
| 191 | // For inputs below zero cutoff, replace output with +0.0f. |
| 192 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 193 | vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0); |
| 194 | vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1); |
| 195 | vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2); |
| 196 | vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3); |
| 197 | vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4); |
| 198 | vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5); |
| 199 | vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6); |
| 200 | vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 201 | vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 202 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 203 | // Store 72 (9x8) outputs at a time. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 204 | _mm256_storeu_ps(output, vf0); |
| 205 | _mm256_storeu_ps(output + 8, vf1); |
| 206 | _mm256_storeu_ps(output + 16, vf2); |
| 207 | _mm256_storeu_ps(output + 24, vf3); |
| 208 | _mm256_storeu_ps(output + 32, vf4); |
| 209 | _mm256_storeu_ps(output + 40, vf5); |
| 210 | _mm256_storeu_ps(output + 48, vf6); |
| 211 | _mm256_storeu_ps(output + 56, vf7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 212 | _mm256_storeu_ps(output + 64, vf8); |
| 213 | output += 72; |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 214 | |
| 215 | // Accumulate computed exponents. |
| 216 | vacc0 = _mm256_add_ps(vacc0, vf0); |
| 217 | vacc1 = _mm256_add_ps(vacc1, vf1); |
| 218 | vacc2 = _mm256_add_ps(vacc2, vf2); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 219 | vacc0 = _mm256_add_ps(vacc0, vf3); |
| 220 | vacc1 = _mm256_add_ps(vacc1, vf4); |
| 221 | vacc2 = _mm256_add_ps(vacc2, vf5); |
| 222 | vacc0 = _mm256_add_ps(vacc0, vf6); |
| 223 | vacc1 = _mm256_add_ps(vacc1, vf7); |
| 224 | vacc2 = _mm256_add_ps(vacc2, vf8); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 225 | } |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 226 | // Add up all accumulators to vacc0 |
| 227 | vacc0 = _mm256_add_ps(vacc0, vacc1); |
| 228 | vacc0 = _mm256_add_ps(vacc0, vacc2); |
| 229 | |
| 230 | __m256 vacc = vacc0; |
| 231 | for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) { |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 232 | // Load 8 inputs at a time. |
| 233 | const __m256 vi = _mm256_loadu_ps(input); |
| 234 | input += 8; |
| 235 | |
| 236 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 237 | const __m256 vx = _mm256_sub_ps(vi, vi_max); |
| 238 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 239 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 240 | __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias); |
| 241 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 242 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 243 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 244 | const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); |
| 245 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 246 | // Subtract the large number back to get final elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 247 | vn = _mm256_sub_ps(vn, vmagic_bias); |
| 248 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 249 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 250 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 251 | __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx); |
| 252 | vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); |
| 253 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 254 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 255 | __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); |
| 256 | vp = _mm256_fmadd_ps(vp, vt, vc3); |
| 257 | vp = _mm256_fmadd_ps(vp, vt, vc2); |
| 258 | vp = _mm256_fmadd_ps(vp, vt, vc1); |
| 259 | |
| 260 | // Reconstruct the final f value: |
| 261 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 262 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 263 | // = s + (t * s) * p |
| 264 | vt = _mm256_mul_ps(vt, vs); |
| 265 | __m256 vf = _mm256_fmadd_ps(vt, vp, vs); |
| 266 | |
| 267 | // For inputs below zero cutoff, replace output with +0.0f. |
| 268 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 269 | vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf); |
| 270 | |
| 271 | // Store 8 outputs at a time. |
| 272 | _mm256_storeu_ps(output, vf); |
| 273 | output += 8; |
| 274 | |
| 275 | // Accumulate computed exponents. |
| 276 | vacc = _mm256_add_ps(vacc, vf); |
| 277 | } |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 278 | if (elements != 0) { |
| 279 | assert(elements >= 1 * sizeof(float)); |
| 280 | assert(elements <= 7 * sizeof(float)); |
| 281 | const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements)); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 282 | |
| 283 | // Load up to 7 inputs at a time. |
| 284 | const __m256 vi = _mm256_maskload_ps(input, vmask); |
| 285 | |
| 286 | // Subtract maximum input x := i - i_max. This implies x <= 0. |
| 287 | const __m256 vx = _mm256_sub_ps(vi, vi_max); |
| 288 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 289 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 290 | __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias); |
| 291 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 292 | // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e. |
| 293 | // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 294 | const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23)); |
| 295 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 296 | // Subtract the large number back to get final elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 297 | vn = _mm256_sub_ps(vn, vmagic_bias); |
| 298 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 299 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 300 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 301 | __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx); |
| 302 | vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt); |
| 303 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 304 | // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2]. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 305 | __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4); |
| 306 | vp = _mm256_fmadd_ps(vp, vt, vc3); |
| 307 | vp = _mm256_fmadd_ps(vp, vt, vc2); |
| 308 | vp = _mm256_fmadd_ps(vp, vt, vc1); |
| 309 | |
| 310 | // Reconstruct the final f value: |
| 311 | // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 312 | // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))) |
| 313 | // = s + (t * s) * p |
| 314 | vt = _mm256_mul_ps(vt, vs); |
| 315 | __m256 vf = _mm256_fmadd_ps(vt, vp, vs); |
| 316 | |
| 317 | // For inputs below zero cutoff, replace output with +0.0f. |
| 318 | // Note that for NaN inputs, comparison result is false, and outputs are left unchanged. |
| 319 | vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf); |
| 320 | |
| 321 | // Store up to 7 outputs at a time. |
| 322 | _mm256_maskstore_ps(output, vmask, vf); |
| 323 | |
| 324 | // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged. |
| 325 | vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask))); |
| 326 | } |
| 327 | // Reduce 8 elements in the SIMD register |
| 328 | __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1)); |
| 329 | vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo)); |
| 330 | vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo)); |
| 331 | _mm_store_ss(sum, vacc_lo); |
| 332 | _mm256_zeroupper(); |
| 333 | } |