Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 1 | // Auto-generated file. Do not edit! |
| 2 | // Template: src/f32-raddstoreexpminusmax/avx512f-p5-scalef.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 | |
Marat Dukhan | cfb3134 | 2019-12-05 10:42:57 -0800 | [diff] [blame] | 14 | #include <xnnpack/intrinsics-polyfill.h> |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 15 | #include <xnnpack/raddstoreexpminusmax.h> |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 16 | |
| 17 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 18 | void xnn_f32_raddstoreexpminusmax_ukernel__avx512f_p5_scalef_x160_acc5( |
| 19 | size_t elements, |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 20 | const float* input, |
| 21 | float* output, |
| 22 | float* sum, |
| 23 | float max) |
| 24 | { |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 25 | assert(elements % sizeof(float) == 0); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 26 | |
| 27 | const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f); |
| 28 | const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f); |
| 29 | const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f); |
| 30 | |
| 31 | const __m512 vc0 = _mm512_set1_ps(1.0f); |
| 32 | const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f); |
| 33 | const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f); |
| 34 | const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f); |
| 35 | const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f); |
| 36 | const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f); |
| 37 | |
| 38 | const __m512 vi_max = _mm512_set1_ps(max); |
| 39 | |
| 40 | __m512 vacc0 = _mm512_setzero_ps(); |
| 41 | __m512 vacc1 = _mm512_setzero_ps(); |
| 42 | __m512 vacc2 = _mm512_setzero_ps(); |
| 43 | __m512 vacc3 = _mm512_setzero_ps(); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 44 | __m512 vacc4 = _mm512_setzero_ps(); |
| 45 | for (; elements >= 160 * sizeof(float); elements -= 160 * sizeof(float)) { |
| 46 | // Load 160 (10x16) inputs at a time. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 47 | const __m512 vi0 = _mm512_loadu_ps(input); |
| 48 | const __m512 vi1 = _mm512_loadu_ps(input + 16); |
| 49 | const __m512 vi2 = _mm512_loadu_ps(input + 32); |
| 50 | const __m512 vi3 = _mm512_loadu_ps(input + 48); |
| 51 | const __m512 vi4 = _mm512_loadu_ps(input + 64); |
| 52 | const __m512 vi5 = _mm512_loadu_ps(input + 80); |
| 53 | const __m512 vi6 = _mm512_loadu_ps(input + 96); |
| 54 | const __m512 vi7 = _mm512_loadu_ps(input + 112); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 55 | const __m512 vi8 = _mm512_loadu_ps(input + 128); |
| 56 | const __m512 vi9 = _mm512_loadu_ps(input + 144); |
| 57 | input += 160; |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 58 | |
| 59 | // Subtract maximum input x := i - i_max. |
| 60 | const __m512 vx0 = _mm512_sub_ps(vi0, vi_max); |
| 61 | const __m512 vx1 = _mm512_sub_ps(vi1, vi_max); |
| 62 | const __m512 vx2 = _mm512_sub_ps(vi2, vi_max); |
| 63 | const __m512 vx3 = _mm512_sub_ps(vi3, vi_max); |
| 64 | const __m512 vx4 = _mm512_sub_ps(vi4, vi_max); |
| 65 | const __m512 vx5 = _mm512_sub_ps(vi5, vi_max); |
| 66 | const __m512 vx6 = _mm512_sub_ps(vi6, vi_max); |
| 67 | const __m512 vx7 = _mm512_sub_ps(vi7, vi_max); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 68 | const __m512 vx8 = _mm512_sub_ps(vi8, vi_max); |
| 69 | const __m512 vx9 = _mm512_sub_ps(vi9, vi_max); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 70 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 71 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 72 | const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0); |
| 73 | const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0); |
| 74 | const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0); |
| 75 | const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0); |
| 76 | const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0); |
| 77 | const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0); |
| 78 | const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0); |
| 79 | const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 80 | const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0); |
| 81 | const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, vlog2e), 0); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 82 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 83 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 84 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 85 | __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0); |
| 86 | __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1); |
| 87 | __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2); |
| 88 | __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3); |
| 89 | __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4); |
| 90 | __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5); |
| 91 | __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6); |
| 92 | __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 93 | __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8); |
| 94 | __m512 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_hi, vx9); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 95 | |
| 96 | vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0); |
| 97 | vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1); |
| 98 | vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2); |
| 99 | vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3); |
| 100 | vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4); |
| 101 | vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5); |
| 102 | vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6); |
| 103 | vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 104 | vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8); |
| 105 | vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_lo, vt9); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 106 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 107 | // 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] | 108 | __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4); |
| 109 | __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4); |
| 110 | __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4); |
| 111 | __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4); |
| 112 | __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4); |
| 113 | __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4); |
| 114 | __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4); |
| 115 | __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 116 | __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4); |
| 117 | __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 118 | |
| 119 | vp0 = _mm512_fmadd_ps(vp0, vt0, vc3); |
| 120 | vp1 = _mm512_fmadd_ps(vp1, vt1, vc3); |
| 121 | vp2 = _mm512_fmadd_ps(vp2, vt2, vc3); |
| 122 | vp3 = _mm512_fmadd_ps(vp3, vt3, vc3); |
| 123 | vp4 = _mm512_fmadd_ps(vp4, vt4, vc3); |
| 124 | vp5 = _mm512_fmadd_ps(vp5, vt5, vc3); |
| 125 | vp6 = _mm512_fmadd_ps(vp6, vt6, vc3); |
| 126 | vp7 = _mm512_fmadd_ps(vp7, vt7, vc3); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 127 | vp8 = _mm512_fmadd_ps(vp8, vt8, vc3); |
| 128 | vp9 = _mm512_fmadd_ps(vp9, vt9, vc3); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 129 | |
| 130 | vp0 = _mm512_fmadd_ps(vp0, vt0, vc2); |
| 131 | vp1 = _mm512_fmadd_ps(vp1, vt1, vc2); |
| 132 | vp2 = _mm512_fmadd_ps(vp2, vt2, vc2); |
| 133 | vp3 = _mm512_fmadd_ps(vp3, vt3, vc2); |
| 134 | vp4 = _mm512_fmadd_ps(vp4, vt4, vc2); |
| 135 | vp5 = _mm512_fmadd_ps(vp5, vt5, vc2); |
| 136 | vp6 = _mm512_fmadd_ps(vp6, vt6, vc2); |
| 137 | vp7 = _mm512_fmadd_ps(vp7, vt7, vc2); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 138 | vp8 = _mm512_fmadd_ps(vp8, vt8, vc2); |
| 139 | vp9 = _mm512_fmadd_ps(vp9, vt9, vc2); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 140 | |
| 141 | vp0 = _mm512_fmadd_ps(vp0, vt0, vc1); |
| 142 | vp1 = _mm512_fmadd_ps(vp1, vt1, vc1); |
| 143 | vp2 = _mm512_fmadd_ps(vp2, vt2, vc1); |
| 144 | vp3 = _mm512_fmadd_ps(vp3, vt3, vc1); |
| 145 | vp4 = _mm512_fmadd_ps(vp4, vt4, vc1); |
| 146 | vp5 = _mm512_fmadd_ps(vp5, vt5, vc1); |
| 147 | vp6 = _mm512_fmadd_ps(vp6, vt6, vc1); |
| 148 | vp7 = _mm512_fmadd_ps(vp7, vt7, vc1); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 149 | vp8 = _mm512_fmadd_ps(vp8, vt8, vc1); |
| 150 | vp9 = _mm512_fmadd_ps(vp9, vt9, vc1); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 151 | |
| 152 | vp0 = _mm512_fmadd_ps(vp0, vt0, vc0); |
| 153 | vp1 = _mm512_fmadd_ps(vp1, vt1, vc0); |
| 154 | vp2 = _mm512_fmadd_ps(vp2, vt2, vc0); |
| 155 | vp3 = _mm512_fmadd_ps(vp3, vt3, vc0); |
| 156 | vp4 = _mm512_fmadd_ps(vp4, vt4, vc0); |
| 157 | vp5 = _mm512_fmadd_ps(vp5, vt5, vc0); |
| 158 | vp6 = _mm512_fmadd_ps(vp6, vt6, vc0); |
| 159 | vp7 = _mm512_fmadd_ps(vp7, vt7, vc0); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 160 | vp8 = _mm512_fmadd_ps(vp8, vt8, vc0); |
| 161 | vp9 = _mm512_fmadd_ps(vp9, vt9, vc0); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 162 | |
| 163 | // Reconstruct the final f value: |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 164 | // f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 165 | // = 2**elements * p |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 166 | const __m512 vf0 = _mm512_scalef_ps(vp0, vn0); |
| 167 | const __m512 vf1 = _mm512_scalef_ps(vp1, vn1); |
| 168 | const __m512 vf2 = _mm512_scalef_ps(vp2, vn2); |
| 169 | const __m512 vf3 = _mm512_scalef_ps(vp3, vn3); |
| 170 | const __m512 vf4 = _mm512_scalef_ps(vp4, vn4); |
| 171 | const __m512 vf5 = _mm512_scalef_ps(vp5, vn5); |
| 172 | const __m512 vf6 = _mm512_scalef_ps(vp6, vn6); |
| 173 | const __m512 vf7 = _mm512_scalef_ps(vp7, vn7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 174 | const __m512 vf8 = _mm512_scalef_ps(vp8, vn8); |
| 175 | const __m512 vf9 = _mm512_scalef_ps(vp9, vn9); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 176 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 177 | // Store 160 (10x16) outputs at a time. |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 178 | _mm512_storeu_ps(output, vf0); |
| 179 | _mm512_storeu_ps(output + 16, vf1); |
| 180 | _mm512_storeu_ps(output + 32, vf2); |
| 181 | _mm512_storeu_ps(output + 48, vf3); |
| 182 | _mm512_storeu_ps(output + 64, vf4); |
| 183 | _mm512_storeu_ps(output + 80, vf5); |
| 184 | _mm512_storeu_ps(output + 96, vf6); |
| 185 | _mm512_storeu_ps(output + 112, vf7); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 186 | _mm512_storeu_ps(output + 128, vf8); |
| 187 | _mm512_storeu_ps(output + 144, vf9); |
| 188 | output += 160; |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 189 | |
| 190 | // Accumulate computed exponents. |
| 191 | vacc0 = _mm512_add_ps(vacc0, vf0); |
| 192 | vacc1 = _mm512_add_ps(vacc1, vf1); |
| 193 | vacc2 = _mm512_add_ps(vacc2, vf2); |
| 194 | vacc3 = _mm512_add_ps(vacc3, vf3); |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 195 | vacc4 = _mm512_add_ps(vacc4, vf4); |
| 196 | vacc0 = _mm512_add_ps(vacc0, vf5); |
| 197 | vacc1 = _mm512_add_ps(vacc1, vf6); |
| 198 | vacc2 = _mm512_add_ps(vacc2, vf7); |
| 199 | vacc3 = _mm512_add_ps(vacc3, vf8); |
| 200 | vacc4 = _mm512_add_ps(vacc4, vf9); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 201 | } |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 202 | // Add up all accumulators to vacc0 |
| 203 | vacc0 = _mm512_add_ps(vacc0, vacc1); |
| 204 | vacc2 = _mm512_add_ps(vacc2, vacc3); |
| 205 | vacc0 = _mm512_add_ps(vacc0, vacc2); |
| 206 | vacc0 = _mm512_add_ps(vacc0, vacc4); |
| 207 | |
| 208 | __m512 vacc = vacc0; |
| 209 | for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) { |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 210 | // Load 16 inputs at a time. |
| 211 | const __m512 vi = _mm512_loadu_ps(input); |
| 212 | input += 16; |
| 213 | |
| 214 | // Subtract maximum input x := i - i_max. |
| 215 | const __m512 vx = _mm512_sub_ps(vi, vi_max); |
| 216 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 217 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 218 | const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0); |
| 219 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 220 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 221 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 222 | __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx); |
| 223 | vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt); |
| 224 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 225 | // 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] | 226 | __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4); |
| 227 | vp = _mm512_fmadd_ps(vp, vt, vc3); |
| 228 | vp = _mm512_fmadd_ps(vp, vt, vc2); |
| 229 | vp = _mm512_fmadd_ps(vp, vt, vc1); |
| 230 | vp = _mm512_fmadd_ps(vp, vt, vc0); |
| 231 | |
| 232 | // Reconstruct the final f value: |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 233 | // f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 234 | // = 2**elements * p |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 235 | const __m512 vf = _mm512_scalef_ps(vp, vn); |
| 236 | |
| 237 | // Store 16 outputs at a time. |
| 238 | _mm512_storeu_ps(output, vf); |
| 239 | output += 16; |
| 240 | |
| 241 | // Accumulate computed exponents. |
| 242 | vacc = _mm512_add_ps(vacc, vf); |
| 243 | } |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 244 | if (elements != 0) { |
| 245 | // Prepare mask for valid 32-bit elements (depends on elements). |
| 246 | elements >>= 2 /* log2(sizeof(float)) */; |
| 247 | const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1))); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 248 | |
| 249 | // Load up to 15 inputs at a time. |
| 250 | const __m512 vi = _mm512_maskz_loadu_ps(vmask, input); |
| 251 | |
| 252 | // Subtract maximum input x := i - i_max. |
| 253 | const __m512 vx = _mm512_sub_ps(vi, vi_max); |
| 254 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 255 | // Compute reduced argument elements := round(x / log(2)). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 256 | const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0); |
| 257 | |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 258 | // Compute reduced argument t := x - elements * log(2). |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 259 | // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy. |
| 260 | __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx); |
| 261 | vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt); |
| 262 | |
Marat Dukhan | 102a739 | 2020-11-20 01:18:10 -0800 | [diff] [blame^] | 263 | // 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] | 264 | __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4); |
| 265 | vp = _mm512_fmadd_ps(vp, vt, vc3); |
| 266 | vp = _mm512_fmadd_ps(vp, vt, vc2); |
| 267 | vp = _mm512_fmadd_ps(vp, vt, vc1); |
| 268 | vp = _mm512_fmadd_ps(vp, vt, vc0); |
| 269 | |
| 270 | // Reconstruct the final f value: |
Marat Dukhan | 4c4eb00 | 2019-12-08 21:27:49 -0800 | [diff] [blame] | 271 | // f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))) |
| 272 | // = 2**elements * p |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 273 | const __m512 vf = _mm512_scalef_ps(vp, vn); |
| 274 | |
| 275 | // Store up to 15 outputs at a time. |
| 276 | _mm512_mask_storeu_ps(output, vmask, vf); |
| 277 | |
| 278 | // Accumulate computed exponents. |
| 279 | vacc = _mm512_mask_add_ps(vacc, vmask, vacc, vf); |
| 280 | } |
| 281 | *sum = _mm512_reduce_add_ps(vacc); |
Marat Dukhan | 9757953 | 2019-10-18 16:40:39 -0700 | [diff] [blame] | 282 | } |