1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddstoreexpminusmax/avx2-p5.c.in
3 // Generator: tools/xngen
4 //
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
17 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
18
xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x96_acc2(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x96_acc2(
20 size_t elements,
21 const float* input,
22 float* output,
23 float* sum,
24 float max)
25 {
26 assert(elements % sizeof(float) == 0);
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 for (; elements >= 96 * sizeof(float); elements -= 96 * sizeof(float)) {
46 // Load 96 (12x8) inputs at a time.
47 const __m256 vi0 = _mm256_loadu_ps(input);
48 const __m256 vi1 = _mm256_loadu_ps(input + 8);
49 const __m256 vi2 = _mm256_loadu_ps(input + 16);
50 const __m256 vi3 = _mm256_loadu_ps(input + 24);
51 const __m256 vi4 = _mm256_loadu_ps(input + 32);
52 const __m256 vi5 = _mm256_loadu_ps(input + 40);
53 const __m256 vi6 = _mm256_loadu_ps(input + 48);
54 const __m256 vi7 = _mm256_loadu_ps(input + 56);
55 const __m256 vi8 = _mm256_loadu_ps(input + 64);
56 const __m256 vi9 = _mm256_loadu_ps(input + 72);
57 const __m256 vi10 = _mm256_loadu_ps(input + 80);
58 const __m256 vi11 = _mm256_loadu_ps(input + 88);
59 input += 96;
60
61 // Subtract maximum input x := i - i_max. This implies x <= 0.
62 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
63 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
64 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
65 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
66 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
67 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
68 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
69 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
70 const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
71 const __m256 vx9 = _mm256_sub_ps(vi9, vi_max);
72 const __m256 vx10 = _mm256_sub_ps(vi10, vi_max);
73 const __m256 vx11 = _mm256_sub_ps(vi11, vi_max);
74
75 // Compute reduced argument elements := round(x / log(2)).
76 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
77 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
78 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
79 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
80 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
81 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
82 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
83 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
84 __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
85 __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias);
86 __m256 vn10 = _mm256_fmadd_ps(vx10, vlog2e, vmagic_bias);
87 __m256 vn11 = _mm256_fmadd_ps(vx11, vlog2e, vmagic_bias);
88
89 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
90 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
91 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
92 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
93 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
94 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
95 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
96 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
97 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
98 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
99 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
100 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23));
101 const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn10), 23));
102 const __m256 vs11 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn11), 23));
103
104 // Subtract the large number back to get final elements := round(x / log(2)).
105 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
106 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
107 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
108 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
109 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
110 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
111 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
112 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
113 vn8 = _mm256_sub_ps(vn8, vmagic_bias);
114 vn9 = _mm256_sub_ps(vn9, vmagic_bias);
115 vn10 = _mm256_sub_ps(vn10, vmagic_bias);
116 vn11 = _mm256_sub_ps(vn11, vmagic_bias);
117
118 // Compute reduced argument t := x - elements * log(2).
119 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
120 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
121 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
122 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
123 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
124 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
125 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
126 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
127 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
128 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
129 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
130 __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
131 __m256 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_hi, vx11);
132
133 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
134 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
135 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
136 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
137 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
138 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
139 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
140 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
141 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
142 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
143 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
144 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_lo, vt11);
145
146 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
147 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
148 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
149 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
150 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
151 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
152 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
153 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
154 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
155 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
156 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
157 __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
158 __m256 vp11 = _mm256_fmadd_ps(vc5, vt11, vc4);
159
160 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
161 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
162 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
163 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
164 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
165 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
166 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
167 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
168 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
169 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
170 vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
171 vp11 = _mm256_fmadd_ps(vp11, vt11, vc3);
172
173 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
174 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
175 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
176 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
177 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
178 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
179 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
180 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
181 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
182 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
183 vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
184 vp11 = _mm256_fmadd_ps(vp11, vt11, vc2);
185
186 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
187 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
188 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
189 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
190 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
191 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
192 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
193 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
194 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
195 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
196 vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
197 vp11 = _mm256_fmadd_ps(vp11, vt11, vc1);
198
199 // Reconstruct the final f value:
200 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
201 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
202 // = s + (t * s) * p
203 vt0 = _mm256_mul_ps(vt0, vs0);
204 vt1 = _mm256_mul_ps(vt1, vs1);
205 vt2 = _mm256_mul_ps(vt2, vs2);
206 vt3 = _mm256_mul_ps(vt3, vs3);
207 vt4 = _mm256_mul_ps(vt4, vs4);
208 vt5 = _mm256_mul_ps(vt5, vs5);
209 vt6 = _mm256_mul_ps(vt6, vs6);
210 vt7 = _mm256_mul_ps(vt7, vs7);
211 vt8 = _mm256_mul_ps(vt8, vs8);
212 vt9 = _mm256_mul_ps(vt9, vs9);
213 vt10 = _mm256_mul_ps(vt10, vs10);
214 vt11 = _mm256_mul_ps(vt11, vs11);
215
216 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
217 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
218 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
219 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
220 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
221 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
222 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
223 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
224 __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
225 __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9);
226 __m256 vf10 = _mm256_fmadd_ps(vt10, vp10, vs10);
227 __m256 vf11 = _mm256_fmadd_ps(vt11, vp11, vs11);
228
229 // For inputs below zero cutoff, replace output with +0.0f.
230 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
231 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
232 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
233 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
234 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
235 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
236 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
237 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
238 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
239 vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
240 vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9);
241 vf10 = _mm256_andnot_ps(_mm256_cmp_ps(vx10, vdenorm_cutoff, _CMP_LT_OS), vf10);
242 vf11 = _mm256_andnot_ps(_mm256_cmp_ps(vx11, vdenorm_cutoff, _CMP_LT_OS), vf11);
243
244 // Store 96 (12x8) outputs at a time.
245 _mm256_storeu_ps(output, vf0);
246 _mm256_storeu_ps(output + 8, vf1);
247 _mm256_storeu_ps(output + 16, vf2);
248 _mm256_storeu_ps(output + 24, vf3);
249 _mm256_storeu_ps(output + 32, vf4);
250 _mm256_storeu_ps(output + 40, vf5);
251 _mm256_storeu_ps(output + 48, vf6);
252 _mm256_storeu_ps(output + 56, vf7);
253 _mm256_storeu_ps(output + 64, vf8);
254 _mm256_storeu_ps(output + 72, vf9);
255 _mm256_storeu_ps(output + 80, vf10);
256 _mm256_storeu_ps(output + 88, vf11);
257 output += 96;
258
259 // Accumulate computed exponents.
260 vacc0 = _mm256_add_ps(vacc0, vf0);
261 vacc1 = _mm256_add_ps(vacc1, vf1);
262 vacc0 = _mm256_add_ps(vacc0, vf2);
263 vacc1 = _mm256_add_ps(vacc1, vf3);
264 vacc0 = _mm256_add_ps(vacc0, vf4);
265 vacc1 = _mm256_add_ps(vacc1, vf5);
266 vacc0 = _mm256_add_ps(vacc0, vf6);
267 vacc1 = _mm256_add_ps(vacc1, vf7);
268 vacc0 = _mm256_add_ps(vacc0, vf8);
269 vacc1 = _mm256_add_ps(vacc1, vf9);
270 vacc0 = _mm256_add_ps(vacc0, vf10);
271 vacc1 = _mm256_add_ps(vacc1, vf11);
272 }
273 // Add up all accumulators to vacc0
274 vacc0 = _mm256_add_ps(vacc0, vacc1);
275
276 __m256 vacc = vacc0;
277 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
278 // Load 8 inputs at a time.
279 const __m256 vi = _mm256_loadu_ps(input);
280 input += 8;
281
282 // Subtract maximum input x := i - i_max. This implies x <= 0.
283 const __m256 vx = _mm256_sub_ps(vi, vi_max);
284
285 // Compute reduced argument elements := round(x / log(2)).
286 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
287
288 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
289 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
290 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
291
292 // Subtract the large number back to get final elements := round(x / log(2)).
293 vn = _mm256_sub_ps(vn, vmagic_bias);
294
295 // Compute reduced argument t := x - elements * log(2).
296 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
297 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
298 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
299
300 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
301 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
302 vp = _mm256_fmadd_ps(vp, vt, vc3);
303 vp = _mm256_fmadd_ps(vp, vt, vc2);
304 vp = _mm256_fmadd_ps(vp, vt, vc1);
305
306 // Reconstruct the final f value:
307 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
308 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
309 // = s + (t * s) * p
310 vt = _mm256_mul_ps(vt, vs);
311 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
312
313 // For inputs below zero cutoff, replace output with +0.0f.
314 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
315 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
316
317 // Store 8 outputs at a time.
318 _mm256_storeu_ps(output, vf);
319 output += 8;
320
321 // Accumulate computed exponents.
322 vacc = _mm256_add_ps(vacc, vf);
323 }
324 if (elements != 0) {
325 assert(elements >= 1 * sizeof(float));
326 assert(elements <= 7 * sizeof(float));
327 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
328
329 // Load up to 7 inputs at a time.
330 const __m256 vi = _mm256_maskload_ps(input, vmask);
331
332 // Subtract maximum input x := i - i_max. This implies x <= 0.
333 const __m256 vx = _mm256_sub_ps(vi, vi_max);
334
335 // Compute reduced argument elements := round(x / log(2)).
336 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
337
338 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
339 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
340 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
341
342 // Subtract the large number back to get final elements := round(x / log(2)).
343 vn = _mm256_sub_ps(vn, vmagic_bias);
344
345 // Compute reduced argument t := x - elements * log(2).
346 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
347 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
348 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
349
350 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
351 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
352 vp = _mm256_fmadd_ps(vp, vt, vc3);
353 vp = _mm256_fmadd_ps(vp, vt, vc2);
354 vp = _mm256_fmadd_ps(vp, vt, vc1);
355
356 // Reconstruct the final f value:
357 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
358 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
359 // = s + (t * s) * p
360 vt = _mm256_mul_ps(vt, vs);
361 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
362
363 // For inputs below zero cutoff, replace output with +0.0f.
364 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
365 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
366
367 // Store up to 7 outputs at a time.
368 _mm256_maskstore_ps(output, vmask, vf);
369
370 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
371 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
372 }
373 // Reduce 8 elements in the SIMD register
374 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
375 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
376 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
377 _mm_store_ss(sum, vacc_lo);
378 _mm256_zeroupper();
379 }
380