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_acc6(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x96_acc6(
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 __m256 vacc2 = _mm256_setzero_ps();
46 __m256 vacc3 = _mm256_setzero_ps();
47 __m256 vacc4 = _mm256_setzero_ps();
48 __m256 vacc5 = _mm256_setzero_ps();
49 for (; elements >= 96 * sizeof(float); elements -= 96 * sizeof(float)) {
50 // Load 96 (12x8) inputs at a time.
51 const __m256 vi0 = _mm256_loadu_ps(input);
52 const __m256 vi1 = _mm256_loadu_ps(input + 8);
53 const __m256 vi2 = _mm256_loadu_ps(input + 16);
54 const __m256 vi3 = _mm256_loadu_ps(input + 24);
55 const __m256 vi4 = _mm256_loadu_ps(input + 32);
56 const __m256 vi5 = _mm256_loadu_ps(input + 40);
57 const __m256 vi6 = _mm256_loadu_ps(input + 48);
58 const __m256 vi7 = _mm256_loadu_ps(input + 56);
59 const __m256 vi8 = _mm256_loadu_ps(input + 64);
60 const __m256 vi9 = _mm256_loadu_ps(input + 72);
61 const __m256 vi10 = _mm256_loadu_ps(input + 80);
62 const __m256 vi11 = _mm256_loadu_ps(input + 88);
63 input += 96;
64
65 // Subtract maximum input x := i - i_max. This implies x <= 0.
66 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
67 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
68 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
69 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
70 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
71 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
72 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
73 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
74 const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
75 const __m256 vx9 = _mm256_sub_ps(vi9, vi_max);
76 const __m256 vx10 = _mm256_sub_ps(vi10, vi_max);
77 const __m256 vx11 = _mm256_sub_ps(vi11, vi_max);
78
79 // Compute reduced argument elements := round(x / log(2)).
80 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
81 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
82 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
83 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
84 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
85 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
86 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
87 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
88 __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
89 __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias);
90 __m256 vn10 = _mm256_fmadd_ps(vx10, vlog2e, vmagic_bias);
91 __m256 vn11 = _mm256_fmadd_ps(vx11, vlog2e, vmagic_bias);
92
93 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
94 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
95 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
96 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
97 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
98 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
99 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
100 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
101 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
102 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
103 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
104 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23));
105 const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn10), 23));
106 const __m256 vs11 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn11), 23));
107
108 // Subtract the large number back to get final elements := round(x / log(2)).
109 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
110 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
111 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
112 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
113 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
114 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
115 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
116 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
117 vn8 = _mm256_sub_ps(vn8, vmagic_bias);
118 vn9 = _mm256_sub_ps(vn9, vmagic_bias);
119 vn10 = _mm256_sub_ps(vn10, vmagic_bias);
120 vn11 = _mm256_sub_ps(vn11, vmagic_bias);
121
122 // Compute reduced argument t := x - elements * log(2).
123 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
124 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
125 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
126 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
127 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
128 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
129 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
130 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
131 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
132 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
133 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
134 __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
135 __m256 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_hi, vx11);
136
137 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
138 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
139 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
140 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
141 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
142 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
143 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
144 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
145 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
146 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
147 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
148 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_lo, vt11);
149
150 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
151 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
152 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
153 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
154 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
155 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
156 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
157 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
158 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
159 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
160 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
161 __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
162 __m256 vp11 = _mm256_fmadd_ps(vc5, vt11, vc4);
163
164 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
165 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
166 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
167 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
168 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
169 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
170 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
171 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
172 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
173 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
174 vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
175 vp11 = _mm256_fmadd_ps(vp11, vt11, vc3);
176
177 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
178 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
179 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
180 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
181 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
182 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
183 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
184 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
185 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
186 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
187 vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
188 vp11 = _mm256_fmadd_ps(vp11, vt11, vc2);
189
190 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
191 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
192 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
193 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
194 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
195 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
196 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
197 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
198 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
199 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
200 vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
201 vp11 = _mm256_fmadd_ps(vp11, vt11, vc1);
202
203 // Reconstruct the final f value:
204 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
205 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
206 // = s + (t * s) * p
207 vt0 = _mm256_mul_ps(vt0, vs0);
208 vt1 = _mm256_mul_ps(vt1, vs1);
209 vt2 = _mm256_mul_ps(vt2, vs2);
210 vt3 = _mm256_mul_ps(vt3, vs3);
211 vt4 = _mm256_mul_ps(vt4, vs4);
212 vt5 = _mm256_mul_ps(vt5, vs5);
213 vt6 = _mm256_mul_ps(vt6, vs6);
214 vt7 = _mm256_mul_ps(vt7, vs7);
215 vt8 = _mm256_mul_ps(vt8, vs8);
216 vt9 = _mm256_mul_ps(vt9, vs9);
217 vt10 = _mm256_mul_ps(vt10, vs10);
218 vt11 = _mm256_mul_ps(vt11, vs11);
219
220 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
221 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
222 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
223 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
224 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
225 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
226 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
227 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
228 __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
229 __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9);
230 __m256 vf10 = _mm256_fmadd_ps(vt10, vp10, vs10);
231 __m256 vf11 = _mm256_fmadd_ps(vt11, vp11, vs11);
232
233 // For inputs below zero cutoff, replace output with +0.0f.
234 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
235 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
236 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
237 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
238 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
239 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
240 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
241 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
242 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
243 vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
244 vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9);
245 vf10 = _mm256_andnot_ps(_mm256_cmp_ps(vx10, vdenorm_cutoff, _CMP_LT_OS), vf10);
246 vf11 = _mm256_andnot_ps(_mm256_cmp_ps(vx11, vdenorm_cutoff, _CMP_LT_OS), vf11);
247
248 // Store 96 (12x8) outputs at a time.
249 _mm256_storeu_ps(output, vf0);
250 _mm256_storeu_ps(output + 8, vf1);
251 _mm256_storeu_ps(output + 16, vf2);
252 _mm256_storeu_ps(output + 24, vf3);
253 _mm256_storeu_ps(output + 32, vf4);
254 _mm256_storeu_ps(output + 40, vf5);
255 _mm256_storeu_ps(output + 48, vf6);
256 _mm256_storeu_ps(output + 56, vf7);
257 _mm256_storeu_ps(output + 64, vf8);
258 _mm256_storeu_ps(output + 72, vf9);
259 _mm256_storeu_ps(output + 80, vf10);
260 _mm256_storeu_ps(output + 88, vf11);
261 output += 96;
262
263 // Accumulate computed exponents.
264 vacc0 = _mm256_add_ps(vacc0, vf0);
265 vacc1 = _mm256_add_ps(vacc1, vf1);
266 vacc2 = _mm256_add_ps(vacc2, vf2);
267 vacc3 = _mm256_add_ps(vacc3, vf3);
268 vacc4 = _mm256_add_ps(vacc4, vf4);
269 vacc5 = _mm256_add_ps(vacc5, vf5);
270 vacc0 = _mm256_add_ps(vacc0, vf6);
271 vacc1 = _mm256_add_ps(vacc1, vf7);
272 vacc2 = _mm256_add_ps(vacc2, vf8);
273 vacc3 = _mm256_add_ps(vacc3, vf9);
274 vacc4 = _mm256_add_ps(vacc4, vf10);
275 vacc5 = _mm256_add_ps(vacc5, vf11);
276 }
277 // Add up all accumulators to vacc0
278 vacc0 = _mm256_add_ps(vacc0, vacc1);
279 vacc2 = _mm256_add_ps(vacc2, vacc3);
280 vacc4 = _mm256_add_ps(vacc4, vacc5);
281 vacc0 = _mm256_add_ps(vacc0, vacc2);
282 vacc0 = _mm256_add_ps(vacc0, vacc4);
283
284 __m256 vacc = vacc0;
285 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
286 // Load 8 inputs at a time.
287 const __m256 vi = _mm256_loadu_ps(input);
288 input += 8;
289
290 // Subtract maximum input x := i - i_max. This implies x <= 0.
291 const __m256 vx = _mm256_sub_ps(vi, vi_max);
292
293 // Compute reduced argument elements := round(x / log(2)).
294 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
295
296 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
297 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
298 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
299
300 // Subtract the large number back to get final elements := round(x / log(2)).
301 vn = _mm256_sub_ps(vn, vmagic_bias);
302
303 // Compute reduced argument t := x - elements * log(2).
304 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
305 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
306 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
307
308 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
309 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
310 vp = _mm256_fmadd_ps(vp, vt, vc3);
311 vp = _mm256_fmadd_ps(vp, vt, vc2);
312 vp = _mm256_fmadd_ps(vp, vt, vc1);
313
314 // Reconstruct the final f value:
315 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
316 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
317 // = s + (t * s) * p
318 vt = _mm256_mul_ps(vt, vs);
319 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
320
321 // For inputs below zero cutoff, replace output with +0.0f.
322 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
323 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
324
325 // Store 8 outputs at a time.
326 _mm256_storeu_ps(output, vf);
327 output += 8;
328
329 // Accumulate computed exponents.
330 vacc = _mm256_add_ps(vacc, vf);
331 }
332 if (elements != 0) {
333 assert(elements >= 1 * sizeof(float));
334 assert(elements <= 7 * sizeof(float));
335 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
336
337 // Load up to 7 inputs at a time.
338 const __m256 vi = _mm256_maskload_ps(input, vmask);
339
340 // Subtract maximum input x := i - i_max. This implies x <= 0.
341 const __m256 vx = _mm256_sub_ps(vi, vi_max);
342
343 // Compute reduced argument elements := round(x / log(2)).
344 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
345
346 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
347 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
348 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
349
350 // Subtract the large number back to get final elements := round(x / log(2)).
351 vn = _mm256_sub_ps(vn, vmagic_bias);
352
353 // Compute reduced argument t := x - elements * log(2).
354 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
355 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
356 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
357
358 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
359 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
360 vp = _mm256_fmadd_ps(vp, vt, vc3);
361 vp = _mm256_fmadd_ps(vp, vt, vc2);
362 vp = _mm256_fmadd_ps(vp, vt, vc1);
363
364 // Reconstruct the final f value:
365 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
366 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
367 // = s + (t * s) * p
368 vt = _mm256_mul_ps(vt, vs);
369 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
370
371 // For inputs below zero cutoff, replace output with +0.0f.
372 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
373 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
374
375 // Store up to 7 outputs at a time.
376 _mm256_maskstore_ps(output, vmask, vf);
377
378 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
379 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
380 }
381 // Reduce 8 elements in the SIMD register
382 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
383 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
384 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
385 _mm_store_ss(sum, vacc_lo);
386 _mm256_zeroupper();
387 }
388