1 // Auto-generated file. Do not edit!
2 // Template: src/f32-sigmoid/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/common.h>
15 #include <xnnpack/vunary.h>
16
17
18 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
19
xnn_f32_sigmoid_ukernel__avx2_rr1_p5_nr2fma_x56(size_t n,const float * x,float * y,const void * params)20 void xnn_f32_sigmoid_ukernel__avx2_rr1_p5_nr2fma_x56(
21 size_t n,
22 const float* x,
23 float* y,
24 const void* params)
25 {
26 assert(n % sizeof(float) == 0);
27
28 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
29 // The smallest x for which sigmoidf(x) is normalized.
30 // This number is also the smallest x for which expf(x) is normalized.
31 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep+6f);
32 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
33 const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
34 const __m256 vone = _mm256_set1_ps(1.0f);
35 const __m256 vsign_mask = _mm256_set1_ps(-0.0f);
36
37 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
38 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
39 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
40 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
41 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
42
43 for (; n >= 56 * sizeof(float); n -= 56 * sizeof(float)) {
44 const __m256 vx0 = _mm256_loadu_ps(x);
45 const __m256 vx1 = _mm256_loadu_ps(x + 8);
46 const __m256 vx2 = _mm256_loadu_ps(x + 16);
47 const __m256 vx3 = _mm256_loadu_ps(x + 24);
48 const __m256 vx4 = _mm256_loadu_ps(x + 32);
49 const __m256 vx5 = _mm256_loadu_ps(x + 40);
50 const __m256 vx6 = _mm256_loadu_ps(x + 48);
51 x += 56;
52
53 // General structure of the algorithm:
54 // / exp(x) / (1 + exp(x)) if x <= 0
55 // f[x] :=
56 // \ 1 - f[-x] if x >= 0
57 //
58 // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
59 // then replace result with 1 - f[z] if x >= 0.
60 const __m256 vz0 = _mm256_or_ps(vx0, vsign_mask);
61 const __m256 vz1 = _mm256_or_ps(vx1, vsign_mask);
62 const __m256 vz2 = _mm256_or_ps(vx2, vsign_mask);
63 const __m256 vz3 = _mm256_or_ps(vx3, vsign_mask);
64 const __m256 vz4 = _mm256_or_ps(vx4, vsign_mask);
65 const __m256 vz5 = _mm256_or_ps(vx5, vsign_mask);
66 const __m256 vz6 = _mm256_or_ps(vx6, vsign_mask);
67
68 // Compute reduced argument n := round(z / log(2)).
69 // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
70 // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
71 // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
72 // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
73 // the algorithm.
74 __m256 vn0 = _mm256_fmadd_ps(vz0, vlog2e, vmagic_bias);
75 __m256 vn1 = _mm256_fmadd_ps(vz1, vlog2e, vmagic_bias);
76 __m256 vn2 = _mm256_fmadd_ps(vz2, vlog2e, vmagic_bias);
77 __m256 vn3 = _mm256_fmadd_ps(vz3, vlog2e, vmagic_bias);
78 __m256 vn4 = _mm256_fmadd_ps(vz4, vlog2e, vmagic_bias);
79 __m256 vn5 = _mm256_fmadd_ps(vz5, vlog2e, vmagic_bias);
80 __m256 vn6 = _mm256_fmadd_ps(vz6, vlog2e, vmagic_bias);
81
82 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
83 // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
84 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
85 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
86 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
87 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
88 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
89 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
90 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
91
92 // Subtract the large number back to get final n := round(z / log(2)).
93 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
94 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
95 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
96 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
97 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
98 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
99 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
100
101 // Compute reduced argument t := z - n * log(2).
102 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2, vz0);
103 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2, vz1);
104 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2, vz2);
105 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2, vz3);
106 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2, vz4);
107 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2, vz5);
108 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2, vz6);
109
110 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
111 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
112 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
113 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
114 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
115 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
116 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
117 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
118
119 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
120 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
121 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
122 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
123 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
124 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
125 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
126
127 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
128 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
129 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
130 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
131 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
132 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
133 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
134
135 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
136 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
137 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
138 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
139 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
140 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
141 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
142
143 // Reconstruct the exp(z) value:
144 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
145 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
146 // = s + (t * s) * p
147 vt0 = _mm256_mul_ps(vt0, vs0);
148 vt1 = _mm256_mul_ps(vt1, vs1);
149 vt2 = _mm256_mul_ps(vt2, vs2);
150 vt3 = _mm256_mul_ps(vt3, vs3);
151 vt4 = _mm256_mul_ps(vt4, vs4);
152 vt5 = _mm256_mul_ps(vt5, vs5);
153 vt6 = _mm256_mul_ps(vt6, vs6);
154
155 const __m256 ve0 = _mm256_fmadd_ps(vt0, vp0, vs0);
156 const __m256 ve1 = _mm256_fmadd_ps(vt1, vp1, vs1);
157 const __m256 ve2 = _mm256_fmadd_ps(vt2, vp2, vs2);
158 const __m256 ve3 = _mm256_fmadd_ps(vt3, vp3, vs3);
159 const __m256 ve4 = _mm256_fmadd_ps(vt4, vp4, vs4);
160 const __m256 ve5 = _mm256_fmadd_ps(vt5, vp5, vs5);
161 const __m256 ve6 = _mm256_fmadd_ps(vt6, vp6, vs6);
162
163 // Denominator of the sigmoid fraction: 1.0 + exp(z)
164 const __m256 vd0 = _mm256_add_ps(ve0, vone);
165 const __m256 vd1 = _mm256_add_ps(ve1, vone);
166 const __m256 vd2 = _mm256_add_ps(ve2, vone);
167 const __m256 vd3 = _mm256_add_ps(ve3, vone);
168 const __m256 vd4 = _mm256_add_ps(ve4, vone);
169 const __m256 vd5 = _mm256_add_ps(ve5, vone);
170 const __m256 vd6 = _mm256_add_ps(ve6, vone);
171
172 // Use Newton-Raphson method to compute reciprocal of denominator.
173 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
174 // Thus the reciprocal of the denominator never overflows.
175 __m256 vr0 = _mm256_rcp_ps(vd0);
176 __m256 vr1 = _mm256_rcp_ps(vd1);
177 __m256 vr2 = _mm256_rcp_ps(vd2);
178 __m256 vr3 = _mm256_rcp_ps(vd3);
179 __m256 vr4 = _mm256_rcp_ps(vd4);
180 __m256 vr5 = _mm256_rcp_ps(vd5);
181 __m256 vr6 = _mm256_rcp_ps(vd6);
182
183 vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0);
184 vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1);
185 vr2 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr2, vd2, vone), vr2, vr2);
186 vr3 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr3, vd3, vone), vr3, vr3);
187 vr4 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr4, vd4, vone), vr4, vr4);
188 vr5 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr5, vd5, vone), vr5, vr5);
189 vr6 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr6, vd6, vone), vr6, vr6);
190
191 vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0);
192 vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1);
193 vr2 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr2, vd2, vone), vr2, vr2);
194 vr3 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr3, vd3, vone), vr3, vr3);
195 vr4 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr4, vd4, vone), vr4, vr4);
196 vr5 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr5, vd5, vone), vr5, vr5);
197 vr6 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr6, vd6, vone), vr6, vr6);
198
199 // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
200 __m256 vf0 = _mm256_mul_ps(ve0, vr0);
201 __m256 vf1 = _mm256_mul_ps(ve1, vr1);
202 __m256 vf2 = _mm256_mul_ps(ve2, vr2);
203 __m256 vf3 = _mm256_mul_ps(ve3, vr3);
204 __m256 vf4 = _mm256_mul_ps(ve4, vr4);
205 __m256 vf5 = _mm256_mul_ps(ve5, vr5);
206 __m256 vf6 = _mm256_mul_ps(ve6, vr6);
207
208 // For inputs below denormal cutoff, replace output with +0.0f.
209 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
210 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vz0, vdenorm_cutoff, _CMP_LT_OS), vf0);
211 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vz1, vdenorm_cutoff, _CMP_LT_OS), vf1);
212 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vz2, vdenorm_cutoff, _CMP_LT_OS), vf2);
213 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vz3, vdenorm_cutoff, _CMP_LT_OS), vf3);
214 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vz4, vdenorm_cutoff, _CMP_LT_OS), vf4);
215 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vz5, vdenorm_cutoff, _CMP_LT_OS), vf5);
216 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vz6, vdenorm_cutoff, _CMP_LT_OS), vf6);
217
218 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
219 vf0 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf0), vf0, vx0);
220 vf1 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf1), vf1, vx1);
221 vf2 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf2), vf2, vx2);
222 vf3 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf3), vf3, vx3);
223 vf4 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf4), vf4, vx4);
224 vf5 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf5), vf5, vx5);
225 vf6 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf6), vf6, vx6);
226
227 _mm256_storeu_ps(y, vf0);
228 _mm256_storeu_ps(y + 8, vf1);
229 _mm256_storeu_ps(y + 16, vf2);
230 _mm256_storeu_ps(y + 24, vf3);
231 _mm256_storeu_ps(y + 32, vf4);
232 _mm256_storeu_ps(y + 40, vf5);
233 _mm256_storeu_ps(y + 48, vf6);
234 y += 56;
235 }
236 for (; n >= 8 * sizeof(float); n -= 8 * sizeof(float)) {
237 const __m256 vx = _mm256_loadu_ps(x);
238 x += 8;
239
240 // General structure of the algorithm:
241 // / exp(x) / (1 + exp(x)) if x <= 0
242 // f[x] :=
243 // \ 1 - f[-x] if x >= 0
244 //
245 // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
246 // then replace result with 1 - f[z] if x >= 0.
247 const __m256 vz = _mm256_or_ps(vx, vsign_mask);
248
249 // Compute reduced argument n := round(z / log(2)).
250 // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
251 // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
252 // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
253 // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
254 // the algorithm.
255 __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);
256
257 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
258 // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
259 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
260
261 // Subtract the large number back to get final n := round(z / log(2)).
262 vn = _mm256_sub_ps(vn, vmagic_bias);
263
264 // Compute reduced argument t := z - n * log(2).
265 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
266
267 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
268 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
269 vp = _mm256_fmadd_ps(vp, vt, vc3);
270 vp = _mm256_fmadd_ps(vp, vt, vc2);
271 vp = _mm256_fmadd_ps(vp, vt, vc1);
272
273 // Reconstruct the exp(z) value:
274 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
275 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
276 // = s + (t * s) * p
277 vt = _mm256_mul_ps(vt, vs);
278 const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);
279
280 // Denominator of the sigmoid fraction: 1.0 + exp(z)
281 const __m256 vd = _mm256_add_ps(ve, vone);
282
283 // Use Newton-Raphson method to compute reciprocal of denominator.
284 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
285 // Thus the reciprocal of the denominator never overflows.
286 __m256 vr = _mm256_rcp_ps(vd);
287 vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
288 vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
289
290 // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
291 __m256 vf = _mm256_mul_ps(ve, vr);
292
293 // For inputs below denormal cutoff, replace output with +0.0f.
294 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
295 vf = _mm256_andnot_ps(_mm256_cmp_ps(vz, vdenorm_cutoff, _CMP_LT_OS), vf);
296
297 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
298 vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);
299
300 _mm256_storeu_ps(y, vf);
301 y += 8;
302 }
303 if XNN_UNLIKELY(n != 0) {
304 assert(n >= 1 * sizeof(float));
305 assert(n <= 7 * sizeof(float));
306 __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - n));
307
308 const __m256 vx = _mm256_maskload_ps(x, vmask);
309
310 // General structure of the algorithm:
311 // / exp(x) / (1 + exp(x)) if x <= 0
312 // f[x] :=
313 // \ 1 - f[-x] if x >= 0
314 //
315 // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
316 // then replace result with 1 - f[z] if x >= 0.
317 const __m256 vz = _mm256_or_ps(vx, vsign_mask);
318
319 // Compute reduced argument n := round(z / log(2)).
320 // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
321 // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
322 // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
323 // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
324 // the algorithm.
325 __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);
326
327 // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
328 // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
329 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
330
331 // Subtract the large number back to get final n := round(z / log(2)).
332 vn = _mm256_sub_ps(vn, vmagic_bias);
333
334 // Compute reduced argument t := z - n * log(2).
335 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);
336
337 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
338 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
339 vp = _mm256_fmadd_ps(vp, vt, vc3);
340 vp = _mm256_fmadd_ps(vp, vt, vc2);
341 vp = _mm256_fmadd_ps(vp, vt, vc1);
342
343 // Reconstruct the exp(z) value:
344 // e = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
345 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
346 // = s + (t * s) * p
347 vt = _mm256_mul_ps(vt, vs);
348 const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);
349
350 // Denominator of the sigmoid fraction: 1.0 + exp(z)
351 const __m256 vd = _mm256_add_ps(ve, vone);
352
353 // Use Newton-Raphson method to compute reciprocal of denominator.
354 // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
355 // Thus the reciprocal of the denominator never overflows.
356 __m256 vr = _mm256_rcp_ps(vd);
357 vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
358 vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
359
360 // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
361 __m256 vf = _mm256_mul_ps(ve, vr);
362
363 // For inputs below denormal 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(vz, vdenorm_cutoff, _CMP_LT_OS), vf);
366
367 // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
368 vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);
369
370 // _mm256_maskstore_ps(y, vmask, vf) could be used here, but triggers msan failures (probably an msan bug).
371 __m128 vf_lo = _mm256_castps256_ps128(vf);
372 if (n & (4 * sizeof(float))) {
373 _mm_storeu_ps(y, vf_lo);
374 vf_lo = _mm256_extractf128_ps(vf, 1);
375 y += 4;
376 }
377 if (n & (2 * sizeof(float))) {
378 _mm_storel_pi((__m64*) y, vf_lo);
379 vf_lo = _mm_movehl_ps(vf_lo, vf_lo);
380 y += 2;
381 }
382 if (n & (1 * sizeof(float))) {
383 _mm_store_ss(y, vf_lo);
384 }
385 }
386 }
387