1 // Auto-generated file. Do not edit!
2 // Template: src/f32-vscaleexpminusmax/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/vscaleexpminusmax.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_vscaleexpminusmax_ukernel__avx2_p5_x80(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x80(
21 size_t elements,
22 const float* input,
23 float* output,
24 float scale,
25 float max)
26 {
27 assert(elements % sizeof(float) == 0);
28
29 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
30 // The smallest x for which expf(x) is normalized.
31 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
32 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
33 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
34 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
35
36 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
37 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
38 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
39 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
40 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
41
42 const __m256 vscale = _mm256_set1_ps(scale);
43 const __m256 vi_max = _mm256_set1_ps(max);
44
45 for (; elements >= 80 * sizeof(float); elements -= 80 * sizeof(float)) {
46 // Load 80 (10x8) 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 input += 80;
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);
68 const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
69 const __m256 vx9 = _mm256_sub_ps(vi9, vi_max);
70
71 // Compute reduced argument elements := round(x / log(2)).
72 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
73 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
74 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
75 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
76 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
77 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
78 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
79 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
80 __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
81 __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias);
82
83 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
84 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
85 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
86 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
87 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
88 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
89 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
90 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
91 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
92 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
93 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
94 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23));
95
96 // Subtract the large number back to get final elements := round(x / log(2)).
97 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
98 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
99 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
100 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
101 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
102 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
103 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
104 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
105 vn8 = _mm256_sub_ps(vn8, vmagic_bias);
106 vn9 = _mm256_sub_ps(vn9, vmagic_bias);
107
108 // Compute reduced argument t := x - elements * log(2).
109 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
110 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
111 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
112 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
113 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
114 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
115 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
116 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
117 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
118 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
119 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
120
121 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
122 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
123 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
124 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
125 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
126 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
127 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
128 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
129 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
130 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
131
132 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
133 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
134 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
135 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
136 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
137 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
138 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
139 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
140 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
141 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
142 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
143
144 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
145 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
146 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
147 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
148 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
149 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
150 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
151 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
152 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
153 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
154
155 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
156 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
157 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
158 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
159 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
160 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
161 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
162 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
163 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
164 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
165
166 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
167 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
168 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
169 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
170 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
171 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
172 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
173 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
174 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
175 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
176
177 // Reconstruct the final f value:
178 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
179 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
180 // = s + (t * s) * p
181 vt0 = _mm256_mul_ps(vt0, vs0);
182 vt1 = _mm256_mul_ps(vt1, vs1);
183 vt2 = _mm256_mul_ps(vt2, vs2);
184 vt3 = _mm256_mul_ps(vt3, vs3);
185 vt4 = _mm256_mul_ps(vt4, vs4);
186 vt5 = _mm256_mul_ps(vt5, vs5);
187 vt6 = _mm256_mul_ps(vt6, vs6);
188 vt7 = _mm256_mul_ps(vt7, vs7);
189 vt8 = _mm256_mul_ps(vt8, vs8);
190 vt9 = _mm256_mul_ps(vt9, vs9);
191
192 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
193 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
194 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
195 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
196 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
197 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
198 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
199 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
200 __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
201 __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9);
202
203 // For inputs below zero cutoff, replace output with +0.0f.
204 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
205 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
206 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
207 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
208 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
209 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
210 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
211 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
212 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
213 vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
214 vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9);
215
216 // Multiply by scale.
217 vf0 = _mm256_mul_ps(vf0, vscale);
218 vf1 = _mm256_mul_ps(vf1, vscale);
219 vf2 = _mm256_mul_ps(vf2, vscale);
220 vf3 = _mm256_mul_ps(vf3, vscale);
221 vf4 = _mm256_mul_ps(vf4, vscale);
222 vf5 = _mm256_mul_ps(vf5, vscale);
223 vf6 = _mm256_mul_ps(vf6, vscale);
224 vf7 = _mm256_mul_ps(vf7, vscale);
225 vf8 = _mm256_mul_ps(vf8, vscale);
226 vf9 = _mm256_mul_ps(vf9, vscale);
227
228 // Store 80 (10x8) outputs at a time.
229 _mm256_storeu_ps(output, vf0);
230 _mm256_storeu_ps(output + 8, vf1);
231 _mm256_storeu_ps(output + 16, vf2);
232 _mm256_storeu_ps(output + 24, vf3);
233 _mm256_storeu_ps(output + 32, vf4);
234 _mm256_storeu_ps(output + 40, vf5);
235 _mm256_storeu_ps(output + 48, vf6);
236 _mm256_storeu_ps(output + 56, vf7);
237 _mm256_storeu_ps(output + 64, vf8);
238 _mm256_storeu_ps(output + 72, vf9);
239 output += 80;
240 }
241 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
242 // Load 8 inputs at a time.
243 const __m256 vi = _mm256_loadu_ps(input);
244 input += 8;
245
246 // Subtract maximum input x := i - i_max. This implies x <= 0.
247 const __m256 vx = _mm256_sub_ps(vi, vi_max);
248
249 // Compute reduced argument elements := round(x / log(2)).
250 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
251
252 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
253 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
254 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
255
256 // Subtract the large number back to get final elements := round(x / log(2)).
257 vn = _mm256_sub_ps(vn, vmagic_bias);
258
259 // Compute reduced argument t := x - elements * log(2).
260 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
261 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
262 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
263
264 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
265 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
266 vp = _mm256_fmadd_ps(vp, vt, vc3);
267 vp = _mm256_fmadd_ps(vp, vt, vc2);
268 vp = _mm256_fmadd_ps(vp, vt, vc1);
269
270 // Reconstruct the final f value:
271 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
272 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
273 // = s + (t * s) * p
274 vt = _mm256_mul_ps(vt, vs);
275 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
276
277 // For inputs below zero cutoff, replace output with +0.0f.
278 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
279 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
280
281 // Multiply by scale.
282 vf = _mm256_mul_ps(vf, vscale);
283
284 // Store 64 (8x8) outputs at a time.
285 _mm256_storeu_ps(output, vf);
286 output += 8;
287 }
288 if (elements != 0) {
289 assert(elements >= 1 * sizeof(float));
290 assert(elements <= 7 * sizeof(float));
291 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
292
293 // Load up to 7 inputs at a time.
294 const __m256 vi = _mm256_maskload_ps(input, vmask);
295
296 // Subtract maximum input x := i - i_max. This implies x <= 0.
297 const __m256 vx = _mm256_sub_ps(vi, vi_max);
298
299 // Compute reduced argument elements := round(x / log(2)).
300 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
301
302 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
303 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
304 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
305
306 // Subtract the large number back to get final elements := round(x / log(2)).
307 vn = _mm256_sub_ps(vn, vmagic_bias);
308
309 // Compute reduced argument t := x - elements * log(2).
310 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
311 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
312 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
313
314 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
315 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
316 vp = _mm256_fmadd_ps(vp, vt, vc3);
317 vp = _mm256_fmadd_ps(vp, vt, vc2);
318 vp = _mm256_fmadd_ps(vp, vt, vc1);
319
320 // Reconstruct the final f value:
321 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
322 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
323 // = s + (t * s) * p
324 vt = _mm256_mul_ps(vt, vs);
325 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
326
327 // For inputs below zero cutoff, replace output with +0.0f.
328 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
329 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
330
331 // Multiply by scale.
332 vf = _mm256_mul_ps(vf, vscale);
333
334 // Store up to 7 outputs at a time.
335 _mm256_maskstore_ps(output, vmask, vf);
336 }
337 }
338