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_x64(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x64(
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 >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
46 // Load 64 (8x8) 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 input += 64;
56
57 // Subtract maximum input x := i - i_max. This implies x <= 0.
58 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
59 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
60 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
61 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
62 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
63 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
64 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
65 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
66
67 // Compute reduced argument elements := round(x / log(2)).
68 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
69 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
70 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
71 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
72 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
73 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
74 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
75 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
76
77 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
78 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
79 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
80 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
81 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
82 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
83 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
84 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
85 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
86 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
87
88 // Subtract the large number back to get final elements := round(x / log(2)).
89 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
90 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
91 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
92 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
93 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
94 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
95 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
96 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
97
98 // Compute reduced argument t := x - elements * log(2).
99 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
100 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
101 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
102 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
103 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
104 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
105 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
106 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
107 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
108
109 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
110 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
111 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
112 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
113 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
114 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
115 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
116 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
117
118 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
119 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
120 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
121 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
122 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
123 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
124 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
125 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
126 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
127
128 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
129 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
130 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
131 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
132 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
133 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
134 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
135 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
136
137 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
138 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
139 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
140 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
141 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
142 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
143 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
144 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
145
146 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
147 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
148 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
149 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
150 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
151 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
152 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
153 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
154
155 // Reconstruct the final f value:
156 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
157 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
158 // = s + (t * s) * p
159 vt0 = _mm256_mul_ps(vt0, vs0);
160 vt1 = _mm256_mul_ps(vt1, vs1);
161 vt2 = _mm256_mul_ps(vt2, vs2);
162 vt3 = _mm256_mul_ps(vt3, vs3);
163 vt4 = _mm256_mul_ps(vt4, vs4);
164 vt5 = _mm256_mul_ps(vt5, vs5);
165 vt6 = _mm256_mul_ps(vt6, vs6);
166 vt7 = _mm256_mul_ps(vt7, vs7);
167
168 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
169 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
170 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
171 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
172 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
173 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
174 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
175 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
176
177 // For inputs below zero cutoff, replace output with +0.0f.
178 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
179 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
180 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
181 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
182 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
183 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
184 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
185 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
186 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
187
188 // Multiply by scale.
189 vf0 = _mm256_mul_ps(vf0, vscale);
190 vf1 = _mm256_mul_ps(vf1, vscale);
191 vf2 = _mm256_mul_ps(vf2, vscale);
192 vf3 = _mm256_mul_ps(vf3, vscale);
193 vf4 = _mm256_mul_ps(vf4, vscale);
194 vf5 = _mm256_mul_ps(vf5, vscale);
195 vf6 = _mm256_mul_ps(vf6, vscale);
196 vf7 = _mm256_mul_ps(vf7, vscale);
197
198 // Store 64 (8x8) outputs at a time.
199 _mm256_storeu_ps(output, vf0);
200 _mm256_storeu_ps(output + 8, vf1);
201 _mm256_storeu_ps(output + 16, vf2);
202 _mm256_storeu_ps(output + 24, vf3);
203 _mm256_storeu_ps(output + 32, vf4);
204 _mm256_storeu_ps(output + 40, vf5);
205 _mm256_storeu_ps(output + 48, vf6);
206 _mm256_storeu_ps(output + 56, vf7);
207 output += 64;
208 }
209 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
210 // Load 8 inputs at a time.
211 const __m256 vi = _mm256_loadu_ps(input);
212 input += 8;
213
214 // Subtract maximum input x := i - i_max. This implies x <= 0.
215 const __m256 vx = _mm256_sub_ps(vi, vi_max);
216
217 // Compute reduced argument elements := round(x / log(2)).
218 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
219
220 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
221 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
222 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
223
224 // Subtract the large number back to get final elements := round(x / log(2)).
225 vn = _mm256_sub_ps(vn, vmagic_bias);
226
227 // Compute reduced argument t := x - elements * log(2).
228 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
229 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
230 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
231
232 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
233 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
234 vp = _mm256_fmadd_ps(vp, vt, vc3);
235 vp = _mm256_fmadd_ps(vp, vt, vc2);
236 vp = _mm256_fmadd_ps(vp, vt, vc1);
237
238 // Reconstruct the final f value:
239 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
240 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
241 // = s + (t * s) * p
242 vt = _mm256_mul_ps(vt, vs);
243 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
244
245 // For inputs below zero cutoff, replace output with +0.0f.
246 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
247 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
248
249 // Multiply by scale.
250 vf = _mm256_mul_ps(vf, vscale);
251
252 // Store 64 (8x8) outputs at a time.
253 _mm256_storeu_ps(output, vf);
254 output += 8;
255 }
256 if (elements != 0) {
257 assert(elements >= 1 * sizeof(float));
258 assert(elements <= 7 * sizeof(float));
259 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
260
261 // Load up to 7 inputs at a time.
262 const __m256 vi = _mm256_maskload_ps(input, vmask);
263
264 // Subtract maximum input x := i - i_max. This implies x <= 0.
265 const __m256 vx = _mm256_sub_ps(vi, vi_max);
266
267 // Compute reduced argument elements := round(x / log(2)).
268 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
269
270 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
271 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
272 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
273
274 // Subtract the large number back to get final elements := round(x / log(2)).
275 vn = _mm256_sub_ps(vn, vmagic_bias);
276
277 // Compute reduced argument t := x - elements * log(2).
278 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
279 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
280 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
281
282 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
283 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
284 vp = _mm256_fmadd_ps(vp, vt, vc3);
285 vp = _mm256_fmadd_ps(vp, vt, vc2);
286 vp = _mm256_fmadd_ps(vp, vt, vc1);
287
288 // Reconstruct the final f value:
289 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
290 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
291 // = s + (t * s) * p
292 vt = _mm256_mul_ps(vt, vs);
293 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
294
295 // For inputs below zero cutoff, replace output with +0.0f.
296 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
297 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
298
299 // Multiply by scale.
300 vf = _mm256_mul_ps(vf, vscale);
301
302 // Store up to 7 outputs at a time.
303 _mm256_maskstore_ps(output, vmask, vf);
304 }
305 }
306