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_x80_acc5(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x80_acc5(
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 for (; elements >= 80 * sizeof(float); elements -= 80 * sizeof(float)) {
49 // Load 80 (10x8) inputs at a time.
50 const __m256 vi0 = _mm256_loadu_ps(input);
51 const __m256 vi1 = _mm256_loadu_ps(input + 8);
52 const __m256 vi2 = _mm256_loadu_ps(input + 16);
53 const __m256 vi3 = _mm256_loadu_ps(input + 24);
54 const __m256 vi4 = _mm256_loadu_ps(input + 32);
55 const __m256 vi5 = _mm256_loadu_ps(input + 40);
56 const __m256 vi6 = _mm256_loadu_ps(input + 48);
57 const __m256 vi7 = _mm256_loadu_ps(input + 56);
58 const __m256 vi8 = _mm256_loadu_ps(input + 64);
59 const __m256 vi9 = _mm256_loadu_ps(input + 72);
60 input += 80;
61
62 // Subtract maximum input x := i - i_max. This implies x <= 0.
63 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
64 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
65 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
66 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
67 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
68 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
69 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
70 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
71 const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
72 const __m256 vx9 = _mm256_sub_ps(vi9, vi_max);
73
74 // Compute reduced argument elements := round(x / log(2)).
75 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
76 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
77 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
78 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
79 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
80 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
81 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
82 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
83 __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
84 __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias);
85
86 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
87 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
88 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
89 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
90 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
91 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
92 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
93 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
94 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
95 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
96 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
97 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23));
98
99 // Subtract the large number back to get final elements := round(x / log(2)).
100 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
101 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
102 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
103 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
104 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
105 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
106 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
107 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
108 vn8 = _mm256_sub_ps(vn8, vmagic_bias);
109 vn9 = _mm256_sub_ps(vn9, vmagic_bias);
110
111 // Compute reduced argument t := x - elements * log(2).
112 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
113 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
114 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
115 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
116 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
117 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
118 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
119 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
120 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
121 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
122 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
123
124 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
125 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
126 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
127 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
128 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
129 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
130 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
131 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
132 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
133 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
134
135 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
136 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
137 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
138 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
139 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
140 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
141 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
142 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
143 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
144 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
145 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
146
147 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
148 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
149 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
150 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
151 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
152 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
153 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
154 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
155 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
156 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
157
158 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
159 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
160 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
161 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
162 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
163 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
164 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
165 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
166 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
167 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
168
169 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
170 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
171 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
172 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
173 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
174 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
175 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
176 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
177 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
178 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
179
180 // Reconstruct the final f value:
181 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
182 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
183 // = s + (t * s) * p
184 vt0 = _mm256_mul_ps(vt0, vs0);
185 vt1 = _mm256_mul_ps(vt1, vs1);
186 vt2 = _mm256_mul_ps(vt2, vs2);
187 vt3 = _mm256_mul_ps(vt3, vs3);
188 vt4 = _mm256_mul_ps(vt4, vs4);
189 vt5 = _mm256_mul_ps(vt5, vs5);
190 vt6 = _mm256_mul_ps(vt6, vs6);
191 vt7 = _mm256_mul_ps(vt7, vs7);
192 vt8 = _mm256_mul_ps(vt8, vs8);
193 vt9 = _mm256_mul_ps(vt9, vs9);
194
195 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
196 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
197 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
198 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
199 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
200 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
201 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
202 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
203 __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
204 __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9);
205
206 // For inputs below zero cutoff, replace output with +0.0f.
207 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
208 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
209 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
210 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
211 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
212 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
213 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
214 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
215 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
216 vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
217 vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9);
218
219 // Store 80 (10x8) outputs at a time.
220 _mm256_storeu_ps(output, vf0);
221 _mm256_storeu_ps(output + 8, vf1);
222 _mm256_storeu_ps(output + 16, vf2);
223 _mm256_storeu_ps(output + 24, vf3);
224 _mm256_storeu_ps(output + 32, vf4);
225 _mm256_storeu_ps(output + 40, vf5);
226 _mm256_storeu_ps(output + 48, vf6);
227 _mm256_storeu_ps(output + 56, vf7);
228 _mm256_storeu_ps(output + 64, vf8);
229 _mm256_storeu_ps(output + 72, vf9);
230 output += 80;
231
232 // Accumulate computed exponents.
233 vacc0 = _mm256_add_ps(vacc0, vf0);
234 vacc1 = _mm256_add_ps(vacc1, vf1);
235 vacc2 = _mm256_add_ps(vacc2, vf2);
236 vacc3 = _mm256_add_ps(vacc3, vf3);
237 vacc4 = _mm256_add_ps(vacc4, vf4);
238 vacc0 = _mm256_add_ps(vacc0, vf5);
239 vacc1 = _mm256_add_ps(vacc1, vf6);
240 vacc2 = _mm256_add_ps(vacc2, vf7);
241 vacc3 = _mm256_add_ps(vacc3, vf8);
242 vacc4 = _mm256_add_ps(vacc4, vf9);
243 }
244 // Add up all accumulators to vacc0
245 vacc0 = _mm256_add_ps(vacc0, vacc1);
246 vacc2 = _mm256_add_ps(vacc2, vacc3);
247 vacc0 = _mm256_add_ps(vacc0, vacc2);
248 vacc0 = _mm256_add_ps(vacc0, vacc4);
249
250 __m256 vacc = vacc0;
251 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
252 // Load 8 inputs at a time.
253 const __m256 vi = _mm256_loadu_ps(input);
254 input += 8;
255
256 // Subtract maximum input x := i - i_max. This implies x <= 0.
257 const __m256 vx = _mm256_sub_ps(vi, vi_max);
258
259 // Compute reduced argument elements := round(x / log(2)).
260 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
261
262 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
263 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
264 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
265
266 // Subtract the large number back to get final elements := round(x / log(2)).
267 vn = _mm256_sub_ps(vn, vmagic_bias);
268
269 // Compute reduced argument t := x - elements * log(2).
270 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
271 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
272 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
273
274 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
275 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
276 vp = _mm256_fmadd_ps(vp, vt, vc3);
277 vp = _mm256_fmadd_ps(vp, vt, vc2);
278 vp = _mm256_fmadd_ps(vp, vt, vc1);
279
280 // Reconstruct the final f value:
281 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
282 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
283 // = s + (t * s) * p
284 vt = _mm256_mul_ps(vt, vs);
285 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
286
287 // For inputs below zero cutoff, replace output with +0.0f.
288 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
289 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
290
291 // Store 8 outputs at a time.
292 _mm256_storeu_ps(output, vf);
293 output += 8;
294
295 // Accumulate computed exponents.
296 vacc = _mm256_add_ps(vacc, vf);
297 }
298 if (elements != 0) {
299 assert(elements >= 1 * sizeof(float));
300 assert(elements <= 7 * sizeof(float));
301 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
302
303 // Load up to 7 inputs at a time.
304 const __m256 vi = _mm256_maskload_ps(input, vmask);
305
306 // Subtract maximum input x := i - i_max. This implies x <= 0.
307 const __m256 vx = _mm256_sub_ps(vi, vi_max);
308
309 // Compute reduced argument elements := round(x / log(2)).
310 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
311
312 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
313 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
314 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
315
316 // Subtract the large number back to get final elements := round(x / log(2)).
317 vn = _mm256_sub_ps(vn, vmagic_bias);
318
319 // Compute reduced argument t := x - elements * log(2).
320 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
321 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
322 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
323
324 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
325 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
326 vp = _mm256_fmadd_ps(vp, vt, vc3);
327 vp = _mm256_fmadd_ps(vp, vt, vc2);
328 vp = _mm256_fmadd_ps(vp, vt, vc1);
329
330 // Reconstruct the final f value:
331 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
332 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
333 // = s + (t * s) * p
334 vt = _mm256_mul_ps(vt, vs);
335 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
336
337 // For inputs below zero cutoff, replace output with +0.0f.
338 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
339 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
340
341 // Store up to 7 outputs at a time.
342 _mm256_maskstore_ps(output, vmask, vf);
343
344 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
345 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
346 }
347 // Reduce 8 elements in the SIMD register
348 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
349 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
350 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
351 _mm_store_ss(sum, vacc_lo);
352 _mm256_zeroupper();
353 }
354