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_x64_acc4(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x64_acc4(
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 for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
48 // Load 64 (8x8) inputs at a time.
49 const __m256 vi0 = _mm256_loadu_ps(input);
50 const __m256 vi1 = _mm256_loadu_ps(input + 8);
51 const __m256 vi2 = _mm256_loadu_ps(input + 16);
52 const __m256 vi3 = _mm256_loadu_ps(input + 24);
53 const __m256 vi4 = _mm256_loadu_ps(input + 32);
54 const __m256 vi5 = _mm256_loadu_ps(input + 40);
55 const __m256 vi6 = _mm256_loadu_ps(input + 48);
56 const __m256 vi7 = _mm256_loadu_ps(input + 56);
57 input += 64;
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
69 // Compute reduced argument elements := round(x / log(2)).
70 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
71 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
72 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
73 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
74 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
75 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
76 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
77 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
78
79 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
80 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
81 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
82 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
83 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
84 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
85 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
86 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
87 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
88 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
89
90 // Subtract the large number back to get final elements := round(x / log(2)).
91 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
92 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
93 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
94 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
95 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
96 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
97 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
98 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
99
100 // Compute reduced argument t := x - elements * log(2).
101 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
102 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
103 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
104 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
105 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
106 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
107 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
108 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
109 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
110
111 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
112 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
113 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
114 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
115 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
116 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
117 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
118 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
119
120 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
121 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
122 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
123 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
124 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
125 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
126 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
127 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
128 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
129
130 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
131 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
132 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
133 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
134 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
135 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
136 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
137 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
138
139 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
140 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
141 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
142 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
143 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
144 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
145 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
146 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
147
148 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
149 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
150 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
151 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
152 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
153 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
154 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
155 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
156
157 // Reconstruct the final f value:
158 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
159 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
160 // = s + (t * s) * p
161 vt0 = _mm256_mul_ps(vt0, vs0);
162 vt1 = _mm256_mul_ps(vt1, vs1);
163 vt2 = _mm256_mul_ps(vt2, vs2);
164 vt3 = _mm256_mul_ps(vt3, vs3);
165 vt4 = _mm256_mul_ps(vt4, vs4);
166 vt5 = _mm256_mul_ps(vt5, vs5);
167 vt6 = _mm256_mul_ps(vt6, vs6);
168 vt7 = _mm256_mul_ps(vt7, vs7);
169
170 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
171 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
172 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
173 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
174 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
175 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
176 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
177 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
178
179 // For inputs below zero cutoff, replace output with +0.0f.
180 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
181 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
182 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
183 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
184 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
185 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
186 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
187 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
188 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
189
190 // Store 64 (8x8) outputs at a time.
191 _mm256_storeu_ps(output, vf0);
192 _mm256_storeu_ps(output + 8, vf1);
193 _mm256_storeu_ps(output + 16, vf2);
194 _mm256_storeu_ps(output + 24, vf3);
195 _mm256_storeu_ps(output + 32, vf4);
196 _mm256_storeu_ps(output + 40, vf5);
197 _mm256_storeu_ps(output + 48, vf6);
198 _mm256_storeu_ps(output + 56, vf7);
199 output += 64;
200
201 // Accumulate computed exponents.
202 vacc0 = _mm256_add_ps(vacc0, vf0);
203 vacc1 = _mm256_add_ps(vacc1, vf1);
204 vacc2 = _mm256_add_ps(vacc2, vf2);
205 vacc3 = _mm256_add_ps(vacc3, vf3);
206 vacc0 = _mm256_add_ps(vacc0, vf4);
207 vacc1 = _mm256_add_ps(vacc1, vf5);
208 vacc2 = _mm256_add_ps(vacc2, vf6);
209 vacc3 = _mm256_add_ps(vacc3, vf7);
210 }
211 // Add up all accumulators to vacc0
212 vacc0 = _mm256_add_ps(vacc0, vacc1);
213 vacc2 = _mm256_add_ps(vacc2, vacc3);
214 vacc0 = _mm256_add_ps(vacc0, vacc2);
215
216 __m256 vacc = vacc0;
217 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
218 // Load 8 inputs at a time.
219 const __m256 vi = _mm256_loadu_ps(input);
220 input += 8;
221
222 // Subtract maximum input x := i - i_max. This implies x <= 0.
223 const __m256 vx = _mm256_sub_ps(vi, vi_max);
224
225 // Compute reduced argument elements := round(x / log(2)).
226 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
227
228 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
229 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
230 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
231
232 // Subtract the large number back to get final elements := round(x / log(2)).
233 vn = _mm256_sub_ps(vn, vmagic_bias);
234
235 // Compute reduced argument t := x - elements * log(2).
236 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
237 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
238 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
239
240 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
241 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
242 vp = _mm256_fmadd_ps(vp, vt, vc3);
243 vp = _mm256_fmadd_ps(vp, vt, vc2);
244 vp = _mm256_fmadd_ps(vp, vt, vc1);
245
246 // Reconstruct the final f value:
247 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
248 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
249 // = s + (t * s) * p
250 vt = _mm256_mul_ps(vt, vs);
251 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
252
253 // For inputs below zero cutoff, replace output with +0.0f.
254 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
255 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
256
257 // Store 8 outputs at a time.
258 _mm256_storeu_ps(output, vf);
259 output += 8;
260
261 // Accumulate computed exponents.
262 vacc = _mm256_add_ps(vacc, vf);
263 }
264 if (elements != 0) {
265 assert(elements >= 1 * sizeof(float));
266 assert(elements <= 7 * sizeof(float));
267 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
268
269 // Load up to 7 inputs at a time.
270 const __m256 vi = _mm256_maskload_ps(input, vmask);
271
272 // Subtract maximum input x := i - i_max. This implies x <= 0.
273 const __m256 vx = _mm256_sub_ps(vi, vi_max);
274
275 // Compute reduced argument elements := round(x / log(2)).
276 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
277
278 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
279 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
280 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
281
282 // Subtract the large number back to get final elements := round(x / log(2)).
283 vn = _mm256_sub_ps(vn, vmagic_bias);
284
285 // Compute reduced argument t := x - elements * log(2).
286 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
287 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
288 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
289
290 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
291 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
292 vp = _mm256_fmadd_ps(vp, vt, vc3);
293 vp = _mm256_fmadd_ps(vp, vt, vc2);
294 vp = _mm256_fmadd_ps(vp, vt, vc1);
295
296 // Reconstruct the final f value:
297 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
298 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
299 // = s + (t * s) * p
300 vt = _mm256_mul_ps(vt, vs);
301 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
302
303 // For inputs below zero cutoff, replace output with +0.0f.
304 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
305 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
306
307 // Store up to 7 outputs at a time.
308 _mm256_maskstore_ps(output, vmask, vf);
309
310 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
311 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
312 }
313 // Reduce 8 elements in the SIMD register
314 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
315 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
316 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
317 _mm_store_ss(sum, vacc_lo);
318 _mm256_zeroupper();
319 }
320