1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddexpminusmax/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/raddexpminusmax.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_raddexpminusmax_ukernel__avx2_p5_x72_acc3(size_t elements,const float * input,float * sum,float max)19 void xnn_f32_raddexpminusmax_ukernel__avx2_p5_x72_acc3(
20 size_t elements,
21 const float* input,
22 float* sum,
23 float max)
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
28 // The smallest x for which expf(x) is normalized.
29 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
30 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
31 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
32 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
33
34 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
35 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
36 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
37 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
38 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
39
40 const __m256 vi_max = _mm256_set1_ps(max);
41
42 __m256 vacc0 = _mm256_setzero_ps();
43 __m256 vacc1 = _mm256_setzero_ps();
44 __m256 vacc2 = _mm256_setzero_ps();
45 for (; elements >= 72 * sizeof(float); elements -= 72 * sizeof(float)) {
46 // Load 72 (9x8) 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 input += 72;
57
58 // Subtract maximum input x := i - i_max. This implies x <= 0.
59 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
60 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
61 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
62 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
63 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
64 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
65 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
66 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
67 const __m256 vx8 = _mm256_sub_ps(vi8, 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 __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
79
80 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
81 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
82 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
83 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
84 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
85 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
86 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
87 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
88 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
89 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
90 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
91
92 // Subtract the large number back to get final elements := round(x / 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 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
101 vn8 = _mm256_sub_ps(vn8, vmagic_bias);
102
103 // Compute reduced argument t := x - elements * log(2).
104 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
105 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
106 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
107 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
108 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
109 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
110 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
111 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
112 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
113 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
114
115 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
116 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
117 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
118 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
119 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
120 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
121 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
122 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
123 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
124
125 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
126 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
127 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
128 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
129 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
130 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
131 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
132 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
133 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
134 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
135
136 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
137 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
138 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
139 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
140 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
141 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
142 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
143 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
144 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
145
146 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
147 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
148 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
149 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
150 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
151 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
152 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
153 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
154 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
155
156 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
157 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
158 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
159 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
160 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
161 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
162 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
163 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
164 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
165
166 // Reconstruct the final f value:
167 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
168 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
169 // = s + (t * s) * p
170 vt0 = _mm256_mul_ps(vt0, vs0);
171 vt1 = _mm256_mul_ps(vt1, vs1);
172 vt2 = _mm256_mul_ps(vt2, vs2);
173 vt3 = _mm256_mul_ps(vt3, vs3);
174 vt4 = _mm256_mul_ps(vt4, vs4);
175 vt5 = _mm256_mul_ps(vt5, vs5);
176 vt6 = _mm256_mul_ps(vt6, vs6);
177 vt7 = _mm256_mul_ps(vt7, vs7);
178 vt8 = _mm256_mul_ps(vt8, vs8);
179
180 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
181 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
182 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
183 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
184 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
185 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
186 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
187 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
188 __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
189
190 // For inputs below zero cutoff, replace output with +0.0f.
191 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
192 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
193 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
194 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
195 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
196 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
197 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
198 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
199 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
200 vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
201
202 // Accumulate computed exponents.
203 vacc0 = _mm256_add_ps(vacc0, vf0);
204 vacc1 = _mm256_add_ps(vacc1, vf1);
205 vacc2 = _mm256_add_ps(vacc2, vf2);
206 vacc0 = _mm256_add_ps(vacc0, vf3);
207 vacc1 = _mm256_add_ps(vacc1, vf4);
208 vacc2 = _mm256_add_ps(vacc2, vf5);
209 vacc0 = _mm256_add_ps(vacc0, vf6);
210 vacc1 = _mm256_add_ps(vacc1, vf7);
211 vacc2 = _mm256_add_ps(vacc2, vf8);
212 }
213 // Add up all accumulators to vacc0
214 vacc0 = _mm256_add_ps(vacc0, vacc1);
215 vacc0 = _mm256_add_ps(vacc0, vacc2);
216
217 __m256 vacc = vacc0;
218 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
219 // Load 8 inputs at a time.
220 const __m256 vi = _mm256_loadu_ps(input);
221 input += 8;
222
223 // Subtract maximum input x := i - i_max. This implies x <= 0.
224 const __m256 vx = _mm256_sub_ps(vi, vi_max);
225
226 // Compute reduced argument elements := round(x / log(2)).
227 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
228
229 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
230 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
231 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
232
233 // Subtract the large number back to get final elements := round(x / log(2)).
234 vn = _mm256_sub_ps(vn, vmagic_bias);
235
236 // Compute reduced argument t := x - elements * log(2).
237 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
238 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
239 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
240
241 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
242 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
243 vp = _mm256_fmadd_ps(vp, vt, vc3);
244 vp = _mm256_fmadd_ps(vp, vt, vc2);
245 vp = _mm256_fmadd_ps(vp, vt, vc1);
246
247 // Reconstruct the final f value:
248 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
249 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
250 // = s + (t * s) * p
251 vt = _mm256_mul_ps(vt, vs);
252 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
253
254 // For inputs below zero cutoff, replace output with +0.0f.
255 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
256 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
257
258 // Accumulate computed exponents.
259 vacc = _mm256_add_ps(vacc, vf);
260 }
261 if (elements != 0) {
262 assert(elements >= 1 * sizeof(float));
263 assert(elements <= 7 * sizeof(float));
264 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
265
266 // Load up to 7 inputs at a time.
267 const __m256 vi = _mm256_maskload_ps(input, vmask);
268
269 // Subtract maximum input x := i - i_max. This implies x <= 0.
270 const __m256 vx = _mm256_sub_ps(vi, vi_max);
271
272 // Compute reduced argument elements := round(x / log(2)).
273 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
274
275 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
276 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
277 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
278
279 // Subtract the large number back to get final elements := round(x / log(2)).
280 vn = _mm256_sub_ps(vn, vmagic_bias);
281
282 // Compute reduced argument t := x - elements * log(2).
283 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
284 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
285 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
286
287 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
288 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
289 vp = _mm256_fmadd_ps(vp, vt, vc3);
290 vp = _mm256_fmadd_ps(vp, vt, vc2);
291 vp = _mm256_fmadd_ps(vp, vt, vc1);
292
293 // Reconstruct the final f value:
294 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
295 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
296 // = s + (t * s) * p
297 vt = _mm256_mul_ps(vt, vs);
298 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
299
300 // For inputs below zero cutoff, replace output with +0.0f.
301 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
302 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
303
304 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
305 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
306 }
307 // Reduce 8 elements in the SIMD register
308 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
309 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
310 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
311 _mm_store_ss(sum, vacc_lo);
312 _mm256_zeroupper();
313 }
314