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_x64_acc2(size_t elements,const float * input,float * sum,float max)19 void xnn_f32_raddexpminusmax_ukernel__avx2_p5_x64_acc2(
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 for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
45 // Load 64 (8x8) inputs at a time.
46 const __m256 vi0 = _mm256_loadu_ps(input);
47 const __m256 vi1 = _mm256_loadu_ps(input + 8);
48 const __m256 vi2 = _mm256_loadu_ps(input + 16);
49 const __m256 vi3 = _mm256_loadu_ps(input + 24);
50 const __m256 vi4 = _mm256_loadu_ps(input + 32);
51 const __m256 vi5 = _mm256_loadu_ps(input + 40);
52 const __m256 vi6 = _mm256_loadu_ps(input + 48);
53 const __m256 vi7 = _mm256_loadu_ps(input + 56);
54 input += 64;
55
56 // Subtract maximum input x := i - i_max. This implies x <= 0.
57 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
58 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
59 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
60 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
61 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
62 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
63 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
64 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
65
66 // Compute reduced argument elements := round(x / log(2)).
67 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
68 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
69 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
70 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
71 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
72 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
73 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
74 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
75
76 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
77 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
78 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
79 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
80 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
81 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
82 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
83 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
84 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
85 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
86
87 // Subtract the large number back to get final elements := round(x / log(2)).
88 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
89 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
90 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
91 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
92 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
93 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
94 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
95 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
96
97 // Compute reduced argument t := x - elements * log(2).
98 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
99 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
100 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
101 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
102 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
103 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
104 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
105 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
106 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
107
108 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
109 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
110 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
111 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
112 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
113 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
114 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
115 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
116
117 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
118 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
119 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
120 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
121 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
122 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
123 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
124 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
125 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
126
127 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
128 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
129 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
130 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
131 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
132 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
133 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
134 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
135
136 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
137 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
138 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
139 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
140 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
141 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
142 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
143 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
144
145 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
146 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
147 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
148 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
149 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
150 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
151 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
152 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
153
154 // Reconstruct the final f value:
155 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
156 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
157 // = s + (t * s) * p
158 vt0 = _mm256_mul_ps(vt0, vs0);
159 vt1 = _mm256_mul_ps(vt1, vs1);
160 vt2 = _mm256_mul_ps(vt2, vs2);
161 vt3 = _mm256_mul_ps(vt3, vs3);
162 vt4 = _mm256_mul_ps(vt4, vs4);
163 vt5 = _mm256_mul_ps(vt5, vs5);
164 vt6 = _mm256_mul_ps(vt6, vs6);
165 vt7 = _mm256_mul_ps(vt7, vs7);
166
167 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
168 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
169 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
170 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
171 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
172 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
173 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
174 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
175
176 // For inputs below zero cutoff, replace output with +0.0f.
177 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
178 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
179 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
180 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
181 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
182 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
183 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
184 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
185 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
186
187 // Accumulate computed exponents.
188 vacc0 = _mm256_add_ps(vacc0, vf0);
189 vacc1 = _mm256_add_ps(vacc1, vf1);
190 vacc0 = _mm256_add_ps(vacc0, vf2);
191 vacc1 = _mm256_add_ps(vacc1, vf3);
192 vacc0 = _mm256_add_ps(vacc0, vf4);
193 vacc1 = _mm256_add_ps(vacc1, vf5);
194 vacc0 = _mm256_add_ps(vacc0, vf6);
195 vacc1 = _mm256_add_ps(vacc1, vf7);
196 }
197 // Add up all accumulators to vacc0
198 vacc0 = _mm256_add_ps(vacc0, vacc1);
199
200 __m256 vacc = vacc0;
201 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
202 // Load 8 inputs at a time.
203 const __m256 vi = _mm256_loadu_ps(input);
204 input += 8;
205
206 // Subtract maximum input x := i - i_max. This implies x <= 0.
207 const __m256 vx = _mm256_sub_ps(vi, vi_max);
208
209 // Compute reduced argument elements := round(x / log(2)).
210 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
211
212 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
213 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
214 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
215
216 // Subtract the large number back to get final elements := round(x / log(2)).
217 vn = _mm256_sub_ps(vn, vmagic_bias);
218
219 // Compute reduced argument t := x - elements * log(2).
220 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
221 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
222 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
223
224 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
225 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
226 vp = _mm256_fmadd_ps(vp, vt, vc3);
227 vp = _mm256_fmadd_ps(vp, vt, vc2);
228 vp = _mm256_fmadd_ps(vp, vt, vc1);
229
230 // Reconstruct the final f value:
231 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
232 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
233 // = s + (t * s) * p
234 vt = _mm256_mul_ps(vt, vs);
235 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
236
237 // For inputs below zero cutoff, replace output with +0.0f.
238 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
239 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
240
241 // Accumulate computed exponents.
242 vacc = _mm256_add_ps(vacc, vf);
243 }
244 if (elements != 0) {
245 assert(elements >= 1 * sizeof(float));
246 assert(elements <= 7 * sizeof(float));
247 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
248
249 // Load up to 7 inputs at a time.
250 const __m256 vi = _mm256_maskload_ps(input, vmask);
251
252 // Subtract maximum input x := i - i_max. This implies x <= 0.
253 const __m256 vx = _mm256_sub_ps(vi, vi_max);
254
255 // Compute reduced argument elements := round(x / log(2)).
256 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
257
258 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
259 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
260 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
261
262 // Subtract the large number back to get final elements := round(x / log(2)).
263 vn = _mm256_sub_ps(vn, vmagic_bias);
264
265 // Compute reduced argument t := x - elements * log(2).
266 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
267 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
268 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
269
270 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
271 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
272 vp = _mm256_fmadd_ps(vp, vt, vc3);
273 vp = _mm256_fmadd_ps(vp, vt, vc2);
274 vp = _mm256_fmadd_ps(vp, vt, vc1);
275
276 // Reconstruct the final f value:
277 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
278 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
279 // = s + (t * s) * p
280 vt = _mm256_mul_ps(vt, vs);
281 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
282
283 // For inputs below zero cutoff, replace output with +0.0f.
284 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
285 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
286
287 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
288 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
289 }
290 // Reduce 8 elements in the SIMD register
291 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
292 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
293 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
294 _mm_store_ss(sum, vacc_lo);
295 _mm256_zeroupper();
296 }
297