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(size_t elements,const float * input,float * sum,float max)19 void xnn_f32_raddexpminusmax_ukernel__avx2_p5_x64(
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 for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
44 // Load 64 (8x8) inputs at a time.
45 const __m256 vi0 = _mm256_loadu_ps(input);
46 const __m256 vi1 = _mm256_loadu_ps(input + 8);
47 const __m256 vi2 = _mm256_loadu_ps(input + 16);
48 const __m256 vi3 = _mm256_loadu_ps(input + 24);
49 const __m256 vi4 = _mm256_loadu_ps(input + 32);
50 const __m256 vi5 = _mm256_loadu_ps(input + 40);
51 const __m256 vi6 = _mm256_loadu_ps(input + 48);
52 const __m256 vi7 = _mm256_loadu_ps(input + 56);
53 input += 64;
54
55 // Subtract maximum input x := i - i_max. This implies x <= 0.
56 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
57 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
58 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
59 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
60 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
61 const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
62 const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
63 const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
64
65 // Compute reduced argument elements := round(x / log(2)).
66 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
67 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
68 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
69 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
70 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
71 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
72 __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
73 __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
74
75 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
76 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
77 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
78 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
79 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
80 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
81 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
82 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
83 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
84 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
85
86 // Subtract the large number back to get final elements := round(x / log(2)).
87 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
88 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
89 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
90 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
91 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
92 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
93 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
94 vn7 = _mm256_sub_ps(vn7, vmagic_bias);
95
96 // Compute reduced argument t := x - elements * log(2).
97 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
98 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
99 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
100 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
101 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
102 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
103 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
104 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
105 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
106
107 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
108 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
109 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
110 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
111 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
112 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
113 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
114 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
115
116 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
117 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
118 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
119 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
120 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
121 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
122 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
123 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
124 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
125
126 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
127 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
128 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
129 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
130 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
131 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
132 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
133 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
134
135 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
136 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
137 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
138 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
139 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
140 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
141 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
142 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
143
144 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
145 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
146 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
147 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
148 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
149 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
150 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
151 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
152
153 // Reconstruct the final f value:
154 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
155 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
156 // = s + (t * s) * p
157 vt0 = _mm256_mul_ps(vt0, vs0);
158 vt1 = _mm256_mul_ps(vt1, vs1);
159 vt2 = _mm256_mul_ps(vt2, vs2);
160 vt3 = _mm256_mul_ps(vt3, vs3);
161 vt4 = _mm256_mul_ps(vt4, vs4);
162 vt5 = _mm256_mul_ps(vt5, vs5);
163 vt6 = _mm256_mul_ps(vt6, vs6);
164 vt7 = _mm256_mul_ps(vt7, vs7);
165
166 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
167 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
168 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
169 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
170 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
171 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
172 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
173 __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
174
175 // For inputs below zero cutoff, replace output with +0.0f.
176 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
177 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
178 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
179 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
180 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
181 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
182 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
183 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
184 vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
185
186 // Accumulate computed exponents.
187 vacc0 = _mm256_add_ps(vacc0, vf0);
188 vacc0 = _mm256_add_ps(vacc0, vf1);
189 vacc0 = _mm256_add_ps(vacc0, vf2);
190 vacc0 = _mm256_add_ps(vacc0, vf3);
191 vacc0 = _mm256_add_ps(vacc0, vf4);
192 vacc0 = _mm256_add_ps(vacc0, vf5);
193 vacc0 = _mm256_add_ps(vacc0, vf6);
194 vacc0 = _mm256_add_ps(vacc0, vf7);
195 }
196
197 __m256 vacc = vacc0;
198 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
199 // Load 8 inputs at a time.
200 const __m256 vi = _mm256_loadu_ps(input);
201 input += 8;
202
203 // Subtract maximum input x := i - i_max. This implies x <= 0.
204 const __m256 vx = _mm256_sub_ps(vi, vi_max);
205
206 // Compute reduced argument elements := round(x / log(2)).
207 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
208
209 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
210 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
211 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
212
213 // Subtract the large number back to get final elements := round(x / log(2)).
214 vn = _mm256_sub_ps(vn, vmagic_bias);
215
216 // Compute reduced argument t := x - elements * log(2).
217 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
218 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
219 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
220
221 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
222 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
223 vp = _mm256_fmadd_ps(vp, vt, vc3);
224 vp = _mm256_fmadd_ps(vp, vt, vc2);
225 vp = _mm256_fmadd_ps(vp, vt, vc1);
226
227 // Reconstruct the final f value:
228 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
229 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
230 // = s + (t * s) * p
231 vt = _mm256_mul_ps(vt, vs);
232 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
233
234 // For inputs below zero cutoff, replace output with +0.0f.
235 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
236 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
237
238 // Accumulate computed exponents.
239 vacc = _mm256_add_ps(vacc, vf);
240 }
241 if (elements != 0) {
242 assert(elements >= 1 * sizeof(float));
243 assert(elements <= 7 * sizeof(float));
244 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
245
246 // Load up to 7 inputs at a time.
247 const __m256 vi = _mm256_maskload_ps(input, vmask);
248
249 // Subtract maximum input x := i - i_max. This implies x <= 0.
250 const __m256 vx = _mm256_sub_ps(vi, vi_max);
251
252 // Compute reduced argument elements := round(x / log(2)).
253 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
254
255 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
256 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
257 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
258
259 // Subtract the large number back to get final elements := round(x / log(2)).
260 vn = _mm256_sub_ps(vn, vmagic_bias);
261
262 // Compute reduced argument t := x - elements * log(2).
263 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
264 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
265 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
266
267 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
268 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
269 vp = _mm256_fmadd_ps(vp, vt, vc3);
270 vp = _mm256_fmadd_ps(vp, vt, vc2);
271 vp = _mm256_fmadd_ps(vp, vt, vc1);
272
273 // Reconstruct the final f value:
274 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
275 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
276 // = s + (t * s) * p
277 vt = _mm256_mul_ps(vt, vs);
278 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
279
280 // For inputs below zero cutoff, replace output with +0.0f.
281 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
282 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
283
284 // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
285 vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
286 }
287 // Reduce 8 elements in the SIMD register
288 __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
289 vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
290 vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
291 _mm_store_ss(sum, vacc_lo);
292 _mm256_zeroupper();
293 }
294