1 // Auto-generated file. Do not edit!
2 // Template: src/f32-vscaleexpminusmax/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/common.h>
15 #include <xnnpack/vscaleexpminusmax.h>
16
17
18 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
19
xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x56(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x56(
21 size_t elements,
22 const float* input,
23 float* output,
24 float scale,
25 float max)
26 {
27 assert(elements % sizeof(float) == 0);
28
29 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
30 // The smallest x for which expf(x) is normalized.
31 const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
32 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
33 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
34 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
35
36 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
37 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
38 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
39 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
40 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
41
42 const __m256 vscale = _mm256_set1_ps(scale);
43 const __m256 vi_max = _mm256_set1_ps(max);
44
45 for (; elements >= 56 * sizeof(float); elements -= 56 * sizeof(float)) {
46 // Load 56 (7x8) 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 input += 56;
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
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
74 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
75 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
76 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
77 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
78 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
79 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
80 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
81 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
82 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
83
84 // Subtract the large number back to get final elements := round(x / log(2)).
85 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
86 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
87 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
88 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
89 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
90 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
91 vn6 = _mm256_sub_ps(vn6, vmagic_bias);
92
93 // Compute reduced argument t := x - elements * log(2).
94 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
95 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
96 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
97 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
98 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
99 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
100 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
101 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
102
103 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
104 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
105 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
106 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
107 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
108 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
109 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
110
111 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
112 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
113 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
114 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
115 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
116 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
117 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
118 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
119
120 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
121 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
122 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
123 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
124 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
125 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
126 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
127
128 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
129 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
130 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
131 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
132 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
133 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
134 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
135
136 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
137 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
138 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
139 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
140 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
141 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
142 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
143
144 // Reconstruct the final f value:
145 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
146 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
147 // = s + (t * s) * p
148 vt0 = _mm256_mul_ps(vt0, vs0);
149 vt1 = _mm256_mul_ps(vt1, vs1);
150 vt2 = _mm256_mul_ps(vt2, vs2);
151 vt3 = _mm256_mul_ps(vt3, vs3);
152 vt4 = _mm256_mul_ps(vt4, vs4);
153 vt5 = _mm256_mul_ps(vt5, vs5);
154 vt6 = _mm256_mul_ps(vt6, vs6);
155
156 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
157 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
158 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
159 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
160 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
161 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
162 __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
163
164 // For inputs below zero cutoff, replace output with +0.0f.
165 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
166 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
167 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
168 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
169 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
170 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
171 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
172 vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
173
174 // Multiply by scale.
175 vf0 = _mm256_mul_ps(vf0, vscale);
176 vf1 = _mm256_mul_ps(vf1, vscale);
177 vf2 = _mm256_mul_ps(vf2, vscale);
178 vf3 = _mm256_mul_ps(vf3, vscale);
179 vf4 = _mm256_mul_ps(vf4, vscale);
180 vf5 = _mm256_mul_ps(vf5, vscale);
181 vf6 = _mm256_mul_ps(vf6, vscale);
182
183 // Store 56 (7x8) outputs at a time.
184 _mm256_storeu_ps(output, vf0);
185 _mm256_storeu_ps(output + 8, vf1);
186 _mm256_storeu_ps(output + 16, vf2);
187 _mm256_storeu_ps(output + 24, vf3);
188 _mm256_storeu_ps(output + 32, vf4);
189 _mm256_storeu_ps(output + 40, vf5);
190 _mm256_storeu_ps(output + 48, vf6);
191 output += 56;
192 }
193 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
194 // Load 8 inputs at a time.
195 const __m256 vi = _mm256_loadu_ps(input);
196 input += 8;
197
198 // Subtract maximum input x := i - i_max. This implies x <= 0.
199 const __m256 vx = _mm256_sub_ps(vi, vi_max);
200
201 // Compute reduced argument elements := round(x / log(2)).
202 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
203
204 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
205 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
206 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
207
208 // Subtract the large number back to get final elements := round(x / log(2)).
209 vn = _mm256_sub_ps(vn, vmagic_bias);
210
211 // Compute reduced argument t := x - elements * log(2).
212 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
213 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
214 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
215
216 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
217 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
218 vp = _mm256_fmadd_ps(vp, vt, vc3);
219 vp = _mm256_fmadd_ps(vp, vt, vc2);
220 vp = _mm256_fmadd_ps(vp, vt, vc1);
221
222 // Reconstruct the final f value:
223 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
224 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
225 // = s + (t * s) * p
226 vt = _mm256_mul_ps(vt, vs);
227 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
228
229 // For inputs below zero cutoff, replace output with +0.0f.
230 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
231 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
232
233 // Multiply by scale.
234 vf = _mm256_mul_ps(vf, vscale);
235
236 // Store 64 (8x8) outputs at a time.
237 _mm256_storeu_ps(output, vf);
238 output += 8;
239 }
240 if (elements != 0) {
241 assert(elements >= 1 * sizeof(float));
242 assert(elements <= 7 * sizeof(float));
243 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
244
245 // Load up to 7 inputs at a time.
246 const __m256 vi = _mm256_maskload_ps(input, vmask);
247
248 // Subtract maximum input x := i - i_max. This implies x <= 0.
249 const __m256 vx = _mm256_sub_ps(vi, vi_max);
250
251 // Compute reduced argument elements := round(x / log(2)).
252 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
253
254 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
255 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
256 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
257
258 // Subtract the large number back to get final elements := round(x / log(2)).
259 vn = _mm256_sub_ps(vn, vmagic_bias);
260
261 // Compute reduced argument t := x - elements * log(2).
262 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
263 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
264 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
265
266 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
267 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
268 vp = _mm256_fmadd_ps(vp, vt, vc3);
269 vp = _mm256_fmadd_ps(vp, vt, vc2);
270 vp = _mm256_fmadd_ps(vp, vt, vc1);
271
272 // Reconstruct the final f value:
273 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
274 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
275 // = s + (t * s) * p
276 vt = _mm256_mul_ps(vt, vs);
277 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
278
279 // For inputs below zero cutoff, replace output with +0.0f.
280 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
281 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
282
283 // Multiply by scale.
284 vf = _mm256_mul_ps(vf, vscale);
285
286 // Store up to 7 outputs at a time.
287 _mm256_maskstore_ps(output, vmask, vf);
288 }
289 }
290