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_x48(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x48(
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 >= 48 * sizeof(float); elements -= 48 * sizeof(float)) {
46 // Load 48 (6x8) 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 input += 48;
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
63 // Compute reduced argument elements := round(x / log(2)).
64 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
65 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
66 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
67 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
68 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
69 __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
70
71 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
72 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
73 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
74 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
75 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
76 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
77 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
78 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
79
80 // Subtract the large number back to get final elements := round(x / log(2)).
81 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
82 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
83 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
84 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
85 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
86 vn5 = _mm256_sub_ps(vn5, vmagic_bias);
87
88 // Compute reduced argument t := x - elements * log(2).
89 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
90 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
91 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
92 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
93 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
94 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
95 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
96
97 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
98 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
99 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
100 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
101 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
102 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
103
104 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
105 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
106 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
107 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
108 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
109 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
110 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
111
112 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
113 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
114 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
115 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
116 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
117 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
118
119 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
120 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
121 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
122 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
123 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
124 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
125
126 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
127 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
128 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
129 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
130 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
131 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
132
133 // Reconstruct the final f value:
134 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
135 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
136 // = s + (t * s) * p
137 vt0 = _mm256_mul_ps(vt0, vs0);
138 vt1 = _mm256_mul_ps(vt1, vs1);
139 vt2 = _mm256_mul_ps(vt2, vs2);
140 vt3 = _mm256_mul_ps(vt3, vs3);
141 vt4 = _mm256_mul_ps(vt4, vs4);
142 vt5 = _mm256_mul_ps(vt5, vs5);
143
144 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
145 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
146 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
147 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
148 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
149 __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
150
151 // For inputs below zero cutoff, replace output with +0.0f.
152 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
153 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
154 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
155 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
156 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
157 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
158 vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
159
160 // Multiply by scale.
161 vf0 = _mm256_mul_ps(vf0, vscale);
162 vf1 = _mm256_mul_ps(vf1, vscale);
163 vf2 = _mm256_mul_ps(vf2, vscale);
164 vf3 = _mm256_mul_ps(vf3, vscale);
165 vf4 = _mm256_mul_ps(vf4, vscale);
166 vf5 = _mm256_mul_ps(vf5, vscale);
167
168 // Store 48 (6x8) outputs at a time.
169 _mm256_storeu_ps(output, vf0);
170 _mm256_storeu_ps(output + 8, vf1);
171 _mm256_storeu_ps(output + 16, vf2);
172 _mm256_storeu_ps(output + 24, vf3);
173 _mm256_storeu_ps(output + 32, vf4);
174 _mm256_storeu_ps(output + 40, vf5);
175 output += 48;
176 }
177 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
178 // Load 8 inputs at a time.
179 const __m256 vi = _mm256_loadu_ps(input);
180 input += 8;
181
182 // Subtract maximum input x := i - i_max. This implies x <= 0.
183 const __m256 vx = _mm256_sub_ps(vi, vi_max);
184
185 // Compute reduced argument elements := round(x / log(2)).
186 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
187
188 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
189 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
190 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
191
192 // Subtract the large number back to get final elements := round(x / log(2)).
193 vn = _mm256_sub_ps(vn, vmagic_bias);
194
195 // Compute reduced argument t := x - elements * log(2).
196 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
197 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
198 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
199
200 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
201 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
202 vp = _mm256_fmadd_ps(vp, vt, vc3);
203 vp = _mm256_fmadd_ps(vp, vt, vc2);
204 vp = _mm256_fmadd_ps(vp, vt, vc1);
205
206 // Reconstruct the final f value:
207 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
208 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
209 // = s + (t * s) * p
210 vt = _mm256_mul_ps(vt, vs);
211 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
212
213 // For inputs below zero cutoff, replace output with +0.0f.
214 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
215 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
216
217 // Multiply by scale.
218 vf = _mm256_mul_ps(vf, vscale);
219
220 // Store 64 (8x8) outputs at a time.
221 _mm256_storeu_ps(output, vf);
222 output += 8;
223 }
224 if (elements != 0) {
225 assert(elements >= 1 * sizeof(float));
226 assert(elements <= 7 * sizeof(float));
227 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
228
229 // Load up to 7 inputs at a time.
230 const __m256 vi = _mm256_maskload_ps(input, vmask);
231
232 // Subtract maximum input x := i - i_max. This implies x <= 0.
233 const __m256 vx = _mm256_sub_ps(vi, vi_max);
234
235 // Compute reduced argument elements := round(x / log(2)).
236 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
237
238 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
239 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
240 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
241
242 // Subtract the large number back to get final elements := round(x / log(2)).
243 vn = _mm256_sub_ps(vn, vmagic_bias);
244
245 // Compute reduced argument t := x - elements * log(2).
246 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
247 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
248 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
249
250 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
251 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
252 vp = _mm256_fmadd_ps(vp, vt, vc3);
253 vp = _mm256_fmadd_ps(vp, vt, vc2);
254 vp = _mm256_fmadd_ps(vp, vt, vc1);
255
256 // Reconstruct the final f value:
257 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
258 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
259 // = s + (t * s) * p
260 vt = _mm256_mul_ps(vt, vs);
261 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
262
263 // For inputs below zero cutoff, replace output with +0.0f.
264 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
265 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
266
267 // Multiply by scale.
268 vf = _mm256_mul_ps(vf, vscale);
269
270 // Store up to 7 outputs at a time.
271 _mm256_maskstore_ps(output, vmask, vf);
272 }
273 }
274