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_x40(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x40(
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 >= 40 * sizeof(float); elements -= 40 * sizeof(float)) {
46 // Load 40 (5x8) 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 input += 40;
53
54 // Subtract maximum input x := i - i_max. This implies x <= 0.
55 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
56 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
57 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
58 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
59 const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
60
61 // Compute reduced argument elements := round(x / log(2)).
62 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
63 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
64 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
65 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
66 __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
67
68 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
69 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
70 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
71 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
72 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
73 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
74 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
75
76 // Subtract the large number back to get final elements := round(x / log(2)).
77 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
78 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
79 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
80 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
81 vn4 = _mm256_sub_ps(vn4, vmagic_bias);
82
83 // Compute reduced argument t := x - elements * log(2).
84 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
85 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
86 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
87 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
88 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
89 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
90
91 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
92 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
93 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
94 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
95 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
96
97 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
98 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
99 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
100 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
101 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
102 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
103
104 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
105 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
106 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
107 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
108 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
109
110 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
111 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
112 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
113 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
114 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
115
116 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
117 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
118 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
119 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
120 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
121
122 // Reconstruct the final f value:
123 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
124 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
125 // = s + (t * s) * p
126 vt0 = _mm256_mul_ps(vt0, vs0);
127 vt1 = _mm256_mul_ps(vt1, vs1);
128 vt2 = _mm256_mul_ps(vt2, vs2);
129 vt3 = _mm256_mul_ps(vt3, vs3);
130 vt4 = _mm256_mul_ps(vt4, vs4);
131
132 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
133 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
134 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
135 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
136 __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
137
138 // For inputs below zero cutoff, replace output with +0.0f.
139 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
140 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
141 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
142 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
143 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
144 vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
145
146 // Multiply by scale.
147 vf0 = _mm256_mul_ps(vf0, vscale);
148 vf1 = _mm256_mul_ps(vf1, vscale);
149 vf2 = _mm256_mul_ps(vf2, vscale);
150 vf3 = _mm256_mul_ps(vf3, vscale);
151 vf4 = _mm256_mul_ps(vf4, vscale);
152
153 // Store 40 (5x8) outputs at a time.
154 _mm256_storeu_ps(output, vf0);
155 _mm256_storeu_ps(output + 8, vf1);
156 _mm256_storeu_ps(output + 16, vf2);
157 _mm256_storeu_ps(output + 24, vf3);
158 _mm256_storeu_ps(output + 32, vf4);
159 output += 40;
160 }
161 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
162 // Load 8 inputs at a time.
163 const __m256 vi = _mm256_loadu_ps(input);
164 input += 8;
165
166 // Subtract maximum input x := i - i_max. This implies x <= 0.
167 const __m256 vx = _mm256_sub_ps(vi, vi_max);
168
169 // Compute reduced argument elements := round(x / log(2)).
170 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
171
172 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
173 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
174 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
175
176 // Subtract the large number back to get final elements := round(x / log(2)).
177 vn = _mm256_sub_ps(vn, vmagic_bias);
178
179 // Compute reduced argument t := x - elements * log(2).
180 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
181 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
182 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
183
184 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
185 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
186 vp = _mm256_fmadd_ps(vp, vt, vc3);
187 vp = _mm256_fmadd_ps(vp, vt, vc2);
188 vp = _mm256_fmadd_ps(vp, vt, vc1);
189
190 // Reconstruct the final f value:
191 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
192 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
193 // = s + (t * s) * p
194 vt = _mm256_mul_ps(vt, vs);
195 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
196
197 // For inputs below zero cutoff, replace output with +0.0f.
198 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
199 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
200
201 // Multiply by scale.
202 vf = _mm256_mul_ps(vf, vscale);
203
204 // Store 64 (8x8) outputs at a time.
205 _mm256_storeu_ps(output, vf);
206 output += 8;
207 }
208 if (elements != 0) {
209 assert(elements >= 1 * sizeof(float));
210 assert(elements <= 7 * sizeof(float));
211 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
212
213 // Load up to 7 inputs at a time.
214 const __m256 vi = _mm256_maskload_ps(input, vmask);
215
216 // Subtract maximum input x := i - i_max. This implies x <= 0.
217 const __m256 vx = _mm256_sub_ps(vi, vi_max);
218
219 // Compute reduced argument elements := round(x / log(2)).
220 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
221
222 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
223 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
224 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
225
226 // Subtract the large number back to get final elements := round(x / log(2)).
227 vn = _mm256_sub_ps(vn, vmagic_bias);
228
229 // Compute reduced argument t := x - elements * log(2).
230 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
231 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
232 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
233
234 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
235 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
236 vp = _mm256_fmadd_ps(vp, vt, vc3);
237 vp = _mm256_fmadd_ps(vp, vt, vc2);
238 vp = _mm256_fmadd_ps(vp, vt, vc1);
239
240 // Reconstruct the final f value:
241 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
242 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
243 // = s + (t * s) * p
244 vt = _mm256_mul_ps(vt, vs);
245 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
246
247 // For inputs below zero cutoff, replace output with +0.0f.
248 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
249 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
250
251 // Multiply by scale.
252 vf = _mm256_mul_ps(vf, vscale);
253
254 // Store up to 7 outputs at a time.
255 _mm256_maskstore_ps(output, vmask, vf);
256 }
257 }
258