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_x32(size_t elements,const float * input,float * output,float scale,float max)20 void xnn_f32_vscaleexpminusmax_ukernel__avx2_p5_x32(
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 >= 32 * sizeof(float); elements -= 32 * sizeof(float)) {
46 // Load 32 (4x8) 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 input += 32;
52
53 // Subtract maximum input x := i - i_max. This implies x <= 0.
54 const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
55 const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
56 const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
57 const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
58
59 // Compute reduced argument elements := round(x / log(2)).
60 __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
61 __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
62 __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
63 __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
64
65 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
66 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
67 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
68 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
69 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
70 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
71
72 // Subtract the large number back to get final elements := round(x / log(2)).
73 vn0 = _mm256_sub_ps(vn0, vmagic_bias);
74 vn1 = _mm256_sub_ps(vn1, vmagic_bias);
75 vn2 = _mm256_sub_ps(vn2, vmagic_bias);
76 vn3 = _mm256_sub_ps(vn3, vmagic_bias);
77
78 // Compute reduced argument t := x - elements * log(2).
79 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
80 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
81 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
82 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
83 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
84
85 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
86 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
87 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
88 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
89
90 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
91 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
92 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
93 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
94 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
95
96 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
97 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
98 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
99 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
100
101 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
102 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
103 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
104 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
105
106 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
107 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
108 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
109 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
110
111 // Reconstruct the final f value:
112 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
113 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
114 // = s + (t * s) * p
115 vt0 = _mm256_mul_ps(vt0, vs0);
116 vt1 = _mm256_mul_ps(vt1, vs1);
117 vt2 = _mm256_mul_ps(vt2, vs2);
118 vt3 = _mm256_mul_ps(vt3, vs3);
119
120 __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
121 __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
122 __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
123 __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
124
125 // For inputs below zero cutoff, replace output with +0.0f.
126 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
127 vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
128 vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
129 vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
130 vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
131
132 // Multiply by scale.
133 vf0 = _mm256_mul_ps(vf0, vscale);
134 vf1 = _mm256_mul_ps(vf1, vscale);
135 vf2 = _mm256_mul_ps(vf2, vscale);
136 vf3 = _mm256_mul_ps(vf3, vscale);
137
138 // Store 32 (4x8) outputs at a time.
139 _mm256_storeu_ps(output, vf0);
140 _mm256_storeu_ps(output + 8, vf1);
141 _mm256_storeu_ps(output + 16, vf2);
142 _mm256_storeu_ps(output + 24, vf3);
143 output += 32;
144 }
145 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
146 // Load 8 inputs at a time.
147 const __m256 vi = _mm256_loadu_ps(input);
148 input += 8;
149
150 // Subtract maximum input x := i - i_max. This implies x <= 0.
151 const __m256 vx = _mm256_sub_ps(vi, vi_max);
152
153 // Compute reduced argument elements := round(x / log(2)).
154 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
155
156 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
157 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
158 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
159
160 // Subtract the large number back to get final elements := round(x / log(2)).
161 vn = _mm256_sub_ps(vn, vmagic_bias);
162
163 // Compute reduced argument t := x - elements * log(2).
164 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
165 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
166 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
167
168 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
169 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
170 vp = _mm256_fmadd_ps(vp, vt, vc3);
171 vp = _mm256_fmadd_ps(vp, vt, vc2);
172 vp = _mm256_fmadd_ps(vp, vt, vc1);
173
174 // Reconstruct the final f value:
175 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
176 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
177 // = s + (t * s) * p
178 vt = _mm256_mul_ps(vt, vs);
179 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
180
181 // For inputs below zero cutoff, replace output with +0.0f.
182 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
183 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
184
185 // Multiply by scale.
186 vf = _mm256_mul_ps(vf, vscale);
187
188 // Store 64 (8x8) outputs at a time.
189 _mm256_storeu_ps(output, vf);
190 output += 8;
191 }
192 if (elements != 0) {
193 assert(elements >= 1 * sizeof(float));
194 assert(elements <= 7 * sizeof(float));
195 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
196
197 // Load up to 7 inputs at a time.
198 const __m256 vi = _mm256_maskload_ps(input, vmask);
199
200 // Subtract maximum input x := i - i_max. This implies x <= 0.
201 const __m256 vx = _mm256_sub_ps(vi, vi_max);
202
203 // Compute reduced argument elements := round(x / log(2)).
204 __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
205
206 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
207 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
208 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
209
210 // Subtract the large number back to get final elements := round(x / log(2)).
211 vn = _mm256_sub_ps(vn, vmagic_bias);
212
213 // Compute reduced argument t := x - elements * log(2).
214 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
215 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
216 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
217
218 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
219 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
220 vp = _mm256_fmadd_ps(vp, vt, vc3);
221 vp = _mm256_fmadd_ps(vp, vt, vc2);
222 vp = _mm256_fmadd_ps(vp, vt, vc1);
223
224 // Reconstruct the final f value:
225 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
226 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
227 // = s + (t * s) * p
228 vt = _mm256_mul_ps(vt, vs);
229 __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
230
231 // For inputs below zero cutoff, replace output with +0.0f.
232 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
233 vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
234
235 // Multiply by scale.
236 vf = _mm256_mul_ps(vf, vscale);
237
238 // Store up to 7 outputs at a time.
239 _mm256_maskstore_ps(output, vmask, vf);
240 }
241 }
242