1 // Auto-generated file. Do not edit!
2 // Template: src/f32-vscaleextexp/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/vscaleextexp.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_vscaleextexp_ukernel__avx2_p5_x64(size_t elements,const float * x,float * y,float scale_value,float scale_exp)20 void xnn_f32_vscaleextexp_ukernel__avx2_p5_x64(
21 size_t elements,
22 const float* x,
23 float* y,
24 float scale_value,
25 float scale_exp)
26 {
27 assert(elements % sizeof(float) == 0);
28
29 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
30 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
31 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
32
33 // The smallest elements such that 2**elements is considered non-negligible.
34 // For smaller elements, 2**elements is replaced with zero.
35 const __m256 vmin_exponent = _mm256_set1_ps(-127.0f);
36 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
37
38 const __m256 vc0 = _mm256_set1_ps(1.0f);
39 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
40 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
41 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
42 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
43 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
44
45 const __m256 vscalev = _mm256_set1_ps(scale_value);
46 const __m256 vscalee = _mm256_set1_ps(scale_exp);
47
48 for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
49 // Load 64 (8x8) inputs at a time.
50 const __m256 vx0 = _mm256_loadu_ps(x);
51 const __m256 vx1 = _mm256_loadu_ps(x + 8);
52 const __m256 vx2 = _mm256_loadu_ps(x + 16);
53 const __m256 vx3 = _mm256_loadu_ps(x + 24);
54 const __m256 vx4 = _mm256_loadu_ps(x + 32);
55 const __m256 vx5 = _mm256_loadu_ps(x + 40);
56 const __m256 vx6 = _mm256_loadu_ps(x + 48);
57 const __m256 vx7 = _mm256_loadu_ps(x + 56);
58 x += 64;
59
60 // Compute reduced argument elements := round(x / log(2)).
61 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
62 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
63 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
64 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69
70 // Compute reduced argument t := x - elements * log(2).
71 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
72 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
73 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
74 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
75 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
76 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
77 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
78 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
79 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
80
81 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
82 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
83 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
84 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
85 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
86 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
87 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
88 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
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 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
96 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
97 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
98 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
99
100 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
101 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
102 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
103 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
104 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
105 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
106 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
107 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
108
109 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
110 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
111 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
112 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
113 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
114 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
115 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
116 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
117
118 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
119 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
120 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
121 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
122 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
123 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
124 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
125 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
126
127 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
128 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
129 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
130 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
131 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
132 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
133 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
134 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
135
136 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation where
137 // - vnX is "exponent"
138 // - vpX is "mantissa"
139 //
140 // exp2(ae) * av * exp2(be) * bv =
141 // = exp2(ae + be) * (av * bv)
142 __m256 vf0 = _mm256_mul_ps(vp0, vscalev);
143 __m256 vf1 = _mm256_mul_ps(vp1, vscalev);
144 __m256 vf2 = _mm256_mul_ps(vp2, vscalev);
145 __m256 vf3 = _mm256_mul_ps(vp3, vscalev);
146 __m256 vf4 = _mm256_mul_ps(vp4, vscalev);
147 __m256 vf5 = _mm256_mul_ps(vp5, vscalev);
148 __m256 vf6 = _mm256_mul_ps(vp6, vscalev);
149 __m256 vf7 = _mm256_mul_ps(vp7, vscalev);
150
151 __m256 ve0 = _mm256_add_ps(vn0, vscalee);
152 __m256 ve1 = _mm256_add_ps(vn1, vscalee);
153 __m256 ve2 = _mm256_add_ps(vn2, vscalee);
154 __m256 ve3 = _mm256_add_ps(vn3, vscalee);
155 __m256 ve4 = _mm256_add_ps(vn4, vscalee);
156 __m256 ve5 = _mm256_add_ps(vn5, vscalee);
157 __m256 ve6 = _mm256_add_ps(vn6, vscalee);
158 __m256 ve7 = _mm256_add_ps(vn7, vscalee);
159
160 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
161 // This replacement is done in two steps:
162 // 1. Clamp minimum e at -127.0.
163 // 2. Map e to scale factor 0.0 when e == -127.0
164 ve0 = _mm256_max_ps(ve0, vmin_exponent);
165 ve1 = _mm256_max_ps(ve1, vmin_exponent);
166 ve2 = _mm256_max_ps(ve2, vmin_exponent);
167 ve3 = _mm256_max_ps(ve3, vmin_exponent);
168 ve4 = _mm256_max_ps(ve4, vmin_exponent);
169 ve5 = _mm256_max_ps(ve5, vmin_exponent);
170 ve6 = _mm256_max_ps(ve6, vmin_exponent);
171 ve7 = _mm256_max_ps(ve7, vmin_exponent);
172
173 // Convert exponents into scale factors:
174 // - s = exp2(e) when e > -127.0
175 // - s = 0.0 when e <= -127.0
176 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve0, vmagic_bias)), 23));
177 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve1, vmagic_bias)), 23));
178 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve2, vmagic_bias)), 23));
179 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve3, vmagic_bias)), 23));
180 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve4, vmagic_bias)), 23));
181 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve5, vmagic_bias)), 23));
182 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve6, vmagic_bias)), 23));
183 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve7, vmagic_bias)), 23));
184
185 // Multiply "mantissa" by the scale factor.
186 vf0 = _mm256_mul_ps(vf0, vs0);
187 vf1 = _mm256_mul_ps(vf1, vs1);
188 vf2 = _mm256_mul_ps(vf2, vs2);
189 vf3 = _mm256_mul_ps(vf3, vs3);
190 vf4 = _mm256_mul_ps(vf4, vs4);
191 vf5 = _mm256_mul_ps(vf5, vs5);
192 vf6 = _mm256_mul_ps(vf6, vs6);
193 vf7 = _mm256_mul_ps(vf7, vs7);
194
195 // Store 64 (8x8) outputs at a time.
196 _mm256_storeu_ps(y, vf0);
197 _mm256_storeu_ps(y + 8, vf1);
198 _mm256_storeu_ps(y + 16, vf2);
199 _mm256_storeu_ps(y + 24, vf3);
200 _mm256_storeu_ps(y + 32, vf4);
201 _mm256_storeu_ps(y + 40, vf5);
202 _mm256_storeu_ps(y + 48, vf6);
203 _mm256_storeu_ps(y + 56, vf7);
204 y += 64;
205 }
206
207 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
208 // Load 8 inputs at a time.
209 const __m256 vx = _mm256_loadu_ps(x);
210 x += 8;
211
212 // Compute reduced argument elements := round(x / log(2)).
213 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
214
215 // Compute reduced argument t := x - elements * log(2).
216 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
217 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
218 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
219
220 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
221 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
222 vp = _mm256_fmadd_ps(vp, vt, vc3);
223 vp = _mm256_fmadd_ps(vp, vt, vc2);
224 vp = _mm256_fmadd_ps(vp, vt, vc1);
225 vp = _mm256_fmadd_ps(vp, vt, vc0);
226
227 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
228 __m256 vf = _mm256_mul_ps(vp, vscalev);
229 __m256 ve = _mm256_add_ps(vn, vscalee);
230
231 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
232 ve = _mm256_max_ps(ve, vmin_exponent);
233
234 // Convert exponents into scale factors.
235 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
236
237 // Multiply "mantissa" by the scale factor.
238 vf = _mm256_mul_ps(vf, vs);
239
240 // Store 8 results at a time.
241 _mm256_storeu_ps(y, vf);
242 y += 8;
243 }
244 if XNN_UNLIKELY(elements != 0) {
245 assert(elements >= 1 * sizeof(float));
246 assert(elements <= 7 * sizeof(float));
247 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
248
249 // Load up to 7 inputs at a time.
250 const __m256 vx = _mm256_maskload_ps(x, vmask);
251
252 // Compute reduced argument elements := round(x / log(2)).
253 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
254
255 // Compute reduced argument t := x - elements * log(2).
256 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
257 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
258 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
259
260 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
261 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
262 vp = _mm256_fmadd_ps(vp, vt, vc3);
263 vp = _mm256_fmadd_ps(vp, vt, vc2);
264 vp = _mm256_fmadd_ps(vp, vt, vc1);
265 vp = _mm256_fmadd_ps(vp, vt, vc0);
266
267 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
268 __m256 vf = _mm256_mul_ps(vp, vscalev);
269 __m256 ve = _mm256_add_ps(vn, vscalee);
270
271 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
272 ve = _mm256_max_ps(ve, vmin_exponent);
273
274 // Convert exponents into scale factors.
275 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
276
277 // Multiply "mantissa" by the scale factor.
278 vf = _mm256_mul_ps(vf, vs);
279
280 // Store up to 7 inputs at a time.
281 _mm256_maskstore_ps(y, vmask, vf);
282 }
283 _mm256_zeroupper();
284 }
285