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_x72(size_t elements,const float * x,float * y,float scale_value,float scale_exp)20 void xnn_f32_vscaleextexp_ukernel__avx2_p5_x72(
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 >= 72 * sizeof(float); elements -= 72 * sizeof(float)) {
49 // Load 72 (9x8) 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 const __m256 vx8 = _mm256_loadu_ps(x + 64);
59 x += 72;
60
61 // Compute reduced argument elements := round(x / log(2)).
62 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
63 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
64 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70 const __m256 vn8 = _mm256_round_ps(_mm256_mul_ps(vx8, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71
72 // Compute reduced argument t := x - elements * log(2).
73 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
74 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
75 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
76 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
77 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
78 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
79 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
80 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
81 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
82 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
83
84 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
85 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
86 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
87 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
88 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
89 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
90 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
91 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
92 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
93
94 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
95 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
96 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
97 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
98 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
99 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
100 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
101 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
102 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
103 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
104
105 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
106 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
107 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
108 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
109 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
110 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
111 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
112 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
113 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
114
115 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
116 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
117 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
118 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
119 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
120 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
121 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
122 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
123 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
124
125 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
126 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
127 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
128 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
129 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
130 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
131 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
132 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
133 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
134
135 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
136 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
137 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
138 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
139 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
140 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
141 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
142 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
143 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
144
145 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation where
146 // - vnX is "exponent"
147 // - vpX is "mantissa"
148 //
149 // exp2(ae) * av * exp2(be) * bv =
150 // = exp2(ae + be) * (av * bv)
151 __m256 vf0 = _mm256_mul_ps(vp0, vscalev);
152 __m256 vf1 = _mm256_mul_ps(vp1, vscalev);
153 __m256 vf2 = _mm256_mul_ps(vp2, vscalev);
154 __m256 vf3 = _mm256_mul_ps(vp3, vscalev);
155 __m256 vf4 = _mm256_mul_ps(vp4, vscalev);
156 __m256 vf5 = _mm256_mul_ps(vp5, vscalev);
157 __m256 vf6 = _mm256_mul_ps(vp6, vscalev);
158 __m256 vf7 = _mm256_mul_ps(vp7, vscalev);
159 __m256 vf8 = _mm256_mul_ps(vp8, vscalev);
160
161 __m256 ve0 = _mm256_add_ps(vn0, vscalee);
162 __m256 ve1 = _mm256_add_ps(vn1, vscalee);
163 __m256 ve2 = _mm256_add_ps(vn2, vscalee);
164 __m256 ve3 = _mm256_add_ps(vn3, vscalee);
165 __m256 ve4 = _mm256_add_ps(vn4, vscalee);
166 __m256 ve5 = _mm256_add_ps(vn5, vscalee);
167 __m256 ve6 = _mm256_add_ps(vn6, vscalee);
168 __m256 ve7 = _mm256_add_ps(vn7, vscalee);
169 __m256 ve8 = _mm256_add_ps(vn8, vscalee);
170
171 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
172 // This replacement is done in two steps:
173 // 1. Clamp minimum e at -127.0.
174 // 2. Map e to scale factor 0.0 when e == -127.0
175 ve0 = _mm256_max_ps(ve0, vmin_exponent);
176 ve1 = _mm256_max_ps(ve1, vmin_exponent);
177 ve2 = _mm256_max_ps(ve2, vmin_exponent);
178 ve3 = _mm256_max_ps(ve3, vmin_exponent);
179 ve4 = _mm256_max_ps(ve4, vmin_exponent);
180 ve5 = _mm256_max_ps(ve5, vmin_exponent);
181 ve6 = _mm256_max_ps(ve6, vmin_exponent);
182 ve7 = _mm256_max_ps(ve7, vmin_exponent);
183 ve8 = _mm256_max_ps(ve8, vmin_exponent);
184
185 // Convert exponents into scale factors:
186 // - s = exp2(e) when e > -127.0
187 // - s = 0.0 when e <= -127.0
188 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve0, vmagic_bias)), 23));
189 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve1, vmagic_bias)), 23));
190 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve2, vmagic_bias)), 23));
191 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve3, vmagic_bias)), 23));
192 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve4, vmagic_bias)), 23));
193 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve5, vmagic_bias)), 23));
194 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve6, vmagic_bias)), 23));
195 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve7, vmagic_bias)), 23));
196 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve8, vmagic_bias)), 23));
197
198 // Multiply "mantissa" by the scale factor.
199 vf0 = _mm256_mul_ps(vf0, vs0);
200 vf1 = _mm256_mul_ps(vf1, vs1);
201 vf2 = _mm256_mul_ps(vf2, vs2);
202 vf3 = _mm256_mul_ps(vf3, vs3);
203 vf4 = _mm256_mul_ps(vf4, vs4);
204 vf5 = _mm256_mul_ps(vf5, vs5);
205 vf6 = _mm256_mul_ps(vf6, vs6);
206 vf7 = _mm256_mul_ps(vf7, vs7);
207 vf8 = _mm256_mul_ps(vf8, vs8);
208
209 // Store 72 (9x8) outputs at a time.
210 _mm256_storeu_ps(y, vf0);
211 _mm256_storeu_ps(y + 8, vf1);
212 _mm256_storeu_ps(y + 16, vf2);
213 _mm256_storeu_ps(y + 24, vf3);
214 _mm256_storeu_ps(y + 32, vf4);
215 _mm256_storeu_ps(y + 40, vf5);
216 _mm256_storeu_ps(y + 48, vf6);
217 _mm256_storeu_ps(y + 56, vf7);
218 _mm256_storeu_ps(y + 64, vf8);
219 y += 72;
220 }
221
222 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
223 // Load 8 inputs at a time.
224 const __m256 vx = _mm256_loadu_ps(x);
225 x += 8;
226
227 // Compute reduced argument elements := round(x / log(2)).
228 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
229
230 // Compute reduced argument t := x - elements * log(2).
231 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
232 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
233 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
234
235 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
236 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
237 vp = _mm256_fmadd_ps(vp, vt, vc3);
238 vp = _mm256_fmadd_ps(vp, vt, vc2);
239 vp = _mm256_fmadd_ps(vp, vt, vc1);
240 vp = _mm256_fmadd_ps(vp, vt, vc0);
241
242 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
243 __m256 vf = _mm256_mul_ps(vp, vscalev);
244 __m256 ve = _mm256_add_ps(vn, vscalee);
245
246 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
247 ve = _mm256_max_ps(ve, vmin_exponent);
248
249 // Convert exponents into scale factors.
250 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
251
252 // Multiply "mantissa" by the scale factor.
253 vf = _mm256_mul_ps(vf, vs);
254
255 // Store 8 results at a time.
256 _mm256_storeu_ps(y, vf);
257 y += 8;
258 }
259 if XNN_UNLIKELY(elements != 0) {
260 assert(elements >= 1 * sizeof(float));
261 assert(elements <= 7 * sizeof(float));
262 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
263
264 // Load up to 7 inputs at a time.
265 const __m256 vx = _mm256_maskload_ps(x, vmask);
266
267 // Compute reduced argument elements := round(x / log(2)).
268 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
269
270 // Compute reduced argument t := x - elements * log(2).
271 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
272 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
273 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
274
275 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
276 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
277 vp = _mm256_fmadd_ps(vp, vt, vc3);
278 vp = _mm256_fmadd_ps(vp, vt, vc2);
279 vp = _mm256_fmadd_ps(vp, vt, vc1);
280 vp = _mm256_fmadd_ps(vp, vt, vc0);
281
282 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
283 __m256 vf = _mm256_mul_ps(vp, vscalev);
284 __m256 ve = _mm256_add_ps(vn, vscalee);
285
286 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
287 ve = _mm256_max_ps(ve, vmin_exponent);
288
289 // Convert exponents into scale factors.
290 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
291
292 // Multiply "mantissa" by the scale factor.
293 vf = _mm256_mul_ps(vf, vs);
294
295 // Store up to 7 inputs at a time.
296 _mm256_maskstore_ps(y, vmask, vf);
297 }
298 _mm256_zeroupper();
299 }
300