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_x88(size_t elements,const float * x,float * y,float scale_value,float scale_exp)20 void xnn_f32_vscaleextexp_ukernel__avx2_p5_x88(
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 >= 88 * sizeof(float); elements -= 88 * sizeof(float)) {
49 // Load 88 (11x8) 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 const __m256 vx9 = _mm256_loadu_ps(x + 72);
60 const __m256 vx10 = _mm256_loadu_ps(x + 80);
61 x += 88;
62
63 // Compute reduced argument elements := round(x / log(2)).
64 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
72 const __m256 vn8 = _mm256_round_ps(_mm256_mul_ps(vx8, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
73 const __m256 vn9 = _mm256_round_ps(_mm256_mul_ps(vx9, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
74 const __m256 vn10 = _mm256_round_ps(_mm256_mul_ps(vx10, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
75
76 // Compute reduced argument t := x - elements * log(2).
77 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
78 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
79 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
80 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
81 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
82 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
83 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
84 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
85 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
86 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
87 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
88 __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
89
90 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
91 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
92 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
93 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
94 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
95 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
96 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
97 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
98 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
99 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
100 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
101
102 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
103 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
104 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
105 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
106 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
107 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
108 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
109 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
110 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
111 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
112 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
113 __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
114
115 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
116 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
117 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
118 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
119 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
120 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
121 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
122 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
123 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
124 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
125 vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
126
127 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
128 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
129 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
130 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
131 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
132 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
133 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
134 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
135 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
136 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
137 vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
138
139 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
140 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
141 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
142 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
143 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
144 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
145 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
146 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
147 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
148 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
149 vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
150
151 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
152 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
153 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
154 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
155 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
156 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
157 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
158 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
159 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
160 vp9 = _mm256_fmadd_ps(vp9, vt9, vc0);
161 vp10 = _mm256_fmadd_ps(vp10, vt10, vc0);
162
163 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation where
164 // - vnX is "exponent"
165 // - vpX is "mantissa"
166 //
167 // exp2(ae) * av * exp2(be) * bv =
168 // = exp2(ae + be) * (av * bv)
169 __m256 vf0 = _mm256_mul_ps(vp0, vscalev);
170 __m256 vf1 = _mm256_mul_ps(vp1, vscalev);
171 __m256 vf2 = _mm256_mul_ps(vp2, vscalev);
172 __m256 vf3 = _mm256_mul_ps(vp3, vscalev);
173 __m256 vf4 = _mm256_mul_ps(vp4, vscalev);
174 __m256 vf5 = _mm256_mul_ps(vp5, vscalev);
175 __m256 vf6 = _mm256_mul_ps(vp6, vscalev);
176 __m256 vf7 = _mm256_mul_ps(vp7, vscalev);
177 __m256 vf8 = _mm256_mul_ps(vp8, vscalev);
178 __m256 vf9 = _mm256_mul_ps(vp9, vscalev);
179 __m256 vf10 = _mm256_mul_ps(vp10, vscalev);
180
181 __m256 ve0 = _mm256_add_ps(vn0, vscalee);
182 __m256 ve1 = _mm256_add_ps(vn1, vscalee);
183 __m256 ve2 = _mm256_add_ps(vn2, vscalee);
184 __m256 ve3 = _mm256_add_ps(vn3, vscalee);
185 __m256 ve4 = _mm256_add_ps(vn4, vscalee);
186 __m256 ve5 = _mm256_add_ps(vn5, vscalee);
187 __m256 ve6 = _mm256_add_ps(vn6, vscalee);
188 __m256 ve7 = _mm256_add_ps(vn7, vscalee);
189 __m256 ve8 = _mm256_add_ps(vn8, vscalee);
190 __m256 ve9 = _mm256_add_ps(vn9, vscalee);
191 __m256 ve10 = _mm256_add_ps(vn10, vscalee);
192
193 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
194 // This replacement is done in two steps:
195 // 1. Clamp minimum e at -127.0.
196 // 2. Map e to scale factor 0.0 when e == -127.0
197 ve0 = _mm256_max_ps(ve0, vmin_exponent);
198 ve1 = _mm256_max_ps(ve1, vmin_exponent);
199 ve2 = _mm256_max_ps(ve2, vmin_exponent);
200 ve3 = _mm256_max_ps(ve3, vmin_exponent);
201 ve4 = _mm256_max_ps(ve4, vmin_exponent);
202 ve5 = _mm256_max_ps(ve5, vmin_exponent);
203 ve6 = _mm256_max_ps(ve6, vmin_exponent);
204 ve7 = _mm256_max_ps(ve7, vmin_exponent);
205 ve8 = _mm256_max_ps(ve8, vmin_exponent);
206 ve9 = _mm256_max_ps(ve9, vmin_exponent);
207 ve10 = _mm256_max_ps(ve10, vmin_exponent);
208
209 // Convert exponents into scale factors:
210 // - s = exp2(e) when e > -127.0
211 // - s = 0.0 when e <= -127.0
212 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve0, vmagic_bias)), 23));
213 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve1, vmagic_bias)), 23));
214 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve2, vmagic_bias)), 23));
215 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve3, vmagic_bias)), 23));
216 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve4, vmagic_bias)), 23));
217 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve5, vmagic_bias)), 23));
218 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve6, vmagic_bias)), 23));
219 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve7, vmagic_bias)), 23));
220 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve8, vmagic_bias)), 23));
221 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve9, vmagic_bias)), 23));
222 const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve10, vmagic_bias)), 23));
223
224 // Multiply "mantissa" by the scale factor.
225 vf0 = _mm256_mul_ps(vf0, vs0);
226 vf1 = _mm256_mul_ps(vf1, vs1);
227 vf2 = _mm256_mul_ps(vf2, vs2);
228 vf3 = _mm256_mul_ps(vf3, vs3);
229 vf4 = _mm256_mul_ps(vf4, vs4);
230 vf5 = _mm256_mul_ps(vf5, vs5);
231 vf6 = _mm256_mul_ps(vf6, vs6);
232 vf7 = _mm256_mul_ps(vf7, vs7);
233 vf8 = _mm256_mul_ps(vf8, vs8);
234 vf9 = _mm256_mul_ps(vf9, vs9);
235 vf10 = _mm256_mul_ps(vf10, vs10);
236
237 // Store 88 (11x8) outputs at a time.
238 _mm256_storeu_ps(y, vf0);
239 _mm256_storeu_ps(y + 8, vf1);
240 _mm256_storeu_ps(y + 16, vf2);
241 _mm256_storeu_ps(y + 24, vf3);
242 _mm256_storeu_ps(y + 32, vf4);
243 _mm256_storeu_ps(y + 40, vf5);
244 _mm256_storeu_ps(y + 48, vf6);
245 _mm256_storeu_ps(y + 56, vf7);
246 _mm256_storeu_ps(y + 64, vf8);
247 _mm256_storeu_ps(y + 72, vf9);
248 _mm256_storeu_ps(y + 80, vf10);
249 y += 88;
250 }
251
252 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
253 // Load 8 inputs at a time.
254 const __m256 vx = _mm256_loadu_ps(x);
255 x += 8;
256
257 // Compute reduced argument elements := round(x / log(2)).
258 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
259
260 // Compute reduced argument t := x - elements * log(2).
261 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
262 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
263 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
264
265 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
266 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
267 vp = _mm256_fmadd_ps(vp, vt, vc3);
268 vp = _mm256_fmadd_ps(vp, vt, vc2);
269 vp = _mm256_fmadd_ps(vp, vt, vc1);
270 vp = _mm256_fmadd_ps(vp, vt, vc0);
271
272 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
273 __m256 vf = _mm256_mul_ps(vp, vscalev);
274 __m256 ve = _mm256_add_ps(vn, vscalee);
275
276 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
277 ve = _mm256_max_ps(ve, vmin_exponent);
278
279 // Convert exponents into scale factors.
280 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
281
282 // Multiply "mantissa" by the scale factor.
283 vf = _mm256_mul_ps(vf, vs);
284
285 // Store 8 results at a time.
286 _mm256_storeu_ps(y, vf);
287 y += 8;
288 }
289 if XNN_UNLIKELY(elements != 0) {
290 assert(elements >= 1 * sizeof(float));
291 assert(elements <= 7 * sizeof(float));
292 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
293
294 // Load up to 7 inputs at a time.
295 const __m256 vx = _mm256_maskload_ps(x, vmask);
296
297 // Compute reduced argument elements := round(x / log(2)).
298 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
299
300 // Compute reduced argument t := x - elements * log(2).
301 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
302 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
303 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
304
305 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
306 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
307 vp = _mm256_fmadd_ps(vp, vt, vc3);
308 vp = _mm256_fmadd_ps(vp, vt, vc2);
309 vp = _mm256_fmadd_ps(vp, vt, vc1);
310 vp = _mm256_fmadd_ps(vp, vt, vc0);
311
312 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
313 __m256 vf = _mm256_mul_ps(vp, vscalev);
314 __m256 ve = _mm256_add_ps(vn, vscalee);
315
316 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
317 ve = _mm256_max_ps(ve, vmin_exponent);
318
319 // Convert exponents into scale factors.
320 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
321
322 // Multiply "mantissa" by the scale factor.
323 vf = _mm256_mul_ps(vf, vs);
324
325 // Store up to 7 inputs at a time.
326 _mm256_maskstore_ps(y, vmask, vf);
327 }
328 _mm256_zeroupper();
329 }
330