1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddextexp/avx512f-p5-scalef.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 #include <math.h>
12
13 #include <immintrin.h>
14
15 #include <xnnpack/common.h>
16 #include <xnnpack/intrinsics-polyfill.h>
17 #include <xnnpack/raddextexp.h>
18
19
xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x192_acc3(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x192_acc3(
21 size_t elements,
22 const float* x,
23 float* sum)
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
28 const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f);
29 const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f);
30
31 const __m512 vc0 = _mm512_set1_ps(1.0f);
32 const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f);
33 const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f);
34 const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f);
35 const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f);
36 const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f);
37
38 const __m512 vminus_inf = _mm512_set1_ps(-INFINITY);
39
40 __m512 vaccv0 = _mm512_setzero_ps();
41 __m512 vaccv1 = _mm512_setzero_ps();
42 __m512 vaccv2 = _mm512_setzero_ps();
43 __m512 vacce0 = vminus_inf;
44 __m512 vacce1 = vminus_inf;
45 __m512 vacce2 = vminus_inf;
46 for (; elements >= 192 * sizeof(float); elements -= 192 * sizeof(float)) {
47 // Load 192 (12x16) inputs at a time.
48 const __m512 vx0 = _mm512_loadu_ps(x);
49 const __m512 vx1 = _mm512_loadu_ps(x + 16);
50 const __m512 vx2 = _mm512_loadu_ps(x + 32);
51 const __m512 vx3 = _mm512_loadu_ps(x + 48);
52 const __m512 vx4 = _mm512_loadu_ps(x + 64);
53 const __m512 vx5 = _mm512_loadu_ps(x + 80);
54 const __m512 vx6 = _mm512_loadu_ps(x + 96);
55 const __m512 vx7 = _mm512_loadu_ps(x + 112);
56 const __m512 vx8 = _mm512_loadu_ps(x + 128);
57 const __m512 vx9 = _mm512_loadu_ps(x + 144);
58 const __m512 vx10 = _mm512_loadu_ps(x + 160);
59 const __m512 vx11 = _mm512_loadu_ps(x + 176);
60 x += 192;
61
62 // Compute reduced argument elements := round(x / log(2)).
63 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
64 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
65 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
66 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
67 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
68 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
69 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
70 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
71 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
72 const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, vlog2e), 0);
73 const __m512 vn10 = _mm512_roundscale_ps(_mm512_mul_ps(vx10, vlog2e), 0);
74 const __m512 vn11 = _mm512_roundscale_ps(_mm512_mul_ps(vx11, vlog2e), 0);
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 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
79 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
80 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
81 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
82 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
83 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
84 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
85 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
86 __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8);
87 __m512 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_hi, vx9);
88 __m512 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_hi, vx10);
89 __m512 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_hi, vx11);
90
91 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
92 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
93 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
94 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
95 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
96 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
97 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
98 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
99 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
100 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_lo, vt9);
101 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_lo, vt10);
102 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_lo, vt11);
103
104 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
105 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
106 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
107 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
108 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
109 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
110 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
111 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
112 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
113 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
114 __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4);
115 __m512 vp10 = _mm512_fmadd_ps(vc5, vt10, vc4);
116 __m512 vp11 = _mm512_fmadd_ps(vc5, vt11, vc4);
117
118 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
119 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
120 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
121 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
122 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
123 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
124 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
125 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
126 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
127 vp9 = _mm512_fmadd_ps(vp9, vt9, vc3);
128 vp10 = _mm512_fmadd_ps(vp10, vt10, vc3);
129 vp11 = _mm512_fmadd_ps(vp11, vt11, vc3);
130
131 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
132 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
133 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
134 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
135 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
136 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
137 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
138 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
139 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
140 vp9 = _mm512_fmadd_ps(vp9, vt9, vc2);
141 vp10 = _mm512_fmadd_ps(vp10, vt10, vc2);
142 vp11 = _mm512_fmadd_ps(vp11, vt11, vc2);
143
144 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
145 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
146 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
147 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
148 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
149 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
150 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
151 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
152 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
153 vp9 = _mm512_fmadd_ps(vp9, vt9, vc1);
154 vp10 = _mm512_fmadd_ps(vp10, vt10, vc1);
155 vp11 = _mm512_fmadd_ps(vp11, vt11, vc1);
156
157 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
158 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
159 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
160 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
161 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
162 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
163 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
164 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
165 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
166 vp9 = _mm512_fmadd_ps(vp9, vt9, vc0);
167 vp10 = _mm512_fmadd_ps(vp10, vt10, vc0);
168 vp11 = _mm512_fmadd_ps(vp11, vt11, vc0);
169
170 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
171 // - vnX is "exponent"
172 // - vpX is "mantissa"
173 //
174 // exp2(ae) * av + exp2(be) * bv =
175 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
176 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
177 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
178 //
179 // For computational efficiency we add three "extended" floating-point numbers at a time.
180 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
181 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
182 __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2);
183 vmax_e0 = _mm512_max_ps(vmax_e0, vn3);
184 vmax_e1 = _mm512_max_ps(vmax_e1, vn4);
185 vmax_e2 = _mm512_max_ps(vmax_e2, vn5);
186 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
187 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
188 vmax_e2 = _mm512_max_ps(vmax_e2, vn8);
189 vmax_e0 = _mm512_max_ps(vmax_e0, vn9);
190 vmax_e1 = _mm512_max_ps(vmax_e1, vn10);
191 vmax_e2 = _mm512_max_ps(vmax_e2, vn11);
192
193 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
194 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
195 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2);
196 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
197 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
198 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2);
199 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e0);
200 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e1);
201 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e2);
202 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
203 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
204 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e2);
205 const __m512 vdelta_e9 = _mm512_sub_ps(vn9, vmax_e0);
206 const __m512 vdelta_e10 = _mm512_sub_ps(vn10, vmax_e1);
207 const __m512 vdelta_e11 = _mm512_sub_ps(vn11, vmax_e2);
208
209 // Update accumulated "mantissa" and "exponent" values
210 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
211 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
212 vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2);
213 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
214 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
215 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2));
216 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp3, vdelta_e3));
217 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp4, vdelta_e4));
218 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp5, vdelta_e5));
219 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
220 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
221 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp8, vdelta_e8));
222 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp9, vdelta_e9));
223 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp10, vdelta_e10));
224 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp11, vdelta_e11));
225
226 vacce0 = vmax_e0;
227 vacce1 = vmax_e1;
228 vacce2 = vmax_e2;
229 }
230
231 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
232 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
233 const __m512 vmax_acce2 = vacce2;
234 const __m512 vmax_acce012 = _mm512_max_ps(vmax_acce01, vmax_acce2);
235
236 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce012);
237 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce012);
238 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce012);
239
240 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
241 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
242 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2));
243 __m512 vacce = vmax_acce012;
244
245 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
246 // Load 16 inputs at a time.
247 const __m512 vx = _mm512_loadu_ps(x);
248 x += 16;
249
250 // Compute reduced argument elements := round(x / log(2)).
251 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
252
253 // Compute reduced argument t := x - elements * log(2).
254 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
255 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
256 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
257
258 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
259 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
260 vp = _mm512_fmadd_ps(vp, vt, vc3);
261 vp = _mm512_fmadd_ps(vp, vt, vc2);
262 vp = _mm512_fmadd_ps(vp, vt, vc1);
263 vp = _mm512_fmadd_ps(vp, vt, vc0);
264
265 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
266 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
267 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
268 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
269 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
270 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
271
272 vacce = vmax_e;
273 }
274 if XNN_UNLIKELY(elements != 0) {
275 // Prepare mask for valid 32-bit elements (depends on elements).
276 elements >>= 2 /* log2(sizeof(float)) */;
277 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
278
279 // Load up to 15 inputs at a time.
280 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
281
282 // Compute reduced argument elements := round(x / log(2)).
283 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
284
285 // Compute reduced argument t := x - elements * log(2).
286 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
287 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
288 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
289
290 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
291 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
292 vp = _mm512_fmadd_ps(vp, vt, vc3);
293 vp = _mm512_fmadd_ps(vp, vt, vc2);
294 vp = _mm512_fmadd_ps(vp, vt, vc1);
295 vp = _mm512_fmadd_ps(vp, vt, vc0);
296
297 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
298 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
299 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
300 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
301 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
302 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
303 vacce = vmax_e;
304 }
305
306 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
307 const float vmax_acce = _mm512_reduce_max_ps(vacce);
308 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
309
310 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
311 sum[1] = vmax_acce;
312
313 _mm256_zeroupper();
314 }
315