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_acc6(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x192_acc6(
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 vaccv3 = _mm512_setzero_ps();
44 __m512 vaccv4 = _mm512_setzero_ps();
45 __m512 vaccv5 = _mm512_setzero_ps();
46 __m512 vacce0 = vminus_inf;
47 __m512 vacce1 = vminus_inf;
48 __m512 vacce2 = vminus_inf;
49 __m512 vacce3 = vminus_inf;
50 __m512 vacce4 = vminus_inf;
51 __m512 vacce5 = vminus_inf;
52 for (; elements >= 192 * sizeof(float); elements -= 192 * sizeof(float)) {
53 // Load 192 (12x16) inputs at a time.
54 const __m512 vx0 = _mm512_loadu_ps(x);
55 const __m512 vx1 = _mm512_loadu_ps(x + 16);
56 const __m512 vx2 = _mm512_loadu_ps(x + 32);
57 const __m512 vx3 = _mm512_loadu_ps(x + 48);
58 const __m512 vx4 = _mm512_loadu_ps(x + 64);
59 const __m512 vx5 = _mm512_loadu_ps(x + 80);
60 const __m512 vx6 = _mm512_loadu_ps(x + 96);
61 const __m512 vx7 = _mm512_loadu_ps(x + 112);
62 const __m512 vx8 = _mm512_loadu_ps(x + 128);
63 const __m512 vx9 = _mm512_loadu_ps(x + 144);
64 const __m512 vx10 = _mm512_loadu_ps(x + 160);
65 const __m512 vx11 = _mm512_loadu_ps(x + 176);
66 x += 192;
67
68 // Compute reduced argument elements := round(x / log(2)).
69 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
70 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
71 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
72 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
73 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
74 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
75 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
76 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
77 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
78 const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, vlog2e), 0);
79 const __m512 vn10 = _mm512_roundscale_ps(_mm512_mul_ps(vx10, vlog2e), 0);
80 const __m512 vn11 = _mm512_roundscale_ps(_mm512_mul_ps(vx11, vlog2e), 0);
81
82 // Compute reduced argument t := x - elements * log(2).
83 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
84 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
85 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
86 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
87 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
88 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
89 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
90 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
91 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
92 __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8);
93 __m512 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_hi, vx9);
94 __m512 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_hi, vx10);
95 __m512 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_hi, vx11);
96
97 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
98 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
99 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
100 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
101 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
102 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
103 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
104 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
105 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
106 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_lo, vt9);
107 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_lo, vt10);
108 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_lo, vt11);
109
110 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
111 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
112 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
113 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
114 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
115 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
116 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
117 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
118 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
119 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
120 __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4);
121 __m512 vp10 = _mm512_fmadd_ps(vc5, vt10, vc4);
122 __m512 vp11 = _mm512_fmadd_ps(vc5, vt11, vc4);
123
124 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
125 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
126 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
127 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
128 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
129 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
130 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
131 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
132 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
133 vp9 = _mm512_fmadd_ps(vp9, vt9, vc3);
134 vp10 = _mm512_fmadd_ps(vp10, vt10, vc3);
135 vp11 = _mm512_fmadd_ps(vp11, vt11, vc3);
136
137 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
138 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
139 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
140 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
141 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
142 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
143 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
144 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
145 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
146 vp9 = _mm512_fmadd_ps(vp9, vt9, vc2);
147 vp10 = _mm512_fmadd_ps(vp10, vt10, vc2);
148 vp11 = _mm512_fmadd_ps(vp11, vt11, vc2);
149
150 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
151 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
152 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
153 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
154 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
155 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
156 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
157 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
158 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
159 vp9 = _mm512_fmadd_ps(vp9, vt9, vc1);
160 vp10 = _mm512_fmadd_ps(vp10, vt10, vc1);
161 vp11 = _mm512_fmadd_ps(vp11, vt11, vc1);
162
163 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
164 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
165 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
166 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
167 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
168 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
169 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
170 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
171 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
172 vp9 = _mm512_fmadd_ps(vp9, vt9, vc0);
173 vp10 = _mm512_fmadd_ps(vp10, vt10, vc0);
174 vp11 = _mm512_fmadd_ps(vp11, vt11, vc0);
175
176 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
177 // - vnX is "exponent"
178 // - vpX is "mantissa"
179 //
180 // exp2(ae) * av + exp2(be) * bv =
181 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
182 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
183 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
184 //
185 // For computational efficiency we add three "extended" floating-point numbers at a time.
186 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
187 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
188 __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2);
189 __m512 vmax_e3 = _mm512_max_ps(vacce3, vn3);
190 __m512 vmax_e4 = _mm512_max_ps(vacce4, vn4);
191 __m512 vmax_e5 = _mm512_max_ps(vacce5, vn5);
192 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
193 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
194 vmax_e2 = _mm512_max_ps(vmax_e2, vn8);
195 vmax_e3 = _mm512_max_ps(vmax_e3, vn9);
196 vmax_e4 = _mm512_max_ps(vmax_e4, vn10);
197 vmax_e5 = _mm512_max_ps(vmax_e5, vn11);
198
199 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
200 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
201 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2);
202 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_e3);
203 const __m512 vdelta_acce4 = _mm512_sub_ps(vacce4, vmax_e4);
204 const __m512 vdelta_acce5 = _mm512_sub_ps(vacce5, vmax_e5);
205 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
206 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
207 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2);
208 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e3);
209 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e4);
210 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e5);
211 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
212 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
213 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e2);
214 const __m512 vdelta_e9 = _mm512_sub_ps(vn9, vmax_e3);
215 const __m512 vdelta_e10 = _mm512_sub_ps(vn10, vmax_e4);
216 const __m512 vdelta_e11 = _mm512_sub_ps(vn11, vmax_e5);
217
218 // Update accumulated "mantissa" and "exponent" values
219 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
220 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
221 vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2);
222 vaccv3 = _mm512_scalef_ps(vaccv3, vdelta_acce3);
223 vaccv4 = _mm512_scalef_ps(vaccv4, vdelta_acce4);
224 vaccv5 = _mm512_scalef_ps(vaccv5, vdelta_acce5);
225 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
226 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
227 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2));
228 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp3, vdelta_e3));
229 vaccv4 = _mm512_add_ps(vaccv4, _mm512_scalef_ps(vp4, vdelta_e4));
230 vaccv5 = _mm512_add_ps(vaccv5, _mm512_scalef_ps(vp5, vdelta_e5));
231 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
232 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
233 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp8, vdelta_e8));
234 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp9, vdelta_e9));
235 vaccv4 = _mm512_add_ps(vaccv4, _mm512_scalef_ps(vp10, vdelta_e10));
236 vaccv5 = _mm512_add_ps(vaccv5, _mm512_scalef_ps(vp11, vdelta_e11));
237
238 vacce0 = vmax_e0;
239 vacce1 = vmax_e1;
240 vacce2 = vmax_e2;
241 vacce3 = vmax_e3;
242 vacce4 = vmax_e4;
243 vacce5 = vmax_e5;
244 }
245
246 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
247 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
248 const __m512 vmax_acce23 = _mm512_max_ps(vacce2, vacce3);
249 const __m512 vmax_acce45 = _mm512_max_ps(vacce4, vacce5);
250 const __m512 vmax_acce0123 = _mm512_max_ps(vmax_acce01, vmax_acce23);
251 const __m512 vmax_acce012345 = _mm512_max_ps(vmax_acce0123, vmax_acce45);
252
253 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce012345);
254 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce012345);
255 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce012345);
256 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_acce012345);
257 const __m512 vdelta_acce4 = _mm512_sub_ps(vacce4, vmax_acce012345);
258 const __m512 vdelta_acce5 = _mm512_sub_ps(vacce5, vmax_acce012345);
259
260 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
261 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
262 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2));
263 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv3, vdelta_acce3));
264 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv4, vdelta_acce4));
265 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv5, vdelta_acce5));
266 __m512 vacce = vmax_acce012345;
267
268 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
269 // Load 16 inputs at a time.
270 const __m512 vx = _mm512_loadu_ps(x);
271 x += 16;
272
273 // Compute reduced argument elements := round(x / log(2)).
274 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
275
276 // Compute reduced argument t := x - elements * log(2).
277 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
278 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
279 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
280
281 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
282 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
283 vp = _mm512_fmadd_ps(vp, vt, vc3);
284 vp = _mm512_fmadd_ps(vp, vt, vc2);
285 vp = _mm512_fmadd_ps(vp, vt, vc1);
286 vp = _mm512_fmadd_ps(vp, vt, vc0);
287
288 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
289 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
290 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
291 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
292 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
293 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
294
295 vacce = vmax_e;
296 }
297 if XNN_UNLIKELY(elements != 0) {
298 // Prepare mask for valid 32-bit elements (depends on elements).
299 elements >>= 2 /* log2(sizeof(float)) */;
300 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
301
302 // Load up to 15 inputs at a time.
303 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
304
305 // Compute reduced argument elements := round(x / log(2)).
306 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
307
308 // Compute reduced argument t := x - elements * log(2).
309 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
310 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
311 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
312
313 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
314 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
315 vp = _mm512_fmadd_ps(vp, vt, vc3);
316 vp = _mm512_fmadd_ps(vp, vt, vc2);
317 vp = _mm512_fmadd_ps(vp, vt, vc1);
318 vp = _mm512_fmadd_ps(vp, vt, vc0);
319
320 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
321 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
322 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
323 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
324 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
325 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
326 vacce = vmax_e;
327 }
328
329 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
330 const float vmax_acce = _mm512_reduce_max_ps(vacce);
331 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
332
333 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
334 sum[1] = vmax_acce;
335
336 _mm256_zeroupper();
337 }
338