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_x160_acc5(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x160_acc5(
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 vacce0 = vminus_inf;
46 __m512 vacce1 = vminus_inf;
47 __m512 vacce2 = vminus_inf;
48 __m512 vacce3 = vminus_inf;
49 __m512 vacce4 = vminus_inf;
50 for (; elements >= 160 * sizeof(float); elements -= 160 * sizeof(float)) {
51 // Load 160 (10x16) inputs at a time.
52 const __m512 vx0 = _mm512_loadu_ps(x);
53 const __m512 vx1 = _mm512_loadu_ps(x + 16);
54 const __m512 vx2 = _mm512_loadu_ps(x + 32);
55 const __m512 vx3 = _mm512_loadu_ps(x + 48);
56 const __m512 vx4 = _mm512_loadu_ps(x + 64);
57 const __m512 vx5 = _mm512_loadu_ps(x + 80);
58 const __m512 vx6 = _mm512_loadu_ps(x + 96);
59 const __m512 vx7 = _mm512_loadu_ps(x + 112);
60 const __m512 vx8 = _mm512_loadu_ps(x + 128);
61 const __m512 vx9 = _mm512_loadu_ps(x + 144);
62 x += 160;
63
64 // Compute reduced argument elements := round(x / log(2)).
65 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
66 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
67 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
68 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
69 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
70 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
71 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
72 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
73 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
74 const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, 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
89 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
90 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
91 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
92 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
93 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
94 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
95 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
96 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
97 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
98 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_lo, vt9);
99
100 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
101 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
102 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
103 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
104 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
105 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
106 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
107 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
108 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
109 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
110 __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4);
111
112 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
113 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
114 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
115 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
116 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
117 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
118 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
119 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
120 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
121 vp9 = _mm512_fmadd_ps(vp9, vt9, vc3);
122
123 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
124 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
125 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
126 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
127 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
128 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
129 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
130 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
131 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
132 vp9 = _mm512_fmadd_ps(vp9, vt9, vc2);
133
134 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
135 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
136 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
137 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
138 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
139 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
140 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
141 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
142 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
143 vp9 = _mm512_fmadd_ps(vp9, vt9, vc1);
144
145 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
146 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
147 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
148 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
149 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
150 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
151 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
152 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
153 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
154 vp9 = _mm512_fmadd_ps(vp9, vt9, vc0);
155
156 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
157 // - vnX is "exponent"
158 // - vpX is "mantissa"
159 //
160 // exp2(ae) * av + exp2(be) * bv =
161 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
162 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
163 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
164 //
165 // For computational efficiency we add three "extended" floating-point numbers at a time.
166 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
167 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
168 __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2);
169 __m512 vmax_e3 = _mm512_max_ps(vacce3, vn3);
170 __m512 vmax_e4 = _mm512_max_ps(vacce4, vn4);
171 vmax_e0 = _mm512_max_ps(vmax_e0, vn5);
172 vmax_e1 = _mm512_max_ps(vmax_e1, vn6);
173 vmax_e2 = _mm512_max_ps(vmax_e2, vn7);
174 vmax_e3 = _mm512_max_ps(vmax_e3, vn8);
175 vmax_e4 = _mm512_max_ps(vmax_e4, vn9);
176
177 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
178 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
179 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2);
180 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_e3);
181 const __m512 vdelta_acce4 = _mm512_sub_ps(vacce4, vmax_e4);
182 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
183 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
184 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2);
185 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e3);
186 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e4);
187 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e0);
188 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e1);
189 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e2);
190 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e3);
191 const __m512 vdelta_e9 = _mm512_sub_ps(vn9, vmax_e4);
192
193 // Update accumulated "mantissa" and "exponent" values
194 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
195 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
196 vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2);
197 vaccv3 = _mm512_scalef_ps(vaccv3, vdelta_acce3);
198 vaccv4 = _mm512_scalef_ps(vaccv4, vdelta_acce4);
199 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
200 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
201 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2));
202 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp3, vdelta_e3));
203 vaccv4 = _mm512_add_ps(vaccv4, _mm512_scalef_ps(vp4, vdelta_e4));
204 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp5, vdelta_e5));
205 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp6, vdelta_e6));
206 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp7, vdelta_e7));
207 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp8, vdelta_e8));
208 vaccv4 = _mm512_add_ps(vaccv4, _mm512_scalef_ps(vp9, vdelta_e9));
209
210 vacce0 = vmax_e0;
211 vacce1 = vmax_e1;
212 vacce2 = vmax_e2;
213 vacce3 = vmax_e3;
214 vacce4 = vmax_e4;
215 }
216
217 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
218 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
219 const __m512 vmax_acce23 = _mm512_max_ps(vacce2, vacce3);
220 const __m512 vmax_acce4 = vacce4;
221 const __m512 vmax_acce0123 = _mm512_max_ps(vmax_acce01, vmax_acce23);
222 const __m512 vmax_acce01234 = _mm512_max_ps(vmax_acce0123, vmax_acce4);
223
224 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce01234);
225 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce01234);
226 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce01234);
227 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_acce01234);
228 const __m512 vdelta_acce4 = _mm512_sub_ps(vacce4, vmax_acce01234);
229
230 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
231 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
232 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2));
233 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv3, vdelta_acce3));
234 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv4, vdelta_acce4));
235 __m512 vacce = vmax_acce01234;
236
237 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
238 // Load 16 inputs at a time.
239 const __m512 vx = _mm512_loadu_ps(x);
240 x += 16;
241
242 // Compute reduced argument elements := round(x / log(2)).
243 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
244
245 // Compute reduced argument t := x - elements * log(2).
246 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
247 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
248 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
249
250 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
251 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
252 vp = _mm512_fmadd_ps(vp, vt, vc3);
253 vp = _mm512_fmadd_ps(vp, vt, vc2);
254 vp = _mm512_fmadd_ps(vp, vt, vc1);
255 vp = _mm512_fmadd_ps(vp, vt, vc0);
256
257 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
258 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
259 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
260 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
261 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
262 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
263
264 vacce = vmax_e;
265 }
266 if XNN_UNLIKELY(elements != 0) {
267 // Prepare mask for valid 32-bit elements (depends on elements).
268 elements >>= 2 /* log2(sizeof(float)) */;
269 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
270
271 // Load up to 15 inputs at a time.
272 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
273
274 // Compute reduced argument elements := round(x / log(2)).
275 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
276
277 // Compute reduced argument t := x - elements * log(2).
278 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
279 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
280 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
281
282 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
283 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
284 vp = _mm512_fmadd_ps(vp, vt, vc3);
285 vp = _mm512_fmadd_ps(vp, vt, vc2);
286 vp = _mm512_fmadd_ps(vp, vt, vc1);
287 vp = _mm512_fmadd_ps(vp, vt, vc0);
288
289 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
290 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
291 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
292 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
293 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
294 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
295 vacce = vmax_e;
296 }
297
298 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
299 const float vmax_acce = _mm512_reduce_max_ps(vacce);
300 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
301
302 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
303 sum[1] = vmax_acce;
304
305 _mm256_zeroupper();
306 }
307