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_acc2(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x192_acc2(
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 vacce0 = vminus_inf;
43 __m512 vacce1 = vminus_inf;
44 for (; elements >= 192 * sizeof(float); elements -= 192 * sizeof(float)) {
45 // Load 192 (12x16) inputs at a time.
46 const __m512 vx0 = _mm512_loadu_ps(x);
47 const __m512 vx1 = _mm512_loadu_ps(x + 16);
48 const __m512 vx2 = _mm512_loadu_ps(x + 32);
49 const __m512 vx3 = _mm512_loadu_ps(x + 48);
50 const __m512 vx4 = _mm512_loadu_ps(x + 64);
51 const __m512 vx5 = _mm512_loadu_ps(x + 80);
52 const __m512 vx6 = _mm512_loadu_ps(x + 96);
53 const __m512 vx7 = _mm512_loadu_ps(x + 112);
54 const __m512 vx8 = _mm512_loadu_ps(x + 128);
55 const __m512 vx9 = _mm512_loadu_ps(x + 144);
56 const __m512 vx10 = _mm512_loadu_ps(x + 160);
57 const __m512 vx11 = _mm512_loadu_ps(x + 176);
58 x += 192;
59
60 // Compute reduced argument elements := round(x / log(2)).
61 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
62 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
63 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
64 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
65 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
66 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
67 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
68 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
69 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
70 const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, vlog2e), 0);
71 const __m512 vn10 = _mm512_roundscale_ps(_mm512_mul_ps(vx10, vlog2e), 0);
72 const __m512 vn11 = _mm512_roundscale_ps(_mm512_mul_ps(vx11, vlog2e), 0);
73
74 // Compute reduced argument t := x - elements * log(2).
75 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
76 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
77 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
78 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
79 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
80 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
81 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
82 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
83 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
84 __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8);
85 __m512 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_hi, vx9);
86 __m512 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_hi, vx10);
87 __m512 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_hi, vx11);
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 vt10 = _mm512_fmadd_ps(vn10, vminus_ln2_lo, vt10);
100 vt11 = _mm512_fmadd_ps(vn11, vminus_ln2_lo, vt11);
101
102 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
103 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
104 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
105 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
106 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
107 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
108 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
109 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
110 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
111 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
112 __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4);
113 __m512 vp10 = _mm512_fmadd_ps(vc5, vt10, vc4);
114 __m512 vp11 = _mm512_fmadd_ps(vc5, vt11, vc4);
115
116 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
117 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
118 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
119 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
120 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
121 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
122 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
123 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
124 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
125 vp9 = _mm512_fmadd_ps(vp9, vt9, vc3);
126 vp10 = _mm512_fmadd_ps(vp10, vt10, vc3);
127 vp11 = _mm512_fmadd_ps(vp11, vt11, vc3);
128
129 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
130 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
131 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
132 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
133 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
134 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
135 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
136 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
137 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
138 vp9 = _mm512_fmadd_ps(vp9, vt9, vc2);
139 vp10 = _mm512_fmadd_ps(vp10, vt10, vc2);
140 vp11 = _mm512_fmadd_ps(vp11, vt11, vc2);
141
142 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
143 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
144 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
145 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
146 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
147 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
148 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
149 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
150 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
151 vp9 = _mm512_fmadd_ps(vp9, vt9, vc1);
152 vp10 = _mm512_fmadd_ps(vp10, vt10, vc1);
153 vp11 = _mm512_fmadd_ps(vp11, vt11, vc1);
154
155 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
156 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
157 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
158 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
159 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
160 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
161 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
162 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
163 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
164 vp9 = _mm512_fmadd_ps(vp9, vt9, vc0);
165 vp10 = _mm512_fmadd_ps(vp10, vt10, vc0);
166 vp11 = _mm512_fmadd_ps(vp11, vt11, vc0);
167
168 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
169 // - vnX is "exponent"
170 // - vpX is "mantissa"
171 //
172 // exp2(ae) * av + exp2(be) * bv =
173 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
174 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
175 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
176 //
177 // For computational efficiency we add three "extended" floating-point numbers at a time.
178 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
179 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
180 vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
181 vmax_e1 = _mm512_max_ps(vmax_e1, vn3);
182 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
183 vmax_e1 = _mm512_max_ps(vmax_e1, vn5);
184 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
185 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
186 vmax_e0 = _mm512_max_ps(vmax_e0, vn8);
187 vmax_e1 = _mm512_max_ps(vmax_e1, vn9);
188 vmax_e0 = _mm512_max_ps(vmax_e0, vn10);
189 vmax_e1 = _mm512_max_ps(vmax_e1, vn11);
190
191 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
192 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
193 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
194 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
195 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
196 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e1);
197 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
198 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e1);
199 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
200 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
201 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e0);
202 const __m512 vdelta_e9 = _mm512_sub_ps(vn9, vmax_e1);
203 const __m512 vdelta_e10 = _mm512_sub_ps(vn10, vmax_e0);
204 const __m512 vdelta_e11 = _mm512_sub_ps(vn11, vmax_e1);
205
206 // Update accumulated "mantissa" and "exponent" values
207 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
208 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
209 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
210 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
211 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
212 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp3, vdelta_e3));
213 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
214 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp5, vdelta_e5));
215 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
216 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
217 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp8, vdelta_e8));
218 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp9, vdelta_e9));
219 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp10, vdelta_e10));
220 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp11, vdelta_e11));
221
222 vacce0 = vmax_e0;
223 vacce1 = vmax_e1;
224 }
225
226 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
227 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
228
229 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce01);
230 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce01);
231
232 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
233 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
234 __m512 vacce = vmax_acce01;
235
236 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
237 // Load 16 inputs at a time.
238 const __m512 vx = _mm512_loadu_ps(x);
239 x += 16;
240
241 // Compute reduced argument elements := round(x / log(2)).
242 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
243
244 // Compute reduced argument t := x - elements * log(2).
245 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
246 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
247 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
248
249 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
250 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
251 vp = _mm512_fmadd_ps(vp, vt, vc3);
252 vp = _mm512_fmadd_ps(vp, vt, vc2);
253 vp = _mm512_fmadd_ps(vp, vt, vc1);
254 vp = _mm512_fmadd_ps(vp, vt, vc0);
255
256 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
257 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
258 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
259 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
260 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
261 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
262
263 vacce = vmax_e;
264 }
265 if XNN_UNLIKELY(elements != 0) {
266 // Prepare mask for valid 32-bit elements (depends on elements).
267 elements >>= 2 /* log2(sizeof(float)) */;
268 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
269
270 // Load up to 15 inputs at a time.
271 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
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_mask_max_ps(vacce, vmask, 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_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
293 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
294 vacce = vmax_e;
295 }
296
297 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
298 const float vmax_acce = _mm512_reduce_max_ps(vacce);
299 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
300
301 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
302 sum[1] = vmax_acce;
303
304 _mm256_zeroupper();
305 }
306