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_x144_acc3(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x144_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 >= 144 * sizeof(float); elements -= 144 * sizeof(float)) {
47 // Load 144 (9x16) 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 x += 144;
58
59 // Compute reduced argument elements := round(x / log(2)).
60 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
61 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
62 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
63 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
64 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
65 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
66 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
67 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
68 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
69
70 // Compute reduced argument t := x - elements * log(2).
71 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
72 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
73 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
74 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
75 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
76 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
77 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
78 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
79 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
80 __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8);
81
82 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
83 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
84 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
85 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
86 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
87 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
88 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
89 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
90 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
91
92 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
93 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
94 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
95 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
96 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
97 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
98 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
99 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
100 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
101 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
102
103 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
104 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
105 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
106 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
107 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
108 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
109 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
110 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
111 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
112
113 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
114 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
115 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
116 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
117 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
118 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
119 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
120 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
121 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
122
123 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
124 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
125 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
126 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
127 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
128 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
129 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
130 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
131 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
132
133 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
134 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
135 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
136 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
137 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
138 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
139 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
140 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
141 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
142
143 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
144 // - vnX is "exponent"
145 // - vpX is "mantissa"
146 //
147 // exp2(ae) * av + exp2(be) * bv =
148 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
149 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
150 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
151 //
152 // For computational efficiency we add three "extended" floating-point numbers at a time.
153 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
154 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
155 __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2);
156 vmax_e0 = _mm512_max_ps(vmax_e0, vn3);
157 vmax_e1 = _mm512_max_ps(vmax_e1, vn4);
158 vmax_e2 = _mm512_max_ps(vmax_e2, vn5);
159 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
160 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
161 vmax_e2 = _mm512_max_ps(vmax_e2, vn8);
162
163 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
164 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
165 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2);
166 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
167 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
168 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2);
169 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e0);
170 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e1);
171 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e2);
172 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
173 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
174 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e2);
175
176 // Update accumulated "mantissa" and "exponent" values
177 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
178 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
179 vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2);
180 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
181 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
182 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2));
183 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp3, vdelta_e3));
184 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp4, vdelta_e4));
185 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp5, vdelta_e5));
186 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
187 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
188 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp8, vdelta_e8));
189
190 vacce0 = vmax_e0;
191 vacce1 = vmax_e1;
192 vacce2 = vmax_e2;
193 }
194
195 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
196 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
197 const __m512 vmax_acce2 = vacce2;
198 const __m512 vmax_acce012 = _mm512_max_ps(vmax_acce01, vmax_acce2);
199
200 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce012);
201 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce012);
202 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce012);
203
204 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
205 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
206 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2));
207 __m512 vacce = vmax_acce012;
208
209 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
210 // Load 16 inputs at a time.
211 const __m512 vx = _mm512_loadu_ps(x);
212 x += 16;
213
214 // Compute reduced argument elements := round(x / log(2)).
215 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
216
217 // Compute reduced argument t := x - elements * log(2).
218 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
219 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
220 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
221
222 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
223 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
224 vp = _mm512_fmadd_ps(vp, vt, vc3);
225 vp = _mm512_fmadd_ps(vp, vt, vc2);
226 vp = _mm512_fmadd_ps(vp, vt, vc1);
227 vp = _mm512_fmadd_ps(vp, vt, vc0);
228
229 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
230 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
231 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
232 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
233 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
234 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
235
236 vacce = vmax_e;
237 }
238 if XNN_UNLIKELY(elements != 0) {
239 // Prepare mask for valid 32-bit elements (depends on elements).
240 elements >>= 2 /* log2(sizeof(float)) */;
241 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
242
243 // Load up to 15 inputs at a time.
244 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
245
246 // Compute reduced argument elements := round(x / log(2)).
247 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
248
249 // Compute reduced argument t := x - elements * log(2).
250 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
251 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
252 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
253
254 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
255 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
256 vp = _mm512_fmadd_ps(vp, vt, vc3);
257 vp = _mm512_fmadd_ps(vp, vt, vc2);
258 vp = _mm512_fmadd_ps(vp, vt, vc1);
259 vp = _mm512_fmadd_ps(vp, vt, vc0);
260
261 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
262 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
263 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
264 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
265 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
266 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
267 vacce = vmax_e;
268 }
269
270 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
271 const float vmax_acce = _mm512_reduce_max_ps(vacce);
272 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
273
274 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
275 sum[1] = vmax_acce;
276
277 _mm256_zeroupper();
278 }
279