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_acc2(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x160_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 >= 160 * sizeof(float); elements -= 160 * sizeof(float)) {
45 // Load 160 (10x16) 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 x += 160;
57
58 // Compute reduced argument elements := round(x / log(2)).
59 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
60 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
61 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
62 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
63 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
64 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
65 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
66 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
67 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
68 const __m512 vn9 = _mm512_roundscale_ps(_mm512_mul_ps(vx9, 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 __m512 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_hi, vx9);
82
83 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
84 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
85 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
86 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
87 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
88 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
89 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
90 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
91 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
92 vt9 = _mm512_fmadd_ps(vn9, vminus_ln2_lo, vt9);
93
94 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
95 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
96 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
97 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
98 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
99 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
100 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
101 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
102 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
103 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
104 __m512 vp9 = _mm512_fmadd_ps(vc5, vt9, vc4);
105
106 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
107 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
108 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
109 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
110 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
111 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
112 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
113 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
114 vp8 = _mm512_fmadd_ps(vp8, vt8, vc3);
115 vp9 = _mm512_fmadd_ps(vp9, vt9, vc3);
116
117 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
118 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
119 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
120 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
121 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
122 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
123 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
124 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
125 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
126 vp9 = _mm512_fmadd_ps(vp9, vt9, vc2);
127
128 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
129 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
130 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
131 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
132 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
133 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
134 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
135 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
136 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
137 vp9 = _mm512_fmadd_ps(vp9, vt9, vc1);
138
139 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
140 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
141 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
142 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
143 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
144 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
145 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
146 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
147 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
148 vp9 = _mm512_fmadd_ps(vp9, vt9, vc0);
149
150 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
151 // - vnX is "exponent"
152 // - vpX is "mantissa"
153 //
154 // exp2(ae) * av + exp2(be) * bv =
155 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
156 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
157 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
158 //
159 // For computational efficiency we add three "extended" floating-point numbers at a time.
160 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
161 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
162 vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
163 vmax_e1 = _mm512_max_ps(vmax_e1, vn3);
164 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
165 vmax_e1 = _mm512_max_ps(vmax_e1, vn5);
166 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
167 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
168 vmax_e0 = _mm512_max_ps(vmax_e0, vn8);
169 vmax_e1 = _mm512_max_ps(vmax_e1, vn9);
170
171 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
172 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
173 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
174 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
175 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
176 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e1);
177 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
178 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e1);
179 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
180 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
181 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e0);
182 const __m512 vdelta_e9 = _mm512_sub_ps(vn9, vmax_e1);
183
184 // Update accumulated "mantissa" and "exponent" values
185 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
186 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
187 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
188 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
189 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
190 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp3, vdelta_e3));
191 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
192 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp5, vdelta_e5));
193 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
194 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
195 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp8, vdelta_e8));
196 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp9, vdelta_e9));
197
198 vacce0 = vmax_e0;
199 vacce1 = vmax_e1;
200 }
201
202 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
203 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
204
205 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce01);
206 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce01);
207
208 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
209 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
210 __m512 vacce = vmax_acce01;
211
212 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
213 // Load 16 inputs at a time.
214 const __m512 vx = _mm512_loadu_ps(x);
215 x += 16;
216
217 // Compute reduced argument elements := round(x / log(2)).
218 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
219
220 // Compute reduced argument t := x - elements * log(2).
221 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
222 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
223 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
224
225 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
226 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
227 vp = _mm512_fmadd_ps(vp, vt, vc3);
228 vp = _mm512_fmadd_ps(vp, vt, vc2);
229 vp = _mm512_fmadd_ps(vp, vt, vc1);
230 vp = _mm512_fmadd_ps(vp, vt, vc0);
231
232 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
233 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
234 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
235 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
236 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
237 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
238
239 vacce = vmax_e;
240 }
241 if XNN_UNLIKELY(elements != 0) {
242 // Prepare mask for valid 32-bit elements (depends on elements).
243 elements >>= 2 /* log2(sizeof(float)) */;
244 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
245
246 // Load up to 15 inputs at a time.
247 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
248
249 // Compute reduced argument elements := round(x / log(2)).
250 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
251
252 // Compute reduced argument t := x - elements * log(2).
253 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
254 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
255 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
256
257 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
258 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
259 vp = _mm512_fmadd_ps(vp, vt, vc3);
260 vp = _mm512_fmadd_ps(vp, vt, vc2);
261 vp = _mm512_fmadd_ps(vp, vt, vc1);
262 vp = _mm512_fmadd_ps(vp, vt, vc0);
263
264 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
265 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
266 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
267 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
268 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
269 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
270 vacce = vmax_e;
271 }
272
273 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
274 const float vmax_acce = _mm512_reduce_max_ps(vacce);
275 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
276
277 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
278 sum[1] = vmax_acce;
279
280 _mm256_zeroupper();
281 }
282