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_x128_acc4(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x128_acc4(
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 vacce0 = vminus_inf;
45 __m512 vacce1 = vminus_inf;
46 __m512 vacce2 = vminus_inf;
47 __m512 vacce3 = vminus_inf;
48 for (; elements >= 128 * sizeof(float); elements -= 128 * sizeof(float)) {
49 // Load 128 (8x16) inputs at a time.
50 const __m512 vx0 = _mm512_loadu_ps(x);
51 const __m512 vx1 = _mm512_loadu_ps(x + 16);
52 const __m512 vx2 = _mm512_loadu_ps(x + 32);
53 const __m512 vx3 = _mm512_loadu_ps(x + 48);
54 const __m512 vx4 = _mm512_loadu_ps(x + 64);
55 const __m512 vx5 = _mm512_loadu_ps(x + 80);
56 const __m512 vx6 = _mm512_loadu_ps(x + 96);
57 const __m512 vx7 = _mm512_loadu_ps(x + 112);
58 x += 128;
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
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
81 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
82 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
83 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
84 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
85 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
86 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
87 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
88 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
89
90 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
91 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
92 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
93 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
94 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
95 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
96 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
97 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
98 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
99
100 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
101 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
102 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
103 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
104 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
105 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
106 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
107 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
108
109 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
110 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
111 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
112 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
113 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
114 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
115 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
116 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
117
118 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
119 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
120 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
121 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
122 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
123 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
124 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
125 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
126
127 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
128 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
129 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
130 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
131 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
132 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
133 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
134 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
135
136 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
137 // - vnX is "exponent"
138 // - vpX is "mantissa"
139 //
140 // exp2(ae) * av + exp2(be) * bv =
141 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
142 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
143 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
144 //
145 // For computational efficiency we add three "extended" floating-point numbers at a time.
146 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
147 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
148 __m512 vmax_e2 = _mm512_max_ps(vacce2, vn2);
149 __m512 vmax_e3 = _mm512_max_ps(vacce3, vn3);
150 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
151 vmax_e1 = _mm512_max_ps(vmax_e1, vn5);
152 vmax_e2 = _mm512_max_ps(vmax_e2, vn6);
153 vmax_e3 = _mm512_max_ps(vmax_e3, vn7);
154
155 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
156 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
157 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_e2);
158 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_e3);
159 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
160 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
161 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e2);
162 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e3);
163 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
164 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e1);
165 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e2);
166 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e3);
167
168 // Update accumulated "mantissa" and "exponent" values
169 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
170 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
171 vaccv2 = _mm512_scalef_ps(vaccv2, vdelta_acce2);
172 vaccv3 = _mm512_scalef_ps(vaccv3, vdelta_acce3);
173 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
174 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
175 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp2, vdelta_e2));
176 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp3, vdelta_e3));
177 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
178 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp5, vdelta_e5));
179 vaccv2 = _mm512_add_ps(vaccv2, _mm512_scalef_ps(vp6, vdelta_e6));
180 vaccv3 = _mm512_add_ps(vaccv3, _mm512_scalef_ps(vp7, vdelta_e7));
181
182 vacce0 = vmax_e0;
183 vacce1 = vmax_e1;
184 vacce2 = vmax_e2;
185 vacce3 = vmax_e3;
186 }
187
188 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
189 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
190 const __m512 vmax_acce23 = _mm512_max_ps(vacce2, vacce3);
191 const __m512 vmax_acce0123 = _mm512_max_ps(vmax_acce01, vmax_acce23);
192
193 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce0123);
194 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce0123);
195 const __m512 vdelta_acce2 = _mm512_sub_ps(vacce2, vmax_acce0123);
196 const __m512 vdelta_acce3 = _mm512_sub_ps(vacce3, vmax_acce0123);
197
198 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
199 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
200 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv2, vdelta_acce2));
201 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv3, vdelta_acce3));
202 __m512 vacce = vmax_acce0123;
203
204 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
205 // Load 16 inputs at a time.
206 const __m512 vx = _mm512_loadu_ps(x);
207 x += 16;
208
209 // Compute reduced argument elements := round(x / log(2)).
210 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
211
212 // Compute reduced argument t := x - elements * log(2).
213 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
214 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
215 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
216
217 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
218 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
219 vp = _mm512_fmadd_ps(vp, vt, vc3);
220 vp = _mm512_fmadd_ps(vp, vt, vc2);
221 vp = _mm512_fmadd_ps(vp, vt, vc1);
222 vp = _mm512_fmadd_ps(vp, vt, vc0);
223
224 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
225 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
226 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
227 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
228 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
229 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
230
231 vacce = vmax_e;
232 }
233 if XNN_UNLIKELY(elements != 0) {
234 // Prepare mask for valid 32-bit elements (depends on elements).
235 elements >>= 2 /* log2(sizeof(float)) */;
236 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
237
238 // Load up to 15 inputs at a time.
239 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
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 approximation 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_mask_max_ps(vacce, vmask, 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_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
261 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
262 vacce = vmax_e;
263 }
264
265 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
266 const float vmax_acce = _mm512_reduce_max_ps(vacce);
267 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
268
269 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
270 sum[1] = vmax_acce;
271
272 _mm256_zeroupper();
273 }
274