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(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x144(
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 vacce0 = vminus_inf;
42 for (; elements >= 144 * sizeof(float); elements -= 144 * sizeof(float)) {
43 // Load 144 (9x16) inputs at a time.
44 const __m512 vx0 = _mm512_loadu_ps(x);
45 const __m512 vx1 = _mm512_loadu_ps(x + 16);
46 const __m512 vx2 = _mm512_loadu_ps(x + 32);
47 const __m512 vx3 = _mm512_loadu_ps(x + 48);
48 const __m512 vx4 = _mm512_loadu_ps(x + 64);
49 const __m512 vx5 = _mm512_loadu_ps(x + 80);
50 const __m512 vx6 = _mm512_loadu_ps(x + 96);
51 const __m512 vx7 = _mm512_loadu_ps(x + 112);
52 const __m512 vx8 = _mm512_loadu_ps(x + 128);
53 x += 144;
54
55 // Compute reduced argument elements := round(x / log(2)).
56 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
57 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
58 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
59 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
60 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
61 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
62 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
63 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
64 const __m512 vn8 = _mm512_roundscale_ps(_mm512_mul_ps(vx8, vlog2e), 0);
65
66 // Compute reduced argument t := x - elements * log(2).
67 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
68 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
69 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
70 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
71 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
72 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
73 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
74 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
75 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
76 __m512 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_hi, vx8);
77
78 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
79 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
80 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
81 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
82 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
83 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
84 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
85 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
86 vt8 = _mm512_fmadd_ps(vn8, vminus_ln2_lo, vt8);
87
88 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
89 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
90 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
91 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
92 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
93 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
94 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
95 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
96 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
97 __m512 vp8 = _mm512_fmadd_ps(vc5, vt8, vc4);
98
99 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
100 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
101 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
102 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
103 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
104 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
105 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
106 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
107 vp8 = _mm512_fmadd_ps(vp8, vt8, 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 vp8 = _mm512_fmadd_ps(vp8, vt8, vc2);
118
119 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
120 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
121 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
122 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
123 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
124 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
125 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
126 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
127 vp8 = _mm512_fmadd_ps(vp8, vt8, vc1);
128
129 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
130 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
131 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
132 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
133 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
134 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
135 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
136 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
137 vp8 = _mm512_fmadd_ps(vp8, vt8, vc0);
138
139 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
140 // - vnX is "exponent"
141 // - vpX is "mantissa"
142 //
143 // exp2(ae) * av + exp2(be) * bv =
144 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
145 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
146 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
147 //
148 // For computational efficiency we add three "extended" floating-point numbers at a time.
149 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
150 vmax_e0 = _mm512_max_ps(vmax_e0, vn1);
151 vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
152 vmax_e0 = _mm512_max_ps(vmax_e0, vn3);
153 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
154 vmax_e0 = _mm512_max_ps(vmax_e0, vn5);
155 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
156 vmax_e0 = _mm512_max_ps(vmax_e0, vn7);
157 vmax_e0 = _mm512_max_ps(vmax_e0, vn8);
158
159 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
160 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
161 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e0);
162 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
163 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e0);
164 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
165 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e0);
166 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
167 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e0);
168 const __m512 vdelta_e8 = _mm512_sub_ps(vn8, vmax_e0);
169
170 // Update accumulated "mantissa" and "exponent" values
171 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
172 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
173 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp1, vdelta_e1));
174 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
175 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp3, vdelta_e3));
176 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
177 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp5, vdelta_e5));
178 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
179 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp7, vdelta_e7));
180 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp8, vdelta_e8));
181
182 vacce0 = vmax_e0;
183 }
184
185 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
186 __m512 vaccv = vaccv0;
187 __m512 vacce = vacce0;
188
189 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
190 // Load 16 inputs at a time.
191 const __m512 vx = _mm512_loadu_ps(x);
192 x += 16;
193
194 // Compute reduced argument elements := round(x / log(2)).
195 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
196
197 // Compute reduced argument t := x - elements * log(2).
198 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
199 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
200 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
201
202 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
203 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
204 vp = _mm512_fmadd_ps(vp, vt, vc3);
205 vp = _mm512_fmadd_ps(vp, vt, vc2);
206 vp = _mm512_fmadd_ps(vp, vt, vc1);
207 vp = _mm512_fmadd_ps(vp, vt, vc0);
208
209 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
210 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
211 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
212 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
213 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
214 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
215
216 vacce = vmax_e;
217 }
218 if XNN_UNLIKELY(elements != 0) {
219 // Prepare mask for valid 32-bit elements (depends on elements).
220 elements >>= 2 /* log2(sizeof(float)) */;
221 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
222
223 // Load up to 15 inputs at a time.
224 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
225
226 // Compute reduced argument elements := round(x / log(2)).
227 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
228
229 // Compute reduced argument t := x - elements * log(2).
230 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
231 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
232 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
233
234 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
235 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
236 vp = _mm512_fmadd_ps(vp, vt, vc3);
237 vp = _mm512_fmadd_ps(vp, vt, vc2);
238 vp = _mm512_fmadd_ps(vp, vt, vc1);
239 vp = _mm512_fmadd_ps(vp, vt, vc0);
240
241 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
242 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
243 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
244 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
245 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
246 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
247 vacce = vmax_e;
248 }
249
250 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
251 const float vmax_acce = _mm512_reduce_max_ps(vacce);
252 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
253
254 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
255 sum[1] = vmax_acce;
256
257 _mm256_zeroupper();
258 }
259