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_acc2(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x128_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 >= 128 * sizeof(float); elements -= 128 * sizeof(float)) {
45 // Load 128 (8x16) 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 x += 128;
55
56 // Compute reduced argument elements := round(x / log(2)).
57 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
58 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
59 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
60 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
61 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
62 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
63 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
64 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, 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
77 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
78 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
79 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
80 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
81 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
82 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
83 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
84 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
85
86 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
87 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
88 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
89 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
90 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
91 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
92 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
93 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
94 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
95
96 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
97 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
98 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
99 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
100 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
101 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
102 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
103 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
104
105 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
106 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
107 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
108 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
109 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
110 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
111 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
112 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
113
114 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
115 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
116 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
117 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
118 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
119 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
120 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
121 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
122
123 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
124 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
125 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
126 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
127 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
128 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
129 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
130 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
131
132 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
133 // - vnX is "exponent"
134 // - vpX is "mantissa"
135 //
136 // exp2(ae) * av + exp2(be) * bv =
137 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
138 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
139 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
140 //
141 // For computational efficiency we add three "extended" floating-point numbers at a time.
142 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
143 __m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
144 vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
145 vmax_e1 = _mm512_max_ps(vmax_e1, vn3);
146 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
147 vmax_e1 = _mm512_max_ps(vmax_e1, vn5);
148 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
149 vmax_e1 = _mm512_max_ps(vmax_e1, vn7);
150
151 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
152 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
153 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
154 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
155 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
156 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e1);
157 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
158 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e1);
159 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
160 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e1);
161
162 // Update accumulated "mantissa" and "exponent" values
163 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
164 vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
165 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
166 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
167 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
168 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp3, vdelta_e3));
169 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
170 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp5, vdelta_e5));
171 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
172 vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp7, vdelta_e7));
173
174 vacce0 = vmax_e0;
175 vacce1 = vmax_e1;
176 }
177
178 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
179 const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
180
181 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce01);
182 const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce01);
183
184 __m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
185 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
186 __m512 vacce = vmax_acce01;
187
188 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
189 // Load 16 inputs at a time.
190 const __m512 vx = _mm512_loadu_ps(x);
191 x += 16;
192
193 // Compute reduced argument elements := round(x / log(2)).
194 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
195
196 // Compute reduced argument t := x - elements * log(2).
197 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
198 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
199 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
200
201 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
202 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
203 vp = _mm512_fmadd_ps(vp, vt, vc3);
204 vp = _mm512_fmadd_ps(vp, vt, vc2);
205 vp = _mm512_fmadd_ps(vp, vt, vc1);
206 vp = _mm512_fmadd_ps(vp, vt, vc0);
207
208 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
209 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
210 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
211 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
212 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
213 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
214
215 vacce = vmax_e;
216 }
217 if XNN_UNLIKELY(elements != 0) {
218 // Prepare mask for valid 32-bit elements (depends on elements).
219 elements >>= 2 /* log2(sizeof(float)) */;
220 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
221
222 // Load up to 15 inputs at a time.
223 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
224
225 // Compute reduced argument elements := round(x / log(2)).
226 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
227
228 // Compute reduced argument t := x - elements * log(2).
229 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
230 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
231 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
232
233 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
234 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
235 vp = _mm512_fmadd_ps(vp, vt, vc3);
236 vp = _mm512_fmadd_ps(vp, vt, vc2);
237 vp = _mm512_fmadd_ps(vp, vt, vc1);
238 vp = _mm512_fmadd_ps(vp, vt, vc0);
239
240 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
241 const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
242 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
243 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
244 vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
245 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
246 vacce = vmax_e;
247 }
248
249 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
250 const float vmax_acce = _mm512_reduce_max_ps(vacce);
251 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
252
253 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
254 sum[1] = vmax_acce;
255
256 _mm256_zeroupper();
257 }
258