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(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_x128(
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 >= 128 * sizeof(float); elements -= 128 * sizeof(float)) {
43 // Load 128 (8x16) 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 x += 128;
53
54 // Compute reduced argument elements := round(x / log(2)).
55 const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
56 const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
57 const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
58 const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
59 const __m512 vn4 = _mm512_roundscale_ps(_mm512_mul_ps(vx4, vlog2e), 0);
60 const __m512 vn5 = _mm512_roundscale_ps(_mm512_mul_ps(vx5, vlog2e), 0);
61 const __m512 vn6 = _mm512_roundscale_ps(_mm512_mul_ps(vx6, vlog2e), 0);
62 const __m512 vn7 = _mm512_roundscale_ps(_mm512_mul_ps(vx7, vlog2e), 0);
63
64 // Compute reduced argument t := x - elements * log(2).
65 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
66 __m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
67 __m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
68 __m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
69 __m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
70 __m512 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_hi, vx4);
71 __m512 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_hi, vx5);
72 __m512 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_hi, vx6);
73 __m512 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_hi, vx7);
74
75 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
76 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
77 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
78 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
79 vt4 = _mm512_fmadd_ps(vn4, vminus_ln2_lo, vt4);
80 vt5 = _mm512_fmadd_ps(vn5, vminus_ln2_lo, vt5);
81 vt6 = _mm512_fmadd_ps(vn6, vminus_ln2_lo, vt6);
82 vt7 = _mm512_fmadd_ps(vn7, vminus_ln2_lo, vt7);
83
84 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
85 __m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
86 __m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
87 __m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
88 __m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
89 __m512 vp4 = _mm512_fmadd_ps(vc5, vt4, vc4);
90 __m512 vp5 = _mm512_fmadd_ps(vc5, vt5, vc4);
91 __m512 vp6 = _mm512_fmadd_ps(vc5, vt6, vc4);
92 __m512 vp7 = _mm512_fmadd_ps(vc5, vt7, vc4);
93
94 vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
95 vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
96 vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
97 vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
98 vp4 = _mm512_fmadd_ps(vp4, vt4, vc3);
99 vp5 = _mm512_fmadd_ps(vp5, vt5, vc3);
100 vp6 = _mm512_fmadd_ps(vp6, vt6, vc3);
101 vp7 = _mm512_fmadd_ps(vp7, vt7, vc3);
102
103 vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
104 vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
105 vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
106 vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
107 vp4 = _mm512_fmadd_ps(vp4, vt4, vc2);
108 vp5 = _mm512_fmadd_ps(vp5, vt5, vc2);
109 vp6 = _mm512_fmadd_ps(vp6, vt6, vc2);
110 vp7 = _mm512_fmadd_ps(vp7, vt7, vc2);
111
112 vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
113 vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
114 vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
115 vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
116 vp4 = _mm512_fmadd_ps(vp4, vt4, vc1);
117 vp5 = _mm512_fmadd_ps(vp5, vt5, vc1);
118 vp6 = _mm512_fmadd_ps(vp6, vt6, vc1);
119 vp7 = _mm512_fmadd_ps(vp7, vt7, vc1);
120
121 vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
122 vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
123 vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
124 vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
125 vp4 = _mm512_fmadd_ps(vp4, vt4, vc0);
126 vp5 = _mm512_fmadd_ps(vp5, vt5, vc0);
127 vp6 = _mm512_fmadd_ps(vp6, vt6, vc0);
128 vp7 = _mm512_fmadd_ps(vp7, vt7, vc0);
129
130 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
131 // - vnX is "exponent"
132 // - vpX is "mantissa"
133 //
134 // exp2(ae) * av + exp2(be) * bv =
135 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
136 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
137 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
138 //
139 // For computational efficiency we add three "extended" floating-point numbers at a time.
140 __m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
141 vmax_e0 = _mm512_max_ps(vmax_e0, vn1);
142 vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
143 vmax_e0 = _mm512_max_ps(vmax_e0, vn3);
144 vmax_e0 = _mm512_max_ps(vmax_e0, vn4);
145 vmax_e0 = _mm512_max_ps(vmax_e0, vn5);
146 vmax_e0 = _mm512_max_ps(vmax_e0, vn6);
147 vmax_e0 = _mm512_max_ps(vmax_e0, vn7);
148
149 const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
150 const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
151 const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e0);
152 const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
153 const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e0);
154 const __m512 vdelta_e4 = _mm512_sub_ps(vn4, vmax_e0);
155 const __m512 vdelta_e5 = _mm512_sub_ps(vn5, vmax_e0);
156 const __m512 vdelta_e6 = _mm512_sub_ps(vn6, vmax_e0);
157 const __m512 vdelta_e7 = _mm512_sub_ps(vn7, vmax_e0);
158
159 // Update accumulated "mantissa" and "exponent" values
160 vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
161 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
162 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp1, vdelta_e1));
163 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
164 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp3, vdelta_e3));
165 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp4, vdelta_e4));
166 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp5, vdelta_e5));
167 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp6, vdelta_e6));
168 vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp7, vdelta_e7));
169
170 vacce0 = vmax_e0;
171 }
172
173 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
174 __m512 vaccv = vaccv0;
175 __m512 vacce = vacce0;
176
177 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
178 // Load 16 inputs at a time.
179 const __m512 vx = _mm512_loadu_ps(x);
180 x += 16;
181
182 // Compute reduced argument elements := round(x / log(2)).
183 const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
184
185 // Compute reduced argument t := x - elements * log(2).
186 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
187 __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
188 vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
189
190 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
191 __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
192 vp = _mm512_fmadd_ps(vp, vt, vc3);
193 vp = _mm512_fmadd_ps(vp, vt, vc2);
194 vp = _mm512_fmadd_ps(vp, vt, vc1);
195 vp = _mm512_fmadd_ps(vp, vt, vc0);
196
197 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
198 const __m512 vmax_e = _mm512_max_ps(vacce, vn);
199 const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
200 const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
201 vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
202 vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
203
204 vacce = vmax_e;
205 }
206 if XNN_UNLIKELY(elements != 0) {
207 // Prepare mask for valid 32-bit elements (depends on elements).
208 elements >>= 2 /* log2(sizeof(float)) */;
209 const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));
210
211 // Load up to 15 inputs at a time.
212 const __m512 vx = _mm512_maskz_loadu_ps(vmask, x);
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 approximation 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_mask_max_ps(vacce, vmask, 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_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
234 vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
235 vacce = vmax_e;
236 }
237
238 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
239 const float vmax_acce = _mm512_reduce_max_ps(vacce);
240 const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
241
242 sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
243 sum[1] = vmax_acce;
244
245 _mm256_zeroupper();
246 }
247