1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddextexp/avx2-p5.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/raddextexp.h>
16
17
18 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
19
xnn_f32_raddextexp_ukernel__avx2_p5_x96_acc3(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx2_p5_x96_acc3(
21 size_t elements,
22 const float* x,
23 float* sum)
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
28 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
29 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
30
31 // The smallest elements such that 2**elements is considered non-negligible.
32 // For smaller elements, 2**elements is replaced with zero.
33 const __m256 vmin_exponent = _mm256_set1_ps(-127.0f);
34 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
35 const __m256 vminus_inf = _mm256_set1_ps(-INFINITY);
36
37 const __m256 vc0 = _mm256_set1_ps(1.0f);
38 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
39 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
40 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
41 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
42 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
43
44 __m256 vaccv0 = _mm256_setzero_ps();
45 __m256 vaccv1 = _mm256_setzero_ps();
46 __m256 vaccv2 = _mm256_setzero_ps();
47 __m256 vacce0 = vminus_inf;
48 __m256 vacce1 = vminus_inf;
49 __m256 vacce2 = vminus_inf;
50 for (; elements >= 96 * sizeof(float); elements -= 96 * sizeof(float)) {
51 // Load 96 (12x8) inputs at a time.
52 const __m256 vx0 = _mm256_loadu_ps(x);
53 const __m256 vx1 = _mm256_loadu_ps(x + 8);
54 const __m256 vx2 = _mm256_loadu_ps(x + 16);
55 const __m256 vx3 = _mm256_loadu_ps(x + 24);
56 const __m256 vx4 = _mm256_loadu_ps(x + 32);
57 const __m256 vx5 = _mm256_loadu_ps(x + 40);
58 const __m256 vx6 = _mm256_loadu_ps(x + 48);
59 const __m256 vx7 = _mm256_loadu_ps(x + 56);
60 const __m256 vx8 = _mm256_loadu_ps(x + 64);
61 const __m256 vx9 = _mm256_loadu_ps(x + 72);
62 const __m256 vx10 = _mm256_loadu_ps(x + 80);
63 const __m256 vx11 = _mm256_loadu_ps(x + 88);
64 x += 96;
65
66 // Compute reduced argument elements := round(x / log(2)).
67 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
72 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
73 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
74 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
75 const __m256 vn8 = _mm256_round_ps(_mm256_mul_ps(vx8, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
76 const __m256 vn9 = _mm256_round_ps(_mm256_mul_ps(vx9, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
77 const __m256 vn10 = _mm256_round_ps(_mm256_mul_ps(vx10, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
78 const __m256 vn11 = _mm256_round_ps(_mm256_mul_ps(vx11, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
79
80 // Compute reduced argument t := x - elements * log(2).
81 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
82 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
83 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
84 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
85 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
86 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
87 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
88 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
89 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
90 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
91 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
92 __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
93 __m256 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_hi, vx11);
94
95 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
96 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
97 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
98 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
99 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
100 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
101 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
102 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
103 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
104 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
105 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
106 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_lo, vt11);
107
108 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
109 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
110 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
111 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
112 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
113 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
114 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
115 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
116 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
117 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
118 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
119 __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
120 __m256 vp11 = _mm256_fmadd_ps(vc5, vt11, vc4);
121
122 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
123 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
124 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
125 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
126 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
127 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
128 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
129 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
130 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
131 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
132 vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
133 vp11 = _mm256_fmadd_ps(vp11, vt11, vc3);
134
135 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
136 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
137 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
138 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
139 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
140 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
141 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
142 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
143 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
144 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
145 vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
146 vp11 = _mm256_fmadd_ps(vp11, vt11, vc2);
147
148 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
149 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
150 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
151 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
152 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
153 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
154 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
155 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
156 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
157 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
158 vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
159 vp11 = _mm256_fmadd_ps(vp11, vt11, vc1);
160
161 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
162 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
163 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
164 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
165 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
166 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
167 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
168 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
169 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
170 vp9 = _mm256_fmadd_ps(vp9, vt9, vc0);
171 vp10 = _mm256_fmadd_ps(vp10, vt10, vc0);
172 vp11 = _mm256_fmadd_ps(vp11, vt11, vc0);
173
174 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
175 // - vnX is "exponent"
176 // - vpX is "mantissa"
177 //
178 // exp2(ae) * av + exp2(be) * bv =
179 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
180 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
181 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
182 //
183 // For computational efficiency we may add several "extended" floating-point numbers at a time.
184 __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0);
185 __m256 vmax_e1 = _mm256_max_ps(vacce1, vn1);
186 __m256 vmax_e2 = _mm256_max_ps(vacce2, vn2);
187 vmax_e0 = _mm256_max_ps(vmax_e0, vn3);
188 vmax_e1 = _mm256_max_ps(vmax_e1, vn4);
189 vmax_e2 = _mm256_max_ps(vmax_e2, vn5);
190 vmax_e0 = _mm256_max_ps(vmax_e0, vn6);
191 vmax_e1 = _mm256_max_ps(vmax_e1, vn7);
192 vmax_e2 = _mm256_max_ps(vmax_e2, vn8);
193 vmax_e0 = _mm256_max_ps(vmax_e0, vn9);
194 vmax_e1 = _mm256_max_ps(vmax_e1, vn10);
195 vmax_e2 = _mm256_max_ps(vmax_e2, vn11);
196
197 // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0.
198 // This replacement is done in two steps:
199 // 1. Clamp minimum delta_e at -127.0.
200 // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0
201 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent);
202 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_e1), vmin_exponent);
203 const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_e2), vmin_exponent);
204 const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent);
205 const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e1), vmin_exponent);
206 const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e2), vmin_exponent);
207 const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e0), vmin_exponent);
208 const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e1), vmin_exponent);
209 const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e2), vmin_exponent);
210 const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e0), vmin_exponent);
211 const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e1), vmin_exponent);
212 const __m256 vdelta_e8 = _mm256_max_ps(_mm256_sub_ps(vn8, vmax_e2), vmin_exponent);
213 const __m256 vdelta_e9 = _mm256_max_ps(_mm256_sub_ps(vn9, vmax_e0), vmin_exponent);
214 const __m256 vdelta_e10 = _mm256_max_ps(_mm256_sub_ps(vn10, vmax_e1), vmin_exponent);
215 const __m256 vdelta_e11 = _mm256_max_ps(_mm256_sub_ps(vn11, vmax_e2), vmin_exponent);
216
217 // Convert delta-exponents into scale factors:
218 // - s = exp2(delta_e) when delta_e > -127.0
219 // - s = 0.0 when delta_e <= -127.0
220 //
221 // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0.
222 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
223 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
224 const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
225 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23));
226 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23));
227 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23));
228 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23));
229 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23));
230 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23));
231 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23));
232 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23));
233 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e8, vmagic_bias)), 23));
234 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e9, vmagic_bias)), 23));
235 const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e10, vmagic_bias)), 23));
236 const __m256 vs11 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e11, vmagic_bias)), 23));
237
238 // Update accumulated "mantissa" and "exponent" values
239 vaccv0 = _mm256_mul_ps(vaccv0, vaccs0);
240 vaccv1 = _mm256_mul_ps(vaccv1, vaccs1);
241 vaccv2 = _mm256_mul_ps(vaccv2, vaccs2);
242 vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0);
243 vaccv1 = _mm256_fmadd_ps(vp1, vs1, vaccv1);
244 vaccv2 = _mm256_fmadd_ps(vp2, vs2, vaccv2);
245 vaccv0 = _mm256_fmadd_ps(vp3, vs3, vaccv0);
246 vaccv1 = _mm256_fmadd_ps(vp4, vs4, vaccv1);
247 vaccv2 = _mm256_fmadd_ps(vp5, vs5, vaccv2);
248 vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0);
249 vaccv1 = _mm256_fmadd_ps(vp7, vs7, vaccv1);
250 vaccv2 = _mm256_fmadd_ps(vp8, vs8, vaccv2);
251 vaccv0 = _mm256_fmadd_ps(vp9, vs9, vaccv0);
252 vaccv1 = _mm256_fmadd_ps(vp10, vs10, vaccv1);
253 vaccv2 = _mm256_fmadd_ps(vp11, vs11, vaccv2);
254
255 vacce0 = vmax_e0;
256 vacce1 = vmax_e1;
257 vacce2 = vmax_e2;
258 }
259
260 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
261 const __m256 vmax_acce01 = _mm256_max_ps(vacce0, vacce1);
262 const __m256 vmax_acce2 = vacce2;
263 const __m256 vmax_acce012 = _mm256_max_ps(vmax_acce01, vmax_acce2);
264
265 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_acce012), vmin_exponent);
266 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_acce012), vmin_exponent);
267 const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_acce012), vmin_exponent);
268
269 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
270 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
271 const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
272
273 __m256 vaccv = _mm256_mul_ps(vaccv0, vaccs0);
274 vaccv = _mm256_fmadd_ps(vaccv1, vaccs1, vaccv);
275 vaccv = _mm256_fmadd_ps(vaccv2, vaccs2, vaccv);
276 __m256 vacce = vmax_acce012;
277
278 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
279 // Load 8 inputs at a time.
280 const __m256 vx = _mm256_loadu_ps(x);
281 x += 8;
282
283 // Compute reduced argument elements := round(x / log(2)).
284 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
285
286 // Compute reduced argument t := x - elements * log(2).
287 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
288 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
289 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
290
291 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
292 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
293 vp = _mm256_fmadd_ps(vp, vt, vc3);
294 vp = _mm256_fmadd_ps(vp, vt, vc2);
295 vp = _mm256_fmadd_ps(vp, vt, vc1);
296 vp = _mm256_fmadd_ps(vp, vt, vc0);
297
298 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
299 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
300
301 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
302 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
303 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
304
305 // Convert exponents into scale factors.
306 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
307 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
308
309 // Update accumulated "mantissa" and "exponent" values.
310 vaccv = _mm256_mul_ps(vaccv, vaccs);
311 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
312
313 vacce = vmax_e;
314 }
315 if XNN_UNLIKELY(elements != 0) {
316 assert(elements >= 1 * sizeof(float));
317 assert(elements <= 7 * sizeof(float));
318 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
319
320 // Load up to 7 inputs at a time.
321 const __m256 vx = _mm256_maskload_ps(x, vmask);
322
323 // Compute reduced argument elements := round(x / log(2)).
324 __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
325
326 // Compute reduced argument t := x - elements * log(2).
327 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
328 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
329 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
330
331 // Correct reduced argument elements for masked out elements.
332 vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask));
333
334 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
335 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
336 vp = _mm256_fmadd_ps(vp, vt, vc3);
337 vp = _mm256_fmadd_ps(vp, vt, vc2);
338 vp = _mm256_fmadd_ps(vp, vt, vc1);
339 vp = _mm256_fmadd_ps(vp, vt, vc0);
340 vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask));
341
342 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
343 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
344
345 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
346 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
347 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
348
349 // Convert exponents into scale factors.
350 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
351 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
352
353 // Update accumulated "mantissa" and "exponent" values.
354 vaccv = _mm256_mul_ps(vaccv, vaccs);
355 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
356
357 vacce = vmax_e;
358 }
359
360 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
361 __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1));
362 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2)));
363 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1)));
364 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent);
365 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
366
367 vaccv = _mm256_mul_ps(vaccv, vaccs);
368 __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1));
369 vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum));
370 vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum));
371
372 _mm_store_ss(&sum[0], vaccv_sum);
373 _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce));
374
375 _mm256_zeroupper();
376 }
377