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(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx2_p5_x96(
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 vacce0 = vminus_inf;
46 for (; elements >= 96 * sizeof(float); elements -= 96 * sizeof(float)) {
47 // Load 96 (12x8) inputs at a time.
48 const __m256 vx0 = _mm256_loadu_ps(x);
49 const __m256 vx1 = _mm256_loadu_ps(x + 8);
50 const __m256 vx2 = _mm256_loadu_ps(x + 16);
51 const __m256 vx3 = _mm256_loadu_ps(x + 24);
52 const __m256 vx4 = _mm256_loadu_ps(x + 32);
53 const __m256 vx5 = _mm256_loadu_ps(x + 40);
54 const __m256 vx6 = _mm256_loadu_ps(x + 48);
55 const __m256 vx7 = _mm256_loadu_ps(x + 56);
56 const __m256 vx8 = _mm256_loadu_ps(x + 64);
57 const __m256 vx9 = _mm256_loadu_ps(x + 72);
58 const __m256 vx10 = _mm256_loadu_ps(x + 80);
59 const __m256 vx11 = _mm256_loadu_ps(x + 88);
60 x += 96;
61
62 // Compute reduced argument elements := round(x / log(2)).
63 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
64 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71 const __m256 vn8 = _mm256_round_ps(_mm256_mul_ps(vx8, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
72 const __m256 vn9 = _mm256_round_ps(_mm256_mul_ps(vx9, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
73 const __m256 vn10 = _mm256_round_ps(_mm256_mul_ps(vx10, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
74 const __m256 vn11 = _mm256_round_ps(_mm256_mul_ps(vx11, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
75
76 // Compute reduced argument t := x - elements * log(2).
77 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
78 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
79 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
80 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
81 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
82 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
83 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
84 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
85 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
86 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
87 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
88 __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
89 __m256 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_hi, vx11);
90
91 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
92 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
93 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
94 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
95 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
96 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
97 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
98 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
99 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
100 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
101 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
102 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_lo, vt11);
103
104 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
105 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
106 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
107 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
108 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
109 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
110 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
111 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
112 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
113 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
114 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
115 __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
116 __m256 vp11 = _mm256_fmadd_ps(vc5, vt11, vc4);
117
118 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
119 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
120 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
121 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
122 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
123 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
124 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
125 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
126 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
127 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
128 vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
129 vp11 = _mm256_fmadd_ps(vp11, vt11, vc3);
130
131 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
132 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
133 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
134 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
135 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
136 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
137 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
138 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
139 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
140 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
141 vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
142 vp11 = _mm256_fmadd_ps(vp11, vt11, vc2);
143
144 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
145 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
146 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
147 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
148 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
149 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
150 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
151 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
152 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
153 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
154 vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
155 vp11 = _mm256_fmadd_ps(vp11, vt11, vc1);
156
157 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
158 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
159 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
160 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
161 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
162 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
163 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
164 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
165 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
166 vp9 = _mm256_fmadd_ps(vp9, vt9, vc0);
167 vp10 = _mm256_fmadd_ps(vp10, vt10, vc0);
168 vp11 = _mm256_fmadd_ps(vp11, vt11, vc0);
169
170 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
171 // - vnX is "exponent"
172 // - vpX is "mantissa"
173 //
174 // exp2(ae) * av + exp2(be) * bv =
175 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
176 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
177 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
178 //
179 // For computational efficiency we may add several "extended" floating-point numbers at a time.
180 __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0);
181 vmax_e0 = _mm256_max_ps(vmax_e0, vn1);
182 vmax_e0 = _mm256_max_ps(vmax_e0, vn2);
183 vmax_e0 = _mm256_max_ps(vmax_e0, vn3);
184 vmax_e0 = _mm256_max_ps(vmax_e0, vn4);
185 vmax_e0 = _mm256_max_ps(vmax_e0, vn5);
186 vmax_e0 = _mm256_max_ps(vmax_e0, vn6);
187 vmax_e0 = _mm256_max_ps(vmax_e0, vn7);
188 vmax_e0 = _mm256_max_ps(vmax_e0, vn8);
189 vmax_e0 = _mm256_max_ps(vmax_e0, vn9);
190 vmax_e0 = _mm256_max_ps(vmax_e0, vn10);
191 vmax_e0 = _mm256_max_ps(vmax_e0, vn11);
192
193 // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0.
194 // This replacement is done in two steps:
195 // 1. Clamp minimum delta_e at -127.0.
196 // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0
197 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent);
198 const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent);
199 const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e0), vmin_exponent);
200 const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e0), vmin_exponent);
201 const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e0), vmin_exponent);
202 const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e0), vmin_exponent);
203 const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e0), vmin_exponent);
204 const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e0), vmin_exponent);
205 const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e0), vmin_exponent);
206 const __m256 vdelta_e8 = _mm256_max_ps(_mm256_sub_ps(vn8, vmax_e0), vmin_exponent);
207 const __m256 vdelta_e9 = _mm256_max_ps(_mm256_sub_ps(vn9, vmax_e0), vmin_exponent);
208 const __m256 vdelta_e10 = _mm256_max_ps(_mm256_sub_ps(vn10, vmax_e0), vmin_exponent);
209 const __m256 vdelta_e11 = _mm256_max_ps(_mm256_sub_ps(vn11, vmax_e0), vmin_exponent);
210
211 // Convert delta-exponents into scale factors:
212 // - s = exp2(delta_e) when delta_e > -127.0
213 // - s = 0.0 when delta_e <= -127.0
214 //
215 // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0.
216 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
217 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23));
218 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23));
219 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23));
220 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23));
221 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23));
222 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23));
223 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23));
224 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23));
225 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e8, vmagic_bias)), 23));
226 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e9, vmagic_bias)), 23));
227 const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e10, vmagic_bias)), 23));
228 const __m256 vs11 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e11, vmagic_bias)), 23));
229
230 // Update accumulated "mantissa" and "exponent" values
231 vaccv0 = _mm256_mul_ps(vaccv0, vaccs0);
232 vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0);
233 vaccv0 = _mm256_fmadd_ps(vp1, vs1, vaccv0);
234 vaccv0 = _mm256_fmadd_ps(vp2, vs2, vaccv0);
235 vaccv0 = _mm256_fmadd_ps(vp3, vs3, vaccv0);
236 vaccv0 = _mm256_fmadd_ps(vp4, vs4, vaccv0);
237 vaccv0 = _mm256_fmadd_ps(vp5, vs5, vaccv0);
238 vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0);
239 vaccv0 = _mm256_fmadd_ps(vp7, vs7, vaccv0);
240 vaccv0 = _mm256_fmadd_ps(vp8, vs8, vaccv0);
241 vaccv0 = _mm256_fmadd_ps(vp9, vs9, vaccv0);
242 vaccv0 = _mm256_fmadd_ps(vp10, vs10, vaccv0);
243 vaccv0 = _mm256_fmadd_ps(vp11, vs11, vaccv0);
244
245 vacce0 = vmax_e0;
246 }
247
248 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
249 __m256 vaccv = vaccv0;
250 __m256 vacce = vacce0;
251
252 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
253 // Load 8 inputs at a time.
254 const __m256 vx = _mm256_loadu_ps(x);
255 x += 8;
256
257 // Compute reduced argument elements := round(x / log(2)).
258 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
259
260 // Compute reduced argument t := x - elements * log(2).
261 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
262 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
263 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
264
265 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
266 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
267 vp = _mm256_fmadd_ps(vp, vt, vc3);
268 vp = _mm256_fmadd_ps(vp, vt, vc2);
269 vp = _mm256_fmadd_ps(vp, vt, vc1);
270 vp = _mm256_fmadd_ps(vp, vt, vc0);
271
272 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
273 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
274
275 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
276 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
277 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
278
279 // Convert exponents into scale factors.
280 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
281 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
282
283 // Update accumulated "mantissa" and "exponent" values.
284 vaccv = _mm256_mul_ps(vaccv, vaccs);
285 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
286
287 vacce = vmax_e;
288 }
289 if XNN_UNLIKELY(elements != 0) {
290 assert(elements >= 1 * sizeof(float));
291 assert(elements <= 7 * sizeof(float));
292 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
293
294 // Load up to 7 inputs at a time.
295 const __m256 vx = _mm256_maskload_ps(x, vmask);
296
297 // Compute reduced argument elements := round(x / log(2)).
298 __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
299
300 // Compute reduced argument t := x - elements * log(2).
301 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
302 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
303 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
304
305 // Correct reduced argument elements for masked out elements.
306 vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask));
307
308 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
309 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
310 vp = _mm256_fmadd_ps(vp, vt, vc3);
311 vp = _mm256_fmadd_ps(vp, vt, vc2);
312 vp = _mm256_fmadd_ps(vp, vt, vc1);
313 vp = _mm256_fmadd_ps(vp, vt, vc0);
314 vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask));
315
316 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
317 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
318
319 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
320 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
321 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
322
323 // Convert exponents into scale factors.
324 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
325 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
326
327 // Update accumulated "mantissa" and "exponent" values.
328 vaccv = _mm256_mul_ps(vaccv, vaccs);
329 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
330
331 vacce = vmax_e;
332 }
333
334 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
335 __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1));
336 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2)));
337 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1)));
338 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent);
339 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
340
341 vaccv = _mm256_mul_ps(vaccv, vaccs);
342 __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1));
343 vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum));
344 vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum));
345
346 _mm_store_ss(&sum[0], vaccv_sum);
347 _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce));
348
349 _mm256_zeroupper();
350 }
351