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_x72_acc3(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx2_p5_x72_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 >= 72 * sizeof(float); elements -= 72 * sizeof(float)) {
51 // Load 72 (9x8) 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 x += 72;
62
63 // Compute reduced argument elements := round(x / log(2)).
64 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70 const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71 const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
72 const __m256 vn8 = _mm256_round_ps(_mm256_mul_ps(vx8, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
73
74 // Compute reduced argument t := x - elements * log(2).
75 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
76 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
77 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
78 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
79 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
80 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
81 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
82 __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
83 __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
84 __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
85
86 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
87 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
88 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
89 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
90 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
91 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
92 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
93 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
94 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
95
96 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
97 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
98 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
99 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
100 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
101 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
102 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
103 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
104 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
105 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
106
107 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
108 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
109 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
110 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
111 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
112 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
113 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
114 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
115 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
116
117 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
118 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
119 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
120 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
121 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
122 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
123 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
124 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
125 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
126
127 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
128 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
129 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
130 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
131 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
132 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
133 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
134 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
135 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
136
137 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
138 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
139 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
140 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
141 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
142 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
143 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
144 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
145 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
146
147 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
148 // - vnX is "exponent"
149 // - vpX is "mantissa"
150 //
151 // exp2(ae) * av + exp2(be) * bv =
152 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
153 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
154 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
155 //
156 // For computational efficiency we may add several "extended" floating-point numbers at a time.
157 __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0);
158 __m256 vmax_e1 = _mm256_max_ps(vacce1, vn1);
159 __m256 vmax_e2 = _mm256_max_ps(vacce2, vn2);
160 vmax_e0 = _mm256_max_ps(vmax_e0, vn3);
161 vmax_e1 = _mm256_max_ps(vmax_e1, vn4);
162 vmax_e2 = _mm256_max_ps(vmax_e2, vn5);
163 vmax_e0 = _mm256_max_ps(vmax_e0, vn6);
164 vmax_e1 = _mm256_max_ps(vmax_e1, vn7);
165 vmax_e2 = _mm256_max_ps(vmax_e2, vn8);
166
167 // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0.
168 // This replacement is done in two steps:
169 // 1. Clamp minimum delta_e at -127.0.
170 // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0
171 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent);
172 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_e1), vmin_exponent);
173 const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_e2), vmin_exponent);
174 const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent);
175 const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e1), vmin_exponent);
176 const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e2), vmin_exponent);
177 const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e0), vmin_exponent);
178 const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e1), vmin_exponent);
179 const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e2), vmin_exponent);
180 const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e0), vmin_exponent);
181 const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e1), vmin_exponent);
182 const __m256 vdelta_e8 = _mm256_max_ps(_mm256_sub_ps(vn8, vmax_e2), vmin_exponent);
183
184 // Convert delta-exponents into scale factors:
185 // - s = exp2(delta_e) when delta_e > -127.0
186 // - s = 0.0 when delta_e <= -127.0
187 //
188 // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0.
189 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
190 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
191 const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
192 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23));
193 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23));
194 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23));
195 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23));
196 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23));
197 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23));
198 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23));
199 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23));
200 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e8, vmagic_bias)), 23));
201
202 // Update accumulated "mantissa" and "exponent" values
203 vaccv0 = _mm256_mul_ps(vaccv0, vaccs0);
204 vaccv1 = _mm256_mul_ps(vaccv1, vaccs1);
205 vaccv2 = _mm256_mul_ps(vaccv2, vaccs2);
206 vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0);
207 vaccv1 = _mm256_fmadd_ps(vp1, vs1, vaccv1);
208 vaccv2 = _mm256_fmadd_ps(vp2, vs2, vaccv2);
209 vaccv0 = _mm256_fmadd_ps(vp3, vs3, vaccv0);
210 vaccv1 = _mm256_fmadd_ps(vp4, vs4, vaccv1);
211 vaccv2 = _mm256_fmadd_ps(vp5, vs5, vaccv2);
212 vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0);
213 vaccv1 = _mm256_fmadd_ps(vp7, vs7, vaccv1);
214 vaccv2 = _mm256_fmadd_ps(vp8, vs8, vaccv2);
215
216 vacce0 = vmax_e0;
217 vacce1 = vmax_e1;
218 vacce2 = vmax_e2;
219 }
220
221 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
222 const __m256 vmax_acce01 = _mm256_max_ps(vacce0, vacce1);
223 const __m256 vmax_acce2 = vacce2;
224 const __m256 vmax_acce012 = _mm256_max_ps(vmax_acce01, vmax_acce2);
225
226 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_acce012), vmin_exponent);
227 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_acce012), vmin_exponent);
228 const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_acce012), vmin_exponent);
229
230 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
231 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
232 const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
233
234 __m256 vaccv = _mm256_mul_ps(vaccv0, vaccs0);
235 vaccv = _mm256_fmadd_ps(vaccv1, vaccs1, vaccv);
236 vaccv = _mm256_fmadd_ps(vaccv2, vaccs2, vaccv);
237 __m256 vacce = vmax_acce012;
238
239 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
240 // Load 8 inputs at a time.
241 const __m256 vx = _mm256_loadu_ps(x);
242 x += 8;
243
244 // Compute reduced argument elements := round(x / log(2)).
245 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
246
247 // Compute reduced argument t := x - elements * log(2).
248 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
249 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
250 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
251
252 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
253 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
254 vp = _mm256_fmadd_ps(vp, vt, vc3);
255 vp = _mm256_fmadd_ps(vp, vt, vc2);
256 vp = _mm256_fmadd_ps(vp, vt, vc1);
257 vp = _mm256_fmadd_ps(vp, vt, vc0);
258
259 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
260 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
261
262 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
263 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
264 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
265
266 // Convert exponents into scale factors.
267 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
268 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
269
270 // Update accumulated "mantissa" and "exponent" values.
271 vaccv = _mm256_mul_ps(vaccv, vaccs);
272 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
273
274 vacce = vmax_e;
275 }
276 if XNN_UNLIKELY(elements != 0) {
277 assert(elements >= 1 * sizeof(float));
278 assert(elements <= 7 * sizeof(float));
279 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
280
281 // Load up to 7 inputs at a time.
282 const __m256 vx = _mm256_maskload_ps(x, vmask);
283
284 // Compute reduced argument elements := round(x / log(2)).
285 __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
286
287 // Compute reduced argument t := x - elements * log(2).
288 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
289 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
290 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
291
292 // Correct reduced argument elements for masked out elements.
293 vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask));
294
295 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
296 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
297 vp = _mm256_fmadd_ps(vp, vt, vc3);
298 vp = _mm256_fmadd_ps(vp, vt, vc2);
299 vp = _mm256_fmadd_ps(vp, vt, vc1);
300 vp = _mm256_fmadd_ps(vp, vt, vc0);
301 vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask));
302
303 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
304 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
305
306 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
307 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
308 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
309
310 // Convert exponents into scale factors.
311 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
312 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
313
314 // Update accumulated "mantissa" and "exponent" values.
315 vaccv = _mm256_mul_ps(vaccv, vaccs);
316 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
317
318 vacce = vmax_e;
319 }
320
321 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
322 __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1));
323 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2)));
324 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1)));
325 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent);
326 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
327
328 vaccv = _mm256_mul_ps(vaccv, vaccs);
329 __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1));
330 vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum));
331 vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum));
332
333 _mm_store_ss(&sum[0], vaccv_sum);
334 _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce));
335
336 _mm256_zeroupper();
337 }
338