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_x80_acc2(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx2_p5_x80_acc2(
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 vacce0 = vminus_inf;
47 __m256 vacce1 = vminus_inf;
48 for (; elements >= 80 * sizeof(float); elements -= 80 * sizeof(float)) {
49 // Load 80 (10x8) inputs at a time.
50 const __m256 vx0 = _mm256_loadu_ps(x);
51 const __m256 vx1 = _mm256_loadu_ps(x + 8);
52 const __m256 vx2 = _mm256_loadu_ps(x + 16);
53 const __m256 vx3 = _mm256_loadu_ps(x + 24);
54 const __m256 vx4 = _mm256_loadu_ps(x + 32);
55 const __m256 vx5 = _mm256_loadu_ps(x + 40);
56 const __m256 vx6 = _mm256_loadu_ps(x + 48);
57 const __m256 vx7 = _mm256_loadu_ps(x + 56);
58 const __m256 vx8 = _mm256_loadu_ps(x + 64);
59 const __m256 vx9 = _mm256_loadu_ps(x + 72);
60 x += 80;
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
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 __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
86
87 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
88 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
89 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
90 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
91 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
92 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
93 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
94 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
95 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
96 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
97
98 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
99 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
100 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
101 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
102 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
103 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
104 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
105 __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
106 __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
107 __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
108 __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
109
110 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
111 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
112 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
113 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
114 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
115 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
116 vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
117 vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
118 vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
119 vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
120
121 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
122 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
123 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
124 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
125 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
126 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
127 vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
128 vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
129 vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
130 vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
131
132 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
133 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
134 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
135 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
136 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
137 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
138 vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
139 vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
140 vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
141 vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
142
143 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
144 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
145 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
146 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
147 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
148 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
149 vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
150 vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
151 vp8 = _mm256_fmadd_ps(vp8, vt8, vc0);
152 vp9 = _mm256_fmadd_ps(vp9, vt9, vc0);
153
154 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
155 // - vnX is "exponent"
156 // - vpX is "mantissa"
157 //
158 // exp2(ae) * av + exp2(be) * bv =
159 // = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
160 // = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
161 // = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
162 //
163 // For computational efficiency we may add several "extended" floating-point numbers at a time.
164 __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0);
165 __m256 vmax_e1 = _mm256_max_ps(vacce1, vn1);
166 vmax_e0 = _mm256_max_ps(vmax_e0, vn2);
167 vmax_e1 = _mm256_max_ps(vmax_e1, vn3);
168 vmax_e0 = _mm256_max_ps(vmax_e0, vn4);
169 vmax_e1 = _mm256_max_ps(vmax_e1, vn5);
170 vmax_e0 = _mm256_max_ps(vmax_e0, vn6);
171 vmax_e1 = _mm256_max_ps(vmax_e1, vn7);
172 vmax_e0 = _mm256_max_ps(vmax_e0, vn8);
173 vmax_e1 = _mm256_max_ps(vmax_e1, vn9);
174
175 // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0.
176 // This replacement is done in two steps:
177 // 1. Clamp minimum delta_e at -127.0.
178 // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0
179 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent);
180 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_e1), vmin_exponent);
181 const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent);
182 const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e1), vmin_exponent);
183 const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e0), vmin_exponent);
184 const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e1), vmin_exponent);
185 const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e0), vmin_exponent);
186 const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e1), vmin_exponent);
187 const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e0), vmin_exponent);
188 const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e1), vmin_exponent);
189 const __m256 vdelta_e8 = _mm256_max_ps(_mm256_sub_ps(vn8, vmax_e0), vmin_exponent);
190 const __m256 vdelta_e9 = _mm256_max_ps(_mm256_sub_ps(vn9, vmax_e1), vmin_exponent);
191
192 // Convert delta-exponents into scale factors:
193 // - s = exp2(delta_e) when delta_e > -127.0
194 // - s = 0.0 when delta_e <= -127.0
195 //
196 // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0.
197 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
198 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
199 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23));
200 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23));
201 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23));
202 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23));
203 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23));
204 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23));
205 const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23));
206 const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23));
207 const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e8, vmagic_bias)), 23));
208 const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e9, vmagic_bias)), 23));
209
210 // Update accumulated "mantissa" and "exponent" values
211 vaccv0 = _mm256_mul_ps(vaccv0, vaccs0);
212 vaccv1 = _mm256_mul_ps(vaccv1, vaccs1);
213 vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0);
214 vaccv1 = _mm256_fmadd_ps(vp1, vs1, vaccv1);
215 vaccv0 = _mm256_fmadd_ps(vp2, vs2, vaccv0);
216 vaccv1 = _mm256_fmadd_ps(vp3, vs3, vaccv1);
217 vaccv0 = _mm256_fmadd_ps(vp4, vs4, vaccv0);
218 vaccv1 = _mm256_fmadd_ps(vp5, vs5, vaccv1);
219 vaccv0 = _mm256_fmadd_ps(vp6, vs6, vaccv0);
220 vaccv1 = _mm256_fmadd_ps(vp7, vs7, vaccv1);
221 vaccv0 = _mm256_fmadd_ps(vp8, vs8, vaccv0);
222 vaccv1 = _mm256_fmadd_ps(vp9, vs9, vaccv1);
223
224 vacce0 = vmax_e0;
225 vacce1 = vmax_e1;
226 }
227
228 // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
229 const __m256 vmax_acce01 = _mm256_max_ps(vacce0, vacce1);
230
231 const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_acce01), vmin_exponent);
232 const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_acce01), vmin_exponent);
233
234 const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
235 const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
236
237 __m256 vaccv = _mm256_mul_ps(vaccv0, vaccs0);
238 vaccv = _mm256_fmadd_ps(vaccv1, vaccs1, vaccv);
239 __m256 vacce = vmax_acce01;
240
241 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
242 // Load 8 inputs at a time.
243 const __m256 vx = _mm256_loadu_ps(x);
244 x += 8;
245
246 // Compute reduced argument elements := round(x / log(2)).
247 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
248
249 // Compute reduced argument t := x - elements * log(2).
250 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
251 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
252 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
253
254 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
255 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
256 vp = _mm256_fmadd_ps(vp, vt, vc3);
257 vp = _mm256_fmadd_ps(vp, vt, vc2);
258 vp = _mm256_fmadd_ps(vp, vt, vc1);
259 vp = _mm256_fmadd_ps(vp, vt, vc0);
260
261 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
262 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
263
264 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
265 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
266 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
267
268 // Convert exponents into scale factors.
269 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
270 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
271
272 // Update accumulated "mantissa" and "exponent" values.
273 vaccv = _mm256_mul_ps(vaccv, vaccs);
274 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
275
276 vacce = vmax_e;
277 }
278 if XNN_UNLIKELY(elements != 0) {
279 assert(elements >= 1 * sizeof(float));
280 assert(elements <= 7 * sizeof(float));
281 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
282
283 // Load up to 7 inputs at a time.
284 const __m256 vx = _mm256_maskload_ps(x, vmask);
285
286 // Compute reduced argument elements := round(x / log(2)).
287 __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
288
289 // Compute reduced argument t := x - elements * log(2).
290 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
291 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
292 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
293
294 // Correct reduced argument elements for masked out elements.
295 vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask));
296
297 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
298 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
299 vp = _mm256_fmadd_ps(vp, vt, vc3);
300 vp = _mm256_fmadd_ps(vp, vt, vc2);
301 vp = _mm256_fmadd_ps(vp, vt, vc1);
302 vp = _mm256_fmadd_ps(vp, vt, vc0);
303 vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask));
304
305 // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
306 const __m256 vmax_e = _mm256_max_ps(vacce, vn);
307
308 // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
309 const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
310 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
311
312 // Convert exponents into scale factors.
313 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
314 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
315
316 // Update accumulated "mantissa" and "exponent" values.
317 vaccv = _mm256_mul_ps(vaccv, vaccs);
318 vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
319
320 vacce = vmax_e;
321 }
322
323 // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
324 __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1));
325 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2)));
326 vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1)));
327 const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent);
328 const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
329
330 vaccv = _mm256_mul_ps(vaccv, vaccs);
331 __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1));
332 vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum));
333 vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum));
334
335 _mm_store_ss(&sum[0], vaccv_sum);
336 _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce));
337
338 _mm256_zeroupper();
339 }
340