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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_x64_acc4(size_t elements,const float * x,float * sum)20 void xnn_f32_raddextexp_ukernel__avx2_p5_x64_acc4(
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 vaccv3 = _mm256_setzero_ps();
48   __m256 vacce0 = vminus_inf;
49   __m256 vacce1 = vminus_inf;
50   __m256 vacce2 = vminus_inf;
51   __m256 vacce3 = vminus_inf;
52   for (; elements >= 64 * sizeof(float); elements -= 64 * sizeof(float)) {
53     // Load 64 (8x8) inputs at a time.
54     const __m256 vx0 = _mm256_loadu_ps(x);
55     const __m256 vx1 = _mm256_loadu_ps(x + 8);
56     const __m256 vx2 = _mm256_loadu_ps(x + 16);
57     const __m256 vx3 = _mm256_loadu_ps(x + 24);
58     const __m256 vx4 = _mm256_loadu_ps(x + 32);
59     const __m256 vx5 = _mm256_loadu_ps(x + 40);
60     const __m256 vx6 = _mm256_loadu_ps(x + 48);
61     const __m256 vx7 = _mm256_loadu_ps(x + 56);
62     x += 64;
63 
64     // Compute reduced argument elements := round(x / log(2)).
65     const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
66     const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
67     const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
68     const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
69     const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
70     const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
71     const __m256 vn6 = _mm256_round_ps(_mm256_mul_ps(vx6, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
72     const __m256 vn7 = _mm256_round_ps(_mm256_mul_ps(vx7, 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 
85     vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
86     vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
87     vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
88     vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
89     vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
90     vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
91     vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
92     vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
93 
94     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
95     __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
96     __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
97     __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
98     __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
99     __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
100     __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
101     __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
102     __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
103 
104     vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
105     vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
106     vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
107     vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
108     vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
109     vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
110     vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
111     vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
112 
113     vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
114     vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
115     vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
116     vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
117     vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
118     vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
119     vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
120     vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
121 
122     vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
123     vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
124     vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
125     vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
126     vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
127     vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
128     vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
129     vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
130 
131     vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
132     vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
133     vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
134     vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
135     vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
136     vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
137     vp6 = _mm256_fmadd_ps(vp6, vt6, vc0);
138     vp7 = _mm256_fmadd_ps(vp7, vt7, vc0);
139 
140     // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
141     //  - vnX is "exponent"
142     //  - vpX is "mantissa"
143     //
144     // exp2(ae) * av + exp2(be) * bv =
145     //   = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
146     //   = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
147     //   = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
148     //
149     // For computational efficiency we may add several "extended" floating-point numbers at a time.
150     __m256 vmax_e0 = _mm256_max_ps(vacce0, vn0);
151     __m256 vmax_e1 = _mm256_max_ps(vacce1, vn1);
152     __m256 vmax_e2 = _mm256_max_ps(vacce2, vn2);
153     __m256 vmax_e3 = _mm256_max_ps(vacce3, vn3);
154     vmax_e0 = _mm256_max_ps(vmax_e0, vn4);
155     vmax_e1 = _mm256_max_ps(vmax_e1, vn5);
156     vmax_e2 = _mm256_max_ps(vmax_e2, vn6);
157     vmax_e3 = _mm256_max_ps(vmax_e3, vn7);
158 
159     // For computational efficiency, replace exp2(delta_e) with 0.0f when delta_e <= -127.0.
160     // This replacement is done in two steps:
161     // 1. Clamp minimum delta_e at -127.0.
162     // 2. Map delta_e to scale factor 0.0 when delta_e == -127.0
163     const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_e0), vmin_exponent);
164     const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_e1), vmin_exponent);
165     const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_e2), vmin_exponent);
166     const __m256 vdelta_acce3 = _mm256_max_ps(_mm256_sub_ps(vacce3, vmax_e3), vmin_exponent);
167     const __m256 vdelta_e0 = _mm256_max_ps(_mm256_sub_ps(vn0, vmax_e0), vmin_exponent);
168     const __m256 vdelta_e1 = _mm256_max_ps(_mm256_sub_ps(vn1, vmax_e1), vmin_exponent);
169     const __m256 vdelta_e2 = _mm256_max_ps(_mm256_sub_ps(vn2, vmax_e2), vmin_exponent);
170     const __m256 vdelta_e3 = _mm256_max_ps(_mm256_sub_ps(vn3, vmax_e3), vmin_exponent);
171     const __m256 vdelta_e4 = _mm256_max_ps(_mm256_sub_ps(vn4, vmax_e0), vmin_exponent);
172     const __m256 vdelta_e5 = _mm256_max_ps(_mm256_sub_ps(vn5, vmax_e1), vmin_exponent);
173     const __m256 vdelta_e6 = _mm256_max_ps(_mm256_sub_ps(vn6, vmax_e2), vmin_exponent);
174     const __m256 vdelta_e7 = _mm256_max_ps(_mm256_sub_ps(vn7, vmax_e3), vmin_exponent);
175 
176     // Convert delta-exponents into scale factors:
177     // - s = exp2(delta_e) when delta_e > -127.0
178     // - s = 0.0 when delta_e <= -127.0
179     //
180     // Note: delta-exponents can not exceed 0.0, thus scale factors can not exceed 1.0.
181     const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
182     const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
183     const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
184     const __m256 vaccs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce3, vmagic_bias)), 23));
185     const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e0, vmagic_bias)), 23));
186     const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e1, vmagic_bias)), 23));
187     const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e2, vmagic_bias)), 23));
188     const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e3, vmagic_bias)), 23));
189     const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e4, vmagic_bias)), 23));
190     const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e5, vmagic_bias)), 23));
191     const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e6, vmagic_bias)), 23));
192     const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e7, vmagic_bias)), 23));
193 
194     // Update accumulated "mantissa" and "exponent" values
195     vaccv0 = _mm256_mul_ps(vaccv0, vaccs0);
196     vaccv1 = _mm256_mul_ps(vaccv1, vaccs1);
197     vaccv2 = _mm256_mul_ps(vaccv2, vaccs2);
198     vaccv3 = _mm256_mul_ps(vaccv3, vaccs3);
199     vaccv0 = _mm256_fmadd_ps(vp0, vs0, vaccv0);
200     vaccv1 = _mm256_fmadd_ps(vp1, vs1, vaccv1);
201     vaccv2 = _mm256_fmadd_ps(vp2, vs2, vaccv2);
202     vaccv3 = _mm256_fmadd_ps(vp3, vs3, vaccv3);
203     vaccv0 = _mm256_fmadd_ps(vp4, vs4, vaccv0);
204     vaccv1 = _mm256_fmadd_ps(vp5, vs5, vaccv1);
205     vaccv2 = _mm256_fmadd_ps(vp6, vs6, vaccv2);
206     vaccv3 = _mm256_fmadd_ps(vp7, vs7, vaccv3);
207 
208     vacce0 = vmax_e0;
209     vacce1 = vmax_e1;
210     vacce2 = vmax_e2;
211     vacce3 = vmax_e3;
212   }
213 
214   // Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
215   const __m256 vmax_acce01 = _mm256_max_ps(vacce0, vacce1);
216   const __m256 vmax_acce23 = _mm256_max_ps(vacce2, vacce3);
217   const __m256 vmax_acce0123 = _mm256_max_ps(vmax_acce01, vmax_acce23);
218 
219   const __m256 vdelta_acce0 = _mm256_max_ps(_mm256_sub_ps(vacce0, vmax_acce0123), vmin_exponent);
220   const __m256 vdelta_acce1 = _mm256_max_ps(_mm256_sub_ps(vacce1, vmax_acce0123), vmin_exponent);
221   const __m256 vdelta_acce2 = _mm256_max_ps(_mm256_sub_ps(vacce2, vmax_acce0123), vmin_exponent);
222   const __m256 vdelta_acce3 = _mm256_max_ps(_mm256_sub_ps(vacce3, vmax_acce0123), vmin_exponent);
223 
224   const __m256 vaccs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce0, vmagic_bias)), 23));
225   const __m256 vaccs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce1, vmagic_bias)), 23));
226   const __m256 vaccs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce2, vmagic_bias)), 23));
227   const __m256 vaccs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce3, vmagic_bias)), 23));
228 
229   __m256 vaccv = _mm256_mul_ps(vaccv0, vaccs0);
230   vaccv = _mm256_fmadd_ps(vaccv1, vaccs1, vaccv);
231   vaccv = _mm256_fmadd_ps(vaccv2, vaccs2, vaccv);
232   vaccv = _mm256_fmadd_ps(vaccv3, vaccs3, vaccv);
233   __m256 vacce = vmax_acce0123;
234 
235   for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
236     // Load 8 inputs at a time.
237     const __m256 vx = _mm256_loadu_ps(x);
238     x += 8;
239 
240     // Compute reduced argument elements := round(x / log(2)).
241     const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
242 
243     // Compute reduced argument t := x - elements * log(2).
244     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
245     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
246     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
247 
248     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
249     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
250     vp = _mm256_fmadd_ps(vp, vt, vc3);
251     vp = _mm256_fmadd_ps(vp, vt, vc2);
252     vp = _mm256_fmadd_ps(vp, vt, vc1);
253     vp = _mm256_fmadd_ps(vp, vt, vc0);
254 
255     // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
256     const __m256 vmax_e = _mm256_max_ps(vacce, vn);
257 
258     // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
259     const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
260     const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
261 
262     // Convert exponents into scale factors.
263     const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
264     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
265 
266     // Update accumulated "mantissa" and "exponent" values.
267     vaccv = _mm256_mul_ps(vaccv, vaccs);
268     vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
269 
270     vacce = vmax_e;
271   }
272   if XNN_UNLIKELY(elements != 0) {
273     assert(elements >= 1 * sizeof(float));
274     assert(elements <= 7 * sizeof(float));
275     const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
276 
277     // Load up to 7 inputs at a time.
278     const __m256 vx = _mm256_maskload_ps(x, vmask);
279 
280     // Compute reduced argument elements := round(x / log(2)).
281     __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
282 
283     // Compute reduced argument t := x - elements * log(2).
284     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
285     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
286     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
287 
288     // Correct reduced argument elements for masked out elements.
289     vn = _mm256_blendv_ps(vacce, vn, _mm256_castsi256_ps(vmask));
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     vp = _mm256_and_ps(vp, _mm256_castsi256_ps(vmask));
298 
299     // Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
300     const __m256 vmax_e = _mm256_max_ps(vacce, vn);
301 
302     // For computational efficiency, clamp minimum exp2(delta_e) at -127.0. It will be mapped to 0.0 scale factor later.
303     const __m256 vdelta_e = _mm256_max_ps(_mm256_sub_ps(vn, vmax_e), vmin_exponent);
304     const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_e), vmin_exponent);
305 
306     // Convert exponents into scale factors.
307     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_e, vmagic_bias)), 23));
308     const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
309 
310     // Update accumulated "mantissa" and "exponent" values.
311     vaccv = _mm256_mul_ps(vaccv, vaccs);
312     vaccv = _mm256_fmadd_ps(vp, vs, vaccv);
313 
314     vacce = vmax_e;
315   }
316 
317   // Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
318   __m256 vmax_acce = _mm256_max_ps(vacce, _mm256_permute2f128_ps(vacce, vacce, 1));
319   vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(1, 0, 3, 2)));
320   vmax_acce = _mm256_max_ps(vmax_acce, _mm256_shuffle_ps(vmax_acce, vmax_acce, _MM_SHUFFLE(2, 3, 0, 1)));
321   const __m256 vdelta_acce = _mm256_max_ps(_mm256_sub_ps(vacce, vmax_acce), vmin_exponent);
322   const __m256 vaccs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(vdelta_acce, vmagic_bias)), 23));
323 
324   vaccv = _mm256_mul_ps(vaccv, vaccs);
325   __m128 vaccv_sum = _mm_add_ps(_mm256_castps256_ps128(vaccv), _mm256_extractf128_ps(vaccv, 1));
326   vaccv_sum = _mm_add_ps(vaccv_sum, _mm_movehl_ps(vaccv_sum, vaccv_sum));
327   vaccv_sum = _mm_add_ss(vaccv_sum, _mm_movehdup_ps(vaccv_sum));
328 
329   _mm_store_ss(&sum[0], vaccv_sum);
330   _mm_store_ss(&sum[1], _mm256_castps256_ps128(vmax_acce));
331 
332   _mm256_zeroupper();
333 }
334