• Home
  • Line#
  • Scopes#
  • Navigate#
  • Raw
  • Download
1 // Auto-generated file. Do not edit!
2 //   Template: src/f32-raddstoreexpminusmax/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 
12 #include <immintrin.h>
13 
14 #include <xnnpack/raddstoreexpminusmax.h>
15 
16 
17 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
18 
xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x96(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x96(
20     size_t elements,
21     const float* input,
22     float* output,
23     float* sum,
24     float max)
25 {
26   assert(elements % sizeof(float) == 0);
27 
28   const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
29   // The smallest x for which expf(x) is normalized.
30   const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
31   const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
32   const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
33   const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
34 
35   const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
36   const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
37   const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
38   const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
39   const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
40 
41   const __m256 vi_max = _mm256_set1_ps(max);
42 
43   __m256 vacc0 = _mm256_setzero_ps();
44   for (; elements >= 96 * sizeof(float); elements -= 96 * sizeof(float)) {
45     // Load 96 (12x8) inputs at a time.
46     const __m256 vi0 = _mm256_loadu_ps(input);
47     const __m256 vi1 = _mm256_loadu_ps(input + 8);
48     const __m256 vi2 = _mm256_loadu_ps(input + 16);
49     const __m256 vi3 = _mm256_loadu_ps(input + 24);
50     const __m256 vi4 = _mm256_loadu_ps(input + 32);
51     const __m256 vi5 = _mm256_loadu_ps(input + 40);
52     const __m256 vi6 = _mm256_loadu_ps(input + 48);
53     const __m256 vi7 = _mm256_loadu_ps(input + 56);
54     const __m256 vi8 = _mm256_loadu_ps(input + 64);
55     const __m256 vi9 = _mm256_loadu_ps(input + 72);
56     const __m256 vi10 = _mm256_loadu_ps(input + 80);
57     const __m256 vi11 = _mm256_loadu_ps(input + 88);
58     input += 96;
59 
60     // Subtract maximum input x := i - i_max. This implies x <= 0.
61     const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
62     const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
63     const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
64     const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
65     const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
66     const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
67     const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
68     const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
69     const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
70     const __m256 vx9 = _mm256_sub_ps(vi9, vi_max);
71     const __m256 vx10 = _mm256_sub_ps(vi10, vi_max);
72     const __m256 vx11 = _mm256_sub_ps(vi11, vi_max);
73 
74     // Compute reduced argument elements := round(x / log(2)).
75     __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
76     __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
77     __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
78     __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
79     __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
80     __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
81     __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
82     __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
83     __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
84     __m256 vn9 = _mm256_fmadd_ps(vx9, vlog2e, vmagic_bias);
85     __m256 vn10 = _mm256_fmadd_ps(vx10, vlog2e, vmagic_bias);
86     __m256 vn11 = _mm256_fmadd_ps(vx11, vlog2e, vmagic_bias);
87 
88     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
89     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
90     const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
91     const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
92     const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
93     const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
94     const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
95     const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
96     const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
97     const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
98     const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
99     const __m256 vs9 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn9), 23));
100     const __m256 vs10 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn10), 23));
101     const __m256 vs11 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn11), 23));
102 
103     // Subtract the large number back to get final elements := round(x / log(2)).
104     vn0 = _mm256_sub_ps(vn0, vmagic_bias);
105     vn1 = _mm256_sub_ps(vn1, vmagic_bias);
106     vn2 = _mm256_sub_ps(vn2, vmagic_bias);
107     vn3 = _mm256_sub_ps(vn3, vmagic_bias);
108     vn4 = _mm256_sub_ps(vn4, vmagic_bias);
109     vn5 = _mm256_sub_ps(vn5, vmagic_bias);
110     vn6 = _mm256_sub_ps(vn6, vmagic_bias);
111     vn7 = _mm256_sub_ps(vn7, vmagic_bias);
112     vn8 = _mm256_sub_ps(vn8, vmagic_bias);
113     vn9 = _mm256_sub_ps(vn9, vmagic_bias);
114     vn10 = _mm256_sub_ps(vn10, vmagic_bias);
115     vn11 = _mm256_sub_ps(vn11, vmagic_bias);
116 
117     // Compute reduced argument t := x - elements * log(2).
118     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
119     __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
120     __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
121     __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
122     __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
123     __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
124     __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
125     __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
126     __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
127     __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
128     __m256 vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_hi, vx9);
129     __m256 vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_hi, vx10);
130     __m256 vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_hi, vx11);
131 
132     vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
133     vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
134     vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
135     vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
136     vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
137     vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
138     vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
139     vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
140     vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
141     vt9 = _mm256_fmadd_ps(vn9, vminus_ln2_lo, vt9);
142     vt10 = _mm256_fmadd_ps(vn10, vminus_ln2_lo, vt10);
143     vt11 = _mm256_fmadd_ps(vn11, vminus_ln2_lo, vt11);
144 
145     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
146     __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
147     __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
148     __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
149     __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
150     __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
151     __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
152     __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
153     __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
154     __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
155     __m256 vp9 = _mm256_fmadd_ps(vc5, vt9, vc4);
156     __m256 vp10 = _mm256_fmadd_ps(vc5, vt10, vc4);
157     __m256 vp11 = _mm256_fmadd_ps(vc5, vt11, vc4);
158 
159     vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
160     vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
161     vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
162     vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
163     vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
164     vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
165     vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
166     vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
167     vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
168     vp9 = _mm256_fmadd_ps(vp9, vt9, vc3);
169     vp10 = _mm256_fmadd_ps(vp10, vt10, vc3);
170     vp11 = _mm256_fmadd_ps(vp11, vt11, vc3);
171 
172     vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
173     vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
174     vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
175     vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
176     vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
177     vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
178     vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
179     vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
180     vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
181     vp9 = _mm256_fmadd_ps(vp9, vt9, vc2);
182     vp10 = _mm256_fmadd_ps(vp10, vt10, vc2);
183     vp11 = _mm256_fmadd_ps(vp11, vt11, vc2);
184 
185     vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
186     vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
187     vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
188     vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
189     vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
190     vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
191     vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
192     vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
193     vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
194     vp9 = _mm256_fmadd_ps(vp9, vt9, vc1);
195     vp10 = _mm256_fmadd_ps(vp10, vt10, vc1);
196     vp11 = _mm256_fmadd_ps(vp11, vt11, vc1);
197 
198     // Reconstruct the final f value:
199     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
200     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
201     //     = s + (t * s) * p
202     vt0 = _mm256_mul_ps(vt0, vs0);
203     vt1 = _mm256_mul_ps(vt1, vs1);
204     vt2 = _mm256_mul_ps(vt2, vs2);
205     vt3 = _mm256_mul_ps(vt3, vs3);
206     vt4 = _mm256_mul_ps(vt4, vs4);
207     vt5 = _mm256_mul_ps(vt5, vs5);
208     vt6 = _mm256_mul_ps(vt6, vs6);
209     vt7 = _mm256_mul_ps(vt7, vs7);
210     vt8 = _mm256_mul_ps(vt8, vs8);
211     vt9 = _mm256_mul_ps(vt9, vs9);
212     vt10 = _mm256_mul_ps(vt10, vs10);
213     vt11 = _mm256_mul_ps(vt11, vs11);
214 
215     __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
216     __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
217     __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
218     __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
219     __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
220     __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
221     __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
222     __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
223     __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
224     __m256 vf9 = _mm256_fmadd_ps(vt9, vp9, vs9);
225     __m256 vf10 = _mm256_fmadd_ps(vt10, vp10, vs10);
226     __m256 vf11 = _mm256_fmadd_ps(vt11, vp11, vs11);
227 
228     // For inputs below zero cutoff, replace output with +0.0f.
229     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
230     vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
231     vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
232     vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
233     vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
234     vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
235     vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
236     vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
237     vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
238     vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
239     vf9 = _mm256_andnot_ps(_mm256_cmp_ps(vx9, vdenorm_cutoff, _CMP_LT_OS), vf9);
240     vf10 = _mm256_andnot_ps(_mm256_cmp_ps(vx10, vdenorm_cutoff, _CMP_LT_OS), vf10);
241     vf11 = _mm256_andnot_ps(_mm256_cmp_ps(vx11, vdenorm_cutoff, _CMP_LT_OS), vf11);
242 
243     // Store 96 (12x8) outputs at a time.
244     _mm256_storeu_ps(output, vf0);
245     _mm256_storeu_ps(output + 8, vf1);
246     _mm256_storeu_ps(output + 16, vf2);
247     _mm256_storeu_ps(output + 24, vf3);
248     _mm256_storeu_ps(output + 32, vf4);
249     _mm256_storeu_ps(output + 40, vf5);
250     _mm256_storeu_ps(output + 48, vf6);
251     _mm256_storeu_ps(output + 56, vf7);
252     _mm256_storeu_ps(output + 64, vf8);
253     _mm256_storeu_ps(output + 72, vf9);
254     _mm256_storeu_ps(output + 80, vf10);
255     _mm256_storeu_ps(output + 88, vf11);
256     output += 96;
257 
258     // Accumulate computed exponents.
259     vacc0 = _mm256_add_ps(vacc0, vf0);
260     vacc0 = _mm256_add_ps(vacc0, vf1);
261     vacc0 = _mm256_add_ps(vacc0, vf2);
262     vacc0 = _mm256_add_ps(vacc0, vf3);
263     vacc0 = _mm256_add_ps(vacc0, vf4);
264     vacc0 = _mm256_add_ps(vacc0, vf5);
265     vacc0 = _mm256_add_ps(vacc0, vf6);
266     vacc0 = _mm256_add_ps(vacc0, vf7);
267     vacc0 = _mm256_add_ps(vacc0, vf8);
268     vacc0 = _mm256_add_ps(vacc0, vf9);
269     vacc0 = _mm256_add_ps(vacc0, vf10);
270     vacc0 = _mm256_add_ps(vacc0, vf11);
271   }
272 
273   __m256 vacc = vacc0;
274   for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
275     // Load 8 inputs at a time.
276     const __m256 vi = _mm256_loadu_ps(input);
277     input += 8;
278 
279     // Subtract maximum input x := i - i_max. This implies x <= 0.
280     const __m256 vx = _mm256_sub_ps(vi, vi_max);
281 
282     // Compute reduced argument elements := round(x / log(2)).
283     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
284 
285     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
286     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
287     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
288 
289     // Subtract the large number back to get final elements := round(x / log(2)).
290     vn = _mm256_sub_ps(vn, vmagic_bias);
291 
292     // Compute reduced argument t := x - elements * log(2).
293     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
294     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
295     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
296 
297     // Compute degree-5 polynomial approxiatmion 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 
303     // Reconstruct the final f value:
304     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
305     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
306     //     = s + (t * s) * p
307     vt = _mm256_mul_ps(vt, vs);
308     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
309 
310     // For inputs below zero cutoff, replace output with +0.0f.
311     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
312     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
313 
314     // Store 8 outputs at a time.
315     _mm256_storeu_ps(output, vf);
316     output += 8;
317 
318     // Accumulate computed exponents.
319     vacc = _mm256_add_ps(vacc, vf);
320   }
321   if (elements != 0) {
322     assert(elements >= 1 * sizeof(float));
323     assert(elements <= 7 * sizeof(float));
324     const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
325 
326     // Load up to 7 inputs at a time.
327     const __m256 vi = _mm256_maskload_ps(input, vmask);
328 
329     // Subtract maximum input x := i - i_max. This implies x <= 0.
330     const __m256 vx = _mm256_sub_ps(vi, vi_max);
331 
332     // Compute reduced argument elements := round(x / log(2)).
333     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
334 
335     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
336     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
337     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
338 
339     // Subtract the large number back to get final elements := round(x / log(2)).
340     vn = _mm256_sub_ps(vn, vmagic_bias);
341 
342     // Compute reduced argument t := x - elements * log(2).
343     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
344     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
345     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
346 
347     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
348     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
349     vp = _mm256_fmadd_ps(vp, vt, vc3);
350     vp = _mm256_fmadd_ps(vp, vt, vc2);
351     vp = _mm256_fmadd_ps(vp, vt, vc1);
352 
353     // Reconstruct the final f value:
354     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
355     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
356     //     = s + (t * s) * p
357     vt = _mm256_mul_ps(vt, vs);
358     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
359 
360     // For inputs below zero cutoff, replace output with +0.0f.
361     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
362     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
363 
364     // Store up to 7 outputs at a time.
365     _mm256_maskstore_ps(output, vmask, vf);
366 
367     // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
368     vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
369   }
370   // Reduce 8 elements in the SIMD register
371   __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
372   vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
373   vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
374   _mm_store_ss(sum, vacc_lo);
375   _mm256_zeroupper();
376 }
377