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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_x72_acc3(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x72_acc3(
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   __m256 vacc1 = _mm256_setzero_ps();
45   __m256 vacc2 = _mm256_setzero_ps();
46   for (; elements >= 72 * sizeof(float); elements -= 72 * sizeof(float)) {
47     // Load 72 (9x8) inputs at a time.
48     const __m256 vi0 = _mm256_loadu_ps(input);
49     const __m256 vi1 = _mm256_loadu_ps(input + 8);
50     const __m256 vi2 = _mm256_loadu_ps(input + 16);
51     const __m256 vi3 = _mm256_loadu_ps(input + 24);
52     const __m256 vi4 = _mm256_loadu_ps(input + 32);
53     const __m256 vi5 = _mm256_loadu_ps(input + 40);
54     const __m256 vi6 = _mm256_loadu_ps(input + 48);
55     const __m256 vi7 = _mm256_loadu_ps(input + 56);
56     const __m256 vi8 = _mm256_loadu_ps(input + 64);
57     input += 72;
58 
59     // Subtract maximum input x := i - i_max. This implies x <= 0.
60     const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
61     const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
62     const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
63     const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
64     const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
65     const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
66     const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
67     const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
68     const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
69 
70     // Compute reduced argument elements := round(x / log(2)).
71     __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
72     __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
73     __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
74     __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
75     __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
76     __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
77     __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
78     __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
79     __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
80 
81     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
82     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
83     const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
84     const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
85     const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
86     const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
87     const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
88     const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
89     const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
90     const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
91     const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
92 
93     // Subtract the large number back to get final elements := round(x / log(2)).
94     vn0 = _mm256_sub_ps(vn0, vmagic_bias);
95     vn1 = _mm256_sub_ps(vn1, vmagic_bias);
96     vn2 = _mm256_sub_ps(vn2, vmagic_bias);
97     vn3 = _mm256_sub_ps(vn3, vmagic_bias);
98     vn4 = _mm256_sub_ps(vn4, vmagic_bias);
99     vn5 = _mm256_sub_ps(vn5, vmagic_bias);
100     vn6 = _mm256_sub_ps(vn6, vmagic_bias);
101     vn7 = _mm256_sub_ps(vn7, vmagic_bias);
102     vn8 = _mm256_sub_ps(vn8, vmagic_bias);
103 
104     // Compute reduced argument t := x - elements * log(2).
105     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
106     __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
107     __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
108     __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
109     __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
110     __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
111     __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
112     __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
113     __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
114     __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
115 
116     vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
117     vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
118     vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
119     vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
120     vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
121     vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
122     vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
123     vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
124     vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
125 
126     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
127     __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
128     __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
129     __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
130     __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
131     __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
132     __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
133     __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
134     __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
135     __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
136 
137     vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
138     vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
139     vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
140     vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
141     vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
142     vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
143     vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
144     vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
145     vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
146 
147     vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
148     vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
149     vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
150     vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
151     vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
152     vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
153     vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
154     vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
155     vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
156 
157     vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
158     vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
159     vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
160     vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
161     vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
162     vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
163     vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
164     vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
165     vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
166 
167     // Reconstruct the final f value:
168     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
169     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
170     //     = s + (t * s) * p
171     vt0 = _mm256_mul_ps(vt0, vs0);
172     vt1 = _mm256_mul_ps(vt1, vs1);
173     vt2 = _mm256_mul_ps(vt2, vs2);
174     vt3 = _mm256_mul_ps(vt3, vs3);
175     vt4 = _mm256_mul_ps(vt4, vs4);
176     vt5 = _mm256_mul_ps(vt5, vs5);
177     vt6 = _mm256_mul_ps(vt6, vs6);
178     vt7 = _mm256_mul_ps(vt7, vs7);
179     vt8 = _mm256_mul_ps(vt8, vs8);
180 
181     __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
182     __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
183     __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
184     __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
185     __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
186     __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
187     __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
188     __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
189     __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
190 
191     // For inputs below zero cutoff, replace output with +0.0f.
192     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
193     vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
194     vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
195     vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
196     vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
197     vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
198     vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
199     vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
200     vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
201     vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
202 
203     // Store 72 (9x8) outputs at a time.
204     _mm256_storeu_ps(output, vf0);
205     _mm256_storeu_ps(output + 8, vf1);
206     _mm256_storeu_ps(output + 16, vf2);
207     _mm256_storeu_ps(output + 24, vf3);
208     _mm256_storeu_ps(output + 32, vf4);
209     _mm256_storeu_ps(output + 40, vf5);
210     _mm256_storeu_ps(output + 48, vf6);
211     _mm256_storeu_ps(output + 56, vf7);
212     _mm256_storeu_ps(output + 64, vf8);
213     output += 72;
214 
215     // Accumulate computed exponents.
216     vacc0 = _mm256_add_ps(vacc0, vf0);
217     vacc1 = _mm256_add_ps(vacc1, vf1);
218     vacc2 = _mm256_add_ps(vacc2, vf2);
219     vacc0 = _mm256_add_ps(vacc0, vf3);
220     vacc1 = _mm256_add_ps(vacc1, vf4);
221     vacc2 = _mm256_add_ps(vacc2, vf5);
222     vacc0 = _mm256_add_ps(vacc0, vf6);
223     vacc1 = _mm256_add_ps(vacc1, vf7);
224     vacc2 = _mm256_add_ps(vacc2, vf8);
225   }
226   // Add up all accumulators to vacc0
227   vacc0 = _mm256_add_ps(vacc0, vacc1);
228   vacc0 = _mm256_add_ps(vacc0, vacc2);
229 
230   __m256 vacc = vacc0;
231   for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
232     // Load 8 inputs at a time.
233     const __m256 vi = _mm256_loadu_ps(input);
234     input += 8;
235 
236     // Subtract maximum input x := i - i_max. This implies x <= 0.
237     const __m256 vx = _mm256_sub_ps(vi, vi_max);
238 
239     // Compute reduced argument elements := round(x / log(2)).
240     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
241 
242     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
243     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
244     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
245 
246     // Subtract the large number back to get final elements := round(x / log(2)).
247     vn = _mm256_sub_ps(vn, vmagic_bias);
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 
260     // Reconstruct the final f value:
261     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
262     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
263     //     = s + (t * s) * p
264     vt = _mm256_mul_ps(vt, vs);
265     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
266 
267     // For inputs below zero cutoff, replace output with +0.0f.
268     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
269     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
270 
271     // Store 8 outputs at a time.
272     _mm256_storeu_ps(output, vf);
273     output += 8;
274 
275     // Accumulate computed exponents.
276     vacc = _mm256_add_ps(vacc, vf);
277   }
278   if (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 vi = _mm256_maskload_ps(input, vmask);
285 
286     // Subtract maximum input x := i - i_max. This implies x <= 0.
287     const __m256 vx = _mm256_sub_ps(vi, vi_max);
288 
289     // Compute reduced argument elements := round(x / log(2)).
290     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
291 
292     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
293     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
294     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
295 
296     // Subtract the large number back to get final elements := round(x / log(2)).
297     vn = _mm256_sub_ps(vn, vmagic_bias);
298 
299     // Compute reduced argument t := x - elements * log(2).
300     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
301     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
302     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
303 
304     // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
305     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
306     vp = _mm256_fmadd_ps(vp, vt, vc3);
307     vp = _mm256_fmadd_ps(vp, vt, vc2);
308     vp = _mm256_fmadd_ps(vp, vt, vc1);
309 
310     // Reconstruct the final f value:
311     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
312     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
313     //     = s + (t * s) * p
314     vt = _mm256_mul_ps(vt, vs);
315     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
316 
317     // For inputs below zero cutoff, replace output with +0.0f.
318     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
319     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
320 
321     // Store up to 7 outputs at a time.
322     _mm256_maskstore_ps(output, vmask, vf);
323 
324     // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
325     vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
326   }
327   // Reduce 8 elements in the SIMD register
328   __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
329   vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
330   vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
331   _mm_store_ss(sum, vacc_lo);
332   _mm256_zeroupper();
333 }
334