• 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_x72(size_t elements,const float * input,float * output,float * sum,float max)19 void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x72(
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 >= 72 * sizeof(float); elements -= 72 * sizeof(float)) {
45     // Load 72 (9x8) 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     input += 72;
56 
57     // Subtract maximum input x := i - i_max. This implies x <= 0.
58     const __m256 vx0 = _mm256_sub_ps(vi0, vi_max);
59     const __m256 vx1 = _mm256_sub_ps(vi1, vi_max);
60     const __m256 vx2 = _mm256_sub_ps(vi2, vi_max);
61     const __m256 vx3 = _mm256_sub_ps(vi3, vi_max);
62     const __m256 vx4 = _mm256_sub_ps(vi4, vi_max);
63     const __m256 vx5 = _mm256_sub_ps(vi5, vi_max);
64     const __m256 vx6 = _mm256_sub_ps(vi6, vi_max);
65     const __m256 vx7 = _mm256_sub_ps(vi7, vi_max);
66     const __m256 vx8 = _mm256_sub_ps(vi8, vi_max);
67 
68     // Compute reduced argument elements := round(x / log(2)).
69     __m256 vn0 = _mm256_fmadd_ps(vx0, vlog2e, vmagic_bias);
70     __m256 vn1 = _mm256_fmadd_ps(vx1, vlog2e, vmagic_bias);
71     __m256 vn2 = _mm256_fmadd_ps(vx2, vlog2e, vmagic_bias);
72     __m256 vn3 = _mm256_fmadd_ps(vx3, vlog2e, vmagic_bias);
73     __m256 vn4 = _mm256_fmadd_ps(vx4, vlog2e, vmagic_bias);
74     __m256 vn5 = _mm256_fmadd_ps(vx5, vlog2e, vmagic_bias);
75     __m256 vn6 = _mm256_fmadd_ps(vx6, vlog2e, vmagic_bias);
76     __m256 vn7 = _mm256_fmadd_ps(vx7, vlog2e, vmagic_bias);
77     __m256 vn8 = _mm256_fmadd_ps(vx8, vlog2e, vmagic_bias);
78 
79     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
80     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
81     const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
82     const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));
83     const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn2), 23));
84     const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn3), 23));
85     const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn4), 23));
86     const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn5), 23));
87     const __m256 vs6 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn6), 23));
88     const __m256 vs7 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn7), 23));
89     const __m256 vs8 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn8), 23));
90 
91     // Subtract the large number back to get final elements := round(x / log(2)).
92     vn0 = _mm256_sub_ps(vn0, vmagic_bias);
93     vn1 = _mm256_sub_ps(vn1, vmagic_bias);
94     vn2 = _mm256_sub_ps(vn2, vmagic_bias);
95     vn3 = _mm256_sub_ps(vn3, vmagic_bias);
96     vn4 = _mm256_sub_ps(vn4, vmagic_bias);
97     vn5 = _mm256_sub_ps(vn5, vmagic_bias);
98     vn6 = _mm256_sub_ps(vn6, vmagic_bias);
99     vn7 = _mm256_sub_ps(vn7, vmagic_bias);
100     vn8 = _mm256_sub_ps(vn8, vmagic_bias);
101 
102     // Compute reduced argument t := x - elements * log(2).
103     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
104     __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
105     __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
106     __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
107     __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
108     __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
109     __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
110     __m256 vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_hi, vx6);
111     __m256 vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_hi, vx7);
112     __m256 vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_hi, vx8);
113 
114     vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
115     vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
116     vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
117     vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
118     vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
119     vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
120     vt6 = _mm256_fmadd_ps(vn6, vminus_ln2_lo, vt6);
121     vt7 = _mm256_fmadd_ps(vn7, vminus_ln2_lo, vt7);
122     vt8 = _mm256_fmadd_ps(vn8, vminus_ln2_lo, vt8);
123 
124     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
125     __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
126     __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
127     __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
128     __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
129     __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
130     __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
131     __m256 vp6 = _mm256_fmadd_ps(vc5, vt6, vc4);
132     __m256 vp7 = _mm256_fmadd_ps(vc5, vt7, vc4);
133     __m256 vp8 = _mm256_fmadd_ps(vc5, vt8, vc4);
134 
135     vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
136     vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
137     vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
138     vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
139     vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
140     vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
141     vp6 = _mm256_fmadd_ps(vp6, vt6, vc3);
142     vp7 = _mm256_fmadd_ps(vp7, vt7, vc3);
143     vp8 = _mm256_fmadd_ps(vp8, vt8, vc3);
144 
145     vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
146     vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
147     vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
148     vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
149     vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
150     vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
151     vp6 = _mm256_fmadd_ps(vp6, vt6, vc2);
152     vp7 = _mm256_fmadd_ps(vp7, vt7, vc2);
153     vp8 = _mm256_fmadd_ps(vp8, vt8, vc2);
154 
155     vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
156     vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
157     vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
158     vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
159     vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
160     vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
161     vp6 = _mm256_fmadd_ps(vp6, vt6, vc1);
162     vp7 = _mm256_fmadd_ps(vp7, vt7, vc1);
163     vp8 = _mm256_fmadd_ps(vp8, vt8, vc1);
164 
165     // Reconstruct the final f value:
166     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
167     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
168     //     = s + (t * s) * p
169     vt0 = _mm256_mul_ps(vt0, vs0);
170     vt1 = _mm256_mul_ps(vt1, vs1);
171     vt2 = _mm256_mul_ps(vt2, vs2);
172     vt3 = _mm256_mul_ps(vt3, vs3);
173     vt4 = _mm256_mul_ps(vt4, vs4);
174     vt5 = _mm256_mul_ps(vt5, vs5);
175     vt6 = _mm256_mul_ps(vt6, vs6);
176     vt7 = _mm256_mul_ps(vt7, vs7);
177     vt8 = _mm256_mul_ps(vt8, vs8);
178 
179     __m256 vf0 = _mm256_fmadd_ps(vt0, vp0, vs0);
180     __m256 vf1 = _mm256_fmadd_ps(vt1, vp1, vs1);
181     __m256 vf2 = _mm256_fmadd_ps(vt2, vp2, vs2);
182     __m256 vf3 = _mm256_fmadd_ps(vt3, vp3, vs3);
183     __m256 vf4 = _mm256_fmadd_ps(vt4, vp4, vs4);
184     __m256 vf5 = _mm256_fmadd_ps(vt5, vp5, vs5);
185     __m256 vf6 = _mm256_fmadd_ps(vt6, vp6, vs6);
186     __m256 vf7 = _mm256_fmadd_ps(vt7, vp7, vs7);
187     __m256 vf8 = _mm256_fmadd_ps(vt8, vp8, vs8);
188 
189     // For inputs below zero cutoff, replace output with +0.0f.
190     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
191     vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vx0, vdenorm_cutoff, _CMP_LT_OS), vf0);
192     vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vx1, vdenorm_cutoff, _CMP_LT_OS), vf1);
193     vf2 = _mm256_andnot_ps(_mm256_cmp_ps(vx2, vdenorm_cutoff, _CMP_LT_OS), vf2);
194     vf3 = _mm256_andnot_ps(_mm256_cmp_ps(vx3, vdenorm_cutoff, _CMP_LT_OS), vf3);
195     vf4 = _mm256_andnot_ps(_mm256_cmp_ps(vx4, vdenorm_cutoff, _CMP_LT_OS), vf4);
196     vf5 = _mm256_andnot_ps(_mm256_cmp_ps(vx5, vdenorm_cutoff, _CMP_LT_OS), vf5);
197     vf6 = _mm256_andnot_ps(_mm256_cmp_ps(vx6, vdenorm_cutoff, _CMP_LT_OS), vf6);
198     vf7 = _mm256_andnot_ps(_mm256_cmp_ps(vx7, vdenorm_cutoff, _CMP_LT_OS), vf7);
199     vf8 = _mm256_andnot_ps(_mm256_cmp_ps(vx8, vdenorm_cutoff, _CMP_LT_OS), vf8);
200 
201     // Store 72 (9x8) outputs at a time.
202     _mm256_storeu_ps(output, vf0);
203     _mm256_storeu_ps(output + 8, vf1);
204     _mm256_storeu_ps(output + 16, vf2);
205     _mm256_storeu_ps(output + 24, vf3);
206     _mm256_storeu_ps(output + 32, vf4);
207     _mm256_storeu_ps(output + 40, vf5);
208     _mm256_storeu_ps(output + 48, vf6);
209     _mm256_storeu_ps(output + 56, vf7);
210     _mm256_storeu_ps(output + 64, vf8);
211     output += 72;
212 
213     // Accumulate computed exponents.
214     vacc0 = _mm256_add_ps(vacc0, vf0);
215     vacc0 = _mm256_add_ps(vacc0, vf1);
216     vacc0 = _mm256_add_ps(vacc0, vf2);
217     vacc0 = _mm256_add_ps(vacc0, vf3);
218     vacc0 = _mm256_add_ps(vacc0, vf4);
219     vacc0 = _mm256_add_ps(vacc0, vf5);
220     vacc0 = _mm256_add_ps(vacc0, vf6);
221     vacc0 = _mm256_add_ps(vacc0, vf7);
222     vacc0 = _mm256_add_ps(vacc0, vf8);
223   }
224 
225   __m256 vacc = vacc0;
226   for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
227     // Load 8 inputs at a time.
228     const __m256 vi = _mm256_loadu_ps(input);
229     input += 8;
230 
231     // Subtract maximum input x := i - i_max. This implies x <= 0.
232     const __m256 vx = _mm256_sub_ps(vi, vi_max);
233 
234     // Compute reduced argument elements := round(x / log(2)).
235     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
236 
237     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
238     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
239     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
240 
241     // Subtract the large number back to get final elements := round(x / log(2)).
242     vn = _mm256_sub_ps(vn, vmagic_bias);
243 
244     // Compute reduced argument t := x - elements * log(2).
245     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
246     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
247     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
248 
249     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
250     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
251     vp = _mm256_fmadd_ps(vp, vt, vc3);
252     vp = _mm256_fmadd_ps(vp, vt, vc2);
253     vp = _mm256_fmadd_ps(vp, vt, vc1);
254 
255     // Reconstruct the final f value:
256     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
257     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
258     //     = s + (t * s) * p
259     vt = _mm256_mul_ps(vt, vs);
260     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
261 
262     // For inputs below zero cutoff, replace output with +0.0f.
263     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
264     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
265 
266     // Store 8 outputs at a time.
267     _mm256_storeu_ps(output, vf);
268     output += 8;
269 
270     // Accumulate computed exponents.
271     vacc = _mm256_add_ps(vacc, vf);
272   }
273   if (elements != 0) {
274     assert(elements >= 1 * sizeof(float));
275     assert(elements <= 7 * sizeof(float));
276     const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
277 
278     // Load up to 7 inputs at a time.
279     const __m256 vi = _mm256_maskload_ps(input, vmask);
280 
281     // Subtract maximum input x := i - i_max. This implies x <= 0.
282     const __m256 vx = _mm256_sub_ps(vi, vi_max);
283 
284     // Compute reduced argument elements := round(x / log(2)).
285     __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);
286 
287     // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
288     // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
289     const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));
290 
291     // Subtract the large number back to get final elements := round(x / log(2)).
292     vn = _mm256_sub_ps(vn, vmagic_bias);
293 
294     // Compute reduced argument t := x - elements * log(2).
295     // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
296     __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
297     vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
298 
299     // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
300     __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
301     vp = _mm256_fmadd_ps(vp, vt, vc3);
302     vp = _mm256_fmadd_ps(vp, vt, vc2);
303     vp = _mm256_fmadd_ps(vp, vt, vc1);
304 
305     // Reconstruct the final f value:
306     //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
307     //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
308     //     = s + (t * s) * p
309     vt = _mm256_mul_ps(vt, vs);
310     __m256 vf = _mm256_fmadd_ps(vt, vp, vs);
311 
312     // For inputs below zero cutoff, replace output with +0.0f.
313     // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
314     vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);
315 
316     // Store up to 7 outputs at a time.
317     _mm256_maskstore_ps(output, vmask, vf);
318 
319     // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
320     vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
321   }
322   // Reduce 8 elements in the SIMD register
323   __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
324   vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
325   vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
326   _mm_store_ss(sum, vacc_lo);
327   _mm256_zeroupper();
328 }
329