1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddstoreexpminusmax/sse2-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 <emmintrin.h>
13
14 #include <xnnpack/common.h>
15 #include <xnnpack/raddstoreexpminusmax.h>
16
17
xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x20_acc5(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x20_acc5(
19 size_t elements,
20 const float* input,
21 float* output,
22 float* sum,
23 float max) XNN_DISABLE_TSAN
24 {
25 assert(elements % sizeof(float) == 0);
26
27 const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f);
28 // The smallest x for which expf(x) is normalized.
29 const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f);
30 const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f);
31 // Last 7 bits are zeroes
32 const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f);
33 const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f);
34
35 const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f);
36 const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f);
37 const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f);
38 const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f);
39 const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f);
40
41 const __m128 vi_max = _mm_set1_ps(max);
42
43 __m128 vacc0 = _mm_setzero_ps();
44 __m128 vacc1 = _mm_setzero_ps();
45 __m128 vacc2 = _mm_setzero_ps();
46 __m128 vacc3 = _mm_setzero_ps();
47 __m128 vacc4 = _mm_setzero_ps();
48 for (; elements >= 20 * sizeof(float); elements -= 20 * sizeof(float)) {
49 // Load 20 (5x4) inputs at a time.
50 const __m128 vi0123 = _mm_loadu_ps(input);
51 const __m128 vi4567 = _mm_loadu_ps(input + 4);
52 const __m128 vi89AB = _mm_loadu_ps(input + 8);
53 const __m128 viCDEF = _mm_loadu_ps(input + 12);
54 const __m128 viGHIJ = _mm_loadu_ps(input + 16);
55 input += 20;
56
57 // Subtract maximum input x := i - i_max. This implies x <= 0.
58 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
59 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
60 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
61 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
62 const __m128 vxGHIJ = _mm_sub_ps(viGHIJ, vi_max);
63
64 // Compute reduced argument elements := round(x / log(2)).
65 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
66 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
67 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
68 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
69 __m128 vnGHIJ = _mm_add_ps(_mm_mul_ps(vxGHIJ, vlog2e), vmagic_bias);
70
71 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
72 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
73 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
74 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
75 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
76 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
77 const __m128 vsGHIJ = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnGHIJ), 23));
78
79 // Subtract the large number back to get final elements := round(x / log(2)).
80 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
81 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
82 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
83 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
84 vnGHIJ = _mm_sub_ps(vnGHIJ, vmagic_bias);
85
86 // Compute reduced argument t := x - elements * log(2).
87 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
88 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
89 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
90 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
91 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
92 __m128 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_hi), vxGHIJ);
93
94 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
95 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
96 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
97 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
98 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_lo), vtGHIJ);
99
100 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
101 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
102 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
103 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
104 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
105 __m128 vpGHIJ = _mm_add_ps(_mm_mul_ps(vc5, vtGHIJ), vc4);
106
107 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
108 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
109 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
110 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
111 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc3);
112
113 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
114 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
115 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
116 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
117 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc2);
118
119 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
120 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
121 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
122 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
123 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc1);
124
125 // Reconstruct the final f value:
126 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
127 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
128 // = s + (t * s) * p
129 vt0123 = _mm_mul_ps(vt0123, vs0123);
130 vt4567 = _mm_mul_ps(vt4567, vs4567);
131 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
132 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
133 vtGHIJ = _mm_mul_ps(vtGHIJ, vsGHIJ);
134
135 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
136 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
137 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
138 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
139 __m128 vfGHIJ = _mm_add_ps(_mm_mul_ps(vtGHIJ, vpGHIJ), vsGHIJ);
140
141 // For inputs below zero cutoff, replace output with +0.0f.
142 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
143 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
144 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
145 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
146 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
147 vfGHIJ = _mm_andnot_ps(_mm_cmplt_ps(vxGHIJ, vdenorm_cutoff), vfGHIJ);
148
149 // Store 20 (5x4) outputs at a time.
150 _mm_storeu_ps(output, vf0123);
151 _mm_storeu_ps(output + 4, vf4567);
152 _mm_storeu_ps(output + 8, vf89AB);
153 _mm_storeu_ps(output + 12, vfCDEF);
154 _mm_storeu_ps(output + 16, vfGHIJ);
155 output += 20;
156
157 // Accumulate computed exponents.
158 vacc0 = _mm_add_ps(vacc0, vf0123);
159 vacc4 = _mm_add_ps(vacc4, vf4567);
160 vacc3 = _mm_add_ps(vacc3, vf89AB);
161 vacc2 = _mm_add_ps(vacc2, vfCDEF);
162 vacc1 = _mm_add_ps(vacc1, vfGHIJ);
163 }
164 // Add up all accumulators to vacc0
165 vacc0 = _mm_add_ps(vacc0, vacc1);
166 vacc2 = _mm_add_ps(vacc2, vacc3);
167 vacc0 = _mm_add_ps(vacc0, vacc2);
168 vacc0 = _mm_add_ps(vacc0, vacc4);
169
170 __m128 vacc = vacc0;
171 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
172 // Load 4 inputs at a time.
173 const __m128 vi = _mm_loadu_ps(input);
174 input += 4;
175
176 // Subtract maximum input x := i - i_max. This implies x <= 0.
177 const __m128 vx = _mm_sub_ps(vi, vi_max);
178
179 // Compute reduced argument elements := round(x / log(2)).
180 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
181
182 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
183 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
184 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
185
186 // Subtract the large number back to get final elements := round(x / log(2)).
187 vn = _mm_sub_ps(vn, vmagic_bias);
188
189 // Compute reduced argument t := x - elements * log(2).
190 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
191 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
192 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
193
194 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
195 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
196 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
197 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
198 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
199
200 // Reconstruct the final f value:
201 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
202 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
203 // = s + (t * s) * p
204 vt = _mm_mul_ps(vt, vs);
205 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
206
207 // For inputs below zero cutoff, replace output with +0.0f.
208 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
209 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
210
211 // Store 4 outputs at a time.
212 _mm_storeu_ps(output, vf);
213 output += 4;
214
215 // Accumulate computed exponents.
216 vacc = _mm_add_ps(vacc, vf);
217 }
218 if (elements != 0) {
219 assert(elements >= 1 * sizeof(float));
220 assert(elements <= 3 * sizeof(float));
221 // Load 4 inputs at a time.
222 const __m128 vi = _mm_loadu_ps(input);
223
224 // Subtract maximum input x := i - i_max. This implies x <= 0.
225 const __m128 vx = _mm_sub_ps(vi, vi_max);
226
227 // Compute reduced argument elements := round(x / log(2)).
228 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
229
230 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
231 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
232 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
233
234 // Subtract the large number back to get final elements := round(x / log(2)).
235 vn = _mm_sub_ps(vn, vmagic_bias);
236
237 // Compute reduced argument t := x - elements * log(2).
238 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
239 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
240 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
241
242 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
243 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
244 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
245 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
246 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
247
248 // Reconstruct the final f value:
249 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
250 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
251 // = s + (t * s) * p
252 vt = _mm_mul_ps(vt, vs);
253 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
254
255 // For inputs below zero cutoff, replace output with +0.0f.
256 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
257 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
258
259 if (elements & (2 * sizeof(float))) {
260 // Store 2 outputs at a time.
261 _mm_storel_pi((__m64*) output, vf);
262 output += 2;
263
264 // Accumulate 2 computed exponents.
265 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
266
267 vf = _mm_movehl_ps(vf, vf);
268 }
269 if (elements & (1 * sizeof(float))) {
270 // Store 1 output at a time.
271 _mm_store_ss(output, vf);
272
273 // Accumulate 1 computed exponent.
274 vacc = _mm_add_ss(vacc, vf);
275 }
276 }
277 // Reduce 4 elements in the SIMD register
278 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
279 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
280 _mm_store_ss(sum, vacc);
281 }
282