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(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x20(
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 for (; elements >= 20 * sizeof(float); elements -= 20 * sizeof(float)) {
45 // Load 20 (5x4) inputs at a time.
46 const __m128 vi0123 = _mm_loadu_ps(input);
47 const __m128 vi4567 = _mm_loadu_ps(input + 4);
48 const __m128 vi89AB = _mm_loadu_ps(input + 8);
49 const __m128 viCDEF = _mm_loadu_ps(input + 12);
50 const __m128 viGHIJ = _mm_loadu_ps(input + 16);
51 input += 20;
52
53 // Subtract maximum input x := i - i_max. This implies x <= 0.
54 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
55 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
56 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
57 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
58 const __m128 vxGHIJ = _mm_sub_ps(viGHIJ, vi_max);
59
60 // Compute reduced argument elements := round(x / log(2)).
61 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
62 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
63 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
64 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
65 __m128 vnGHIJ = _mm_add_ps(_mm_mul_ps(vxGHIJ, vlog2e), vmagic_bias);
66
67 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
68 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
69 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
70 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
71 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
72 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
73 const __m128 vsGHIJ = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnGHIJ), 23));
74
75 // Subtract the large number back to get final elements := round(x / log(2)).
76 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
77 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
78 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
79 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
80 vnGHIJ = _mm_sub_ps(vnGHIJ, vmagic_bias);
81
82 // Compute reduced argument t := x - elements * log(2).
83 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
84 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
85 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
86 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
87 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
88 __m128 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_hi), vxGHIJ);
89
90 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
91 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
92 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
93 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
94 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_lo), vtGHIJ);
95
96 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
97 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
98 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
99 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
100 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
101 __m128 vpGHIJ = _mm_add_ps(_mm_mul_ps(vc5, vtGHIJ), vc4);
102
103 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
104 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
105 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
106 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
107 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc3);
108
109 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
110 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
111 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
112 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
113 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc2);
114
115 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
116 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
117 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
118 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
119 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc1);
120
121 // Reconstruct the final f value:
122 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
123 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
124 // = s + (t * s) * p
125 vt0123 = _mm_mul_ps(vt0123, vs0123);
126 vt4567 = _mm_mul_ps(vt4567, vs4567);
127 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
128 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
129 vtGHIJ = _mm_mul_ps(vtGHIJ, vsGHIJ);
130
131 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
132 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
133 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
134 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
135 __m128 vfGHIJ = _mm_add_ps(_mm_mul_ps(vtGHIJ, vpGHIJ), vsGHIJ);
136
137 // For inputs below zero cutoff, replace output with +0.0f.
138 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
139 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
140 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
141 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
142 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
143 vfGHIJ = _mm_andnot_ps(_mm_cmplt_ps(vxGHIJ, vdenorm_cutoff), vfGHIJ);
144
145 // Store 20 (5x4) outputs at a time.
146 _mm_storeu_ps(output, vf0123);
147 _mm_storeu_ps(output + 4, vf4567);
148 _mm_storeu_ps(output + 8, vf89AB);
149 _mm_storeu_ps(output + 12, vfCDEF);
150 _mm_storeu_ps(output + 16, vfGHIJ);
151 output += 20;
152
153 // Accumulate computed exponents.
154 vacc0 = _mm_add_ps(vacc0, vf0123);
155 vacc0 = _mm_add_ps(vacc0, vf4567);
156 vacc0 = _mm_add_ps(vacc0, vf89AB);
157 vacc0 = _mm_add_ps(vacc0, vfCDEF);
158 vacc0 = _mm_add_ps(vacc0, vfGHIJ);
159 }
160
161 __m128 vacc = vacc0;
162 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
163 // Load 4 inputs at a time.
164 const __m128 vi = _mm_loadu_ps(input);
165 input += 4;
166
167 // Subtract maximum input x := i - i_max. This implies x <= 0.
168 const __m128 vx = _mm_sub_ps(vi, vi_max);
169
170 // Compute reduced argument elements := round(x / log(2)).
171 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
172
173 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
174 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
175 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
176
177 // Subtract the large number back to get final elements := round(x / log(2)).
178 vn = _mm_sub_ps(vn, vmagic_bias);
179
180 // Compute reduced argument t := x - elements * log(2).
181 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
182 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
183 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
184
185 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
186 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
187 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
188 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
189 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
190
191 // Reconstruct the final f value:
192 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
193 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
194 // = s + (t * s) * p
195 vt = _mm_mul_ps(vt, vs);
196 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
197
198 // For inputs below zero cutoff, replace output with +0.0f.
199 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
200 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
201
202 // Store 4 outputs at a time.
203 _mm_storeu_ps(output, vf);
204 output += 4;
205
206 // Accumulate computed exponents.
207 vacc = _mm_add_ps(vacc, vf);
208 }
209 if (elements != 0) {
210 assert(elements >= 1 * sizeof(float));
211 assert(elements <= 3 * sizeof(float));
212 // Load 4 inputs at a time.
213 const __m128 vi = _mm_loadu_ps(input);
214
215 // Subtract maximum input x := i - i_max. This implies x <= 0.
216 const __m128 vx = _mm_sub_ps(vi, vi_max);
217
218 // Compute reduced argument elements := round(x / log(2)).
219 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
220
221 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
222 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
223 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
224
225 // Subtract the large number back to get final elements := round(x / log(2)).
226 vn = _mm_sub_ps(vn, vmagic_bias);
227
228 // Compute reduced argument t := x - elements * log(2).
229 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
230 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
231 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
232
233 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
234 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
235 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
236 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
237 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
238
239 // Reconstruct the final f value:
240 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
241 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
242 // = s + (t * s) * p
243 vt = _mm_mul_ps(vt, vs);
244 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
245
246 // For inputs below zero cutoff, replace output with +0.0f.
247 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
248 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
249
250 if (elements & (2 * sizeof(float))) {
251 // Store 2 outputs at a time.
252 _mm_storel_pi((__m64*) output, vf);
253 output += 2;
254
255 // Accumulate 2 computed exponents.
256 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
257
258 vf = _mm_movehl_ps(vf, vf);
259 }
260 if (elements & (1 * sizeof(float))) {
261 // Store 1 output at a time.
262 _mm_store_ss(output, vf);
263
264 // Accumulate 1 computed exponent.
265 vacc = _mm_add_ss(vacc, vf);
266 }
267 }
268 // Reduce 4 elements in the SIMD register
269 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
270 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
271 _mm_store_ss(sum, vacc);
272 }
273