1 // Auto-generated file. Do not edit!
2 // Template: src/f32-raddstoreexpminusmax/sse2-rr2-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_rr2_p5_x20_acc5(size_t elements,const float * input,const float * max,float * output,float * sum,const union xnn_f32_expminus_params params[restrict XNN_MIN_ELEMENTS (1)])18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_rr2_p5_x20_acc5(
19 size_t elements,
20 const float* input,
21 const float* max,
22 float* output,
23 float* sum,
24 const union xnn_f32_expminus_params params[restrict XNN_MIN_ELEMENTS(1)]) XNN_OOB_READS
25 {
26 assert(elements % sizeof(float) == 0);
27
28 const __m128 vi_max = _mm_load1_ps(max);
29 const __m128 vlog2e = _mm_load_ps(params->sse2_rr2_p5.log2e);
30 const __m128 vmagic_bias = _mm_load_ps(params->sse2_rr2_p5.magic_bias);
31 const __m128 vminus_ln2_hi = _mm_load_ps(params->sse2_rr2_p5.minus_ln2_hi);
32 const __m128 vminus_ln2_lo = _mm_load_ps(params->sse2_rr2_p5.minus_ln2_lo);
33 const __m128 vc5 = _mm_load_ps(params->sse2_rr2_p5.c5);
34 const __m128 vc4 = _mm_load_ps(params->sse2_rr2_p5.c4);
35 const __m128 vc3 = _mm_load_ps(params->sse2_rr2_p5.c3);
36 const __m128 vc2 = _mm_load_ps(params->sse2_rr2_p5.c2);
37 const __m128 vc1 = _mm_load_ps(params->sse2_rr2_p5.c1);
38 const __m128 vdenorm_cutoff = _mm_load_ps(params->sse2_rr2_p5.denorm_cutoff);
39
40 __m128 vacc0 = _mm_setzero_ps();
41 __m128 vacc1 = _mm_setzero_ps();
42 __m128 vacc2 = _mm_setzero_ps();
43 __m128 vacc3 = _mm_setzero_ps();
44 __m128 vacc4 = _mm_setzero_ps();
45 for (; elements >= 20 * sizeof(float); elements -= 20 * sizeof(float)) {
46 // Load 20 (5x4) inputs at a time.
47 const __m128 vi0123 = _mm_loadu_ps(input);
48 const __m128 vi4567 = _mm_loadu_ps(input + 4);
49 const __m128 vi89AB = _mm_loadu_ps(input + 8);
50 const __m128 viCDEF = _mm_loadu_ps(input + 12);
51 const __m128 viGHIJ = _mm_loadu_ps(input + 16);
52 input += 20;
53
54 // Subtract maximum input x := i - i_max. This implies x <= 0.
55 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
56 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
57 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
58 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
59 const __m128 vxGHIJ = _mm_sub_ps(viGHIJ, vi_max);
60
61 // Compute reduced argument elements := round(x / log(2)).
62 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
63 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
64 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
65 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
66 __m128 vnGHIJ = _mm_add_ps(_mm_mul_ps(vxGHIJ, vlog2e), vmagic_bias);
67
68 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
69 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
70 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
71 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
72 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
73 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
74 const __m128 vsGHIJ = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnGHIJ), 23));
75
76 // Subtract the large number back to get final elements := round(x / log(2)).
77 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
78 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
79 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
80 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
81 vnGHIJ = _mm_sub_ps(vnGHIJ, vmagic_bias);
82
83 // Compute reduced argument t := x - elements * log(2).
84 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
85 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
86 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
87 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
88 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
89 __m128 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_hi), vxGHIJ);
90
91 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
92 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
93 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
94 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
95 vtGHIJ = _mm_add_ps(_mm_mul_ps(vnGHIJ, vminus_ln2_lo), vtGHIJ);
96
97 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
98 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
99 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
100 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
101 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
102 __m128 vpGHIJ = _mm_add_ps(_mm_mul_ps(vc5, vtGHIJ), vc4);
103
104 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
105 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
106 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
107 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
108 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc3);
109
110 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
111 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
112 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
113 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
114 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc2);
115
116 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
117 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
118 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
119 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
120 vpGHIJ = _mm_add_ps(_mm_mul_ps(vpGHIJ, vtGHIJ), vc1);
121
122 // Reconstruct the final f value:
123 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
124 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
125 // = s + (t * s) * p
126 vt0123 = _mm_mul_ps(vt0123, vs0123);
127 vt4567 = _mm_mul_ps(vt4567, vs4567);
128 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
129 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
130 vtGHIJ = _mm_mul_ps(vtGHIJ, vsGHIJ);
131
132 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
133 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
134 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
135 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
136 __m128 vfGHIJ = _mm_add_ps(_mm_mul_ps(vtGHIJ, vpGHIJ), vsGHIJ);
137
138 // For inputs below zero cutoff, replace output with +0.0f.
139 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
140 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
141 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
142 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
143 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
144 vfGHIJ = _mm_andnot_ps(_mm_cmplt_ps(vxGHIJ, vdenorm_cutoff), vfGHIJ);
145
146 // Store 20 (5x4) outputs at a time.
147 _mm_storeu_ps(output, vf0123);
148 _mm_storeu_ps(output + 4, vf4567);
149 _mm_storeu_ps(output + 8, vf89AB);
150 _mm_storeu_ps(output + 12, vfCDEF);
151 _mm_storeu_ps(output + 16, vfGHIJ);
152 output += 20;
153
154 // Accumulate computed exponents.
155 vacc0 = _mm_add_ps(vacc0, vf0123);
156 vacc4 = _mm_add_ps(vacc4, vf4567);
157 vacc3 = _mm_add_ps(vacc3, vf89AB);
158 vacc2 = _mm_add_ps(vacc2, vfCDEF);
159 vacc1 = _mm_add_ps(vacc1, vfGHIJ);
160 }
161 // Add up all accumulators to vacc0
162 vacc0 = _mm_add_ps(vacc0, vacc1);
163 vacc2 = _mm_add_ps(vacc2, vacc3);
164 vacc0 = _mm_add_ps(vacc0, vacc2);
165 vacc0 = _mm_add_ps(vacc0, vacc4);
166
167 __m128 vacc = vacc0;
168 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
169 // Load 4 inputs at a time.
170 const __m128 vi = _mm_loadu_ps(input);
171 input += 4;
172
173 // Subtract maximum input x := i - i_max. This implies x <= 0.
174 const __m128 vx = _mm_sub_ps(vi, vi_max);
175
176 // Compute reduced argument elements := round(x / log(2)).
177 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
178
179 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
180 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
181 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
182
183 // Subtract the large number back to get final elements := round(x / log(2)).
184 vn = _mm_sub_ps(vn, vmagic_bias);
185
186 // Compute reduced argument t := x - elements * log(2).
187 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
188 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
189 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
190
191 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
192 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
193 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
194 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
195 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
196
197 // Reconstruct the final f value:
198 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
199 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
200 // = s + (t * s) * p
201 vt = _mm_mul_ps(vt, vs);
202 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
203
204 // For inputs below zero cutoff, replace output with +0.0f.
205 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
206 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
207
208 // Store 4 outputs at a time.
209 _mm_storeu_ps(output, vf);
210 output += 4;
211
212 // Accumulate computed exponents.
213 vacc = _mm_add_ps(vacc, vf);
214 }
215 if (elements != 0) {
216 assert(elements >= 1 * sizeof(float));
217 assert(elements <= 3 * sizeof(float));
218 // Load 4 inputs at a time.
219 const __m128 vi = _mm_loadu_ps(input);
220
221 // Subtract maximum input x := i - i_max. This implies x <= 0.
222 const __m128 vx = _mm_sub_ps(vi, vi_max);
223
224 // Compute reduced argument elements := round(x / log(2)).
225 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
226
227 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
228 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
229 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
230
231 // Subtract the large number back to get final elements := round(x / log(2)).
232 vn = _mm_sub_ps(vn, vmagic_bias);
233
234 // Compute reduced argument t := x - elements * log(2).
235 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
236 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
237 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
238
239 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
240 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
241 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
242 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
243 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
244
245 // Reconstruct the final f value:
246 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
247 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
248 // = s + (t * s) * p
249 vt = _mm_mul_ps(vt, vs);
250 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
251
252 // For inputs below zero cutoff, replace output with +0.0f.
253 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
254 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
255
256 if (elements & (2 * sizeof(float))) {
257 // Store 2 outputs at a time.
258 _mm_storel_pi((__m64*) output, vf);
259 output += 2;
260
261 // Accumulate 2 computed exponents.
262 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
263
264 vf = _mm_movehl_ps(vf, vf);
265 }
266 if (elements & (1 * sizeof(float))) {
267 // Store 1 output at a time.
268 _mm_store_ss(output, vf);
269
270 // Accumulate 1 computed exponent.
271 vacc = _mm_add_ss(vacc, vf);
272 }
273 }
274 // Reduce 4 elements in the SIMD register
275 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
276 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
277 _mm_store_ss(sum, vacc);
278 }
279