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_x16(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_x16(
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 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
42 // Load 16 (4x4) inputs at a time.
43 const __m128 vi0123 = _mm_loadu_ps(input);
44 const __m128 vi4567 = _mm_loadu_ps(input + 4);
45 const __m128 vi89AB = _mm_loadu_ps(input + 8);
46 const __m128 viCDEF = _mm_loadu_ps(input + 12);
47 input += 16;
48
49 // Subtract maximum input x := i - i_max. This implies x <= 0.
50 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
51 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
52 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
53 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
54
55 // Compute reduced argument elements := round(x / log(2)).
56 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
57 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
58 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
59 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
60
61 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
62 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
63 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
64 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
65 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
66 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
67
68 // Subtract the large number back to get final elements := round(x / log(2)).
69 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
70 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
71 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
72 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
73
74 // Compute reduced argument t := x - elements * log(2).
75 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
76 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
77 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
78 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
79 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
80
81 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
82 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
83 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
84 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
85
86 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
87 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
88 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
89 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
90 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
91
92 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
93 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
94 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
95 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
96
97 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
98 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
99 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
100 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
101
102 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
103 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
104 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
105 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
106
107 // Reconstruct the final f value:
108 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
109 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
110 // = s + (t * s) * p
111 vt0123 = _mm_mul_ps(vt0123, vs0123);
112 vt4567 = _mm_mul_ps(vt4567, vs4567);
113 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
114 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
115
116 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
117 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
118 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
119 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
120
121 // For inputs below zero cutoff, replace output with +0.0f.
122 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
123 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
124 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
125 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
126 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
127
128 // Store 16 (4x4) outputs at a time.
129 _mm_storeu_ps(output, vf0123);
130 _mm_storeu_ps(output + 4, vf4567);
131 _mm_storeu_ps(output + 8, vf89AB);
132 _mm_storeu_ps(output + 12, vfCDEF);
133 output += 16;
134
135 // Accumulate computed exponents.
136 vacc0 = _mm_add_ps(vacc0, vf0123);
137 vacc0 = _mm_add_ps(vacc0, vf4567);
138 vacc0 = _mm_add_ps(vacc0, vf89AB);
139 vacc0 = _mm_add_ps(vacc0, vfCDEF);
140 }
141
142 __m128 vacc = vacc0;
143 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
144 // Load 4 inputs at a time.
145 const __m128 vi = _mm_loadu_ps(input);
146 input += 4;
147
148 // Subtract maximum input x := i - i_max. This implies x <= 0.
149 const __m128 vx = _mm_sub_ps(vi, vi_max);
150
151 // Compute reduced argument elements := round(x / log(2)).
152 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
153
154 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
155 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
156 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
157
158 // Subtract the large number back to get final elements := round(x / log(2)).
159 vn = _mm_sub_ps(vn, vmagic_bias);
160
161 // Compute reduced argument t := x - elements * log(2).
162 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
163 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
164 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
165
166 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
167 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
168 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
169 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
170 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
171
172 // Reconstruct the final f value:
173 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
174 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
175 // = s + (t * s) * p
176 vt = _mm_mul_ps(vt, vs);
177 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
178
179 // For inputs below zero cutoff, replace output with +0.0f.
180 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
181 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
182
183 // Store 4 outputs at a time.
184 _mm_storeu_ps(output, vf);
185 output += 4;
186
187 // Accumulate computed exponents.
188 vacc = _mm_add_ps(vacc, vf);
189 }
190 if (elements != 0) {
191 assert(elements >= 1 * sizeof(float));
192 assert(elements <= 3 * sizeof(float));
193 // Load 4 inputs at a time.
194 const __m128 vi = _mm_loadu_ps(input);
195
196 // Subtract maximum input x := i - i_max. This implies x <= 0.
197 const __m128 vx = _mm_sub_ps(vi, vi_max);
198
199 // Compute reduced argument elements := round(x / log(2)).
200 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
201
202 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
203 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
204 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
205
206 // Subtract the large number back to get final elements := round(x / log(2)).
207 vn = _mm_sub_ps(vn, vmagic_bias);
208
209 // Compute reduced argument t := x - elements * log(2).
210 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
211 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
212 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
213
214 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
215 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
216 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
217 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
218 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
219
220 // Reconstruct the final f value:
221 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
222 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
223 // = s + (t * s) * p
224 vt = _mm_mul_ps(vt, vs);
225 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
226
227 // For inputs below zero cutoff, replace output with +0.0f.
228 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
229 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
230
231 if (elements & (2 * sizeof(float))) {
232 // Store 2 outputs at a time.
233 _mm_storel_pi((__m64*) output, vf);
234 output += 2;
235
236 // Accumulate 2 computed exponents.
237 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
238
239 vf = _mm_movehl_ps(vf, vf);
240 }
241 if (elements & (1 * sizeof(float))) {
242 // Store 1 output at a time.
243 _mm_store_ss(output, vf);
244
245 // Accumulate 1 computed exponent.
246 vacc = _mm_add_ss(vacc, vf);
247 }
248 }
249 // Reduce 4 elements in the SIMD register
250 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
251 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
252 _mm_store_ss(sum, vacc);
253 }
254