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_acc2(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_acc2(
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 for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
43 // Load 16 (4x4) inputs at a time.
44 const __m128 vi0123 = _mm_loadu_ps(input);
45 const __m128 vi4567 = _mm_loadu_ps(input + 4);
46 const __m128 vi89AB = _mm_loadu_ps(input + 8);
47 const __m128 viCDEF = _mm_loadu_ps(input + 12);
48 input += 16;
49
50 // Subtract maximum input x := i - i_max. This implies x <= 0.
51 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
52 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
53 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
54 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
55
56 // Compute reduced argument elements := round(x / log(2)).
57 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
58 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
59 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
60 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
61
62 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
63 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
64 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
65 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
66 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
67 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
68
69 // Subtract the large number back to get final elements := round(x / log(2)).
70 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
71 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
72 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
73 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
74
75 // Compute reduced argument t := x - elements * log(2).
76 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
77 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
78 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
79 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
80 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
81
82 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
83 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
84 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
85 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
86
87 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
88 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
89 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
90 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
91 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
92
93 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
94 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
95 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
96 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
97
98 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
99 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
100 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
101 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
102
103 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
104 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
105 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
106 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
107
108 // Reconstruct the final f value:
109 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
110 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
111 // = s + (t * s) * p
112 vt0123 = _mm_mul_ps(vt0123, vs0123);
113 vt4567 = _mm_mul_ps(vt4567, vs4567);
114 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
115 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
116
117 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
118 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
119 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
120 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
121
122 // For inputs below zero cutoff, replace output with +0.0f.
123 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
124 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
125 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
126 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
127 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
128
129 // Store 16 (4x4) outputs at a time.
130 _mm_storeu_ps(output, vf0123);
131 _mm_storeu_ps(output + 4, vf4567);
132 _mm_storeu_ps(output + 8, vf89AB);
133 _mm_storeu_ps(output + 12, vfCDEF);
134 output += 16;
135
136 // Accumulate computed exponents.
137 vacc0 = _mm_add_ps(vacc0, vf0123);
138 vacc0 = _mm_add_ps(vacc0, vf4567);
139 vacc0 = _mm_add_ps(vacc0, vf89AB);
140 vacc0 = _mm_add_ps(vacc0, vfCDEF);
141 }
142 // Add up all accumulators to vacc0
143 vacc0 = _mm_add_ps(vacc0, vacc1);
144
145 __m128 vacc = vacc0;
146 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
147 // Load 4 inputs at a time.
148 const __m128 vi = _mm_loadu_ps(input);
149 input += 4;
150
151 // Subtract maximum input x := i - i_max. This implies x <= 0.
152 const __m128 vx = _mm_sub_ps(vi, vi_max);
153
154 // Compute reduced argument elements := round(x / log(2)).
155 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
156
157 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
158 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
159 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
160
161 // Subtract the large number back to get final elements := round(x / log(2)).
162 vn = _mm_sub_ps(vn, vmagic_bias);
163
164 // Compute reduced argument t := x - elements * log(2).
165 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
166 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
167 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
168
169 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
170 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
171 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
172 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
173 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
174
175 // Reconstruct the final f value:
176 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
177 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
178 // = s + (t * s) * p
179 vt = _mm_mul_ps(vt, vs);
180 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
181
182 // For inputs below zero cutoff, replace output with +0.0f.
183 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
184 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
185
186 // Store 4 outputs at a time.
187 _mm_storeu_ps(output, vf);
188 output += 4;
189
190 // Accumulate computed exponents.
191 vacc = _mm_add_ps(vacc, vf);
192 }
193 if (elements != 0) {
194 assert(elements >= 1 * sizeof(float));
195 assert(elements <= 3 * sizeof(float));
196 // Load 4 inputs at a time.
197 const __m128 vi = _mm_loadu_ps(input);
198
199 // Subtract maximum input x := i - i_max. This implies x <= 0.
200 const __m128 vx = _mm_sub_ps(vi, vi_max);
201
202 // Compute reduced argument elements := round(x / log(2)).
203 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
204
205 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
206 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
207 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
208
209 // Subtract the large number back to get final elements := round(x / log(2)).
210 vn = _mm_sub_ps(vn, vmagic_bias);
211
212 // Compute reduced argument t := x - elements * log(2).
213 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
214 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
215 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
216
217 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
218 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
219 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
220 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
221 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
222
223 // Reconstruct the final f value:
224 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
225 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
226 // = s + (t * s) * p
227 vt = _mm_mul_ps(vt, vs);
228 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
229
230 // For inputs below zero cutoff, replace output with +0.0f.
231 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
232 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
233
234 if (elements & (2 * sizeof(float))) {
235 // Store 2 outputs at a time.
236 _mm_storel_pi((__m64*) output, vf);
237 output += 2;
238
239 // Accumulate 2 computed exponents.
240 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
241
242 vf = _mm_movehl_ps(vf, vf);
243 }
244 if (elements & (1 * sizeof(float))) {
245 // Store 1 output at a time.
246 _mm_store_ss(output, vf);
247
248 // Accumulate 1 computed exponent.
249 vacc = _mm_add_ss(vacc, vf);
250 }
251 }
252 // Reduce 4 elements in the SIMD register
253 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
254 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
255 _mm_store_ss(sum, vacc);
256 }
257