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_x16(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x16(
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 >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
45 // Load 16 (4x4) 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 input += 16;
51
52 // Subtract maximum input x := i - i_max. This implies x <= 0.
53 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
54 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
55 const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
56 const __m128 vxCDEF = _mm_sub_ps(viCDEF, vi_max);
57
58 // Compute reduced argument elements := round(x / log(2)).
59 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
60 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
61 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
62 __m128 vnCDEF = _mm_add_ps(_mm_mul_ps(vxCDEF, vlog2e), vmagic_bias);
63
64 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
65 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
66 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
67 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
68 const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
69 const __m128 vsCDEF = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vnCDEF), 23));
70
71 // Subtract the large number back to get final elements := round(x / log(2)).
72 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
73 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
74 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
75 vnCDEF = _mm_sub_ps(vnCDEF, vmagic_bias);
76
77 // Compute reduced argument t := x - elements * log(2).
78 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
79 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
80 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
81 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
82 __m128 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_hi), vxCDEF);
83
84 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
85 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
86 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
87 vtCDEF = _mm_add_ps(_mm_mul_ps(vnCDEF, vminus_ln2_lo), vtCDEF);
88
89 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
90 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
91 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
92 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
93 __m128 vpCDEF = _mm_add_ps(_mm_mul_ps(vc5, vtCDEF), vc4);
94
95 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
96 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
97 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
98 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc3);
99
100 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
101 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
102 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
103 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc2);
104
105 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
106 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
107 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
108 vpCDEF = _mm_add_ps(_mm_mul_ps(vpCDEF, vtCDEF), vc1);
109
110 // Reconstruct the final f value:
111 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
112 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
113 // = s + (t * s) * p
114 vt0123 = _mm_mul_ps(vt0123, vs0123);
115 vt4567 = _mm_mul_ps(vt4567, vs4567);
116 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
117 vtCDEF = _mm_mul_ps(vtCDEF, vsCDEF);
118
119 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
120 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
121 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
122 __m128 vfCDEF = _mm_add_ps(_mm_mul_ps(vtCDEF, vpCDEF), vsCDEF);
123
124 // For inputs below zero cutoff, replace output with +0.0f.
125 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
126 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
127 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
128 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
129 vfCDEF = _mm_andnot_ps(_mm_cmplt_ps(vxCDEF, vdenorm_cutoff), vfCDEF);
130
131 // Store 16 (4x4) outputs at a time.
132 _mm_storeu_ps(output, vf0123);
133 _mm_storeu_ps(output + 4, vf4567);
134 _mm_storeu_ps(output + 8, vf89AB);
135 _mm_storeu_ps(output + 12, vfCDEF);
136 output += 16;
137
138 // Accumulate computed exponents.
139 vacc0 = _mm_add_ps(vacc0, vf0123);
140 vacc0 = _mm_add_ps(vacc0, vf4567);
141 vacc0 = _mm_add_ps(vacc0, vf89AB);
142 vacc0 = _mm_add_ps(vacc0, vfCDEF);
143 }
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