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_x12(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x12(
19 size_t elements,
20 const float* input,
21 float* output,
22 float* sum,
23 float max)
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 >= 12 * sizeof(float); elements -= 12 * sizeof(float)) {
45 // Load 12 (3x4) 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 input += 12;
50
51 // Subtract maximum input x := i - i_max. This implies x <= 0.
52 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
53 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
54 const __m128 vx89AB = _mm_sub_ps(vi89AB, 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
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
67 // Subtract the large number back to get final elements := round(x / log(2)).
68 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
69 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
70 vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
71
72 // Compute reduced argument t := x - elements * log(2).
73 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
74 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
75 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
76 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
77
78 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
79 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
80 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
81
82 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
83 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
84 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
85 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
86
87 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
88 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
89 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
90
91 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
92 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
93 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
94
95 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
96 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
97 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
98
99 // Reconstruct the final f value:
100 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
101 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
102 // = s + (t * s) * p
103 vt0123 = _mm_mul_ps(vt0123, vs0123);
104 vt4567 = _mm_mul_ps(vt4567, vs4567);
105 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
106
107 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
108 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
109 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
110
111 // For inputs below zero cutoff, replace output with +0.0f.
112 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
113 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
114 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
115 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
116
117 // Store 12 (3x4) outputs at a time.
118 _mm_storeu_ps(output, vf0123);
119 _mm_storeu_ps(output + 4, vf4567);
120 _mm_storeu_ps(output + 8, vf89AB);
121 output += 12;
122
123 // Accumulate computed exponents.
124 vacc0 = _mm_add_ps(vacc0, vf0123);
125 vacc0 = _mm_add_ps(vacc0, vf4567);
126 vacc0 = _mm_add_ps(vacc0, vf89AB);
127 }
128
129 __m128 vacc = vacc0;
130 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
131 // Load 4 inputs at a time.
132 const __m128 vi = _mm_loadu_ps(input);
133 input += 4;
134
135 // Subtract maximum input x := i - i_max. This implies x <= 0.
136 const __m128 vx = _mm_sub_ps(vi, vi_max);
137
138 // Compute reduced argument elements := round(x / log(2)).
139 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
140
141 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
142 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
143 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
144
145 // Subtract the large number back to get final elements := round(x / log(2)).
146 vn = _mm_sub_ps(vn, vmagic_bias);
147
148 // Compute reduced argument t := x - elements * log(2).
149 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
150 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
151 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
152
153 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
154 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
155 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
156 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
157 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
158
159 // Reconstruct the final f value:
160 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
161 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
162 // = s + (t * s) * p
163 vt = _mm_mul_ps(vt, vs);
164 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
165
166 // For inputs below zero cutoff, replace output with +0.0f.
167 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
168 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
169
170 // Store 4 outputs at a time.
171 _mm_storeu_ps(output, vf);
172 output += 4;
173
174 // Accumulate computed exponents.
175 vacc = _mm_add_ps(vacc, vf);
176 }
177 if (elements != 0) {
178 assert(elements >= 1 * sizeof(float));
179 assert(elements <= 3 * sizeof(float));
180 // Load 4 inputs at a time.
181 const __m128 vi = _mm_loadu_ps(input);
182
183 // Subtract maximum input x := i - i_max. This implies x <= 0.
184 const __m128 vx = _mm_sub_ps(vi, vi_max);
185
186 // Compute reduced argument elements := round(x / log(2)).
187 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
188
189 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
190 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
191 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
192
193 // Subtract the large number back to get final elements := round(x / log(2)).
194 vn = _mm_sub_ps(vn, vmagic_bias);
195
196 // Compute reduced argument t := x - elements * log(2).
197 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
198 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
199 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
200
201 // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
202 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
203 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
204 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
205 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
206
207 // Reconstruct the final f value:
208 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
209 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
210 // = s + (t * s) * p
211 vt = _mm_mul_ps(vt, vs);
212 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
213
214 // For inputs below zero cutoff, replace output with +0.0f.
215 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
216 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
217
218 if (elements & (2 * sizeof(float))) {
219 // Store 2 outputs at a time.
220 _mm_storel_pi((__m64*) output, vf);
221 output += 2;
222
223 // Accumulate 2 computed exponents.
224 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
225
226 vf = _mm_movehl_ps(vf, vf);
227 }
228 if (elements & (1 * sizeof(float))) {
229 // Store 1 output at a time.
230 _mm_store_ss(output, vf);
231
232 // Accumulate 1 computed exponent.
233 vacc = _mm_add_ss(vacc, vf);
234 }
235 }
236 // Reduce 4 elements in the SIMD register
237 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
238 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
239 _mm_store_ss(sum, vacc);
240 }
241