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_acc2(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x12_acc2(
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 __m128 vacc1 = _mm_setzero_ps();
45 for (; elements >= 12 * sizeof(float); elements -= 12 * sizeof(float)) {
46 // Load 12 (3x4) 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 input += 12;
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
57 // Compute reduced argument elements := round(x / log(2)).
58 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
59 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
60 __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, 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
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
73 // Compute reduced argument t := x - elements * log(2).
74 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
75 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
76 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
77 __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
78
79 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
80 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
81 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
82
83 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
84 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
85 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
86 __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
87
88 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
89 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
90 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
91
92 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
93 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
94 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
95
96 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
97 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
98 vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
99
100 // Reconstruct the final f value:
101 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
102 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
103 // = s + (t * s) * p
104 vt0123 = _mm_mul_ps(vt0123, vs0123);
105 vt4567 = _mm_mul_ps(vt4567, vs4567);
106 vt89AB = _mm_mul_ps(vt89AB, vs89AB);
107
108 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
109 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
110 __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
111
112 // For inputs below zero cutoff, replace output with +0.0f.
113 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
114 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
115 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
116 vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
117
118 // Store 12 (3x4) outputs at a time.
119 _mm_storeu_ps(output, vf0123);
120 _mm_storeu_ps(output + 4, vf4567);
121 _mm_storeu_ps(output + 8, vf89AB);
122 output += 12;
123
124 // Accumulate computed exponents.
125 vacc0 = _mm_add_ps(vacc0, vf0123);
126 vacc0 = _mm_add_ps(vacc0, vf4567);
127 vacc0 = _mm_add_ps(vacc0, vf89AB);
128 }
129 // Add up all accumulators to vacc0
130 vacc0 = _mm_add_ps(vacc0, vacc1);
131
132 __m128 vacc = vacc0;
133 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
134 // Load 4 inputs at a time.
135 const __m128 vi = _mm_loadu_ps(input);
136 input += 4;
137
138 // Subtract maximum input x := i - i_max. This implies x <= 0.
139 const __m128 vx = _mm_sub_ps(vi, vi_max);
140
141 // Compute reduced argument elements := round(x / log(2)).
142 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
143
144 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
145 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
146 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
147
148 // Subtract the large number back to get final elements := round(x / log(2)).
149 vn = _mm_sub_ps(vn, vmagic_bias);
150
151 // Compute reduced argument t := x - elements * log(2).
152 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
153 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
154 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
155
156 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
157 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
158 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
159 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
160 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
161
162 // Reconstruct the final f value:
163 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
164 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
165 // = s + (t * s) * p
166 vt = _mm_mul_ps(vt, vs);
167 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
168
169 // For inputs below zero cutoff, replace output with +0.0f.
170 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
171 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
172
173 // Store 4 outputs at a time.
174 _mm_storeu_ps(output, vf);
175 output += 4;
176
177 // Accumulate computed exponents.
178 vacc = _mm_add_ps(vacc, vf);
179 }
180 if (elements != 0) {
181 assert(elements >= 1 * sizeof(float));
182 assert(elements <= 3 * sizeof(float));
183 // Load 4 inputs at a time.
184 const __m128 vi = _mm_loadu_ps(input);
185
186 // Subtract maximum input x := i - i_max. This implies x <= 0.
187 const __m128 vx = _mm_sub_ps(vi, vi_max);
188
189 // Compute reduced argument elements := round(x / log(2)).
190 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
191
192 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
193 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
194 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
195
196 // Subtract the large number back to get final elements := round(x / log(2)).
197 vn = _mm_sub_ps(vn, vmagic_bias);
198
199 // Compute reduced argument t := x - elements * log(2).
200 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
201 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
202 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
203
204 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
205 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
206 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
207 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
208 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
209
210 // Reconstruct the final f value:
211 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
212 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
213 // = s + (t * s) * p
214 vt = _mm_mul_ps(vt, vs);
215 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
216
217 // For inputs below zero cutoff, replace output with +0.0f.
218 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
219 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
220
221 if (elements & (2 * sizeof(float))) {
222 // Store 2 outputs at a time.
223 _mm_storel_pi((__m64*) output, vf);
224 output += 2;
225
226 // Accumulate 2 computed exponents.
227 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
228
229 vf = _mm_movehl_ps(vf, vf);
230 }
231 if (elements & (1 * sizeof(float))) {
232 // Store 1 output at a time.
233 _mm_store_ss(output, vf);
234
235 // Accumulate 1 computed exponent.
236 vacc = _mm_add_ss(vacc, vf);
237 }
238 }
239 // Reduce 4 elements in the SIMD register
240 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
241 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
242 _mm_store_ss(sum, vacc);
243 }
244