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_x8(size_t elements,const float * input,float * output,float * sum,float max)18 void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x8(
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 >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
45 // Load 8 (2x4) inputs at a time.
46 const __m128 vi0123 = _mm_loadu_ps(input);
47 const __m128 vi4567 = _mm_loadu_ps(input + 4);
48 input += 8;
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
54 // Compute reduced argument elements := round(x / log(2)).
55 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
56 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
57
58 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
59 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
60 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
61 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
62
63 // Subtract the large number back to get final elements := round(x / log(2)).
64 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
65 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
66
67 // Compute reduced argument t := x - elements * log(2).
68 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
69 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
70 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
71
72 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
73 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
74
75 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
76 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
77 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
78
79 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
80 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
81
82 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
83 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
84
85 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
86 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
87
88 // Reconstruct the final f value:
89 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
90 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
91 // = s + (t * s) * p
92 vt0123 = _mm_mul_ps(vt0123, vs0123);
93 vt4567 = _mm_mul_ps(vt4567, vs4567);
94
95 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
96 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
97
98 // For inputs below zero cutoff, replace output with +0.0f.
99 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
100 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
101 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
102
103 // Store 8 (2x4) outputs at a time.
104 _mm_storeu_ps(output, vf0123);
105 _mm_storeu_ps(output + 4, vf4567);
106 output += 8;
107
108 // Accumulate computed exponents.
109 vacc0 = _mm_add_ps(vacc0, vf0123);
110 vacc0 = _mm_add_ps(vacc0, vf4567);
111 }
112
113 __m128 vacc = vacc0;
114 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
115 // Load 4 inputs at a time.
116 const __m128 vi = _mm_loadu_ps(input);
117 input += 4;
118
119 // Subtract maximum input x := i - i_max. This implies x <= 0.
120 const __m128 vx = _mm_sub_ps(vi, vi_max);
121
122 // Compute reduced argument elements := round(x / log(2)).
123 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
124
125 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
126 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
127 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
128
129 // Subtract the large number back to get final elements := round(x / log(2)).
130 vn = _mm_sub_ps(vn, vmagic_bias);
131
132 // Compute reduced argument t := x - elements * log(2).
133 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
134 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
135 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
136
137 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
138 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
139 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
140 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
141 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
142
143 // Reconstruct the final f value:
144 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
145 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
146 // = s + (t * s) * p
147 vt = _mm_mul_ps(vt, vs);
148 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
149
150 // For inputs below zero cutoff, replace output with +0.0f.
151 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
152 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
153
154 // Store 4 outputs at a time.
155 _mm_storeu_ps(output, vf);
156 output += 4;
157
158 // Accumulate computed exponents.
159 vacc = _mm_add_ps(vacc, vf);
160 }
161 if (elements != 0) {
162 assert(elements >= 1 * sizeof(float));
163 assert(elements <= 3 * sizeof(float));
164 // Load 4 inputs at a time.
165 const __m128 vi = _mm_loadu_ps(input);
166
167 // Subtract maximum input x := i - i_max. This implies x <= 0.
168 const __m128 vx = _mm_sub_ps(vi, vi_max);
169
170 // Compute reduced argument elements := round(x / log(2)).
171 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
172
173 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
174 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
175 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
176
177 // Subtract the large number back to get final elements := round(x / log(2)).
178 vn = _mm_sub_ps(vn, vmagic_bias);
179
180 // Compute reduced argument t := x - elements * log(2).
181 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
182 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
183 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
184
185 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
186 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
187 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
188 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
189 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
190
191 // Reconstruct the final f value:
192 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
193 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
194 // = s + (t * s) * p
195 vt = _mm_mul_ps(vt, vs);
196 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
197
198 // For inputs below zero cutoff, replace output with +0.0f.
199 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
200 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
201
202 if (elements & (2 * sizeof(float))) {
203 // Store 2 outputs at a time.
204 _mm_storel_pi((__m64*) output, vf);
205 output += 2;
206
207 // Accumulate 2 computed exponents.
208 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
209
210 vf = _mm_movehl_ps(vf, vf);
211 }
212 if (elements & (1 * sizeof(float))) {
213 // Store 1 output at a time.
214 _mm_store_ss(output, vf);
215
216 // Accumulate 1 computed exponent.
217 vacc = _mm_add_ss(vacc, vf);
218 }
219 }
220 // Reduce 4 elements in the SIMD register
221 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
222 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
223 _mm_store_ss(sum, vacc);
224 }
225