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_x8(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_x8(
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 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
42 // Load 8 (2x4) inputs at a time.
43 const __m128 vi0123 = _mm_loadu_ps(input);
44 const __m128 vi4567 = _mm_loadu_ps(input + 4);
45 input += 8;
46
47 // Subtract maximum input x := i - i_max. This implies x <= 0.
48 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
49 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
50
51 // Compute reduced argument elements := round(x / log(2)).
52 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
53 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
54
55 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
56 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
57 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
58 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
59
60 // Subtract the large number back to get final elements := round(x / log(2)).
61 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
62 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
63
64 // Compute reduced argument t := x - elements * log(2).
65 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
66 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
67 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
68
69 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
70 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
71
72 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
73 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
74 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
75
76 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
77 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
78
79 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
80 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
81
82 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
83 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
84
85 // Reconstruct the final f value:
86 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
87 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
88 // = s + (t * s) * p
89 vt0123 = _mm_mul_ps(vt0123, vs0123);
90 vt4567 = _mm_mul_ps(vt4567, vs4567);
91
92 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
93 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
94
95 // For inputs below zero cutoff, replace output with +0.0f.
96 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
97 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
98 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
99
100 // Store 8 (2x4) outputs at a time.
101 _mm_storeu_ps(output, vf0123);
102 _mm_storeu_ps(output + 4, vf4567);
103 output += 8;
104
105 // Accumulate computed exponents.
106 vacc0 = _mm_add_ps(vacc0, vf0123);
107 vacc0 = _mm_add_ps(vacc0, vf4567);
108 }
109
110 __m128 vacc = vacc0;
111 for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
112 // Load 4 inputs at a time.
113 const __m128 vi = _mm_loadu_ps(input);
114 input += 4;
115
116 // Subtract maximum input x := i - i_max. This implies x <= 0.
117 const __m128 vx = _mm_sub_ps(vi, vi_max);
118
119 // Compute reduced argument elements := round(x / log(2)).
120 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
121
122 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
123 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
124 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
125
126 // Subtract the large number back to get final elements := round(x / log(2)).
127 vn = _mm_sub_ps(vn, vmagic_bias);
128
129 // Compute reduced argument t := x - elements * log(2).
130 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
131 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
132 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
133
134 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
135 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
136 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
137 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
138 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
139
140 // Reconstruct the final f value:
141 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
142 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
143 // = s + (t * s) * p
144 vt = _mm_mul_ps(vt, vs);
145 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
146
147 // For inputs below zero cutoff, replace output with +0.0f.
148 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
149 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
150
151 // Store 4 outputs at a time.
152 _mm_storeu_ps(output, vf);
153 output += 4;
154
155 // Accumulate computed exponents.
156 vacc = _mm_add_ps(vacc, vf);
157 }
158 if (elements != 0) {
159 assert(elements >= 1 * sizeof(float));
160 assert(elements <= 3 * sizeof(float));
161 // Load 4 inputs at a time.
162 const __m128 vi = _mm_loadu_ps(input);
163
164 // Subtract maximum input x := i - i_max. This implies x <= 0.
165 const __m128 vx = _mm_sub_ps(vi, vi_max);
166
167 // Compute reduced argument elements := round(x / log(2)).
168 __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
169
170 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
171 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
172 const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
173
174 // Subtract the large number back to get final elements := round(x / log(2)).
175 vn = _mm_sub_ps(vn, vmagic_bias);
176
177 // Compute reduced argument t := x - elements * log(2).
178 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
179 __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
180 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
181
182 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
183 __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
184 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
185 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
186 vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
187
188 // Reconstruct the final f value:
189 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
190 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
191 // = s + (t * s) * p
192 vt = _mm_mul_ps(vt, vs);
193 __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
194
195 // For inputs below zero cutoff, replace output with +0.0f.
196 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
197 vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
198
199 if (elements & (2 * sizeof(float))) {
200 // Store 2 outputs at a time.
201 _mm_storel_pi((__m64*) output, vf);
202 output += 2;
203
204 // Accumulate 2 computed exponents.
205 vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
206
207 vf = _mm_movehl_ps(vf, vf);
208 }
209 if (elements & (1 * sizeof(float))) {
210 // Store 1 output at a time.
211 _mm_store_ss(output, vf);
212
213 // Accumulate 1 computed exponent.
214 vacc = _mm_add_ss(vacc, vf);
215 }
216 }
217 // Reduce 4 elements in the SIMD register
218 vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
219 vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
220 _mm_store_ss(sum, vacc);
221 }
222