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_acc2(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_acc2(
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 __m128 vacc1 = _mm_setzero_ps();
42 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
43 // Load 8 (2x4) inputs at a time.
44 const __m128 vi0123 = _mm_loadu_ps(input);
45 const __m128 vi4567 = _mm_loadu_ps(input + 4);
46 input += 8;
47
48 // Subtract maximum input x := i - i_max. This implies x <= 0.
49 const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
50 const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
51
52 // Compute reduced argument elements := round(x / log(2)).
53 __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
54 __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
55
56 // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
57 // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
58 const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
59 const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
60
61 // Subtract the large number back to get final elements := round(x / log(2)).
62 vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
63 vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
64
65 // Compute reduced argument t := x - elements * log(2).
66 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
67 __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
68 __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
69
70 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
71 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
72
73 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
74 __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
75 __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
76
77 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
78 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
79
80 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
81 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
82
83 vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
84 vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
85
86 // Reconstruct the final f value:
87 // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
88 // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
89 // = s + (t * s) * p
90 vt0123 = _mm_mul_ps(vt0123, vs0123);
91 vt4567 = _mm_mul_ps(vt4567, vs4567);
92
93 __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
94 __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
95
96 // For inputs below zero cutoff, replace output with +0.0f.
97 // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
98 vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
99 vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
100
101 // Store 8 (2x4) outputs at a time.
102 _mm_storeu_ps(output, vf0123);
103 _mm_storeu_ps(output + 4, vf4567);
104 output += 8;
105
106 // Accumulate computed exponents.
107 vacc0 = _mm_add_ps(vacc0, vf0123);
108 vacc0 = _mm_add_ps(vacc0, vf4567);
109 }
110 // Add up all accumulators to vacc0
111 vacc0 = _mm_add_ps(vacc0, vacc1);
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