1 // Auto-generated file. Do not edit!
2 // Template: src/f32-vscaleextexp/avx2-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 <immintrin.h>
13
14 #include <xnnpack/common.h>
15 #include <xnnpack/vscaleextexp.h>
16
17
18 static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};
19
xnn_f32_vscaleextexp_ukernel__avx2_p5_x48(size_t elements,const float * x,float * y,float scale_value,float scale_exp)20 void xnn_f32_vscaleextexp_ukernel__avx2_p5_x48(
21 size_t elements,
22 const float* x,
23 float* y,
24 float scale_value,
25 float scale_exp)
26 {
27 assert(elements % sizeof(float) == 0);
28
29 const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
30 const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
31 const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);
32
33 // The smallest elements such that 2**elements is considered non-negligible.
34 // For smaller elements, 2**elements is replaced with zero.
35 const __m256 vmin_exponent = _mm256_set1_ps(-127.0f);
36 const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
37
38 const __m256 vc0 = _mm256_set1_ps(1.0f);
39 const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
40 const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
41 const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
42 const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
43 const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);
44
45 const __m256 vscalev = _mm256_set1_ps(scale_value);
46 const __m256 vscalee = _mm256_set1_ps(scale_exp);
47
48 for (; elements >= 48 * sizeof(float); elements -= 48 * sizeof(float)) {
49 // Load 48 (6x8) inputs at a time.
50 const __m256 vx0 = _mm256_loadu_ps(x);
51 const __m256 vx1 = _mm256_loadu_ps(x + 8);
52 const __m256 vx2 = _mm256_loadu_ps(x + 16);
53 const __m256 vx3 = _mm256_loadu_ps(x + 24);
54 const __m256 vx4 = _mm256_loadu_ps(x + 32);
55 const __m256 vx5 = _mm256_loadu_ps(x + 40);
56 x += 48;
57
58 // Compute reduced argument elements := round(x / log(2)).
59 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
60 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
61 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
62 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
63 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
64 const __m256 vn5 = _mm256_round_ps(_mm256_mul_ps(vx5, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
65
66 // Compute reduced argument t := x - elements * log(2).
67 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
68 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
69 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
70 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
71 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
72 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
73 __m256 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_hi, vx5);
74
75 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
76 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
77 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
78 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
79 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
80 vt5 = _mm256_fmadd_ps(vn5, vminus_ln2_lo, vt5);
81
82 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
83 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
84 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
85 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
86 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
87 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
88 __m256 vp5 = _mm256_fmadd_ps(vc5, vt5, vc4);
89
90 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
91 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
92 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
93 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
94 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
95 vp5 = _mm256_fmadd_ps(vp5, vt5, vc3);
96
97 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
98 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
99 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
100 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
101 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
102 vp5 = _mm256_fmadd_ps(vp5, vt5, vc2);
103
104 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
105 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
106 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
107 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
108 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
109 vp5 = _mm256_fmadd_ps(vp5, vt5, vc1);
110
111 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
112 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
113 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
114 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
115 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
116 vp5 = _mm256_fmadd_ps(vp5, vt5, vc0);
117
118 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation where
119 // - vnX is "exponent"
120 // - vpX is "mantissa"
121 //
122 // exp2(ae) * av * exp2(be) * bv =
123 // = exp2(ae + be) * (av * bv)
124 __m256 vf0 = _mm256_mul_ps(vp0, vscalev);
125 __m256 vf1 = _mm256_mul_ps(vp1, vscalev);
126 __m256 vf2 = _mm256_mul_ps(vp2, vscalev);
127 __m256 vf3 = _mm256_mul_ps(vp3, vscalev);
128 __m256 vf4 = _mm256_mul_ps(vp4, vscalev);
129 __m256 vf5 = _mm256_mul_ps(vp5, vscalev);
130
131 __m256 ve0 = _mm256_add_ps(vn0, vscalee);
132 __m256 ve1 = _mm256_add_ps(vn1, vscalee);
133 __m256 ve2 = _mm256_add_ps(vn2, vscalee);
134 __m256 ve3 = _mm256_add_ps(vn3, vscalee);
135 __m256 ve4 = _mm256_add_ps(vn4, vscalee);
136 __m256 ve5 = _mm256_add_ps(vn5, vscalee);
137
138 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
139 // This replacement is done in two steps:
140 // 1. Clamp minimum e at -127.0.
141 // 2. Map e to scale factor 0.0 when e == -127.0
142 ve0 = _mm256_max_ps(ve0, vmin_exponent);
143 ve1 = _mm256_max_ps(ve1, vmin_exponent);
144 ve2 = _mm256_max_ps(ve2, vmin_exponent);
145 ve3 = _mm256_max_ps(ve3, vmin_exponent);
146 ve4 = _mm256_max_ps(ve4, vmin_exponent);
147 ve5 = _mm256_max_ps(ve5, vmin_exponent);
148
149 // Convert exponents into scale factors:
150 // - s = exp2(e) when e > -127.0
151 // - s = 0.0 when e <= -127.0
152 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve0, vmagic_bias)), 23));
153 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve1, vmagic_bias)), 23));
154 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve2, vmagic_bias)), 23));
155 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve3, vmagic_bias)), 23));
156 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve4, vmagic_bias)), 23));
157 const __m256 vs5 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve5, vmagic_bias)), 23));
158
159 // Multiply "mantissa" by the scale factor.
160 vf0 = _mm256_mul_ps(vf0, vs0);
161 vf1 = _mm256_mul_ps(vf1, vs1);
162 vf2 = _mm256_mul_ps(vf2, vs2);
163 vf3 = _mm256_mul_ps(vf3, vs3);
164 vf4 = _mm256_mul_ps(vf4, vs4);
165 vf5 = _mm256_mul_ps(vf5, vs5);
166
167 // Store 48 (6x8) outputs at a time.
168 _mm256_storeu_ps(y, vf0);
169 _mm256_storeu_ps(y + 8, vf1);
170 _mm256_storeu_ps(y + 16, vf2);
171 _mm256_storeu_ps(y + 24, vf3);
172 _mm256_storeu_ps(y + 32, vf4);
173 _mm256_storeu_ps(y + 40, vf5);
174 y += 48;
175 }
176
177 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
178 // Load 8 inputs at a time.
179 const __m256 vx = _mm256_loadu_ps(x);
180 x += 8;
181
182 // Compute reduced argument elements := round(x / log(2)).
183 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
184
185 // Compute reduced argument t := x - elements * log(2).
186 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
187 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
188 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
189
190 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
191 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
192 vp = _mm256_fmadd_ps(vp, vt, vc3);
193 vp = _mm256_fmadd_ps(vp, vt, vc2);
194 vp = _mm256_fmadd_ps(vp, vt, vc1);
195 vp = _mm256_fmadd_ps(vp, vt, vc0);
196
197 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
198 __m256 vf = _mm256_mul_ps(vp, vscalev);
199 __m256 ve = _mm256_add_ps(vn, vscalee);
200
201 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
202 ve = _mm256_max_ps(ve, vmin_exponent);
203
204 // Convert exponents into scale factors.
205 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
206
207 // Multiply "mantissa" by the scale factor.
208 vf = _mm256_mul_ps(vf, vs);
209
210 // Store 8 results at a time.
211 _mm256_storeu_ps(y, vf);
212 y += 8;
213 }
214 if XNN_UNLIKELY(elements != 0) {
215 assert(elements >= 1 * sizeof(float));
216 assert(elements <= 7 * sizeof(float));
217 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
218
219 // Load up to 7 inputs at a time.
220 const __m256 vx = _mm256_maskload_ps(x, vmask);
221
222 // Compute reduced argument elements := round(x / log(2)).
223 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
224
225 // Compute reduced argument t := x - elements * log(2).
226 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
227 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
228 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
229
230 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
231 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
232 vp = _mm256_fmadd_ps(vp, vt, vc3);
233 vp = _mm256_fmadd_ps(vp, vt, vc2);
234 vp = _mm256_fmadd_ps(vp, vt, vc1);
235 vp = _mm256_fmadd_ps(vp, vt, vc0);
236
237 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
238 __m256 vf = _mm256_mul_ps(vp, vscalev);
239 __m256 ve = _mm256_add_ps(vn, vscalee);
240
241 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
242 ve = _mm256_max_ps(ve, vmin_exponent);
243
244 // Convert exponents into scale factors.
245 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
246
247 // Multiply "mantissa" by the scale factor.
248 vf = _mm256_mul_ps(vf, vs);
249
250 // Store up to 7 inputs at a time.
251 _mm256_maskstore_ps(y, vmask, vf);
252 }
253 _mm256_zeroupper();
254 }
255