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_x40(size_t elements,const float * x,float * y,float scale_value,float scale_exp)20 void xnn_f32_vscaleextexp_ukernel__avx2_p5_x40(
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 >= 40 * sizeof(float); elements -= 40 * sizeof(float)) {
49 // Load 40 (5x8) 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 x += 40;
56
57 // Compute reduced argument elements := round(x / log(2)).
58 const __m256 vn0 = _mm256_round_ps(_mm256_mul_ps(vx0, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
59 const __m256 vn1 = _mm256_round_ps(_mm256_mul_ps(vx1, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
60 const __m256 vn2 = _mm256_round_ps(_mm256_mul_ps(vx2, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
61 const __m256 vn3 = _mm256_round_ps(_mm256_mul_ps(vx3, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
62 const __m256 vn4 = _mm256_round_ps(_mm256_mul_ps(vx4, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
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 __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_hi, vx0);
67 __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_hi, vx1);
68 __m256 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_hi, vx2);
69 __m256 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_hi, vx3);
70 __m256 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_hi, vx4);
71
72 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2_lo, vt0);
73 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2_lo, vt1);
74 vt2 = _mm256_fmadd_ps(vn2, vminus_ln2_lo, vt2);
75 vt3 = _mm256_fmadd_ps(vn3, vminus_ln2_lo, vt3);
76 vt4 = _mm256_fmadd_ps(vn4, vminus_ln2_lo, vt4);
77
78 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
79 __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
80 __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);
81 __m256 vp2 = _mm256_fmadd_ps(vc5, vt2, vc4);
82 __m256 vp3 = _mm256_fmadd_ps(vc5, vt3, vc4);
83 __m256 vp4 = _mm256_fmadd_ps(vc5, vt4, vc4);
84
85 vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
86 vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);
87 vp2 = _mm256_fmadd_ps(vp2, vt2, vc3);
88 vp3 = _mm256_fmadd_ps(vp3, vt3, vc3);
89 vp4 = _mm256_fmadd_ps(vp4, vt4, vc3);
90
91 vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
92 vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);
93 vp2 = _mm256_fmadd_ps(vp2, vt2, vc2);
94 vp3 = _mm256_fmadd_ps(vp3, vt3, vc2);
95 vp4 = _mm256_fmadd_ps(vp4, vt4, vc2);
96
97 vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
98 vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);
99 vp2 = _mm256_fmadd_ps(vp2, vt2, vc1);
100 vp3 = _mm256_fmadd_ps(vp3, vt3, vc1);
101 vp4 = _mm256_fmadd_ps(vp4, vt4, vc1);
102
103 vp0 = _mm256_fmadd_ps(vp0, vt0, vc0);
104 vp1 = _mm256_fmadd_ps(vp1, vt1, vc0);
105 vp2 = _mm256_fmadd_ps(vp2, vt2, vc0);
106 vp3 = _mm256_fmadd_ps(vp3, vt3, vc0);
107 vp4 = _mm256_fmadd_ps(vp4, vt4, vc0);
108
109 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation where
110 // - vnX is "exponent"
111 // - vpX is "mantissa"
112 //
113 // exp2(ae) * av * exp2(be) * bv =
114 // = exp2(ae + be) * (av * bv)
115 __m256 vf0 = _mm256_mul_ps(vp0, vscalev);
116 __m256 vf1 = _mm256_mul_ps(vp1, vscalev);
117 __m256 vf2 = _mm256_mul_ps(vp2, vscalev);
118 __m256 vf3 = _mm256_mul_ps(vp3, vscalev);
119 __m256 vf4 = _mm256_mul_ps(vp4, vscalev);
120
121 __m256 ve0 = _mm256_add_ps(vn0, vscalee);
122 __m256 ve1 = _mm256_add_ps(vn1, vscalee);
123 __m256 ve2 = _mm256_add_ps(vn2, vscalee);
124 __m256 ve3 = _mm256_add_ps(vn3, vscalee);
125 __m256 ve4 = _mm256_add_ps(vn4, vscalee);
126
127 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
128 // This replacement is done in two steps:
129 // 1. Clamp minimum e at -127.0.
130 // 2. Map e to scale factor 0.0 when e == -127.0
131 ve0 = _mm256_max_ps(ve0, vmin_exponent);
132 ve1 = _mm256_max_ps(ve1, vmin_exponent);
133 ve2 = _mm256_max_ps(ve2, vmin_exponent);
134 ve3 = _mm256_max_ps(ve3, vmin_exponent);
135 ve4 = _mm256_max_ps(ve4, vmin_exponent);
136
137 // Convert exponents into scale factors:
138 // - s = exp2(e) when e > -127.0
139 // - s = 0.0 when e <= -127.0
140 const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve0, vmagic_bias)), 23));
141 const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve1, vmagic_bias)), 23));
142 const __m256 vs2 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve2, vmagic_bias)), 23));
143 const __m256 vs3 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve3, vmagic_bias)), 23));
144 const __m256 vs4 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve4, vmagic_bias)), 23));
145
146 // Multiply "mantissa" by the scale factor.
147 vf0 = _mm256_mul_ps(vf0, vs0);
148 vf1 = _mm256_mul_ps(vf1, vs1);
149 vf2 = _mm256_mul_ps(vf2, vs2);
150 vf3 = _mm256_mul_ps(vf3, vs3);
151 vf4 = _mm256_mul_ps(vf4, vs4);
152
153 // Store 40 (5x8) outputs at a time.
154 _mm256_storeu_ps(y, vf0);
155 _mm256_storeu_ps(y + 8, vf1);
156 _mm256_storeu_ps(y + 16, vf2);
157 _mm256_storeu_ps(y + 24, vf3);
158 _mm256_storeu_ps(y + 32, vf4);
159 y += 40;
160 }
161
162 for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
163 // Load 8 inputs at a time.
164 const __m256 vx = _mm256_loadu_ps(x);
165 x += 8;
166
167 // Compute reduced argument elements := round(x / log(2)).
168 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
169
170 // Compute reduced argument t := x - elements * log(2).
171 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
172 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
173 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
174
175 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
176 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
177 vp = _mm256_fmadd_ps(vp, vt, vc3);
178 vp = _mm256_fmadd_ps(vp, vt, vc2);
179 vp = _mm256_fmadd_ps(vp, vt, vc1);
180 vp = _mm256_fmadd_ps(vp, vt, vc0);
181
182 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
183 __m256 vf = _mm256_mul_ps(vp, vscalev);
184 __m256 ve = _mm256_add_ps(vn, vscalee);
185
186 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
187 ve = _mm256_max_ps(ve, vmin_exponent);
188
189 // Convert exponents into scale factors.
190 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
191
192 // Multiply "mantissa" by the scale factor.
193 vf = _mm256_mul_ps(vf, vs);
194
195 // Store 8 results at a time.
196 _mm256_storeu_ps(y, vf);
197 y += 8;
198 }
199 if XNN_UNLIKELY(elements != 0) {
200 assert(elements >= 1 * sizeof(float));
201 assert(elements <= 7 * sizeof(float));
202 const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));
203
204 // Load up to 7 inputs at a time.
205 const __m256 vx = _mm256_maskload_ps(x, vmask);
206
207 // Compute reduced argument elements := round(x / log(2)).
208 const __m256 vn = _mm256_round_ps(_mm256_mul_ps(vx, vlog2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
209
210 // Compute reduced argument t := x - elements * log(2).
211 // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
212 __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
213 vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);
214
215 // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
216 __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
217 vp = _mm256_fmadd_ps(vp, vt, vc3);
218 vp = _mm256_fmadd_ps(vp, vt, vc2);
219 vp = _mm256_fmadd_ps(vp, vt, vc1);
220 vp = _mm256_fmadd_ps(vp, vt, vc0);
221
222 // Multiply "extended" floating-point numbers in ("mantissa", "exponent") representation.
223 __m256 vf = _mm256_mul_ps(vp, vscalev);
224 __m256 ve = _mm256_add_ps(vn, vscalee);
225
226 // For computational efficiency, replace exp2(e) with 0.0f when e <= -127.0.
227 ve = _mm256_max_ps(ve, vmin_exponent);
228
229 // Convert exponents into scale factors.
230 const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(_mm256_add_ps(ve, vmagic_bias)), 23));
231
232 // Multiply "mantissa" by the scale factor.
233 vf = _mm256_mul_ps(vf, vs);
234
235 // Store up to 7 inputs at a time.
236 _mm256_maskstore_ps(y, vmask, vf);
237 }
238 _mm256_zeroupper();
239 }
240