1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
|
// Auto-generated file. Do not edit!
// Template: src/f32-raddextexp/avx512f-p5-scalef.c.in
// Generator: tools/xngen
//
// Copyright 2019 Google LLC
//
// This source code is licensed under the BSD-style license found in the
// LICENSE file in the root directory of this source tree.
#include <assert.h>
#include <math.h>
#include <immintrin.h>
#include <xnnpack/common.h>
#include <xnnpack/intrinsics-polyfill.h>
#include <xnnpack/raddextexp.h>
void xnn_f32_raddextexp_ukernel__avx512f_p5_scalef_u64_acc2(
size_t batch,
const float* input,
float* sum)
{
assert(batch != 0);
assert(batch % sizeof(float) == 0);
assert(input != NULL);
assert(sum != NULL);
const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f);
const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f);
const __m512 vc0 = _mm512_set1_ps(1.0f);
const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f);
const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f);
const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f);
const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f);
const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f);
const __m512 vminus_inf = _mm512_set1_ps(-INFINITY);
__m512 vaccv0 = _mm512_setzero_ps();
__m512 vaccv1 = _mm512_setzero_ps();
__m512 vacce0 = vminus_inf;
__m512 vacce1 = vminus_inf;
for (; batch >= 64 * sizeof(float); batch -= 64 * sizeof(float)) {
// Load 64 (4x16) inputs at a time.
const __m512 vx0 = _mm512_loadu_ps(input);
const __m512 vx1 = _mm512_loadu_ps(input + 16);
const __m512 vx2 = _mm512_loadu_ps(input + 32);
const __m512 vx3 = _mm512_loadu_ps(input + 48);
input += 64;
// Compute reduced argument batch := round(input / log(2)).
const __m512 vn0 = _mm512_roundscale_ps(_mm512_mul_ps(vx0, vlog2e), 0);
const __m512 vn1 = _mm512_roundscale_ps(_mm512_mul_ps(vx1, vlog2e), 0);
const __m512 vn2 = _mm512_roundscale_ps(_mm512_mul_ps(vx2, vlog2e), 0);
const __m512 vn3 = _mm512_roundscale_ps(_mm512_mul_ps(vx3, vlog2e), 0);
// Compute reduced argument t := input - batch * log(2).
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
__m512 vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_hi, vx0);
__m512 vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_hi, vx1);
__m512 vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_hi, vx2);
__m512 vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_hi, vx3);
vt0 = _mm512_fmadd_ps(vn0, vminus_ln2_lo, vt0);
vt1 = _mm512_fmadd_ps(vn1, vminus_ln2_lo, vt1);
vt2 = _mm512_fmadd_ps(vn2, vminus_ln2_lo, vt2);
vt3 = _mm512_fmadd_ps(vn3, vminus_ln2_lo, vt3);
// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
__m512 vp0 = _mm512_fmadd_ps(vc5, vt0, vc4);
__m512 vp1 = _mm512_fmadd_ps(vc5, vt1, vc4);
__m512 vp2 = _mm512_fmadd_ps(vc5, vt2, vc4);
__m512 vp3 = _mm512_fmadd_ps(vc5, vt3, vc4);
vp0 = _mm512_fmadd_ps(vp0, vt0, vc3);
vp1 = _mm512_fmadd_ps(vp1, vt1, vc3);
vp2 = _mm512_fmadd_ps(vp2, vt2, vc3);
vp3 = _mm512_fmadd_ps(vp3, vt3, vc3);
vp0 = _mm512_fmadd_ps(vp0, vt0, vc2);
vp1 = _mm512_fmadd_ps(vp1, vt1, vc2);
vp2 = _mm512_fmadd_ps(vp2, vt2, vc2);
vp3 = _mm512_fmadd_ps(vp3, vt3, vc2);
vp0 = _mm512_fmadd_ps(vp0, vt0, vc1);
vp1 = _mm512_fmadd_ps(vp1, vt1, vc1);
vp2 = _mm512_fmadd_ps(vp2, vt2, vc1);
vp3 = _mm512_fmadd_ps(vp3, vt3, vc1);
vp0 = _mm512_fmadd_ps(vp0, vt0, vc0);
vp1 = _mm512_fmadd_ps(vp1, vt1, vc0);
vp2 = _mm512_fmadd_ps(vp2, vt2, vc0);
vp3 = _mm512_fmadd_ps(vp3, vt3, vc0);
// Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation where
// - vnX is "exponent"
// - vpX is "mantissa"
//
// exp2(ae) * av + exp2(be) * bv =
// = exp2(max(ae, be)) * exp2(ae - max(ae, be)) * av + exp2(max(ae, be)) * exp2(be - max(ae, be)) * bv
// = exp2(max_e) * (exp2(ae - max_e) * av + exp2(be - max_e) * bv)
// = exp2(max_e) * (exp2(delta_ae) * av + exp2(delta_be) * bv)
//
// For computational efficiency we add three "extended" floating-point numbers at a time.
__m512 vmax_e0 = _mm512_max_ps(vacce0, vn0);
__m512 vmax_e1 = _mm512_max_ps(vacce1, vn1);
vmax_e0 = _mm512_max_ps(vmax_e0, vn2);
vmax_e1 = _mm512_max_ps(vmax_e1, vn3);
const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_e0);
const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_e1);
const __m512 vdelta_e0 = _mm512_sub_ps(vn0, vmax_e0);
const __m512 vdelta_e1 = _mm512_sub_ps(vn1, vmax_e1);
const __m512 vdelta_e2 = _mm512_sub_ps(vn2, vmax_e0);
const __m512 vdelta_e3 = _mm512_sub_ps(vn3, vmax_e1);
// Update accumulated "mantissa" and "exponent" values
vaccv0 = _mm512_scalef_ps(vaccv0, vdelta_acce0);
vaccv1 = _mm512_scalef_ps(vaccv1, vdelta_acce1);
vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp0, vdelta_e0));
vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp1, vdelta_e1));
vaccv0 = _mm512_add_ps(vaccv0, _mm512_scalef_ps(vp2, vdelta_e2));
vaccv1 = _mm512_add_ps(vaccv1, _mm512_scalef_ps(vp3, vdelta_e3));
vacce0 = vmax_e0;
vacce1 = vmax_e1;
}
// Reduce partial sums of "extended" floating-point numbers into a single "extended" SIMD vector of sums.
const __m512 vmax_acce01 = _mm512_max_ps(vacce0, vacce1);
const __m512 vdelta_acce0 = _mm512_sub_ps(vacce0, vmax_acce01);
const __m512 vdelta_acce1 = _mm512_sub_ps(vacce1, vmax_acce01);
__m512 vaccv = _mm512_scalef_ps(vaccv0, vdelta_acce0);
vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vaccv1, vdelta_acce1));
__m512 vacce = vmax_acce01;
for (; batch >= 16 * sizeof(float); batch -= 16 * sizeof(float)) {
// Load 16 inputs at a time.
const __m512 vx = _mm512_loadu_ps(input);
input += 16;
// Compute reduced argument batch := round(input / log(2)).
const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
// Compute reduced argument t := input - batch * log(2).
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
__m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
__m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
vp = _mm512_fmadd_ps(vp, vt, vc3);
vp = _mm512_fmadd_ps(vp, vt, vc2);
vp = _mm512_fmadd_ps(vp, vt, vc1);
vp = _mm512_fmadd_ps(vp, vt, vc0);
// Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
const __m512 vmax_e = _mm512_max_ps(vacce, vn);
const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
vaccv = _mm512_scalef_ps(vaccv, vdelta_acce);
vaccv = _mm512_add_ps(vaccv, _mm512_scalef_ps(vp, vdelta_e));
vacce = vmax_e;
}
if XNN_UNLIKELY(batch != 0) {
// Prepare mask for valid 32-bit batch (depends on batch).
batch >>= XNN_LOG2_SIZEOF_FLOAT;
const __mmask16 vmask = _cvtu32_mask16((uint32_t) ((UINT32_C(1) << batch) - UINT32_C(1)));
// Load up to 15 inputs at a time.
const __m512 vx = _mm512_maskz_loadu_ps(vmask, input);
// Compute reduced argument batch := round(input / log(2)).
const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);
// Compute reduced argument t := input - batch * log(2).
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
__m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);
// Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
__m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
vp = _mm512_fmadd_ps(vp, vt, vc3);
vp = _mm512_fmadd_ps(vp, vt, vc2);
vp = _mm512_fmadd_ps(vp, vt, vc1);
vp = _mm512_fmadd_ps(vp, vt, vc0);
// Accumulate "extended" floating-point numbers in ("mantissa", "exponent") representation.
const __m512 vmax_e = _mm512_mask_max_ps(vacce, vmask, vacce, vn);
const __m512 vdelta_acce = _mm512_sub_ps(vacce, vmax_e);
const __m512 vdelta_e = _mm512_sub_ps(vn, vmax_e);
vaccv = _mm512_mask_scalef_ps(vaccv, vmask, vaccv, vdelta_acce);
vaccv = _mm512_mask_add_ps(vaccv, vmask, vaccv, _mm512_maskz_scalef_ps(vmask, vp, vdelta_e));
vacce = vmax_e;
}
// Reduce partial sums of "extended" floating-point numbers into a single "extended" floating-point sum.
const float vmax_acce = _mm512_reduce_max_ps(vacce);
const __m512 vdelta_acce = _mm512_sub_ps(vacce, _mm512_set1_ps(vmax_acce));
sum[0] = _mm512_reduce_add_ps(_mm512_scalef_ps(vaccv, vdelta_acce));
sum[1] = vmax_acce;
_mm256_zeroupper();
}
|
