forked from pytorch/pytorch
-
Notifications
You must be signed in to change notification settings - Fork 0
/
adagrad.h
203 lines (177 loc) · 5.93 KB
/
adagrad.h
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
#pragma once
#if defined(__AVX__) && !defined(__NVCC__) && \
(defined(__x86_64__) || defined(_M_X64) || defined(__i386__))
#define CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
#include <immintrin.h>
#endif
#include <c10/util/Half.h>
namespace caffe2 {
namespace internal {
// The following functions inside internal namespace are inlined because they
// are performance critical.
template <typename T>
static inline void adagrad_update_base_inlined(
int N,
const T* w,
const float* g,
const T* h,
T* nw,
T* nh,
float decay,
float epsilon,
float lr,
float weight_decay = 0.f) {
for (auto i = 0; i < N; ++i) {
float gi = std::fma(weight_decay, w[i], g[i]);
float hi = decay * h[i] + gi * gi;
nh[i] = hi;
nw[i] = w[i] + lr * gi / (std::sqrt(hi) + epsilon);
}
}
// version with prefetching
// TODO(msmelyan)
// Crux of the computation is computing a / (sqrt(b) + epsilon),
// where a and b are vectors and epsilon is very small (eg., 10^-5) and does not
// change. Today it's computed using two vector sqrt and vector divide simd
// instructions. It is slow. We can take advantage of existing fast vector
// VRSQRTPS instruction that computes approximate reciprocals of square roots
// of the vector. It is 6x faster than vsrt and vdiv combinations. Since the
// addition of epsilon is just done to avoid division by zero, we approximate a
// / (sqrt(b) + epsilon) by a / (sqrt(b + sqrt(epsilon)) If we do that, we can
// use VRSQRTPS instead now. VRSQRTPS is not very accurate. Specifically, for
// the test on random numbers between 0.1 and 1 the absolute error was about
// 10^-3 compared to using slower but more accurate combination of vsqrt and
// vdiv. Extend Marat's function with more NR iterations to get more accuracy
// for training
// TODO(msmelyan)
// explore streaming stores, but need to have unique indices (deduplication)
inline void adagrad_update_prefetch_inlined(
int N,
const float* w,
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
const float* w_n, // prefetch ptr
#else
const float* /* unused */,
#endif
const float* g,
const float* h,
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
const float* h_n, // prefetch ptr
#else
const float* /* unused */,
#endif
float* nw,
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
float* nw_n, // prefetch ptr
#else
float* /* unused */,
#endif
float* nh,
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
float* nh_n, // prefetch ptr
#else
float* /* unused */,
#endif
float epsilon,
float lr,
float weight_decay = 0.f) {
auto i = 0;
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
constexpr int kSize = 8;
for (; i + kSize <= N; i += kSize) {
_mm_prefetch(reinterpret_cast<const char*>(&w_n[i]), _MM_HINT_T0);
_mm_prefetch(reinterpret_cast<const char*>(&h_n[i]), _MM_HINT_T0);
_mm_prefetch(reinterpret_cast<const char*>(&nw_n[i]), _MM_HINT_T0);
_mm_prefetch(reinterpret_cast<const char*>(&nh_n[i]), _MM_HINT_T0);
__m256 gi = _mm256_loadu_ps(g + i);
__m256 hi = _mm256_loadu_ps(h + i);
__m256 wi = _mm256_loadu_ps(w + i);
#ifdef __AVX2__
gi = _mm256_fmadd_ps(_mm256_set1_ps(weight_decay), wi, gi);
#else
gi = _mm256_add_ps(_mm256_mul_ps(_mm256_set1_ps(weight_decay), wi), gi);
#endif
__m256 nhi = _mm256_add_ps(hi, _mm256_mul_ps(gi, gi));
_mm256_storeu_ps(nh + i, nhi);
__m256 vtmp = _mm256_div_ps(
_mm256_mul_ps(_mm256_set1_ps(lr), gi),
_mm256_add_ps(_mm256_sqrt_ps(nhi), _mm256_set1_ps(epsilon)));
_mm256_storeu_ps(nw + i, _mm256_add_ps(wi, vtmp));
}
#endif
adagrad_update_base_inlined(
N - i,
w + i,
g + i,
h + i,
nw + i,
nh + i,
1.0f,
epsilon,
lr,
weight_decay);
}
} // namespace internal
// version with prefetching
// TODO(msmelyan)
// Crux of the computation is computing a / (sqrt(b) + epsilon),
// where a and b are vectors and epsilon is very small (eg., 10^-5) and does not
// change. Today it's computed using two vector sqrt and vector divide simd
// instructions. It is slow. We can take advantage of existing fast vector
// VRSQRTPS instruction that computes approximate reciprocals of square roots
// of the vector. It is 6x faster than vsrt and vdiv combinations. Since the
// addition of epsilon is just done to avoid division by zero, we approximate a
// / (sqrt(b) + epsilon) by a / (sqrt(b + sqrt(epsilon)) If we do that, we can
// use VRSQRTPS instead now. VRSQRTPS is not very accurate. Specifically, for
// the test on random numbers between 0.1 and 1 the absolute error was about
// 10^-3 compared to using slower but more accurate combination of vsqrt and
// vdiv. Extend Marat's function with more NR iterations to get more accuracy
// for training
// TODO(msmelyan)
// explore streaming stores, but need to have inuque indices (deduplication)
void adagrad_update_prefetch(
int N,
const float* w,
const float* w_n, // prefetch ptr
const float* g,
const float* h,
const float* h_n, // prefetch ptr
float* nw,
float* nw_n, // prefetch ptr
float* nh,
float* nh_n, // prefetch ptr
float epsilon,
float lr,
float weight_decay = 0.f);
// Version with prefetching for embeddings and
// momentum using fp16
void adagrad_fp16_update_prefetch(
int N,
const at::Half* w,
const at::Half* w_n, // prefetch ptr
const float* g,
const at::Half* h,
const at::Half* h_n, // prefetch ptr
at::Half* nw,
at::Half* nw_n, // prefetch ptr
at::Half* nh,
at::Half* nh_n, // prefetch ptr
float epsilon,
float lr,
float weight_decay = 0.f);
// version without prefetching
void adagrad_update(
int N,
const float* w,
const float* g,
const float* h,
float* nw,
float* nh,
float epsilon,
float decay,
float lr,
float weight_decay = 0.f);
} // namespace caffe2
#ifdef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
#undef CAFFE2_PERFKERNELS_ADAGRAD_H_USE_INTRINSIC
#endif