forked from google/gemmlowp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
quantization_example.cc
391 lines (347 loc) · 15.2 KB
/
quantization_example.cc
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
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
// Example code illustrating the theory exposed in doc/quantization.md
/* Command line to build and run on x86:
c++ doc/quantization_example.cc -I . --std=c++11 -msse4.1 -lpthread \
-o /tmp/quantization_example && \
/tmp/quantization_example
*/
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <iostream>
#include <random>
#include <vector>
#include "../public/gemmlowp.h"
#include "../public/output_stages.h"
// We will handle both float and quantized matrices, which we will
// represent as gemmlowp::MatrixMap.
// We will need to be able to print them.
// Output a matrix to a std::ostream
template <typename tScalar, gemmlowp::MapOrder tOrder>
std::ostream& operator<<(std::ostream& s,
const gemmlowp::MatrixMap<tScalar, tOrder>& m) {
for (int i = 0; i < m.rows(); i++) {
for (int j = 0; j < m.cols(); j++) {
if (j) {
s << '\t';
}
s << static_cast<float>(m(i, j));
}
s << '\n';
}
return s;
}
// Find the min and max value in a float matrix.
template <gemmlowp::MapOrder tOrder>
void FindMinMax(const gemmlowp::MatrixMap<float, tOrder>& m, float* min,
float* max) {
*min = *max = m(0, 0);
for (int i = 0; i < m.rows(); i++) {
for (int j = 0; j < m.cols(); j++) {
const float val = m(i, j);
*min = std::min(*min, val);
*max = std::max(*max, val);
}
}
}
// A structure to hold quantization parameters 'scale' and 'zero_point'
// as discussed in doc/quantization.md. As explained there, the meaning
// of these values is as the constants in the quantization equation
//
// real_value = scale * (quantized_value - zero_point)
//
// In other words, 'zero_point' is the quantized value that corresponds
// to the real value 0, and 'scale' is the difference of real values
// corresponding to consecutive quantized values.
struct QuantizationParams {
float scale;
std::uint8_t zero_point;
};
// Given the min and max values of a float array, return
// reasonable quantization parameters to use for this array.
QuantizationParams ChooseQuantizationParams(float min, float max) {
// We extend the [min, max] interval to ensure that it contains 0.
// Otherwise, we would not meet the requirement that 0 be an exactly
// representable value.
min = std::min(min, 0.f);
max = std::max(max, 0.f);
// the min and max quantized values, as floating-point values
const float qmin = 0;
const float qmax = 255;
// First determine the scale.
const double scale = (max - min) / (qmax - qmin);
// Zero-point computation.
// First the initial floating-point computation. The zero-point can be
// determined from solving an affine equation for any known pair
// (real value, corresponding quantized value).
// We know two such pairs: (rmin, qmin) and (rmax, qmax).
// Let's use the first one here.
const double initial_zero_point = qmin - min / scale;
// Now we need to nudge the zero point to be an integer
// (our zero points are integer, and this is motivated by the requirement
// to be able to represent the real value "0" exactly as a quantized value,
// which is required in multiple places, for example in Im2col with SAME
// padding).
std::uint8_t nudged_zero_point = 0;
if (initial_zero_point < qmin) {
nudged_zero_point = qmin;
} else if (initial_zero_point > qmax) {
nudged_zero_point = qmax;
} else {
nudged_zero_point =
static_cast<std::uint8_t>(std::round(initial_zero_point));
}
QuantizationParams result;
result.scale = scale;
result.zero_point = nudged_zero_point;
return result;
}
template <gemmlowp::MapOrder tLhsOrder, gemmlowp::MapOrder tRhsOrder,
gemmlowp::MapOrder tResultOrder>
void FloatMatrixMultiplication(
const gemmlowp::MatrixMap<const float, tLhsOrder>& lhs,
const gemmlowp::MatrixMap<const float, tRhsOrder>& rhs,
gemmlowp::MatrixMap<float, tResultOrder>* result) {
assert(lhs.cols() == rhs.rows());
assert(lhs.rows() == result->rows());
assert(rhs.cols() == result->cols());
for (int i = 0; i < lhs.rows(); i++) {
for (int k = 0; k < rhs.cols(); k++) {
(*result)(i, k) = 0;
for (int j = 0; j < lhs.cols(); j++) {
(*result)(i, k) += lhs(i, j) * rhs(j, k);
}
}
}
}
void Quantize(const QuantizationParams& qparams, const std::vector<float>& src,
std::vector<std::uint8_t>* dst) {
assert(src.size() == dst->size());
for (std::size_t i = 0; i < src.size(); i++) {
const float real_val = src[i];
const float transformed_val = qparams.zero_point + real_val / qparams.scale;
const float clamped_val = std::max(0.f, std::min(255.f, transformed_val));
(*dst)[i] = static_cast<std::uint8_t>(std::round(clamped_val));
}
}
void Dequantize(const QuantizationParams& qparams,
const std::vector<std::uint8_t>& src, std::vector<float>* dst) {
assert(src.size() == dst->size());
for (std::size_t i = 0; i < src.size(); i++) {
const std::uint8_t quantized_val = src[i];
(*dst)[i] = qparams.scale * (quantized_val - qparams.zero_point);
}
}
template <typename tScalar, gemmlowp::MapOrder tOrder>
class MatrixWithStorage {
public:
MatrixWithStorage(int rows, int cols)
: storage(rows * cols), matrix_map(storage.data(), rows, cols) {}
void MakeRandom() {
static std::mt19937 random_engine;
std::uniform_real_distribution<float> distribution(-1, 1);
for (auto& x : storage) {
x = static_cast<tScalar>(distribution(random_engine));
}
}
gemmlowp::MatrixMap<const tScalar, tOrder> ConstMap() const {
return gemmlowp::MatrixMap<const tScalar, tOrder>(
storage.data(), matrix_map.rows(), matrix_map.cols());
}
gemmlowp::MatrixMap<tScalar, tOrder> Map() {
return gemmlowp::MatrixMap<tScalar, tOrder>(
storage.data(), matrix_map.rows(), matrix_map.cols());
}
const std::vector<tScalar>& Storage() const { return storage; }
std::vector<tScalar>& Storage() { return storage; }
private:
std::vector<tScalar> storage;
gemmlowp::MatrixMap<tScalar, tOrder> matrix_map;
};
template <typename tScalar, gemmlowp::MapOrder tOrder>
std::ostream& operator<<(std::ostream& s,
const MatrixWithStorage<tScalar, tOrder>& m) {
return s << m.ConstMap();
}
// Given a real_multiplier in the interval (0, 1),
// produces a pair (quantized_multiplier, right_shift) where
// quantized_multiplier is an int32 representing a fixed-point value
// in the interval [-1, 1) (in practice we only produce positive values)
// and right_shift is an amount to shift right by, so that the
// floating-point multiplication of some int32 input value by real_multiplier,
//
// return static_cast<int32>(int32_value * real_multiplier);
//
// is best approximated by the integer-arithmetic-only code
//
// return RoundingRightShift(
// FixedPointMultiplication(int32_value, quantized_multiplier),
// right_shift);
//
// This is how to obtain the fixed-point multiplier and right shift
// parameters to pass to
// OutputStageQuantizeDownInt32ByFixedPoint.
//
// Note: all this code only needs to run offline to generate the quantized
// neural network workload, not at runtime on the
// device on which quantized neural networks need to run. So it's not
// performance-critical at all.
void QuantizeMultiplierSmallerThanOne(float real_multiplier,
std::int32_t* quantized_multiplier,
int* right_shift) {
assert(real_multiplier > 0.f);
assert(real_multiplier < 1.f);
int s = 0;
// We want to bring the real multiplier into the interval [1/2, 1).
// We can do so by multiplying it by two, and recording how many times
// we multiplied by two so that we can compensate that by a right
// shift by the same amount.
while (real_multiplier < 0.5f) {
real_multiplier *= 2.0f;
s++;
}
// Now that the real multiplier is in [1/2, 1), we convert it
// into a fixed-point number.
std::int64_t q =
static_cast<std::int64_t>(std::round(real_multiplier * (1ll << 31)));
assert(q <= (1ll << 31));
// Handle the special case when the real multiplier was so close to 1
// that its fixed-point approximation was undistinguishable from 1.
// We handle this by dividing it by two, and remembering to decrement
// the right shift amount.
if (q == (1ll << 31)) {
q /= 2;
s--;
}
assert(s >= 0);
assert(q <= std::numeric_limits<std::int32_t>::max());
*quantized_multiplier = static_cast<std::int32_t>(q);
*right_shift = s;
}
int main() {
std::cout.precision(3);
const int rows = 2;
const int depth = 4;
const int cols = 3;
const auto kOrder = gemmlowp::MapOrder::ColMajor;
std::cout << "First, let us make some float matrices LHS and RHS, "
<< "and compute their product.\n"
<< std::endl;
MatrixWithStorage<float, kOrder> float_lhs(rows, depth);
float_lhs.MakeRandom();
MatrixWithStorage<float, kOrder> float_rhs(depth, cols);
float_rhs.MakeRandom();
MatrixWithStorage<float, kOrder> reference_float_result(rows, cols);
auto reference_float_result_map = reference_float_result.Map();
FloatMatrixMultiplication(float_lhs.ConstMap(), float_rhs.ConstMap(),
&reference_float_result_map);
std::cout << "Here is the float LHS matrix:\n" << float_lhs << std::endl;
std::cout << "Here is the float RHS matrix:\n" << float_rhs << std::endl;
std::cout << "Here is the float product (LHS * RHS) matrix obtained by "
<< "ordinary float matrix multiplication, i.e. as far as we are "
<< "concerned, the REFERENCE RESULT:\n"
<< reference_float_result << std::endl;
std::cout
<< "Now we embark on reproducing this result using "
<< "quantized arithmetic. The code below splits into two parts: "
<< "quantization code that only needs to run offline (e.g. to "
<< "generate a quantized neural network workload), and actual "
<< "runtime quantized code, which is typically performance-critical "
<< "and where we typically do not want to use any floating-point "
<< "arithmetic. We want to clearly distinguish between the two.\n"
<< std::endl;
std::cout << "The below is OFFLINE QUANTIZATION CODE. We still use some "
<< "floating-point arithmetic in the process of generating the "
<< "quantized workload to be run on-device.\n"
<< std::endl;
std::cout
<< "Now, let us choose quantization parameters for these matrices. "
<< "You might ask, what good is quantization if we need to pick "
<< "quantization parameters for the result before we can run the "
<< "quantized computation to obtain the result? The idea is that we "
<< "target applications such as neural networks, where unknown results "
<< "are only allowed to vary within preexisting bounds. In practice, the "
<< "bounds for the results are typically learned during the neural "
"network "
<< "training process. The min and max of the result do not have to be "
<< "exact. If they are too broad, we just get lower quantization "
"accuracy. "
<< "If they are too narrow, we just get clamping at the bounds.\n"
<< std::endl;
float lhs_min, lhs_max, rhs_min, rhs_max, result_min, result_max;
FindMinMax(float_lhs.Map(), &lhs_min, &lhs_max);
FindMinMax(float_rhs.Map(), &rhs_min, &rhs_max);
FindMinMax(reference_float_result.Map(), &result_min, &result_max);
const auto lhs_qparams = ChooseQuantizationParams(lhs_min, lhs_max);
const auto rhs_qparams = ChooseQuantizationParams(rhs_min, rhs_max);
const auto result_qparams = ChooseQuantizationParams(result_min, result_max);
std::cout << "For LHS, we have min = " << lhs_min << ", max = " << lhs_max
<< ", scale = " << lhs_qparams.scale
<< ", zero_point = " << static_cast<float>(lhs_qparams.zero_point)
<< std::endl;
std::cout << "For RHS, we have min = " << rhs_min << ", max = " << rhs_max
<< ", scale = " << rhs_qparams.scale
<< ", zero_point = " << static_cast<float>(rhs_qparams.zero_point)
<< std::endl;
std::cout << "For the result, we have min = " << result_min
<< ", max = " << result_max << ", scale = " << result_qparams.scale
<< ", zero_point = "
<< static_cast<float>(result_qparams.zero_point) << std::endl;
std::cout << std::endl;
MatrixWithStorage<std::uint8_t, kOrder> uint8_lhs(rows, depth);
MatrixWithStorage<std::uint8_t, kOrder> uint8_rhs(depth, cols);
MatrixWithStorage<std::uint8_t, kOrder> actual_uint8_result(rows, cols);
Quantize(lhs_qparams, float_lhs.Storage(), &uint8_lhs.Storage());
Quantize(rhs_qparams, float_rhs.Storage(), &uint8_rhs.Storage());
std::cout << "Quantized uint8 LHS matrix:\n" << uint8_lhs << std::endl;
std::cout << "Quantized uint8 RHS matrix:\n" << uint8_rhs << std::endl;
const int lhs_offset = -lhs_qparams.zero_point;
const int rhs_offset = -rhs_qparams.zero_point;
const int result_offset = result_qparams.zero_point;
const float real_multiplier =
lhs_qparams.scale * rhs_qparams.scale / result_qparams.scale;
std::int32_t quantized_multiplier;
int right_shift;
QuantizeMultiplierSmallerThanOne(real_multiplier, &quantized_multiplier,
&right_shift);
std::cout << "End of OFFLINE QUANTIZATION CODE.\n" << std::endl;
std::cout << "The below is ON-DEVICE RUNTIME QUANTIZED CODE. "
<< "This is the part that is performance-critical and may only "
<< "use quantized arithmetic.\n"
<< std::endl;
gemmlowp::OutputStageQuantizeDownInt32ByFixedPoint
quantize_down_stage;
quantize_down_stage.result_offset_after_shift = result_offset;
quantize_down_stage.result_fixedpoint_multiplier = quantized_multiplier;
quantize_down_stage.result_shift = right_shift;
gemmlowp::OutputStageSaturatingCastToUint8 saturating_cast_stage;
const auto& output_pipeline =
std::make_tuple(quantize_down_stage, saturating_cast_stage);
auto actual_uint8_result_map = actual_uint8_result.Map();
gemmlowp::GemmContext gemm_context;
gemmlowp::GemmWithOutputPipeline<std::uint8_t, std::uint8_t,
gemmlowp::DefaultL8R8BitDepthParams>(
&gemm_context, uint8_lhs.ConstMap(), uint8_rhs.ConstMap(),
&actual_uint8_result_map, lhs_offset, rhs_offset, output_pipeline);
std::cout << "Quantized uint8 result matrix obtained by quantized "
<< "multiplication:\n"
<< actual_uint8_result << std::endl;
std::cout << "End of ON-DEVICE RUNTIME QUANTIZED CODE.\n" << std::endl;
MatrixWithStorage<float, kOrder> actual_float_result(rows, cols);
Dequantize(result_qparams, actual_uint8_result.Storage(),
&actual_float_result.Storage());
std::cout
<< "Here is the actual float product (LHS * RHS) matrix obtained by "
<< "dequantizing the above uint8 result, i.e. "
<< "as far as we are concerned, the ACTUAL RESULT:\n"
<< actual_float_result << std::endl;
MatrixWithStorage<float, kOrder> diff_float_result(rows, cols);
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
diff_float_result.Map()(i, j) =
actual_float_result.Map()(i, j) - reference_float_result.Map()(i, j);
}
}
std::cout << "Difference between ACTUAL and REFERENCE float results:\n"
<< diff_float_result << std::endl;
}