oneAPI Deep Neural Network Library (oneDNN)
Performance library for Deep Learning
1.96.0
cpu_matmul_quantization.cpp

Annotated version: MatMul Tutorial: Quantization

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* Copyright 2019-2020 Intel Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <random>
#include <stdexcept>
#include <vector>
#include <type_traits>
#include "example_utils.hpp"
using namespace dnnl;
enum class q10n_scheme_t { DYNAMIC, STATIC };
namespace {
void init_vector(std::vector<float> &v, float min_value, float max_value) {
std::mt19937 gen;
std::uniform_real_distribution<float> u(min_value, max_value);
for (auto &e : v)
e = u(gen);
}
template <typename T>
void find_min_max(const std::vector<T> &v, float &min_value, float &max_value) {
min_value = max_value = v[0];
for (auto &e : v) {
min_value = std::min<float>(min_value, e);
max_value = std::max<float>(max_value, e);
}
}
template <typename T>
void compute_q10n_params(const char *message, const std::vector<float> &v,
float &scale, int32_t &zp) {
// Find property of T integer type
// Simple trick to improve accuracy: shrink the range a little bit
float max_int = (float)std::numeric_limits<T>::max() - 1;
float min_int = (float)std::numeric_limits<T>::lowest() + 1;
#ifndef OMIT_WORKAROUND_FOR_SKX
// Read more in CPU / Section 1 here:
// https://oneapi-src.github.io/oneDNN/dev_guide_int8_computations.html
if (std::is_same<T, uint8_t>::value) max_int /= 2;
#endif
// Find min and max value in array
float min_val = v[0], max_val = v[0];
find_min_max(v, min_val, max_val);
// Compute appropriate scale
scale = (max_val - min_val) / (max_int - min_int);
// Compute appropriate offset
if (std::is_same<T, int8_t>::value)
zp = 0;
else
zp = (int32_t)(max_int - max_val / scale);
printf("\tComputing q10n params for %s\n"
"\t\tData type: %s\n"
"\t\tScale:%.3g (inverse scale:%.3g)\n"
"\t\tZero point:%d\n\n",
message, std::is_same<T, int8_t>::value ? "int8_t" : "uint8_t",
scale, 1 / scale, zp);
}
int compare_vectors(const std::vector<float> &v1,
const std::vector<uint8_t> &v2, float scale_v2, int32_t zp_v2,
float threshold) {
double v1_l2 = 0, diff_l2 = 0;
for (size_t n = 0; n < v1.size(); ++n) {
float v2_n = scale_v2 * (v2[n] - zp_v2); // deq10n v2
float diff = v1[n] - v2_n;
v1_l2 += v1[n] * v1[n];
diff_l2 += diff * diff;
}
v1_l2 = std::sqrt(v1_l2);
diff_l2 = std::sqrt(diff_l2);
bool ok = diff_l2 <= threshold * v1_l2;
printf("\tComparison (using l2-norms)\n"
"\t\tReference matrix:%g\n\t\tError:%g\n\t\tRelative error:%g\n"
"\nAccuracy check: %s\n\n",
v1_l2, diff_l2, diff_l2 / v1_l2, ok ? "OK" : "FAILED");
return ok ? 0 : 1;
}
} // namespace
engine eng(engine::kind::cpu, 0); // We create a global engine for simplicity
// Quantize float data into X_int_m oneDNN memory using the q10n parameters
//
// Inputs:
// - X_f32 -- source f32 matrix
// - scale_X, zp_X -- quantization parameters
// - q10n_scheme -- dynamic or static, to mimic real-world applications wrt to
// how the q10n parameters are passed to reorders
// Outputs:
// - X_int_m -- prepared oneDNN memory that would hold quantized values
void quantize(q10n_scheme_t q10n_scheme, const std::vector<float> &X_f32,
float scale_X, int32_t zp_X, memory &X_int_m) {
// Depending on `q10n_scheme` pretend the values come at run-time (dynamic)
// or were known at creation time (static).
float inv_scale_X = 1.f / scale_X;
const bool is_dynamic_q10n = q10n_scheme == q10n_scheme_t::DYNAMIC;
stream s(eng);
memory::desc x_int_md = X_int_m.get_desc();
const auto &dims = x_int_md.data.dims;
memory::desc x_f32_md({dims[0], dims[1]}, dt::f32, {dims[1], 1});
memory X_f32_m(x_f32_md, eng, (void *)X_f32.data());
primitive_attr q10n_attr;
q10n_attr.set_output_scales(/* mask */ 0,
{is_dynamic_q10n ? DNNL_RUNTIME_F32_VAL : inv_scale_X});
q10n_attr.set_zero_points(DNNL_ARG_DST, /* mask */ 0,
{is_dynamic_q10n ? DNNL_RUNTIME_S32_VAL : zp_X});
reorder::primitive_desc q10n_pd(eng, x_f32_md, eng, x_int_md, q10n_attr);
if (is_dynamic_q10n) {
memory scale_X_m({{1}, dt::f32, {1}}, eng, &inv_scale_X);
memory zp_X_m({{1}, dt::s32, {1}}, eng, &zp_X);
reorder(q10n_pd).execute(s,
{{DNNL_ARG_SRC, X_f32_m}, {DNNL_ARG_DST, X_int_m},
} else {
reorder(q10n_pd).execute(
s, {{DNNL_ARG_SRC, X_f32_m}, {DNNL_ARG_DST, X_int_m}});
}
s.wait();
}
// Floating point MatMul
// Inputs:
// - Shape: M, N, K
// - Matrices A and B
// Outputs:
// - Matrix C
void f32_matmul_compute(int64_t M, int64_t N, int64_t K,
const std::vector<float> &A_f32, const std::vector<float> &B_f32,
std::vector<float> &C_f32) {
// Initialize memory descriptors that describes matrices in Row-Major format
memory::desc a_md({M, K}, memory::data_type::f32, {K, 1});
memory::desc b_md({K, N}, memory::data_type::f32, {N, 1});
memory::desc c_md({M, N}, memory::data_type::f32, {N, 1});
// Wrap raw pointers into oneDNN memory objects
memory A_f32_m(a_md, eng, (void *)A_f32.data());
memory B_f32_m(b_md, eng, (void *)B_f32.data());
memory C_f32_m(c_md, eng, (void *)C_f32.data());
// Create a MatMul primitive
matmul::desc matmul_d(a_md, b_md, c_md);
matmul::primitive_desc matmul_pd(matmul_d, eng);
matmul matmul_p(matmul_pd);
stream s(eng);
matmul_p.execute(s,
{{DNNL_ARG_SRC, A_f32_m}, {DNNL_ARG_WEIGHTS, B_f32_m},
{DNNL_ARG_DST, C_f32_m}});
s.wait();
}
// Reduced precision MatMul with **dynamic** quantization
// Inputs:
// - Shape: M, N, K
// - Matrices A and B in float (would be quantized inside the function)
// Outputs:
// - Matrix C in uint8_t
// - Quantization parameters: scale_C and zp_C
void dynamic_q10n_matmul(int64_t M, int64_t N, int64_t K,
const std::vector<float> &A_f32, const std::vector<float> &B_f32,
std::vector<uint8_t> &C_u8, float &scale_C, int32_t &zp_C) {
stream s(eng);
float scale_A, scale_B;
int32_t zp_A, zp_B;
// We compute q10n parameters here, but in the real world applications for
// inputs these parameters are transferred from the previous layers
compute_q10n_params<uint8_t>("A", A_f32, scale_A, zp_A);
compute_q10n_params<int8_t>("B", B_f32, scale_B, zp_B);
assert(zp_B == 0 && "for int8 q10n we assume zero point = 0");
// Quantize matrix A_u8 using reorder primitive
std::vector<uint8_t> A_u8(M * K, 0);
memory::desc a_u8_md({M, K}, memory::data_type::u8, {K, 1});
memory A_u8_m(a_u8_md, eng, (void *)A_u8.data());
quantize(q10n_scheme_t::DYNAMIC, A_f32, scale_A, zp_A, A_u8_m);
// Quantize matrix B_s8 using reorder primitive
std::vector<uint8_t> B_s8(K * N, 0);
memory::desc b_s8_md({K, N}, memory::data_type::s8, {N, 1});
memory B_s8_m(b_s8_md, eng, (void *)B_s8.data());
quantize(q10n_scheme_t::DYNAMIC, B_f32, scale_B, 0, B_s8_m);
// Compute C_f32. We cannot directly compute C_u8 since we don't know the
// appropriate quantization parameters.
//
// Note: typically the computed data type in this case is int32_t and not
// float. But for brevity we are going to embed the scale_A and
// scale_B directly in this quantized MatMul, and hence will get the
// intermediate computation in floating point anyways, so there is
// no sense to convert the result to int32_t.
// In theory, we could postpone using the scale_A and scale_B, compute
// the exact C_s32 := (A_u8 - zp_A) * B_s8, and then find the
// appropriate quantization parameters for matrix C.
// Let it be an exercise :)
std::vector<float> C_f32(M * N, 0);
memory::desc c_f32_md({M, N}, memory::data_type::f32, {N, 1});
memory C_f32_m(c_f32_md, eng, (void *)C_f32.data());
// Create and compute a reduced precision MatMul primitive
{
primitive_attr matmul_attr;
matmul_attr.set_output_scales(/* mask */ 0, {DNNL_RUNTIME_F32_VAL});
matmul_attr.set_zero_points(
matmul::desc matmul_d(a_u8_md, b_s8_md, c_f32_md);
matmul::primitive_desc matmul_pd(matmul_d, matmul_attr, eng);
matmul matmul_p(matmul_pd);
// Pretend the values come at run-time
float output_scale = scale_A * scale_B;
memory output_scales_m(
{{1}, memory::data_type::f32, {1}}, eng, &output_scale);
memory zp_A_m({{1}, memory::data_type::s32, {1}}, eng, &zp_A);
matmul_p.execute(s,
{{DNNL_ARG_SRC, A_u8_m}, {DNNL_ARG_WEIGHTS, B_s8_m},
{DNNL_ARG_DST, C_f32_m},
{DNNL_ARG_ATTR_OUTPUT_SCALES, output_scales_m},
}
// Find quantization parameters for matrix C
compute_q10n_params<uint8_t>("C", C_f32, scale_C, zp_C);
// Finally quantize the matrix C
memory::desc c_u8_md({M, N}, memory::data_type::u8, {N, 1});
memory C_u8_m(c_u8_md, eng, (void *)C_u8.data());
quantize(q10n_scheme_t::DYNAMIC, C_f32, scale_C, zp_C, C_u8_m);
}
// Reduced precision MatMul with **static** quantization
// Inputs:
// - Shape: M, N, K
// - Matrices A and B in float (would be quantized inside the function using
// given q10n parameters)
// - Quantization parameters for all 3 matrices:
// - scale_A, zp_A
// - scale_B
// - scale_C, zp_C
// Outputs:
// - Matrix C in uint8_t
void static_q10n_matmul(int64_t M, int64_t N, int64_t K,
const std::vector<float> &A_f32, const std::vector<float> &B_f32,
float scale_A, int32_t zp_A, float scale_B, float scale_C, int32_t zp_C,
std::vector<uint8_t> &C_u8) {
stream s(eng);
// Quantize matrix A_u8 using reorder primitive
std::vector<uint8_t> A_u8(M * K, 0);
memory::desc a_u8_md({M, K}, memory::data_type::u8, {K, 1});
memory A_u8_m(a_u8_md, eng, (void *)A_u8.data());
quantize(q10n_scheme_t::STATIC, A_f32, scale_A, zp_A, A_u8_m);
// Quantize matrix B_s8 using reorder primitive
std::vector<uint8_t> B_s8(K * N, 0);
memory::desc b_s8_md({K, N}, memory::data_type::s8, {N, 1});
memory B_s8_m(b_s8_md, eng, (void *)B_s8.data());
quantize(q10n_scheme_t::STATIC, B_f32, scale_B, 0, B_s8_m);
// Directly compute C_u8, since we know quantization parameters for the
// matrix C. This is the key difference compare to **dynamic** quantization.
{
memory::desc c_u8_md({M, N}, memory::data_type::u8, {N, 1});
memory C_u8_m(c_u8_md, eng, (void *)C_u8.data());
primitive_attr matmul_attr;
matmul_attr.set_output_scales(
/* mask */ 0, {scale_A * scale_B / scale_C});
matmul_attr.set_zero_points(DNNL_ARG_SRC, /* mask */ 0, {zp_A});
matmul_attr.set_zero_points(DNNL_ARG_DST, /* mask */ 0, {zp_C});
matmul::desc matmul_d(a_u8_md, b_s8_md, c_u8_md);
matmul::primitive_desc matmul_pd(matmul_d, matmul_attr, eng);
matmul matmul_p(matmul_pd);
matmul_p.execute(s,
{{DNNL_ARG_SRC, A_u8_m}, {DNNL_ARG_WEIGHTS, B_s8_m},
{DNNL_ARG_DST, C_u8_m}});
}
}
void compare_f32_and_quantized_matmuls() {
// MatMul parameters
const int64_t M = 10, N = 20, K = 30;
// Data distribution for matrices A and B
const float param_A_min_val = -2.f;
const float param_A_max_val = 1.4f;
const float param_B_min_val = -1.f;
const float param_B_max_val = -param_B_min_val; // B is centered around 0
// Thresholds
//
// Ideally the threshold for static quantization should be a little higher
// than for dynamic quantization. However, we will slightly cheat on the
// guessed q10n parameters of matrix C (see below), so we will get pretty
// good accuracy as well.
const float threshold_dynamic_q10n = 3 * 1e-2f;
const float threshold_static_q10n = 4 * 1e-2f;
// Prepare matrices
std::vector<float> A_f32(M * K), B_f32(K * N), C_f32(M * N, 0);
init_vector(A_f32, param_A_min_val, param_A_max_val);
init_vector(B_f32, param_B_min_val, param_B_max_val);
// Compute _true_ f32 result
f32_matmul_compute(M, N, K, A_f32, B_f32, C_f32);
// Compute quantized variant (dynamic)
{
printf("# DYNAMIC quantization\n\n");
std::vector<uint8_t> C_u8_dynamic_q10n(M * N, 0);
float scale_C_dynamic_q10n; // Q10n parameters we don't know yet
int zp_C_dynamic_q10n;
dynamic_q10n_matmul(M, N, K, A_f32, B_f32, C_u8_dynamic_q10n,
scale_C_dynamic_q10n, zp_C_dynamic_q10n);
// Compare _true_ f32 result with dynamic q10n
int rc = compare_vectors(C_f32, C_u8_dynamic_q10n, scale_C_dynamic_q10n,
zp_C_dynamic_q10n, threshold_dynamic_q10n);
if (rc) throw std::logic_error("Dynamic quantization accuracy failed.");
}
// Compute quantized variant (static)
{
printf("# STATIC quantization\n\n");
std::vector<uint8_t> C_u8_static_q10n(M * N, 0);
// Let's pretend we know the appropriate q10n parameters (by gathering
// some statistic or whatnot). For matrix C we will slightly _cheat_
// and get the appropriate q10n from the actual C_f32 result that we
// computed earlier. Of course, it is not what one would do in the
// **static** q10n scheme (just by the definition of the **static**
// q10n), but solely for the purpose of this example print "passed" in
// the end :)
const float scale_A_static_q10n
= (param_A_max_val - param_A_min_val) / 128;
const int zp_A_static_q10n
= (int)(128 - param_A_max_val / scale_A_static_q10n);
const float scale_B_static_q10n
= (param_B_max_val - param_B_min_val) / 256;
float scale_C_static_q10n;
int zp_C_static_q10n;
// !!! CHEATING STARTS HERE
const char *warn_message
= "C"
"\n\t*******************************************************"
"\n\t* NOTE: These computation do not happen in real world *"
"\n\t* applications and used here solely to simplify *"
"\n\t* the example. *"
"\n\t* Please refer to the example source code for *"
"\n\t* more information. *"
"\n\t*******************************************************";
compute_q10n_params<uint8_t>(
warn_message, C_f32, scale_C_static_q10n, zp_C_static_q10n);
// !!! CHEATING ENDS HERE
static_q10n_matmul(M, N, K, A_f32, B_f32, scale_A_static_q10n,
zp_A_static_q10n, scale_B_static_q10n, scale_C_static_q10n,
zp_C_static_q10n, C_u8_static_q10n);
// Compare _true_ f32 result with static q10n
int rc = compare_vectors(C_f32, C_u8_static_q10n, scale_C_static_q10n,
zp_C_static_q10n, threshold_static_q10n);
if (rc) throw std::logic_error("Static quantization accuracy failed.");
}
}
int main(int argc, char **argv) {
return handle_example_errors(
{engine::kind::cpu}, compare_f32_and_quantized_matmuls);
}