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// Implements the math functions for CPU.
// The implementation in this file allows us to route the underlying numerical
// computation library to different compiler options (-mno-avx2 or -mavx2).
#include <cfloat>
#include <cmath>
#include <cstdint>
#include "common.h"
// NOLINTNEXTLINE(modernize-deprecated-headers)
#include "math.h"
#include <c10/util/irange.h>
using std::uint64_t;
using std::uint8_t;
namespace caffe2 {
namespace math {
static constexpr double QEPSILON = 1e-8;
void quantize_and_compress__base(
const float* input_data,
uint8_t* output_data,
uint64_t input_size,
uint64_t bitwidth,
bool random,
const float* random_buffer) {
uint64_t data_per_byte = 8 / bitwidth;
uint64_t tail = input_size % data_per_byte;
tail = tail ? data_per_byte - tail : 0;
uint64_t segment_size = (input_size + data_per_byte - 1) / data_per_byte;
// basic info
float minimum_element = INFINITY, maximum_element = -INFINITY;
for (const auto i : c10::irange(input_size)) {
minimum_element =
input_data[i] < minimum_element ? input_data[i] : minimum_element;
maximum_element =
input_data[i] > maximum_element ? input_data[i] : maximum_element;
}
output_data[0] = bitwidth;
output_data[1] = tail;
reinterpret_cast<float*>(output_data + 2)[0] = minimum_element;
reinterpret_cast<float*>(output_data + 2)[1] = maximum_element;
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
float gap = (maximum_element - minimum_element) / ((1 << bitwidth) - 1.0f);
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
float gap_inverse = 1. / (gap + QEPSILON);
uint8_t max_q = (1 << bitwidth) - 1;
uint64_t bit_start = 0;
if (random) {
for (uint64_t start = 0; start < input_size; start += segment_size) {
uint64_t stride = start + segment_size <= input_size ? segment_size
: input_size - start;
uint64_t i = 0;
for (; i < stride; ++i) {
float fval = input_data[start + i];
float thetimes = (fval - minimum_element) * gap_inverse;
float rounded = floor(thetimes + random_buffer[start + i]);
rounded = rounded < static_cast<float>(max_q)
? rounded
: static_cast<float>(max_q);
rounded = rounded > 0.0f ? rounded : 0.0f;
uint8_t qval = rounded;
uint8_t orval = output_data[10 + i];
output_data[10 + i] = orval | static_cast<uint8_t>(qval << bit_start);
}
bit_start += bitwidth;
}
} else {
for (uint64_t start = 0; start < input_size; start += segment_size) {
uint64_t stride = start + segment_size <= input_size ? segment_size
: input_size - start;
uint64_t i = 0;
for (; i < stride; ++i) {
float fval = input_data[start + i];
float thetimes = (fval - minimum_element) * gap_inverse;
thetimes = thetimes < static_cast<float>(max_q)
? thetimes
: static_cast<float>(max_q);
thetimes = thetimes > 0.0f ? thetimes : 0.0f;
uint8_t qval = nearbyint(thetimes);
uint8_t orval = output_data[10 + i];
output_data[10 + i] = orval | static_cast<uint8_t>(qval << bit_start);
}
bit_start += bitwidth;
}
}
}
decltype(quantize_and_compress__base) quantize_and_compress__avx2;
void quantize_and_compress(
const float* input_data,
uint8_t* output_data,
uint64_t input_size,
uint64_t bitwidth,
bool random,
const float* random_buffer) {
AVX2_DO(
quantize_and_compress,
input_data,
output_data,
input_size,
bitwidth,
random,
random_buffer);
BASE_DO(
quantize_and_compress,
input_data,
output_data,
input_size,
bitwidth,
random,
random_buffer);
}
void decompress_and_dequantize__base(
const uint8_t* input_data,
float* output_data,
uint64_t input_size) {
// basic info
const float minimum_element =
reinterpret_cast<const float*>(input_data + 2)[0];
const float maximum_element =
reinterpret_cast<const float*>(input_data + 2)[1];
const uint64_t bitwidth = input_data[0];
const float gap =
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
(maximum_element - minimum_element) / ((1 << bitwidth) - 1.f) +
QEPSILON; // for exact recovering
const uint64_t tail = input_data[1];
const uint64_t output_size = (input_size - 10) * (8 / bitwidth) - tail;
// decoding
uint64_t bit_start = 0;
const uint64_t segment_size = input_size - 10;
for (uint64_t start = 0; start < output_size; start += segment_size) {
uint64_t stride = start + segment_size <= output_size ? segment_size
: output_size - start;
uint8_t mask = (1 << bitwidth) - 1;
uint64_t i = 0;
for (; i < stride; ++i) {
output_data[start + i] =
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-avoid-magic-numbers,cppcoreguidelines-narrowing-conversions)
((input_data[10 + i] >> bit_start) & mask) * gap + minimum_element;
}
bit_start += bitwidth;
}
}
decltype(decompress_and_dequantize__base) decompress_and_dequantize__avx2;
void decompress_and_dequantize(
const uint8_t* input_data,
float* output_data,
uint64_t input_size) {
AVX2_DO(decompress_and_dequantize, input_data, output_data, input_size);
BASE_DO(decompress_and_dequantize, input_data, output_data, input_size);
}
} // namespace math
} // namespace caffe2
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