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#ifndef liblogintpack_h
#define liblogintpack_h
#include <cmath>
#include <cstdint>
namespace logintpack {
constexpr int8_t smallestPositive = 0;
// note that abs(unpack(smallestNegative)) == unpack(1), i.e. there
// is no "x" such that "unpack(x) == -unpack(0)"
constexpr int8_t smallestNegative = -1;
inline int16_t pack16logCeil(double x, double lmin, double lmax, uint16_t base = 32768) {
if (base > 32768)
base = 32768;
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * base;
int16_t r = std::ceil(centered);
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
inline int16_t pack16log(double x, double lmin, double lmax, uint16_t base = 32768) {
if (base > 32768)
base = 32768;
const float delta = (log(1. + exp((lmax - lmin) / base)) - log(2.)) * base / (lmax - lmin);
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * base;
int16_t r = std::floor(centered);
if (centered - r > delta)
r += 1;
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
/// pack a value x distributed in [-1,1], with guarantee that -1 and 1 are preserved exactly in packing and unpacking.
/// tries to keep the best precision for x close to the endpoints, sacrifying that in the middle
inline int16_t pack16logClosed(double x, double lmin, double lmax, uint16_t base = 32768) {
if (base > 32768)
base = 32768;
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * (base - 1);
int16_t r = round(centered);
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
inline double unpack16log(int16_t i, double lmin, double lmax, uint16_t base = 32768) {
if (base > 32768)
base = 32768;
const double basef = base;
const double l = lmin + std::abs(i) / basef * (lmax - lmin);
const double val = std::exp(l);
if (i < 0)
return -val;
else
return val;
}
/// reverse of pack8logClosed
inline double unpack16logClosed(int16_t i, double lmin, double lmax, uint16_t base = 32768) {
if (base > 32768)
base = 32768;
const double basef = base - 1;
double l = lmin + std::abs(i) / basef * (lmax - lmin);
if (std::abs(i) == base - 1)
l = lmax;
const double val = std::exp(l);
if (i < 0)
return -val;
else
return val;
}
inline int8_t pack8logCeil(double x, double lmin, double lmax, uint8_t base = 128) {
if (base > 128)
base = 128;
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * base;
int8_t r = std::ceil(centered);
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
inline int8_t pack8log(double x, double lmin, double lmax, uint8_t base = 128) {
if (base > 128)
base = 128;
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * base;
int8_t r = centered;
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
/// pack a value x distributed in [-1,1], with guarantee that -1 and 1 are preserved exactly in packing and unpacking.
/// tries to keep the best precision for x close to the endpoints, sacrifying that in the middle
inline int8_t pack8logClosed(double x, double lmin, double lmax, uint8_t base = 128) {
if (base > 128)
base = 128;
const double l = std::log(std::abs(x));
const double centered = (l - lmin) / (lmax - lmin) * (base - 1);
int8_t r = round(centered);
if (centered >= base - 1)
r = base - 1;
if (centered < 0)
r = 0;
if (x < 0)
r = r == 0 ? -1 : -r;
return r;
}
inline double unpack8log(int8_t i, double lmin, double lmax, uint8_t base = 128) {
if (base > 128)
base = 128;
const double basef = base;
const double l = lmin + std::abs(i) / basef * (lmax - lmin);
const double val = std::exp(l);
if (i < 0)
return -val;
else
return val;
}
/// reverse of pack8logClosed
inline double unpack8logClosed(int8_t i, double lmin, double lmax, uint8_t base = 128) {
if (base > 128)
base = 128;
const double basef = base - 1;
double l = lmin + std::abs(i) / basef * (lmax - lmin);
if (std::abs(i) == base - 1)
l = lmax;
const double val = std::exp(l);
if (i < 0)
return -val;
else
return val;
}
} // namespace logintpack
#endif
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