liblogintpack.h

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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;
  }

  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;
  }

  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;
  }

  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;
  }

  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