libminifloat.h

Go to the documentation of this file.

#ifndef libminifloat_h
#define libminifloat_h
#include "FWCore/Utilities/interface/thread_safety_macros.h"
#include "FWCore/Utilities/interface/bit_cast.h"
#include <cstdint>
#include <cassert>
#include <algorithm>

// ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf
class MiniFloatConverter {
public:
  MiniFloatConverter();
  inline static float float16to32(uint16_t h) {
    uint32_t i32 = mantissatable[offsettable[h >> 10] + (h & 0x3ff)] + exponenttable[h >> 10];
    return edm::bit_cast<float>(i32);
  }
  inline static uint16_t float32to16(float x) { return float32to16round(x); }
  inline static uint16_t float32to16crop(float x) {
    uint32_t i32 = edm::bit_cast<uint32_t>(x);
    return basetable[(i32 >> 23) & 0x1ff] + ((i32 & 0x007fffff) >> shifttable[(i32 >> 23) & 0x1ff]);
  }
  inline static uint16_t float32to16round(float x) {
    uint32_t i32 = edm::bit_cast<uint32_t>(x);
    uint8_t shift = shifttable[(i32 >> 23) & 0x1ff];
    if (shift == 13) {
      uint16_t base2 = (i32 & 0x007fffff) >> 12;
      uint16_t base = base2 >> 1;
      if (((base2 & 1) != 0) && (base < 1023))
        base++;
      return basetable[(i32 >> 23) & 0x1ff] + base;
    } else {
      return basetable[(i32 >> 23) & 0x1ff] + ((i32 & 0x007fffff) >> shifttable[(i32 >> 23) & 0x1ff]);
    }
  }
  template <int bits>
  inline static float reduceMantissaToNbits(const float &f) {
    static_assert(bits <= 23, "max mantissa size is 23 bits");
    constexpr uint32_t mask = (0xFFFFFFFF >> (23 - bits)) << (23 - bits);
    uint32_t i32 = edm::bit_cast<uint32_t>(f);
    i32 &= mask;
    return edm::bit_cast<float>(i32);
  }
  inline static float reduceMantissaToNbits(const float &f, int bits) {
    uint32_t mask = (0xFFFFFFFF >> (23 - bits)) << (23 - bits);
    uint32_t i32 = edm::bit_cast<uint32_t>(f);
    i32 &= mask;
    return edm::bit_cast<float>(i32);
  }

  class ReduceMantissaToNbitsRounding {
  public:
    ReduceMantissaToNbitsRounding(int bits)
        : shift(23 - bits), mask((0xFFFFFFFF >> (shift)) << (shift)), test(1 << (shift - 1)), maxn((1 << bits) - 2) {
      assert(bits <= 23);  // "max mantissa size is 23 bits"
    }
    float operator()(float f) const {
      constexpr uint32_t low23 = (0x007FFFFF);  // mask to keep lowest 23 bits = mantissa
      constexpr uint32_t hi9 = (0xFF800000);    // mask to keep highest 9 bits = the rest
      uint32_t i32 = edm::bit_cast<uint32_t>(f);
      if (i32 & test) {  // need to round
        uint32_t mantissa = (i32 & low23) >> shift;
        if (mantissa < maxn)
          mantissa++;
        i32 = (i32 & hi9) | (mantissa << shift);
      } else {
        i32 &= mask;
      }
      return edm::bit_cast<float>(i32);
    }

  private:
    const int shift;
    const uint32_t mask, test, maxn;
  };

  template <int bits>
  inline static float reduceMantissaToNbitsRounding(const float &f) {
    static const ReduceMantissaToNbitsRounding reducer(bits);
    return reducer(f);
  }

  inline static float reduceMantissaToNbitsRounding(float f, int bits) {
    return ReduceMantissaToNbitsRounding(bits)(f);
  }

  template <typename InItr, typename OutItr>
  static void reduceMantissaToNbitsRounding(int bits, InItr begin, InItr end, OutItr out) {
    std::transform(begin, end, out, ReduceMantissaToNbitsRounding(bits));
  }

  inline static float max() {
    constexpr uint32_t i32 = 0x477fe000;  // = mantissatable[offsettable[0x1e]+0x3ff]+exponenttable[0x1e]
    return edm::bit_cast<float>(i32);
  }

  // Maximum float32 value that gets rounded to max()
  inline static float max32RoundedToMax16() {
    // 2^16 in float32 is the first to result inf in float16, so
    // 2^16-1 is the last float32 to result max() in float16
    constexpr uint32_t i32 = (0x8f << 23) - 1;
    return edm::bit_cast<float>(i32);
  }

  inline static float min() {
    constexpr uint32_t i32 = 0x38800000;  // = mantissatable[offsettable[1]+0]+exponenttable[1]
    return edm::bit_cast<float>(i32);
  }

  // Minimum float32 value that gets rounded to min()
  inline static float min32RoundedToMin16() {
    // 2^-14-1 in float32 is the first to result denormalized in float16, so
    // 2^-14 is the first float32 to result min() in float16
    constexpr uint32_t i32 = (0x71 << 23);
    return edm::bit_cast<float>(i32);
  }

  inline static float denorm_min() {
    constexpr uint32_t i32 = 0x33800000;  // mantissatable[offsettable[0]+1]+exponenttable[0]
    return edm::bit_cast<float>(i32);
  }

  inline static bool isdenorm(uint16_t h) {
    // if exponent is zero (sign-bit excluded of course) and mantissa is not zero
    return ((h >> 10) & 0x1f) == 0 && (h & 0x3ff) != 0;
  }

private:
  CMS_THREAD_SAFE static uint32_t mantissatable[2048];
  CMS_THREAD_SAFE static uint32_t exponenttable[64];
  CMS_THREAD_SAFE static uint16_t offsettable[64];
  CMS_THREAD_SAFE static uint16_t basetable[512];
  CMS_THREAD_SAFE static uint8_t shifttable[512];
  static void filltables();
};
#endif