FloatPacker.cxx

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/*
  Copyright (C) 2002-2026 CERN for the benefit of the ATLAS collaboration
*/
 
#include "CxxUtils/FloatPacker.h"
#include "CxxUtils/ones.h"
#include "CxxUtils/trapping_fp.h"
#include <limits>
#include <sstream>
#include <iomanip>
#include <stdexcept>
#include <bit>
#include <cstdint>
 
namespace {
  typedef CxxUtils::FloatPacker::Packdest Packdest;
  //
  static_assert(std::numeric_limits<double>::is_iec559);
  static_assert(std::numeric_limits<double>::digits == 53);
  static_assert(std::numeric_limits<Packdest>::digits == 32);
 
  constexpr std::uint64_t double_sign_mask     = 0x8000000000000000ULL;
  constexpr std::uint64_t double_exponent_mask = 0x7ff0000000000000ULL;
  constexpr std::uint64_t double_mantissa_mask = 0x000fffffffffffffULL;
  
  constexpr int ieee754_double_bias = 0x3ff;
  constexpr int ieee754_double_exponent_bits = 11;
  constexpr int ieee754_double_mantissa_bits = 52;
  constexpr int ieee754_double_exponent_shift = 52;
  
  constexpr std::uint64_t
  doubleToBits(double value) noexcept
  {
    return std::bit_cast<std::uint64_t>(value);
  }
  
  constexpr double
  bitsToDouble(std::uint64_t bits) noexcept
  {
    return std::bit_cast<double>(bits);
  }
  
  constexpr bool
  isZeroBits(std::uint64_t bits) noexcept
  {
    return (bits & ~double_sign_mask) == 0;
  }
  
  constexpr bool
  isNegativeBits(std::uint64_t bits) noexcept
  {
    return (bits & double_sign_mask) != 0;
  }
  
  constexpr int
  biasedExponent(std::uint64_t bits) noexcept
  {
    return static_cast<int>(
      (bits & double_exponent_mask) >> ieee754_double_exponent_shift);
  }
  
  constexpr std::uint64_t
  doubleMantissaBits(std::uint64_t bits) noexcept
  {
    return bits & double_mantissa_mask;
  }
 
  
  
  const int packdest_bits = std::numeric_limits<Packdest>::digits;
  
  
  // Handy constant: A Packdest with 1 in the high bit.
  const Packdest high_packdest_bit = (1U << (packdest_bits - 1));
  
  const Packdest ieee754_double_exponent_all_ones =
  (Packdest{1} << ieee754_double_exponent_bits) - 1;
  
  
  inline
  int max_int (int nbits)
  {
    return ((1U << nbits) >> 1) - 1;
  }
  
  
  inline
  int min_int (int nbits)
  {
    return static_cast<int>(~0U << nbits) >> 1;
  }
  
  
  void renormalize_denormal (int& exponent,
                             Packdest& mantissa)
  {
    if (mantissa == 0)
      exponent -= packdest_bits; // Lost precision here.
    else {
      while ((mantissa & high_packdest_bit) == 0) {
        --exponent;
        mantissa <<= 1;
      }
      mantissa <<= 1;
    }
  }

  void underflow_to_denormal (int min_exp,
                              int round_bits,
                              int& exponent,
                              Packdest& mantissa)
  {
    if (exponent <= min_exp) {
      const Packdest mantissa_in = mantissa;
  
      // Denormalize the mantissa.
      mantissa = (mantissa >> 1) | high_packdest_bit;
  
      // Now shift it right.
      int shift = min_exp - exponent;
      if (shift < packdest_bits)
        mantissa >>= shift;
      else
        mantissa = 0; // underflow to 0.
  
      // Flag it as denormal.
      exponent = min_exp;
  
      // Handle rounding, if desired.
      if (round_bits) {
        //
        //                                   +- packdest_bits - round_bits - 1
        //                  |- round_bits  -|v
        //    mantissa:     .................X....
        //                       v- shift+1 -^
        //    mantissa_in:  .....X................
        //                       ^
        //                       +- packdest_bits - round_bits + shift
        //
        int orig_pos = packdest_bits - round_bits + shift;
        if (orig_pos < packdest_bits &&
            ((static_cast<Packdest> (1) << orig_pos) & mantissa_in) != 0)
        {
          Packdest lsb = (static_cast<Packdest> (1) <<
                          (packdest_bits - round_bits));
          Packdest lsbmask = ~ (lsb - 1);
  
          // ??? If we overflow here, it means we have to go back
          //     to a normalized representation.  Just punt for now.
          if ((mantissa & lsbmask) != lsbmask)
            mantissa += lsb;
        }
      }
    }
  }
 
 
} // unnamed namespace
 
 
namespace CxxUtils {
 

FloatPacker::FloatPacker (int nbits,
                          int nmantissa,
                          double scale /*= 1*/,
                          bool is_signed /*= true*/,
                          bool round /*= false*/)
  : m_nmantissa (nmantissa),
    m_scale (scale),
    m_is_signed (is_signed),
    m_round (round)
{
  // scale==0 means not to scale.
  // Use that instead of 1 since it's faster to test for 0.
  if (scale == 1 || scale == 0)
    m_invscale = 0;
  else {
    // Avoid spurious div-zero FPEs with clang.
    CXXUTILS_TRAPPING_FP;
    m_invscale = 1. / m_scale;
  }
 
  // Set up other cached values.
  m_npack = m_nmantissa;
  if (m_is_signed)
    --m_npack;
 
  m_npack_ones = ones<Packdest> (m_npack);
 
  // Sign bit mask.
  if (m_is_signed)
    m_signmask = 1U << (nbits - 1);
  else
    m_signmask = 0;
 
  // Number of exponent bits.
  m_nexp = nbits - m_nmantissa;
  m_nexp_ones = ones<Packdest> (m_nexp);
 
  // Minimum exponent value.
  m_min_exp = min_int (m_nexp);
 
  // Maximum exponent value.
  m_max_exp = max_int (m_nexp);
 
  if (m_npack < 1 || m_npack > nbits)
    throw std::runtime_error ("Bad number of mantissa bits.");
}
 

FloatPacker::Packdest
FloatPacker::pack (double src, std::string* err /*= nullptr*/) const
{
  double d = src;
  std::uint64_t bits = doubleToBits(d);
 
  // Fast-path for zero.  (Purely an optimization.)
  // Note: can't use a double compare here.  On some architectures (eg, MIPS)
  // a denormal will compare equal to zero.
  if (bits == 0) {
    return 0;
  }
 
  // Check for NaN and infinity.
  if (biasedExponent(bits) == ieee754_double_exponent_all_ones) {    
    if (err) {
      std::ostringstream os;
      os << "Bad float number: " << src << " ("
         << std::setbase(16)
         << static_cast<std::uint32_t>(bits)
         << " "
         << static_cast<std::uint32_t>(bits >> 32)
         << ")";
      *err = os.str();
    }
    d = 0;
    bits = doubleToBits(d);
  }
 
  if (m_invscale){
    d *= m_invscale;
    bits = doubleToBits(d);
  }
  bool was_negative = false;
  if (isNegativeBits(bits)) {
    if (m_is_signed) {
      was_negative = true;
      d = -d;
      bits = doubleToBits(d);
    }
    else {
      // Don't complain on -0.
      if (d < 0 && err) {
        std::ostringstream os;
        os << "Float overflow during packing: " << src;
        *err = os.str();
      }
      d = 0;
      bits = doubleToBits(d);
    }
  }
 
  // Check for zero again.
  // (Also need to preserve the sign; the scale division may
  // have underflowed.)
  if (isZeroBits(bits)) {
    return was_negative ? m_signmask : 0;
  }
 
  // Get packdest_bits bits of mantissa.
  const std::uint64_t fullMantissa = doubleMantissaBits(bits);
  Packdest mantissa = static_cast<Packdest>(
    fullMantissa >> (ieee754_double_mantissa_bits - packdest_bits));
  int exponent = biasedExponent(bits) - ieee754_double_bias;
 
  // Do rounding, if requested.
  if (m_round) {
    const Packdest lsbmask = Packdest{1} << (packdest_bits - m_npack);
    Packdest roundmask = ~Packdest{0};
    bool roundbit = false;
 
    if (lsbmask > 1) {
      roundbit = (mantissa & (lsbmask >> 1)) != 0;
      roundmask = ~static_cast<Packdest>((lsbmask >> 1) - 1);
    }
    else {
      // We are keeping all packdest_bits bits of the extracted mantissa.
      // The rounding bit is therefore the next bit below those bits in the
      // original 52-bit double mantissa.
      constexpr int shift = ieee754_double_mantissa_bits - packdest_bits;
      roundbit = (fullMantissa & (std::uint64_t{1} << (shift - 1))) != 0;
    }
 
    if (roundbit) {
      // Handle the case where it would overflow.
      if ((mantissa & roundmask) == roundmask) {
        mantissa >>= 1;
        mantissa |= roundmask;
        exponent += 1;
      }
 
      mantissa += lsbmask;
    }
  }
 
  // If the number is too large, bitch, and reset to the largest number.
  if (exponent > m_max_exp) {
    if (err) {
      std::ostringstream os;
      os << "Float overflow during packing: " << src;
      *err = os.str();
    }
    exponent = m_max_exp;
    mantissa = static_cast<Packdest> (~0);
  }
 
  // Handle denormals.  (We've already handled the zero case.)
  if (exponent == - ieee754_double_bias)
    renormalize_denormal (exponent, mantissa);
 
  // If the number is too small, denormalize, or underflow to 0.
  underflow_to_denormal (m_min_exp, m_round ? m_npack: 0, exponent, mantissa);
 
  // Pack in the mantissa bits.
  Packdest dest = mantissa >> (packdest_bits - m_npack);
 
  // The exponent, if desired.
  if (m_nexp > 0)
    dest |= ((exponent - m_min_exp) << m_npack);
 
  // And the optional sign bit.
  if (was_negative)
    dest |= m_signmask;
 
  return dest;
}
 

double
FloatPacker::unpack(Packdest val, std::string* err /*= nullptr*/) const
{
  // Fast-path for 0.
  if (val == 0) {
    return 0;
  }
 
  // Break apart the packed value.
  const bool was_negative = (val & m_signmask) != 0;
 
  double d = 0;
 
  // Fast path for fixed-point representations.
  if (m_nexp == 0) {
    const Packdest mantissa = val & m_npack_ones;
    d = mantissa / (static_cast<double>(m_npack_ones) + 1);
 
    if (was_negative) {
      d *= -1;
    }
  }
  else {
    // Get the mantissa.
    Packdest mantissa = (val & m_npack_ones) << (packdest_bits - m_npack);
    // General case.
    // Get the exponent.
    int exponent = static_cast<int>((val >> m_npack) & m_nexp_ones);
    exponent += m_min_exp; // unbias.
 
    // Handle denormals.
    if (exponent == m_min_exp) {
      // Maybe it was -0?
      if (mantissa == 0) {
        std::uint64_t bits = 0;
        if (was_negative) {
          bits |= double_sign_mask;
        }
        return bitsToDouble(bits);
      }
      renormalize_denormal(exponent, mantissa);
    }
    // Complain about overflow.
    if (exponent >= max_int(ieee754_double_exponent_bits)) {
      if (err) {
        std::ostringstream os;
        os << "Overflow while unpacking float; exponent: " << exponent;
        *err = os.str();
      }
      exponent = max_int(ieee754_double_exponent_bits) + 1;
      mantissa = 0; // Infinity.
    }
    // Underflow into denormal.
    underflow_to_denormal(-ieee754_double_bias, 0, exponent, mantissa);
    // Pack into a double.
    std::uint64_t bits = 0;
    if (was_negative) {
      bits |= double_sign_mask;
    }
    bits |= static_cast<std::uint64_t>(exponent + ieee754_double_bias)
            << ieee754_double_exponent_shift;
    bits |= static_cast<std::uint64_t>(mantissa)
            << (ieee754_double_mantissa_bits - packdest_bits);
    d = bitsToDouble(bits);
  }
  // Set the result.
  if (m_scale) {
    d *= m_scale;
  }
  return d;
}
 
} // namespace CxxUtils