path: root/contrib/libs/double-conversion/ieee.h

// Copyright 2012 the V8 project authors. All rights reserved. 
// Redistribution and use in source and binary forms, with or without 
// modification, are permitted provided that the following conditions are 
// met: 
// 
//     * Redistributions of source code must retain the above copyright 
//       notice, this list of conditions and the following disclaimer. 
//     * Redistributions in binary form must reproduce the above 
//       copyright notice, this list of conditions and the following 
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//       with the distribution. 
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//       contributors may be used to endorse or promote products derived 
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// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 
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#ifndef DOUBLE_CONVERSION_DOUBLE_H_ 
#define DOUBLE_CONVERSION_DOUBLE_H_ 
 
#include "diy-fp.h" 
 
namespace double_conversion { 
 
// We assume that doubles and uint64_t have the same endianness. 
static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } 
static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } 
static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); } 
static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); } 
 
// Helper functions for doubles. 
class Double { 
 public: 
  static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); 
  static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); 
  static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); 
  static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); 
  static const int kPhysicalSignificandSize = 52;  // Excludes the hidden bit. 
  static const int kSignificandSize = 53; 
 
  Double() : d64_(0) {} 
  explicit Double(double d) : d64_(double_to_uint64(d)) {} 
  explicit Double(uint64_t d64) : d64_(d64) {} 
  explicit Double(DiyFp diy_fp) 
    : d64_(DiyFpToUint64(diy_fp)) {} 
 
  // The value encoded by this Double must be greater or equal to +0.0. 
  // It must not be special (infinity, or NaN). 
  DiyFp AsDiyFp() const { 
    ASSERT(Sign() > 0); 
    ASSERT(!IsSpecial()); 
    return DiyFp(Significand(), Exponent()); 
  } 
 
  // The value encoded by this Double must be strictly greater than 0. 
  DiyFp AsNormalizedDiyFp() const { 
    ASSERT(value() > 0.0); 
    uint64_t f = Significand(); 
    int e = Exponent(); 
 
    // The current double could be a denormal. 
    while ((f & kHiddenBit) == 0) { 
      f <<= 1; 
      e--; 
    } 
    // Do the final shifts in one go. 
    f <<= DiyFp::kSignificandSize - kSignificandSize; 
    e -= DiyFp::kSignificandSize - kSignificandSize; 
    return DiyFp(f, e); 
  } 
 
  // Returns the double's bit as uint64. 
  uint64_t AsUint64() const { 
    return d64_; 
  } 
 
  // Returns the next greater double. Returns +infinity on input +infinity. 
  double NextDouble() const { 
    if (d64_ == kInfinity) return Double(kInfinity).value(); 
    if (Sign() < 0 && Significand() == 0) { 
      // -0.0 
      return 0.0; 
    } 
    if (Sign() < 0) { 
      return Double(d64_ - 1).value(); 
    } else { 
      return Double(d64_ + 1).value(); 
    } 
  } 
 
  double PreviousDouble() const { 
    if (d64_ == (kInfinity | kSignMask)) return -Infinity(); 
    if (Sign() < 0) { 
      return Double(d64_ + 1).value(); 
    } else { 
      if (Significand() == 0) return -0.0; 
      return Double(d64_ - 1).value(); 
    } 
  } 
 
  int Exponent() const { 
    if (IsDenormal()) return kDenormalExponent; 
 
    uint64_t d64 = AsUint64(); 
    int biased_e = 
        static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); 
    return biased_e - kExponentBias; 
  } 
 
  uint64_t Significand() const { 
    uint64_t d64 = AsUint64(); 
    uint64_t significand = d64 & kSignificandMask; 
    if (!IsDenormal()) { 
      return significand + kHiddenBit; 
    } else { 
      return significand; 
    } 
  } 
 
  // Returns true if the double is a denormal. 
  bool IsDenormal() const { 
    uint64_t d64 = AsUint64(); 
    return (d64 & kExponentMask) == 0; 
  } 
 
  // We consider denormals not to be special. 
  // Hence only Infinity and NaN are special. 
  bool IsSpecial() const { 
    uint64_t d64 = AsUint64(); 
    return (d64 & kExponentMask) == kExponentMask; 
  } 
 
  bool IsNan() const { 
    uint64_t d64 = AsUint64(); 
    return ((d64 & kExponentMask) == kExponentMask) && 
        ((d64 & kSignificandMask) != 0); 
  } 
 
  bool IsInfinite() const { 
    uint64_t d64 = AsUint64(); 
    return ((d64 & kExponentMask) == kExponentMask) && 
        ((d64 & kSignificandMask) == 0); 
  } 
 
  int Sign() const { 
    uint64_t d64 = AsUint64(); 
    return (d64 & kSignMask) == 0? 1: -1; 
  } 
 
  // Precondition: the value encoded by this Double must be greater or equal 
  // than +0.0. 
  DiyFp UpperBoundary() const { 
    ASSERT(Sign() > 0); 
    return DiyFp(Significand() * 2 + 1, Exponent() - 1); 
  } 
 
  // Computes the two boundaries of this. 
  // The bigger boundary (m_plus) is normalized. The lower boundary has the same 
  // exponent as m_plus. 
  // Precondition: the value encoded by this Double must be greater than 0. 
  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { 
    ASSERT(value() > 0.0); 
    DiyFp v = this->AsDiyFp(); 
    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); 
    DiyFp m_minus; 
    if (LowerBoundaryIsCloser()) { 
      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); 
    } else { 
      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); 
    } 
    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); 
    m_minus.set_e(m_plus.e()); 
    *out_m_plus = m_plus; 
    *out_m_minus = m_minus; 
  } 
 
  bool LowerBoundaryIsCloser() const { 
    // The boundary is closer if the significand is of the form f == 2^p-1 then 
    // the lower boundary is closer. 
    // Think of v = 1000e10 and v- = 9999e9. 
    // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but 
    // at a distance of 1e8. 
    // The only exception is for the smallest normal: the largest denormal is 
    // at the same distance as its successor. 
    // Note: denormals have the same exponent as the smallest normals. 
    bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0); 
    return physical_significand_is_zero && (Exponent() != kDenormalExponent); 
  } 
 
  double value() const { return uint64_to_double(d64_); } 
 
  // Returns the significand size for a given order of magnitude. 
  // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. 
  // This function returns the number of significant binary digits v will have 
  // once it's encoded into a double. In almost all cases this is equal to 
  // kSignificandSize. The only exceptions are denormals. They start with 
  // leading zeroes and their effective significand-size is hence smaller. 
  static int SignificandSizeForOrderOfMagnitude(int order) { 
    if (order >= (kDenormalExponent + kSignificandSize)) { 
      return kSignificandSize; 
    } 
    if (order <= kDenormalExponent) return 0; 
    return order - kDenormalExponent; 
  } 
 
  static double Infinity() { 
    return Double(kInfinity).value(); 
  } 
 
  static double NaN() { 
    return Double(kNaN).value(); 
  } 
 
 private: 
  static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; 
  static const int kDenormalExponent = -kExponentBias + 1; 
  static const int kMaxExponent = 0x7FF - kExponentBias; 
  static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); 
  static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); 
 
  const uint64_t d64_; 
 
  static uint64_t DiyFpToUint64(DiyFp diy_fp) { 
    uint64_t significand = diy_fp.f(); 
    int exponent = diy_fp.e(); 
    while (significand > kHiddenBit + kSignificandMask) { 
      significand >>= 1; 
      exponent++; 
    } 
    if (exponent >= kMaxExponent) { 
      return kInfinity; 
    } 
    if (exponent < kDenormalExponent) { 
      return 0; 
    } 
    while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { 
      significand <<= 1; 
      exponent--; 
    } 
    uint64_t biased_exponent; 
    if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { 
      biased_exponent = 0; 
    } else { 
      biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); 
    } 
    return (significand & kSignificandMask) | 
        (biased_exponent << kPhysicalSignificandSize); 
  } 
 
  DC_DISALLOW_COPY_AND_ASSIGN(Double);
}; 
 
class Single { 
 public: 
  static const uint32_t kSignMask = 0x80000000; 
  static const uint32_t kExponentMask = 0x7F800000; 
  static const uint32_t kSignificandMask = 0x007FFFFF; 
  static const uint32_t kHiddenBit = 0x00800000; 
  static const int kPhysicalSignificandSize = 23;  // Excludes the hidden bit. 
  static const int kSignificandSize = 24; 
 
  Single() : d32_(0) {} 
  explicit Single(float f) : d32_(float_to_uint32(f)) {} 
  explicit Single(uint32_t d32) : d32_(d32) {} 
 
  // The value encoded by this Single must be greater or equal to +0.0. 
  // It must not be special (infinity, or NaN). 
  DiyFp AsDiyFp() const { 
    ASSERT(Sign() > 0); 
    ASSERT(!IsSpecial()); 
    return DiyFp(Significand(), Exponent()); 
  } 
 
  // Returns the single's bit as uint64. 
  uint32_t AsUint32() const { 
    return d32_; 
  } 
 
  int Exponent() const { 
    if (IsDenormal()) return kDenormalExponent; 
 
    uint32_t d32 = AsUint32(); 
    int biased_e = 
        static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize); 
    return biased_e - kExponentBias; 
  } 
 
  uint32_t Significand() const { 
    uint32_t d32 = AsUint32(); 
    uint32_t significand = d32 & kSignificandMask; 
    if (!IsDenormal()) { 
      return significand + kHiddenBit; 
    } else { 
      return significand; 
    } 
  } 
 
  // Returns true if the single is a denormal. 
  bool IsDenormal() const { 
    uint32_t d32 = AsUint32(); 
    return (d32 & kExponentMask) == 0; 
  } 
 
  // We consider denormals not to be special. 
  // Hence only Infinity and NaN are special. 
  bool IsSpecial() const { 
    uint32_t d32 = AsUint32(); 
    return (d32 & kExponentMask) == kExponentMask; 
  } 
 
  bool IsNan() const { 
    uint32_t d32 = AsUint32(); 
    return ((d32 & kExponentMask) == kExponentMask) && 
        ((d32 & kSignificandMask) != 0); 
  } 
 
  bool IsInfinite() const { 
    uint32_t d32 = AsUint32(); 
    return ((d32 & kExponentMask) == kExponentMask) && 
        ((d32 & kSignificandMask) == 0); 
  } 
 
  int Sign() const { 
    uint32_t d32 = AsUint32(); 
    return (d32 & kSignMask) == 0? 1: -1; 
  } 
 
  // Computes the two boundaries of this. 
  // The bigger boundary (m_plus) is normalized. The lower boundary has the same 
  // exponent as m_plus. 
  // Precondition: the value encoded by this Single must be greater than 0. 
  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { 
    ASSERT(value() > 0.0); 
    DiyFp v = this->AsDiyFp(); 
    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); 
    DiyFp m_minus; 
    if (LowerBoundaryIsCloser()) { 
      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); 
    } else { 
      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); 
    } 
    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); 
    m_minus.set_e(m_plus.e()); 
    *out_m_plus = m_plus; 
    *out_m_minus = m_minus; 
  } 
 
  // Precondition: the value encoded by this Single must be greater or equal 
  // than +0.0. 
  DiyFp UpperBoundary() const { 
    ASSERT(Sign() > 0); 
    return DiyFp(Significand() * 2 + 1, Exponent() - 1); 
  } 
 
  bool LowerBoundaryIsCloser() const { 
    // The boundary is closer if the significand is of the form f == 2^p-1 then 
    // the lower boundary is closer. 
    // Think of v = 1000e10 and v- = 9999e9. 
    // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but 
    // at a distance of 1e8. 
    // The only exception is for the smallest normal: the largest denormal is 
    // at the same distance as its successor. 
    // Note: denormals have the same exponent as the smallest normals. 
    bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0); 
    return physical_significand_is_zero && (Exponent() != kDenormalExponent); 
  } 
 
  float value() const { return uint32_to_float(d32_); } 
 
  static float Infinity() { 
    return Single(kInfinity).value(); 
  } 
 
  static float NaN() { 
    return Single(kNaN).value(); 
  } 
 
 private: 
  static const int kExponentBias = 0x7F + kPhysicalSignificandSize; 
  static const int kDenormalExponent = -kExponentBias + 1; 
  static const int kMaxExponent = 0xFF - kExponentBias; 
  static const uint32_t kInfinity = 0x7F800000; 
  static const uint32_t kNaN = 0x7FC00000; 
 
  const uint32_t d32_; 
 
  DC_DISALLOW_COPY_AND_ASSIGN(Single);
}; 
 
}  // namespace double_conversion 
 
#endif  // DOUBLE_CONVERSION_DOUBLE_H_