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 // 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
 //       disclaimer in the documentation and/or other materials provided
 //       with the distribution.
 //     * Neither the name of Google Inc. nor the names of its
 //       contributors may be used to endorse or promote products derived
 //       from this software without specific prior written permission.
 //
 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
 #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 = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000);
   static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
   static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
   static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000);
   static const uint64_t kQuietNanBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00080000, 00000000);
   static const int kPhysicalSignificandSize = 52;  // Excludes the hidden bit.
   static const int kSignificandSize = 53;
   static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
   static const int kMaxExponent = 0x7FF - kExponentBias;
 
   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 {
     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
     DOUBLE_CONVERSION_ASSERT(!IsSpecial());
     return DiyFp(Significand(), Exponent());
   }
 
   // The value encoded by this Double must be strictly greater than 0.
   DiyFp AsNormalizedDiyFp() const {
     DOUBLE_CONVERSION_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 IsQuietNan() const {
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
     return IsNan() && ((AsUint64() & kQuietNanBit) == 0);
 #else
     return IsNan() && ((AsUint64() & kQuietNanBit) != 0);
 #endif
   }
 
   bool IsSignalingNan() const {
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
     return IsNan() && ((AsUint64() & kQuietNanBit) != 0);
 #else
     return IsNan() && ((AsUint64() & kQuietNanBit) == 0);
 #endif
   }
 
 
   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 {
     DOUBLE_CONVERSION_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 {
     DOUBLE_CONVERSION_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 kDenormalExponent = -kExponentBias + 1;
   static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
   static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF7FFFF, FFFFFFFF);
 #else
   static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000);
 #endif
 
 
   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);
   }
 
   DOUBLE_CONVERSION_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 uint32_t kQuietNanBit = 0x00400000;
   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 {
     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
     DOUBLE_CONVERSION_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 IsQuietNan() const {
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
     return IsNan() && ((AsUint32() & kQuietNanBit) == 0);
 #else
     return IsNan() && ((AsUint32() & kQuietNanBit) != 0);
 #endif
   }
 
   bool IsSignalingNan() const {
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
     return IsNan() && ((AsUint32() & kQuietNanBit) != 0);
 #else
     return IsNan() && ((AsUint32() & kQuietNanBit) == 0);
 #endif
   }
 
 
   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 {
     DOUBLE_CONVERSION_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 {
     DOUBLE_CONVERSION_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;
 #if (defined(__mips__) && !defined(__mips_nan2008)) || defined(__hppa__)
   static const uint32_t kNaN = 0x7FBFFFFF;
 #else
   static const uint32_t kNaN = 0x7FC00000;
 #endif
 
   const uint32_t d32_;
 
   DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single);
 };
 
 }  // namespace double_conversion
 
 #endif  // DOUBLE_CONVERSION_DOUBLE_H_

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