src/ieee.h - third_party/double-conversion - Git at Google

 // 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 = 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 -Double::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);
   }

   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_;

   DISALLOW_COPY_AND_ASSIGN(Single);
 };

 }  // namespace double_conversion

 #endif  // DOUBLE_CONVERSION_DOUBLE_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
	// 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 = 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 -Double::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);
	}

	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_;

	DISALLOW_COPY_AND_ASSIGN(Single);
	};

	} // namespace double_conversion

	#endif // DOUBLE_CONVERSION_DOUBLE_H_