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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 = 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);
+  }
+};
+
+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_;
+};
+
+}  // namespace double_conversion
+
+#endif  // DOUBLE_CONVERSION_DOUBLE_H_