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