double.h   [plain text]

// Copyright 2010 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 WTF {

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); }
    
    // 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();
            }
        }
        
        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();
            bool significand_is_zero = (v.f() == kHiddenBit);
            DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
            DiyFp m_minus;
            if (significand_is_zero && v.e() != kDenormalExponent) {
                // The 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.
                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;
        }
        
        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);
        }
    };
    
}  // namespace double_conversion

} // namespace WTF

#endif  // DOUBLE_CONVERSION_DOUBLE_H_