// 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_