| // Copyright 2011 the V8 project authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| #ifndef V8_DOUBLE_H_ |
| #define V8_DOUBLE_H_ |
| |
| #include "src/diy-fp.h" |
| |
| namespace v8 { |
| namespace internal { |
| |
| // We assume that doubles and uint64_t have the same endianness. |
| inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); } |
| inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); } |
| |
| // Helper functions for doubles. |
| class Double { |
| public: |
| static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000); |
| static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000); |
| static const uint64_t kSignificandMask = |
| V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF); |
| static const uint64_t kHiddenBit = V8_2PART_UINT64_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 { |
| DCHECK_GT(Sign(), 0); |
| DCHECK(!IsSpecial()); |
| return DiyFp(Significand(), Exponent()); |
| } |
| |
| // The value encoded by this Double must be strictly greater than 0. |
| DiyFp AsNormalizedDiyFp() const { |
| DCHECK_GT(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 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 { |
| DCHECK_GT(Sign(), 0); |
| return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| } |
| |
| // Returns 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 { |
| DCHECK_GT(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 its encoded into a double. In almost all cases this is equal to |
| // kSignificandSize. The only exception 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; |
| } |
| |
| private: |
| static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
| static const int kDenormalExponent = -kExponentBias + 1; |
| static const int kMaxExponent = 0x7FF - kExponentBias; |
| static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000); |
| |
| // The field d64_ is not marked as const to permit the usage of the copy |
| // constructor. |
| 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 internal |
| } // namespace v8 |
| |
| #endif // V8_DOUBLE_H_ |