ClickHouse/contrib/libdouble-conversion/double-conversion/ieee.h

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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);
}
DISALLOW_COPY_AND_ASSIGN(Double);
};
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_;
DISALLOW_COPY_AND_ASSIGN(Single);
};
} // namespace double_conversion
#endif // DOUBLE_CONVERSION_DOUBLE_H_