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