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/*
* Copyright (C) 2011 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``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 APPLE INC. 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
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* 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 Uint16WithFraction_h
#define Uint16WithFraction_h
#include <wtf/MathExtras.h>
namespace JSC {
// Would be nice if this was a static const member, but the OS X linker
// seems to want a symbol in the binary in that case...
#define oneGreaterThanMaxUInt16 0x10000
// A uint16_t with an infinite precision fraction. Upon overflowing
// the uint16_t range, this class will clamp to oneGreaterThanMaxUInt16.
// This is used in converting the fraction part of a number to a string.
class Uint16WithFraction {
public:
explicit Uint16WithFraction(double number, uint16_t divideByExponent = 0)
{
ASSERT(number && isfinite(number) && !signbit(number));
// Check for values out of uint16_t range.
if (number >= oneGreaterThanMaxUInt16) {
m_values.append(oneGreaterThanMaxUInt16);
m_leadingZeros = 0;
return;
}
// Append the units to m_values.
double integerPart = floor(number);
m_values.append(static_cast<uint32_t>(integerPart));
bool sign;
int32_t exponent;
uint64_t mantissa;
decomposeDouble(number - integerPart, sign, exponent, mantissa);
ASSERT(!sign && exponent < 0);
exponent -= divideByExponent;
int32_t zeroBits = -exponent;
--zeroBits;
// Append the append words for to m_values.
while (zeroBits >= 32) {
m_values.append(0);
zeroBits -= 32;
}
// Left align the 53 bits of the mantissa within 96 bits.
uint32_t values[3];
values[0] = static_cast<uint32_t>(mantissa >> 21);
values[1] = static_cast<uint32_t>(mantissa << 11);
values[2] = 0;
// Shift based on the remainder of the exponent.
if (zeroBits) {
values[2] = values[1] << (32 - zeroBits);
values[1] = (values[1] >> zeroBits) | (values[0] << (32 - zeroBits));
values[0] = (values[0] >> zeroBits);
}
m_values.append(values[0]);
m_values.append(values[1]);
m_values.append(values[2]);
// Canonicalize; remove any trailing zeros.
while (m_values.size() > 1 && !m_values.last())
m_values.removeLast();
// Count the number of leading zero, this is useful in optimizing multiplies.
m_leadingZeros = 0;
while (m_leadingZeros < m_values.size() && !m_values[m_leadingZeros])
++m_leadingZeros;
}
Uint16WithFraction& operator*=(uint16_t multiplier)
{
ASSERT(checkConsistency());
// iteratate backwards over the fraction until we reach the leading zeros,
// passing the carry from one calculation into the next.
uint64_t accumulator = 0;
for (size_t i = m_values.size(); i > m_leadingZeros; ) {
--i;
accumulator += static_cast<uint64_t>(m_values[i]) * static_cast<uint64_t>(multiplier);
m_values[i] = static_cast<uint32_t>(accumulator);
accumulator >>= 32;
}
if (!m_leadingZeros) {
// With a multiplicand and multiplier in the uint16_t range, this cannot carry
// (even allowing for the infinity value).
ASSERT(!accumulator);
// Check for overflow & clamp to 'infinity'.
if (m_values[0] >= oneGreaterThanMaxUInt16) {
m_values.shrink(1);
m_values[0] = oneGreaterThanMaxUInt16;
m_leadingZeros = 0;
return *this;
}
} else if (accumulator) {
// Check for carry from the last multiply, if so overwrite last leading zero.
m_values[--m_leadingZeros] = static_cast<uint32_t>(accumulator);
// The limited range of the multiplier should mean that even if we carry into
// the units, we don't need to check for overflow of the uint16_t range.
ASSERT(m_values[0] < oneGreaterThanMaxUInt16);
}
// Multiplication by an even value may introduce trailing zeros; if so, clean them
// up. (Keeping the value in a normalized form makes some of the comparison operations
// more efficient).
while (m_values.size() > 1 && !m_values.last())
m_values.removeLast();
ASSERT(checkConsistency());
return *this;
}
bool operator<(const Uint16WithFraction& other)
{
ASSERT(checkConsistency());
ASSERT(other.checkConsistency());
// Iterate over the common lengths of arrays.
size_t minSize = std::min(m_values.size(), other.m_values.size());
for (size_t index = 0; index < minSize; ++index) {
// If we find a value that is not equal, compare and return.
uint32_t fromThis = m_values[index];
uint32_t fromOther = other.m_values[index];
if (fromThis != fromOther)
return fromThis < fromOther;
}
// If these numbers have the same lengths, they are equal,
// otherwise which ever number has a longer fraction in larger.
return other.m_values.size() > minSize;
}
// Return the floor (non-fractional portion) of the number, clearing this to zero,
// leaving the fractional part unchanged.
uint32_t floorAndSubtract()
{
// 'floor' is simple the integer portion of the value.
uint32_t floor = m_values[0];
// If floor is non-zero,
if (floor) {
m_values[0] = 0;
m_leadingZeros = 1;
while (m_leadingZeros < m_values.size() && !m_values[m_leadingZeros])
++m_leadingZeros;
}
return floor;
}
// Compare this value to 0.5, returns -1 for less than, 0 for equal, 1 for greater.
int comparePoint5()
{
ASSERT(checkConsistency());
// If units != 0, this is greater than 0.5.
if (m_values[0])
return 1;
// If size == 1 this value is 0, hence < 0.5.
if (m_values.size() == 1)
return -1;
// Compare to 0.5.
if (m_values[1] > 0x80000000ul)
return 1;
if (m_values[1] < 0x80000000ul)
return -1;
// Check for more words - since normalized numbers have no trailing zeros, if
// there are more that two digits we can assume at least one more is non-zero,
// and hence the value is > 0.5.
return m_values.size() > 2 ? 1 : 0;
}
// Return true if the sum of this plus addend would be greater than 1.
bool sumGreaterThanOne(const Uint16WithFraction& addend)
{
ASSERT(checkConsistency());
ASSERT(addend.checkConsistency());
// First, sum the units. If the result is greater than one, return true.
// If equal to one, return true if either number has a fractional part.
uint32_t sum = m_values[0] + addend.m_values[0];
if (sum)
return sum > 1 || std::max(m_values.size(), addend.m_values.size()) > 1;
// We could still produce a result greater than zero if addition of the next
// word from the fraction were to carry, leaving a result > 0.
// Iterate over the common lengths of arrays.
size_t minSize = std::min(m_values.size(), addend.m_values.size());
for (size_t index = 1; index < minSize; ++index) {
// Sum the next word from this & the addend.
uint32_t fromThis = m_values[index];
uint32_t fromAddend = addend.m_values[index];
sum = fromThis + fromAddend;
// Check for overflow. If so, check whether the remaining result is non-zero,
// or if there are any further words in the fraction.
if (sum < fromThis)
return sum || (index + 1) < std::max(m_values.size(), addend.m_values.size());
// If the sum is uint32_t max, then we would carry a 1 if addition of the next
// digits in the number were to overflow.
if (sum != 0xFFFFFFFF)
return false;
}
return false;
}
private:
bool checkConsistency() const
{
// All values should have at least one value.
return (m_values.size())
// The units value must be a uint16_t, or the value is the overflow value.
&& (m_values[0] < oneGreaterThanMaxUInt16 || (m_values[0] == oneGreaterThanMaxUInt16 && m_values.size() == 1))
// There should be no trailing zeros (unless this value is zero!).
&& (m_values.last() || m_values.size() == 1);
}
// The internal storage of the number. This vector is always at least one entry in size,
// with the first entry holding the portion of the number greater than zero. The first
// value always hold a value in the uint16_t range, or holds the value oneGreaterThanMaxUInt16 to
// indicate the value has overflowed to >= 0x10000. If the units value is oneGreaterThanMaxUInt16,
// there can be no fraction (size must be 1).
//
// Subsequent values in the array represent portions of the fractional part of this number.
// The total value of the number is the sum of (m_values[i] / pow(2^32, i)), for each i
// in the array. The vector should contain no trailing zeros, except for the value '0',
// represented by a vector contianing a single zero value. These constraints are checked
// by 'checkConsistency()', above.
//
// The inline capacity of the vector is set to be able to contain any IEEE double (1 for
// the units column, 32 for zeros introduced due to an exponent up to -3FE, and 2 for
// bits taken from the mantissa).
Vector<uint32_t, 36> m_values;
// Cache a count of the number of leading zeros in m_values. We can use this to optimize
// methods that would otherwise need visit all words in the vector, e.g. multiplication.
size_t m_leadingZeros;
};
}
#endif