Source/JavaScriptCore/runtime/Uint16WithFraction.h - external/github.com/WebKit/webkit - Git at Google

 /*
  * 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
  * 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.
  */

 #pragma once

 #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 && std::isfinite(number) && !std::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;
 };

 } // namespace JSC
	/*
	* 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
	* 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.
	*/

	#pragma once

	#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 && std::isfinite(number) && !std::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;
	};

	} // namespace JSC