/* * 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. */ #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