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#ifndef __FIXED_H_
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#define __FIXED_H_
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#define __STDC_FORMAT_MACROS
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#include <cctype>
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#include <cmath>
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#include <cinttypes>
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#include <cstdio>
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#include <cstdint>
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#include <cstdlib>
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#include <iomanip>
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#include <iostream>
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#include <limits>
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#include <sstream>
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#include <stdexcept>
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#include <type_traits>
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#include <map>
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#if __GNUC__ >= 3
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#define __unlikely(cond) __builtin_expect((cond), 0)
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#define __likely(cond) __builtin_expect((cond), 1)
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#else
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#define __unlikely(cond) (cond)
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#define __likely(cond) (cond)
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#endif
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// Defaults for compile time options
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#ifndef BEHAVIOR_PARSE_TRUNCATE
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#define BEHAVIOR_PARSE_TRUNCATE 0 // Default: disable
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#endif
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#ifndef SUPPORT_PARSE_EXPONENT
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#define SUPPORT_PARSE_EXPONENT 1 // Default: enable
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#endif
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template<typename T>
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constexpr T calculateMax(size_t decimal_digits)
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{
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T val = 0;
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for (uint32_t idx = 0; idx < decimal_digits; ++idx)
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{
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val *= 10;
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val += 9;
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}
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return val;
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}
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template<typename IntegerType, typename FractionalType,
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typename StrToIntegerTypeFunc,
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typename StrToFracTypeFunc>
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class fixed
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{
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static_assert(std::is_integral<IntegerType>::value,
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"IntegerType must be an integral type");
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static_assert(std::is_integral<FractionalType>::value,
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"FractionalType must be an integral type");
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static_assert(std::is_signed<IntegerType>::value,
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"IntegerType must be a signed type");
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static_assert(std::is_unsigned<FractionalType>::value,
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"FractionalType must be an unsigned type");
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public:
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static constexpr size_t integer_bits = sizeof(IntegerType) * 8;
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static constexpr size_t fractional_bits = sizeof(FractionalType) * 8;
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static constexpr size_t integer_decimal_digits =
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std::floor(std::log10(std::numeric_limits<IntegerType>::max()));
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static constexpr size_t fractional_decimal_digits =
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std::floor(std::log10(std::numeric_limits<FractionalType>::max()));
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static constexpr size_t total_decimal_digits = integer_decimal_digits +
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fractional_decimal_digits;
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static constexpr IntegerType MAX_INTEGER_VALUE =
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(calculateMax<IntegerType>(integer_decimal_digits));
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static constexpr IntegerType MIN_INTEGER_VALUE = 0;
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static constexpr FractionalType MAX_FRACTIONAL_VALUE =
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(calculateMax<FractionalType>(fractional_decimal_digits));
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static constexpr FractionalType MIN_FRACTIONAL_VALUE = 0;
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static constexpr IntegerType NEGATIVE_ZERO = MAX_INTEGER_VALUE + 2;
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static const uint64_t SCALE_VALUES[20];
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static const std::map<uint64_t, uint32_t> DIGIT_LOOKUP_TABLE;
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// Constructors
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explicit fixed()
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: m_integer(0),
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m_fractional(0)
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{}
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explicit fixed(IntegerType integerVal)
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: m_integer(__checkIntOverflow(integerVal)),
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m_fractional(0)
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{}
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explicit fixed(IntegerType integerVal, FractionalType fractionalVal)
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: m_integer(__checkIntOverflow(integerVal)),
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m_fractional(__checkFracOverflow(fractionalVal))
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{
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// Scale the fractional value appropriately
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m_fractional = __checkFracOverflow(m_fractional *
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getFracScaleValue(m_fractional));
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}
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explicit fixed(IntegerType integerVal, FractionalType fractionalVal, uint32_t leadingZeros)
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: m_integer(__checkIntOverflow(integerVal)),
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m_fractional(__checkFracOverflow(fractionalVal))
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{
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// Scale the fractional value appropriately
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m_fractional = __checkFracOverflow(m_fractional *
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getFracScaleValue(m_fractional,
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leadingZeros));
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}
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// Default copy constructor, and assignment operator
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fixed(const fixed&) = default;
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fixed& operator=(const fixed&) = default;
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// Reassign value to type with a prescaled fractional value.
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void assign(IntegerType integerVal, FractionalType fractionalVal)
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{
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m_integer = __checkIntOverflow(integerVal);
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// Fractional value is prescaled to fractional type precision
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m_fractional = __checkFracOverflow(fractionalVal);
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}
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// Assign a new value with an *unscaled* fractional part (NOTE: use the
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// "leadingZeros" parameter to represent the number of leading zeros in the
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// unscaled fractional part.
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void assignUnscaledFrac(
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IntegerType integerVal,
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FractionalType fractionalVal,
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uint32_t leadingZeros=0)
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{
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m_integer = __checkIntOverflow(integerVal);
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// Scale the fractional value appropriately
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m_fractional = __checkFracOverflow(fractionalVal *
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getFracScaleValue(fractionalVal,
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leadingZeros));
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}
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// Parse value from string input
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uint32_t parse(const char* input)
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{
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char* endPtr = nullptr;
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m_integer = __checkIntOverflow(strto_inttype(input, &endPtr, 10));
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m_fractional = 0;
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bool negativeZeroFlag = false;
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if (std::isdigit(*endPtr))
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{
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throw std::out_of_range("Integer value is out of range.");
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}
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// Check for negative zero corner case with leading zero digit
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if (__unlikely(m_integer == 0 && endPtr - input >= 2 && *(endPtr - 2) == '-'))
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{
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negativeZeroFlag = true;
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}
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// If the ending char is a period we can now parse the fractional part
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uint32_t fracLen = 0;
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if (*endPtr == '.'|| (endPtr[0] == '-' && endPtr[1] == '.'))
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{
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// Check for negative zero corner case without leading zero digit
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if (__unlikely(endPtr[0] == '-'))
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{
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++endPtr;
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negativeZeroFlag = true;
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}
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char* fracEndPtr = nullptr;
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FractionalType fracTemp =
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__checkFracOverflow(strto_fractype(endPtr + 1, &fracEndPtr, 10));
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fracLen = (fracEndPtr - endPtr) - 1;
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if (__unlikely(fracLen > fractional_decimal_digits))
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{
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#if BEHAVIOR_PARSE_TRUNCATE
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// Fractional length exceeds supported number of fractional
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// decimal digits, downscale value to only include supported
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// number of digits
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uint32_t idx = fracLen - fractional_decimal_digits;
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m_fractional = fracTemp / SCALE_VALUES[idx];
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#else
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throw std::out_of_range("Fractional length exceeds supported "
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"number of fractional decimal digits.");
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#endif
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}
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else
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{
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uint32_t idx = fractional_decimal_digits - fracLen;
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m_fractional = __checkFracOverflow(fracTemp * SCALE_VALUES[idx]);
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}
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endPtr = fracEndPtr;
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}
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#if SUPPORT_PARSE_EXPONENT
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// Attempt to parse exponent
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if (*endPtr == 'e' || *endPtr == 'E')
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{
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// Set negative zero flag here if integer part is negative then
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// clear below if final integer part after exponent adjustment is
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// not zero
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if (m_integer < 0)
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{
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negativeZeroFlag = true;
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}
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char* expEndPtr = nullptr;
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long exponent = strtol(++endPtr, &expEndPtr, 10);
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uint32_t integerLen = 0;
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if (m_integer != 0)
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{
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integerLen = DIGIT_LOOKUP_TABLE.upper_bound(std::abs(m_integer))->second;
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}
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uint32_t scaledFracLen =
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DIGIT_LOOKUP_TABLE.upper_bound(m_fractional)->second;
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if (exponent >= 0)
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{
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// Detect potential overflow based on the exponent
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if ((m_integer != 0) &&
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(integerLen + static_cast<size_t>(exponent)) >
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integer_decimal_digits)
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{
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throw std::out_of_range("Positive exponent exceeds maximum"
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" decimal digit range.");
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}
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else if (scaledFracLen + static_cast<size_t>(exponent)
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> total_decimal_digits)
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{
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throw std::out_of_range("Positive exponent exceeds maximum"
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" decimal digit range (2).");
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}
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long fracExponent = exponent;
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if (static_cast<size_t>(fracExponent) > fractional_decimal_digits)
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{
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fracExponent = fractional_decimal_digits;
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}
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bool intZeroFlag = true;
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if (m_integer != 0)
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{
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// Rescale integer value if it is greater than zero
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intZeroFlag = false;
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m_integer *= static_cast<IntegerType>(SCALE_VALUES[exponent]);
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}
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uint64_t scaler = SCALE_VALUES[fractional_decimal_digits -
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fracExponent];
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IntegerType temp = m_fractional / scaler;
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m_integer += temp;
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m_fractional -= (temp * scaler);
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m_fractional *= SCALE_VALUES[fracExponent];
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if (intZeroFlag)
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{
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// Rescale integer value if it was zero
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m_integer *= SCALE_VALUES[exponent - fracExponent];
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}
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}
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else
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{
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// Handle negative exponent
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// Detect potential overflow based on the exponent
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if (m_fractional != 0 &&
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(static_cast<size_t>(-exponent) >
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(fractional_decimal_digits - fracLen)))
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{
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throw std::out_of_range("Negative exponent exceeds maximum"
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" decimal digit range.");
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}
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else if (static_cast<size_t>(-exponent) >=
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(integerLen + fractional_decimal_digits))
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{
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throw std::out_of_range("Negative exponent exceeds maximum"
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" decimal digit range.");
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}
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FractionalType temp = 0;
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if (m_fractional != 0)
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{
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// CASE 1: fractional non-zero
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m_fractional /= SCALE_VALUES[-exponent];
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temp = std::abs(m_integer) % SCALE_VALUES[-exponent];
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temp *= SCALE_VALUES[fractional_decimal_digits + exponent];
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m_integer /= static_cast<IntegerType>(SCALE_VALUES[-exponent]);
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m_fractional += temp;
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}
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else
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{
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// CASE 2: fractional zero
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long intExponent = std::abs(exponent);
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if (static_cast<size_t>(intExponent) > integer_decimal_digits)
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{
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intExponent = integer_decimal_digits;
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}
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temp = std::abs(m_integer) % SCALE_VALUES[intExponent];
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temp *= SCALE_VALUES[fractional_decimal_digits - intExponent];
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m_integer /= SCALE_VALUES[intExponent];
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m_fractional += temp;
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if (std::abs(exponent) > intExponent)
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{
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long fracExponent = std::abs(exponent) - intExponent;
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m_fractional /= SCALE_VALUES[fracExponent];
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}
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}
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}
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// Clear negative zero flag if final adjusted integer part is not
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// zero. Flag will remain set iff initial integer part was negative
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// and integer part after exponent adjustment is zero.
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if (__likely(m_integer != 0))
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{
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negativeZeroFlag = false;
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}
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}
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#endif
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if (__unlikely(negativeZeroFlag))
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{
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m_integer = NEGATIVE_ZERO;
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}
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// Calculate and return overall length
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return (endPtr - input);
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}
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constexpr inline void absval()
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{
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if (__unlikely(m_integer == NEGATIVE_ZERO))
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{
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m_integer = 0;
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}
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else
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{
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m_integer = std::abs(m_integer);
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}
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}
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// This is modeled after std::signbit() for floating point types
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constexpr inline bool signbit() const
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{
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return (m_integer < 0 || m_integer == NEGATIVE_ZERO);
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}
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constexpr inline void negate()
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{
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if (__unlikely(m_integer == 0))
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{
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m_integer = NEGATIVE_ZERO;
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}
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else
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{
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m_integer *= -1;
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}
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}
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// Disallow conversion operators (for now)
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explicit operator int() = delete;
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explicit operator float() = delete;
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explicit operator double() = delete;
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constexpr inline fixed operator-() const noexcept = delete;
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constexpr inline fixed operator!() const noexcept = delete;
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constexpr inline fixed operator~() const noexcept = delete;
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inline fixed& operator+=(const fixed& y) noexcept = delete;
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inline fixed& operator-=(const fixed& y) noexcept = delete;
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inline fixed& operator*=(const fixed& y) noexcept = delete;
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inline fixed& operator/=(const fixed& y) noexcept = delete;
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// Comparison operators
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator==(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator!=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator<(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator>(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator<=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline bool operator>=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
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// Divide by unsigned int
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template<typename I, typename F, typename STI, typename STF>
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friend constexpr inline fixed<I, F, STI, STF> operator/(
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const fixed<I, F, STI, STF>& x, const int64_t& y);
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// Output stream operator
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template<typename I, typename F, typename STI, typename STF>
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friend inline std::ostream& operator<<(
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std::ostream& os, const fixed<I, F, STI, STF>& rhs);
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private:
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static StrToIntegerTypeFunc strto_inttype;
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static StrToFracTypeFunc strto_fractype;
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static inline IntegerType __checkIntOverflow(IntegerType integerVal)
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{
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if (__unlikely(integerVal > MAX_INTEGER_VALUE))
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{
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std::ostringstream msg;
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msg << "Integer value: " << integerVal << " exceeds maximum "
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<< "integer range of type (" << MAX_INTEGER_VALUE << ")!";
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throw std::out_of_range(msg.str());
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}
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return integerVal;
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}
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static inline FractionalType __checkFracOverflow(FractionalType fractionalVal)
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{
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if (__unlikely(fractionalVal > MAX_FRACTIONAL_VALUE))
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{
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std::ostringstream msg;
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msg << "Fractional value: " << fractionalVal << " exceeds maximum "
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<< "fractional range of type (" << MAX_FRACTIONAL_VALUE << ")!";
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throw std::out_of_range(msg.str());
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}
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return fractionalVal;
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}
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// Helper function to get the approprate scale value for an unscaled input
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// value of the fractional type
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static inline FractionalType getFracScaleValue(
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FractionalType value,
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uint32_t leadingZeros=0)
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{
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uint32_t index = fractional_decimal_digits -
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(DIGIT_LOOKUP_TABLE.upper_bound(value)->second +
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leadingZeros);
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return SCALE_VALUES[index];
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}
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IntegerType m_integer;
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FractionalType m_fractional;
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};
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// Functor for calling std::strtoll()
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struct strtoll_ftor {
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inline int64_t operator()(const char* str, char** str_end, int base)
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{
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return std::strtoll(str, str_end, base);
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}
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};
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// Functor for calling std::strtoull()
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struct strtoull_ftor {
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inline uint64_t operator()(const char* str, char** str_end, int base)
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{
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return std::strtoull(str, str_end, base);
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}
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};
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// Predefined types
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using fixed_8_8 = fixed<int8_t, uint8_t, strtoll_ftor, strtoull_ftor>;
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using fixed_8_16 = fixed<int8_t, uint16_t, strtoll_ftor, strtoull_ftor>;
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using fixed_8_32 = fixed<int8_t, uint32_t, strtoll_ftor, strtoull_ftor>;
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using fixed_8_64 = fixed<int8_t, uint64_t, strtoll_ftor, strtoull_ftor>;
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using fixed_16_8 = fixed<int16_t, uint8_t, strtoll_ftor, strtoull_ftor>;
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using fixed_16_16 = fixed<int16_t, uint16_t, strtoll_ftor, strtoull_ftor>;
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using fixed_16_32 = fixed<int16_t, uint32_t, strtoll_ftor, strtoull_ftor>;
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using fixed_16_64 = fixed<int16_t, uint64_t, strtoll_ftor, strtoull_ftor>;
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using fixed_32_8 = fixed<int32_t, uint8_t, strtoll_ftor, strtoull_ftor>;
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using fixed_32_16 = fixed<int32_t, uint16_t, strtoll_ftor, strtoull_ftor>;
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using fixed_32_32 = fixed<int32_t, uint32_t, strtoll_ftor, strtoull_ftor>;
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using fixed_32_64 = fixed<int32_t, uint64_t, strtoll_ftor, strtoull_ftor>;
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using fixed_64_8 = fixed<int64_t, uint8_t, strtoll_ftor, strtoull_ftor>;
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using fixed_64_16 = fixed<int64_t, uint16_t, strtoll_ftor, strtoull_ftor>;
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using fixed_64_32 = fixed<int64_t, uint32_t, strtoll_ftor, strtoull_ftor>;
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using fixed_64_64 = fixed<int64_t, uint64_t, strtoll_ftor, strtoull_ftor>;
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// Precomputed scale value constants
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template<typename I, typename F, typename STI, typename STF>
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const uint64_t fixed<I, F, STI, STF>::SCALE_VALUES[20] =
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{
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/* 0 */ 1ULL,
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/* 1 */ 10ULL,
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/* 2 */ 100ULL,
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/* 3 */ 1000ULL,
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/* 4 */ 10000ULL,
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/* 5 */ 100000ULL,
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/* 6 */ 1000000ULL,
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/* 7 */ 10000000ULL,
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/* 8 */ 100000000ULL,
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/* 9 */ 1000000000ULL,
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/* 10 */ 10000000000ULL,
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/* 11 */ 100000000000ULL,
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/* 12 */ 1000000000000ULL,
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/* 13 */ 10000000000000ULL,
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/* 14 */ 100000000000000ULL,
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/* 15 */ 1000000000000000ULL,
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/* 16 */ 10000000000000000ULL,
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/* 17 */ 100000000000000000ULL,
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/* 18 */ 1000000000000000000ULL,
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/* 19 */ 10000000000000000000ULL
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};
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template<typename I, typename F, typename STI, typename STF>
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const std::map<uint64_t, uint32_t> fixed<I, F, STI, STF>::DIGIT_LOOKUP_TABLE{
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{1ULL, 0},
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{10ULL, 1},
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{100ULL, 2},
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{1000ULL, 3},
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{10000ULL, 4},
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{100000ULL, 5},
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{1000000ULL, 6},
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{10000000ULL, 7},
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{100000000ULL, 8},
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{1000000000ULL, 9},
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{10000000000ULL, 10},
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{100000000000ULL, 11},
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{1000000000000ULL, 12},
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{10000000000000ULL, 13},
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{100000000000000ULL, 14},
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{1000000000000000ULL, 15},
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{10000000000000000ULL, 16},
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{100000000000000000ULL, 17},
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{1000000000000000000ULL, 18},
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{std::numeric_limits<uint64_t>::max(), 19} // Special case for uint64_t max value
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};
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator==(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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return (x.m_integer == y.m_integer && x.m_fractional == y.m_fractional);
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}
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator!=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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return (! (x == y));
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}
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator<(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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if (x.signbit() && (! y.signbit()))
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{
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return true;
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}
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else if ((! x.signbit()) && y.signbit())
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{
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return false;
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}
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else
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{
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I integerX = x.m_integer;
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if (__unlikely((x.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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integerX = 0;
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}
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I integerY = y.m_integer;
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if (__unlikely((y.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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integerY = 0;
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}
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if (integerX == integerY)
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{
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return (x.m_fractional < y.m_fractional);
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}
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else
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{
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return (integerX < integerY);
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}
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}
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return false;
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}
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator>(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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if (x.signbit() && (! y.signbit()))
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{
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return false;
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}
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else if ((! x.signbit()) && y.signbit())
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{
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return true;
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}
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else
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{
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I integerX = x.m_integer;
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if (__unlikely((x.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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integerX = 0;
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}
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I integerY = y.m_integer;
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if (__unlikely((y.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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integerY = 0;
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}
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if (integerX == integerY)
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{
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return (x.m_fractional > y.m_fractional);
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}
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else
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{
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return (integerX > integerY);
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}
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}
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return false;
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}
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator<=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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return (x == y || x < y);
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}
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline bool operator>=(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
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{
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return (x == y || x > y);
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}
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// Addition -- not yet supported
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline fixed<I, F, STI, STF> operator+(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
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// Subtraction -- not yet supported
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline fixed<I, F, STI, STF> operator-(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
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// Multiplication -- not yet supported
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline fixed<I, F, STI, STF> operator*(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
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// Division -- not yet supported
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline fixed<I, F, STI, STF> operator/(
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const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
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// Division by unsigned int
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template<typename I, typename F, typename STI, typename STF>
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constexpr inline fixed<I, F, STI, STF> operator/(
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const fixed<I, F, STI, STF>& x, const int64_t& y)
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{
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fixed<I, F, STI, STF> newVal;
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bool negativeDivisorFlag = (y < 0);
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bool negativeDividendFlag = (x.m_integer < 0) ||
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(x.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO);
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bool negativeZeroFlag = false;
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I integerX = x.m_integer;
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if (__unlikely((integerX == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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integerX = 0;
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negativeZeroFlag = true;
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}
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newVal.m_integer = integerX / y;
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newVal.m_fractional = std::abs(integerX) % y;
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newVal.m_fractional *= x.getFracScaleValue(newVal.m_fractional);
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newVal.m_fractional += x.m_fractional / std::abs(y);
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// Ensure quotient has correct sign value
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if (newVal.m_integer == 0 && negativeDividendFlag && negativeDivisorFlag)
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{
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newVal.m_integer = 0;
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}
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else if ((newVal.m_integer == 0 && (negativeDividendFlag || negativeDivisorFlag))
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|| __unlikely(negativeZeroFlag))
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{
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newVal.m_integer = fixed<I, F, STI, STF>::NEGATIVE_ZERO;
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}
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return newVal;
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}
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// Stream output
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template<typename I, typename F, typename STI, typename STF>
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inline std::ostream& operator<<(std::ostream& os, const fixed<I, F, STI, STF>& rhs)
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{
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#if 0
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// Print full fractional precision always (even with trailing zeros)
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return os << std::fixed << rhs.m_integer << "."
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<< std::setw(fixed<I, F, STI, STF>::fractional_decimal_digits)
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<< std::setfill('0') << rhs.m_fractional;
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#else
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// Print fractional part without trailing zeros
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char buffer[fixed<I, F, STI, STF>::fractional_decimal_digits + 1]{};
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std::snprintf(buffer, fixed<I, F, STI, STF>::fractional_decimal_digits + 1,
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"%" PRIu64, rhs.m_fractional);
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// NOTE: if fractional part is zero always print at least one zero
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int idx = fixed<I, F, STI, STF>::fractional_decimal_digits;
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bool found = false;
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for (; idx >= 0; --idx)
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{
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if (std::isdigit(buffer[idx]) && buffer[idx] != '0')
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{
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found = true;
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break;
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}
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}
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if (found || idx == -1)
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{
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buffer[idx + 1] = '\0';
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}
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uint32_t leadingZeros = (rhs.m_fractional == 0) ? 1 :
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fixed<I, F, STI, STF>::fractional_decimal_digits -
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fixed<I, F, STI, STF>::DIGIT_LOOKUP_TABLE.upper_bound(rhs.m_fractional)->second;
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// Handle special case of negative zero
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os << std::fixed;
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if (__unlikely((rhs.m_integer == fixed<I, F, STI, STF>::NEGATIVE_ZERO)))
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{
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os << "-0.";
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}
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else
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{
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os << rhs.m_integer << ".";
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}
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// Output any fractional leading zeros
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for (uint32_t idx = 0; idx < leadingZeros; ++idx)
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{
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os << "0";
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}
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return os << buffer;
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#endif
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}
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#endif // FIXED_H_
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