|
|
|
#ifndef __FIXED_H_
|
|
#define __FIXED_H_
|
|
|
|
#define __STDC_FORMAT_MACROS
|
|
|
|
#include <cctype>
|
|
#include <cmath>
|
|
#include <cinttypes>
|
|
#include <cstdio>
|
|
#include <cstdint>
|
|
#include <cstdlib>
|
|
#include <iomanip>
|
|
#include <iostream>
|
|
#include <limits>
|
|
#include <sstream>
|
|
#include <stdexcept>
|
|
#include <type_traits>
|
|
#include <map>
|
|
|
|
|
|
#if __GNUC__ >= 3
|
|
#define __unlikely(cond) __builtin_expect((cond), 0)
|
|
#define __likely(cond) __builtin_expect((cond), 1)
|
|
#else
|
|
#define __unlikely(cond) (cond)
|
|
#define __likely(cond) (cond)
|
|
#endif
|
|
|
|
template<typename T>
|
|
constexpr T calculateMax(size_t decimal_digits)
|
|
{
|
|
T val = 0;
|
|
for (uint32_t idx = 0; idx < decimal_digits; ++idx)
|
|
{
|
|
val *= 10;
|
|
val += 9;
|
|
}
|
|
return val;
|
|
}
|
|
|
|
|
|
template<typename IntegerType, typename FractionalType,
|
|
typename StrToIntegerTypeFunc,
|
|
typename StrToFracTypeFunc>
|
|
class fixed
|
|
{
|
|
static_assert(std::is_integral<IntegerType>::value,
|
|
"IntegerType must be an integral type");
|
|
static_assert(std::is_integral<FractionalType>::value,
|
|
"FractionalType must be an integral type");
|
|
|
|
static_assert(std::is_signed<IntegerType>::value,
|
|
"IntegerType must be a signed type");
|
|
static_assert(std::is_unsigned<FractionalType>::value,
|
|
"FractionalType must be an unsigned type");
|
|
|
|
public:
|
|
|
|
static constexpr size_t integer_bits = sizeof(IntegerType) * 8;
|
|
static constexpr size_t fractional_bits = sizeof(FractionalType) * 8;
|
|
|
|
static constexpr size_t integer_decimal_digits =
|
|
std::floor(std::log10(std::numeric_limits<IntegerType>::max()));
|
|
static constexpr size_t fractional_decimal_digits =
|
|
std::floor(std::log10(std::numeric_limits<FractionalType>::max()));
|
|
|
|
static constexpr IntegerType MAX_INTEGER_VALUE =
|
|
(calculateMax<IntegerType>(integer_decimal_digits));
|
|
static constexpr IntegerType MIN_INTEGER_VALUE = 0;
|
|
|
|
static constexpr FractionalType MAX_FRACTIONAL_VALUE =
|
|
(calculateMax<FractionalType>(fractional_decimal_digits));
|
|
static constexpr FractionalType MIN_FRACTIONAL_VALUE = 0;
|
|
|
|
static const uint64_t SCALE_VALUES[20];
|
|
static const std::map<uint64_t, uint32_t> DIGIT_LOOKUP_TABLE;
|
|
|
|
// Constructors
|
|
fixed()
|
|
: m_integer(0),
|
|
m_fractional(0)
|
|
{}
|
|
|
|
fixed(IntegerType integerVal)
|
|
: m_integer(__checkIntOverflow(integerVal)),
|
|
m_fractional(0)
|
|
{}
|
|
|
|
fixed(IntegerType integerVal, FractionalType fractionalVal)
|
|
: m_integer(__checkIntOverflow(integerVal)),
|
|
m_fractional(__checkFracOverflow(fractionalVal))
|
|
{
|
|
// Scale the fractional value appropriately
|
|
m_fractional = __checkFracOverflow(m_fractional *
|
|
getFracScaleValue(m_fractional));
|
|
}
|
|
|
|
fixed(IntegerType integerVal, FractionalType fractionalVal, uint32_t leadingZeros)
|
|
: m_integer(__checkIntOverflow(integerVal)),
|
|
m_fractional(__checkFracOverflow(fractionalVal))
|
|
{
|
|
// Scale the fractional value appropriately
|
|
m_fractional = __checkFracOverflow(m_fractional *
|
|
getFracScaleValue(m_fractional,
|
|
leadingZeros));
|
|
}
|
|
|
|
// Default copy constructor, and assignment operator
|
|
fixed(const fixed&) = default;
|
|
fixed& operator=(const fixed&) = default;
|
|
|
|
// Reassign value to type with a prescaled fractional value.
|
|
void assign(IntegerType integerVal, FractionalType fractionalVal)
|
|
{
|
|
m_integer = __checkIntOverflow(integerVal);
|
|
|
|
// Fractional value is prescaled to fractional type precision
|
|
m_fractional = __checkFracOverflow(fractionalVal);
|
|
}
|
|
|
|
// Assign a new value with an *unscaled* fractional part (NOTE: use the
|
|
// "leadingZeros" parameter to represent the number of leading zeros in the
|
|
// unscaled fractional part.
|
|
void assignUnscaledFrac(
|
|
IntegerType integerVal,
|
|
FractionalType fractionalVal,
|
|
uint32_t leadingZeros=0)
|
|
{
|
|
m_integer = __checkIntOverflow(integerVal);
|
|
|
|
// Scale the fractional value appropriately
|
|
m_fractional = __checkFracOverflow(fractionalVal *
|
|
getFracScaleValue(fractionalVal,
|
|
leadingZeros));
|
|
}
|
|
|
|
// Parse value from string input
|
|
uint32_t parse(const char* input)
|
|
{
|
|
char* endPtr = nullptr;
|
|
m_integer = __checkIntOverflow(strto_inttype(input, &endPtr, 10));
|
|
m_fractional = 0;
|
|
|
|
if (std::isdigit(*endPtr))
|
|
{
|
|
throw std::out_of_range("Integer value is out of range.");
|
|
}
|
|
|
|
// If the ending char is a period we can now parse the fractional part
|
|
if (*endPtr == '.')
|
|
{
|
|
char* fracEndPtr = nullptr;
|
|
FractionalType fracTemp =
|
|
__checkFracOverflow(strto_fractype(endPtr + 1, &fracEndPtr, 10));
|
|
|
|
uint32_t fracLen = (fracEndPtr - endPtr) - 1;
|
|
fracLen = fractional_decimal_digits - fracLen;
|
|
|
|
m_fractional = __checkFracOverflow(fracTemp * SCALE_VALUES[fracLen]);
|
|
endPtr = fracEndPtr;
|
|
}
|
|
|
|
// Calculate and return overall length
|
|
return (endPtr - input);
|
|
}
|
|
|
|
void absval()
|
|
{
|
|
m_integer = abs(m_integer);
|
|
}
|
|
|
|
constexpr inline fixed operator-() const noexcept = delete;
|
|
constexpr inline fixed operator!() const noexcept = delete;
|
|
constexpr inline fixed operator~() const noexcept = delete;
|
|
inline fixed& operator+=(const fixed& y) noexcept = delete;
|
|
inline fixed& operator-=(const fixed& y) noexcept = delete;
|
|
inline fixed& operator*=(const fixed& y) noexcept = delete;
|
|
inline fixed& operator/=(const fixed& y) noexcept = delete;
|
|
|
|
// Comparison operators
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator==(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator!=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator<(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator>(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator<=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline bool operator>=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept;
|
|
|
|
// Divide by unsigned int
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend constexpr inline fixed<I, F, STI, STF> operator/(
|
|
const fixed<I, F, STI, STF>& x, const uint64_t& y);
|
|
|
|
// Output stream operator
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
friend inline std::ostream& operator<<(
|
|
std::ostream& os, const fixed<I, F, STI, STF>& rhs);
|
|
|
|
|
|
private:
|
|
|
|
static StrToIntegerTypeFunc strto_inttype;
|
|
static StrToFracTypeFunc strto_fractype;
|
|
|
|
static inline IntegerType __checkIntOverflow(IntegerType integerVal)
|
|
{
|
|
if (__unlikely(integerVal > MAX_INTEGER_VALUE))
|
|
{
|
|
std::ostringstream msg;
|
|
msg << "Integer value: " << integerVal << " exceeds maximum "
|
|
<< "integer range of type (" << MAX_INTEGER_VALUE << ")!";
|
|
throw std::out_of_range(msg.str());
|
|
}
|
|
return integerVal;
|
|
}
|
|
|
|
static inline FractionalType __checkFracOverflow(FractionalType fractionalVal)
|
|
{
|
|
if (__unlikely(fractionalVal > MAX_FRACTIONAL_VALUE))
|
|
{
|
|
std::ostringstream msg;
|
|
msg << "Fractional value: " << fractionalVal << " exceeds maximum "
|
|
<< "fractional range of type (" << MAX_FRACTIONAL_VALUE << ")!";
|
|
throw std::out_of_range(msg.str());
|
|
}
|
|
return fractionalVal;
|
|
}
|
|
|
|
public:
|
|
// Helper function to get the approprate scale value for an unscaled input
|
|
// value of the fractional type
|
|
static inline FractionalType getFracScaleValue(
|
|
FractionalType value,
|
|
uint32_t leadingZeros=0)
|
|
{
|
|
uint32_t index = fractional_decimal_digits -
|
|
(DIGIT_LOOKUP_TABLE.upper_bound(value)->second +
|
|
leadingZeros);
|
|
return SCALE_VALUES[index];
|
|
}
|
|
|
|
public:
|
|
IntegerType m_integer;
|
|
FractionalType m_fractional;
|
|
};
|
|
|
|
// Functor for calling std::strtoll()
|
|
struct strtoll_ftor {
|
|
inline int64_t operator()(const char* str, char** str_end, int base)
|
|
{
|
|
return std::strtoll(str, str_end, base);
|
|
}
|
|
};
|
|
|
|
// Functor for calling std::strtoull()
|
|
struct strtoull_ftor {
|
|
inline uint64_t operator()(const char* str, char** str_end, int base)
|
|
{
|
|
return std::strtoull(str, str_end, base);
|
|
}
|
|
};
|
|
|
|
// Predefined types
|
|
using fixed_8_8 = fixed<int8_t, uint8_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_8_16 = fixed<int8_t, uint16_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_8_32 = fixed<int8_t, uint32_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_8_64 = fixed<int8_t, uint64_t, strtoll_ftor, strtoull_ftor>;
|
|
|
|
using fixed_16_8 = fixed<int16_t, uint8_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_16_16 = fixed<int16_t, uint16_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_16_32 = fixed<int16_t, uint32_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_16_64 = fixed<int16_t, uint64_t, strtoll_ftor, strtoull_ftor>;
|
|
|
|
using fixed_32_8 = fixed<int32_t, uint8_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_32_16 = fixed<int32_t, uint16_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_32_32 = fixed<int32_t, uint32_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_32_64 = fixed<int32_t, uint64_t, strtoll_ftor, strtoull_ftor>;
|
|
|
|
using fixed_64_8 = fixed<int64_t, uint8_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_64_16 = fixed<int64_t, uint16_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_64_32 = fixed<int64_t, uint32_t, strtoll_ftor, strtoull_ftor>;
|
|
using fixed_64_64 = fixed<int64_t, uint64_t, strtoll_ftor, strtoull_ftor>;
|
|
|
|
// Precomputed scale value constants
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
const uint64_t fixed<I, F, STI, STF>::SCALE_VALUES[20] =
|
|
{
|
|
/* 0 */ 1ULL,
|
|
/* 1 */ 10ULL,
|
|
/* 2 */ 100ULL,
|
|
/* 3 */ 1000ULL,
|
|
/* 4 */ 10000ULL,
|
|
/* 5 */ 100000ULL,
|
|
/* 6 */ 1000000ULL,
|
|
/* 7 */ 10000000ULL,
|
|
/* 8 */ 100000000ULL,
|
|
/* 9 */ 1000000000ULL,
|
|
/* 10 */ 10000000000ULL,
|
|
/* 11 */ 100000000000ULL,
|
|
/* 12 */ 1000000000000ULL,
|
|
/* 13 */ 10000000000000ULL,
|
|
/* 14 */ 100000000000000ULL,
|
|
/* 15 */ 1000000000000000ULL,
|
|
/* 16 */ 10000000000000000ULL,
|
|
/* 17 */ 100000000000000000ULL,
|
|
/* 18 */ 1000000000000000000ULL,
|
|
/* 19 */ 10000000000000000000ULL
|
|
};
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
const std::map<uint64_t, uint32_t> fixed<I, F, STI, STF>::DIGIT_LOOKUP_TABLE{
|
|
{1ULL, 0},
|
|
{10ULL, 1},
|
|
{100ULL, 2},
|
|
{1000ULL, 3},
|
|
{10000ULL, 4},
|
|
{100000ULL, 5},
|
|
{1000000ULL, 6},
|
|
{10000000ULL, 7},
|
|
{100000000ULL, 8},
|
|
{1000000000ULL, 9},
|
|
{10000000000ULL, 10},
|
|
{100000000000ULL, 11},
|
|
{1000000000000ULL, 12},
|
|
{10000000000000ULL, 13},
|
|
{100000000000000ULL, 14},
|
|
{1000000000000000ULL, 15},
|
|
{10000000000000000ULL, 16},
|
|
{100000000000000000ULL, 17},
|
|
{1000000000000000000ULL, 18},
|
|
{std::numeric_limits<uint64_t>::max(), 19} // Special case for uint64_t max value
|
|
};
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator==(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
return (x.m_integer == y.m_integer && x.m_fractional == y.m_fractional);
|
|
}
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator!=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
return (! (x == y));
|
|
}
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator<(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
if (x.m_integer == y.m_integer)
|
|
{
|
|
return (x.m_fractional < y.m_fractional);
|
|
}
|
|
else
|
|
{
|
|
return (x.m_integer < y.m_integer);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator>(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
if (x.m_integer == y.m_integer)
|
|
{
|
|
return (x.m_fractional > y.m_fractional);
|
|
}
|
|
else
|
|
{
|
|
return (x.m_integer > y.m_integer);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator<=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
if (x.m_integer == y.m_integer)
|
|
{
|
|
return (x.m_fractional <= y.m_fractional);
|
|
}
|
|
else
|
|
{
|
|
return (x.m_integer < y.m_integer);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline bool operator>=(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept
|
|
{
|
|
if (x.m_integer == y.m_integer)
|
|
{
|
|
return (x.m_fractional >= y.m_fractional);
|
|
}
|
|
else
|
|
{
|
|
return (x.m_integer > y.m_integer);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
// Addition -- not yet supported
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline fixed<I, F, STI, STF> operator+(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
|
|
|
|
// Subtraction -- not yet supported
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline fixed<I, F, STI, STF> operator-(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
|
|
|
|
// Multiplication -- not yet supported
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline fixed<I, F, STI, STF> operator*(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
|
|
|
|
// Division -- not yet supported
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline fixed<I, F, STI, STF> operator/(
|
|
const fixed<I, F, STI, STF>& x, const fixed<I, F, STI, STF>& y) noexcept = delete;
|
|
|
|
// Division by unsigned int
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
constexpr inline fixed<I, F, STI, STF> operator/(
|
|
const fixed<I, F, STI, STF>& x, const uint64_t& y)
|
|
{
|
|
fixed<I, F, STI, STF> newVal;
|
|
newVal.m_integer = x.m_integer / y;
|
|
newVal.m_fractional = x.m_integer % y;
|
|
newVal.m_fractional *= x.getFracScaleValue(newVal.m_fractional);
|
|
newVal.m_fractional += x.m_fractional / y;
|
|
return newVal;
|
|
}
|
|
|
|
// Stream output
|
|
template<typename I, typename F, typename STI, typename STF>
|
|
inline std::ostream& operator<<(std::ostream& os, const fixed<I, F, STI, STF>& rhs)
|
|
{
|
|
#if 0
|
|
// Print full fractional precision always (even with trailing zeros)
|
|
return os << std::fixed << rhs.m_integer << "."
|
|
<< std::setw(fixed<I, F, STI, STF>::fractional_decimal_digits)
|
|
<< std::setfill('0') << rhs.m_fractional;
|
|
#else
|
|
// Print fractional part without trailing zeros
|
|
char buffer[fixed<I, F, STI, STF>::fractional_decimal_digits + 1]{};
|
|
std::snprintf(buffer, fixed<I, F, STI, STF>::fractional_decimal_digits + 1,
|
|
"%" PRIu64, rhs.m_fractional);
|
|
|
|
// NOTE: if fractional part is zero always print at least one zero
|
|
int idx = fixed<I, F, STI, STF>::fractional_decimal_digits;
|
|
bool found = false;
|
|
for (; idx >= 0; --idx)
|
|
{
|
|
if (std::isdigit(buffer[idx]) && buffer[idx] != '0')
|
|
{
|
|
found = true;
|
|
break;
|
|
}
|
|
}
|
|
if (found)
|
|
{
|
|
buffer[idx + 1] = '\0';
|
|
}
|
|
|
|
uint32_t leadingZeros =
|
|
fixed<I, F, STI, STF>::fractional_decimal_digits -
|
|
fixed<I, F, STI, STF>::DIGIT_LOOKUP_TABLE.upper_bound(rhs.m_fractional)->second;
|
|
|
|
// Output any leading zeros
|
|
os << std::fixed << rhs.m_integer << ".";
|
|
for (uint32_t idx = 0; idx < leadingZeros; ++idx)
|
|
{
|
|
os << "0";
|
|
}
|
|
|
|
return os << buffer;
|
|
#endif
|
|
}
|
|
|
|
#endif // FIXED_H_
|