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root/software/fixed/examples/fixed.hpp @ ef18eb33

835f4592 David Sorber
#ifndef FPM_FIXED_HPP
#define FPM_FIXED_HPP

#include <cassert>
#include <cmath>
#include <cstdint>
#include <functional>
#include <limits>
#include <type_traits>

namespace fpm
{

//! Fixed-point number type
//! \tparam BaseType the base integer type used to store the fixed-point number. This can be a signed or unsigned type.
//! \tparam IntermediateType the integer type used to store intermediate results during calculations.
//! \tparam FractionBits the number of bits of the BaseType used to store the fraction
template <typename BaseType, typename IntermediateType, unsigned int FractionBits>
class fixed
{
static_assert(std::is_integral<BaseType>::value, "BaseType must be an integral type");
static_assert(FractionBits > 0, "FractionBits must be greater than zero");
static_assert(FractionBits <= sizeof(BaseType) * 8, "BaseType must at least be able to contain entire fraction");
static_assert(FractionBits <= 62, "Fraction may be no more than 62 bits");
static_assert(sizeof(IntermediateType) > sizeof(BaseType), "IntermediateType must be larger than BaseType");
static_assert(std::is_signed<IntermediateType>::value == std::is_signed<BaseType>::value, "IntermediateType must have same signedness as BaseType");

static constexpr BaseType FRACTION_MULT = BaseType(1) << FractionBits;

struct raw_construct_tag {};
constexpr inline fixed(BaseType val, raw_construct_tag) noexcept : m_value(val) {}

public:
inline fixed() noexcept {}

// Converts an integral number to the fixed-point type.
// Like static_cast, this truncates bits that don't fit.
template <typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline explicit fixed(T val) noexcept
: m_value(static_cast<BaseType>(val * FRACTION_MULT))
{}

// Converts an floating-point number to the fixed-point type.
// Like static_cast, this truncates bits that don't fit.
template <typename T, typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
constexpr inline explicit fixed(T val) noexcept
: m_value(static_cast<BaseType>((val >= 0.0) ? (val * FRACTION_MULT + T{0.5}) : (val * FRACTION_MULT - T{0.5})))
{}

// Constructs from another fixed-point type with possibly different underlying representation.
// Like static_cast, this truncates bits that don't fit.
template <typename B, typename I, unsigned int F>
constexpr inline explicit fixed(fixed<B,I,F> val) noexcept
: m_value(from_fixed_point<F>(val.raw_value()).raw_value())
{}

// Explicit conversion to a floating-point type
template <typename T, typename std::enable_if<std::is_floating_point<T>::value>::type* = nullptr>
constexpr inline explicit operator T() const noexcept
{
return static_cast<T>(m_value) / FRACTION_MULT;
}

// Explicit conversion to an integral type
template <typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline explicit operator T() const noexcept
{
return static_cast<T>(m_value / FRACTION_MULT);
}

// Returns the raw underlying value of this type.
// Do not use this unless you know what you're doing.
constexpr inline BaseType raw_value() const noexcept
{
return m_value;
}

//! Constructs a fixed-point number from another fixed-point number.
//! \tparam NumFractionBits the number of bits used by the fraction in \a value.
//! \param value the integer fixed-point number
template <unsigned int NumFractionBits, typename T, typename std::enable_if<(NumFractionBits > FractionBits)>::type* = nullptr>
static constexpr inline fixed from_fixed_point(T value) noexcept
{
// To correctly round the last bit in the result, we need one more bit of information.
// We do this by multiplying by two before dividing and adding the LSB to the real result.
return fixed(static_cast<BaseType>(
value / (T(1) << (NumFractionBits - FractionBits)) +
(value / (T(1) << (NumFractionBits - FractionBits - 1)) % 2)),
raw_construct_tag{});
}

template <unsigned int NumFractionBits, typename T, typename std::enable_if<(NumFractionBits <= FractionBits)>::type* = nullptr>
static constexpr inline fixed from_fixed_point(T value) noexcept
{
return fixed(static_cast<BaseType>(
value * (T(1) << (FractionBits - NumFractionBits))),
raw_construct_tag{});
}

// Constructs a fixed-point number from its raw underlying value.
// Do not use this unless you know what you're doing.
static constexpr inline fixed from_raw_value(BaseType value) noexcept
{
return fixed(value, raw_construct_tag{});
}

//
// Constants
//
static constexpr fixed e() { return from_fixed_point<61>(6267931151224907085ll); }
static constexpr fixed pi() { return from_fixed_point<61>(7244019458077122842ll); }
static constexpr fixed half_pi() { return from_fixed_point<62>(7244019458077122842ll); }
static constexpr fixed two_pi() { return from_fixed_point<60>(7244019458077122842ll); }

//
// Arithmetic member operators
//

constexpr inline fixed operator-() const noexcept
{
return fixed::from_raw_value(-m_value);
}

inline fixed& operator+=(const fixed& y) noexcept
{
m_value += y.m_value;
return *this;
}

template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
inline fixed& operator+=(I y) noexcept
{
m_value += y * FRACTION_MULT;
return *this;
}

inline fixed& operator-=(const fixed& y) noexcept
{
m_value -= y.m_value;
return *this;
}

template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
inline fixed& operator-=(I y) noexcept
{
m_value -= y * FRACTION_MULT;
return *this;
}

inline fixed& operator*=(const fixed& y) noexcept
{
// Normal fixed-point multiplication is: x * y / 2**FractionBits.
// To correctly round the last bit in the result, we need one more bit of information.
// We do this by multiplying by two before dividing and adding the LSB to the real result.
auto value = (static_cast<IntermediateType>(m_value) * y.m_value) / (FRACTION_MULT / 2);
m_value = static_cast<BaseType>((value / 2) + (value % 2));
return *this;
}

template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
inline fixed& operator*=(I y) noexcept
{
m_value *= y;
return *this;
}

inline fixed& operator/=(const fixed& y) noexcept
{
assert(y.m_value != 0);
// Normal fixed-point division is: x * 2**FractionBits / y.
// To correctly round the last bit in the result, we need one more bit of information.
// We do this by multiplying by two before dividing and adding the LSB to the real result.
auto value = (static_cast<IntermediateType>(m_value) * FRACTION_MULT * 2) / y.m_value;
m_value = static_cast<BaseType>((value / 2) + (value % 2));
return *this;
}

template <typename I, typename std::enable_if<std::is_integral<I>::value>::type* = nullptr>
inline fixed& operator/=(I y) noexcept
{
m_value /= y;
return *this;
}

private:
BaseType m_value;
};

//
// Convenience typedefs
//

using fixed_16_16 = fixed<std::int32_t, std::int64_t, 16>;
using fixed_24_8 = fixed<std::int32_t, std::int64_t, 8>;
using fixed_8_24 = fixed<std::int32_t, std::int64_t, 24>;

//
// Addition
//

template <typename B, typename I, unsigned int F>
constexpr inline fixed<B, I, F> operator+(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) += y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator+(const fixed<B, I, F>& x, T y) noexcept
{
return fixed<B, I, F>(x) += y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator+(T x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(y) += x;
}

//
// Subtraction
//

template <typename B, typename I, unsigned int F>
constexpr inline fixed<B, I, F> operator-(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) -= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator-(const fixed<B, I, F>& x, T y) noexcept
{
return fixed<B, I, F>(x) -= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator-(T x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) -= y;
}

//
// Multiplication
//

template <typename B, typename I, unsigned int F>
constexpr inline fixed<B, I, F> operator*(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) *= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator*(const fixed<B, I, F>& x, T y) noexcept
{
return fixed<B, I, F>(x) *= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator*(T x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(y) *= x;
}

//
// Division
//

template <typename B, typename I, unsigned int F>
constexpr inline fixed<B, I, F> operator/(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) /= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator/(const fixed<B, I, F>& x, T y) noexcept
{
return fixed<B, I, F>(x) /= y;
}

template <typename B, typename I, unsigned int F, typename T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr>
constexpr inline fixed<B, I, F> operator/(T x, const fixed<B, I, F>& y) noexcept
{
return fixed<B, I, F>(x) /= y;
}

//
// Comparison operators
//

template <typename B, typename I, unsigned int F>
constexpr inline bool operator==(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() == y.raw_value();
}

template <typename B, typename I, unsigned int F>
constexpr inline bool operator!=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() != y.raw_value();
}

template <typename B, typename I, unsigned int F>
constexpr inline bool operator<(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() < y.raw_value();
}

template <typename B, typename I, unsigned int F>
constexpr inline bool operator>(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() > y.raw_value();
}

template <typename B, typename I, unsigned int F>
constexpr inline bool operator<=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() <= y.raw_value();
}

template <typename B, typename I, unsigned int F>
constexpr inline bool operator>=(const fixed<B, I, F>& x, const fixed<B, I, F>& y) noexcept
{
return x.raw_value() >= y.raw_value();
}

namespace detail
{
// Number of base-10 digits required to fully represent a number of bits
static constexpr int max_digits10(int bits)
{
// 8.24 fixed-point equivalent of (int)ceil(bits * std::log10(2));
using T = long long;
return static_cast<int>((T{bits} * 5050445 + (T{1} << 24) - 1) >> 24);
}

// Number of base-10 digits that can be fully represented by a number of bits
static constexpr int digits10(int bits)
{
// 8.24 fixed-point equivalent of (int)(bits * std::log10(2));
using T = long long;
return static_cast<int>((T{bits} * 5050445) >> 24);
}

} // namespace detail
} // namespace fpm

// Specializations for customization points
namespace std
{

template <typename B, typename I, unsigned int F>
struct hash<fpm::fixed<B,I,F>>
{
using argument_type = fpm::fixed<B, I, F>;
using result_type = std::size_t;

result_type operator()(argument_type arg) const noexcept(noexcept(std::declval<std::hash<B>>()(arg.raw_value()))) {
return m_hash(arg.raw_value());
}

private:
std::hash<B> m_hash;
};

template <typename B, typename I, unsigned int F>
struct numeric_limits<fpm::fixed<B,I,F>>
{
static constexpr bool is_specialized = true;
static constexpr bool is_signed = std::numeric_limits<B>::is_signed;
static constexpr bool is_integer = false;
static constexpr bool is_exact = true;
static constexpr bool has_infinity = false;
static constexpr bool has_quiet_NaN = false;
static constexpr bool has_signaling_NaN = false;
static constexpr bool has_denorm = std::denorm_absent;
static constexpr bool has_denorm_loss = false;
static constexpr std::float_round_style round_style = std::round_to_nearest;
static constexpr bool is_iec_559 = false;
static constexpr bool is_bounded = true;
static constexpr bool is_modulo = std::numeric_limits<B>::is_modulo;
static constexpr int digits = std::numeric_limits<B>::digits;

// Any number with `digits10` significant base-10 digits (that fits in
// the range of the type) is guaranteed to be convertible from text and
// back without change. Worst case, this is 0.000...001, so we can only
// guarantee this case. Nothing more.
static constexpr int digits10 = 1;

// This is equal to max_digits10 for the integer and fractional part together.
static constexpr int max_digits10 =
fpm::detail::max_digits10(std::numeric_limits<B>::digits - F) + fpm::detail::max_digits10(F);

static constexpr int radix = 2;
static constexpr int min_exponent = 1 - F;
static constexpr int min_exponent10 = -fpm::detail::digits10(F);
static constexpr int max_exponent = std::numeric_limits<B>::digits - F;
static constexpr int max_exponent10 = fpm::detail::digits10(std::numeric_limits<B>::digits - F);
static constexpr bool traps = true;
static constexpr bool tinyness_before = false;

static constexpr fpm::fixed<B,I,F> lowest() noexcept {
return fpm::fixed<B,I,F>::from_raw_value(std::numeric_limits<B>::lowest());
};

static constexpr fpm::fixed<B,I,F> min() noexcept {
return lowest();
}

static constexpr fpm::fixed<B,I,F> max() noexcept {
return fpm::fixed<B,I,F>::from_raw_value(std::numeric_limits<B>::max());
};

static constexpr fpm::fixed<B,I,F> epsilon() noexcept {
return fpm::fixed<B,I,F>::from_raw_value(1);
};

static constexpr fpm::fixed<B,I,F> round_error() noexcept {
return fpm::fixed<B,I,F>(1) / 2;
};

static constexpr fpm::fixed<B,I,F> denorm_min() noexcept {
return min();
}
};

template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_specialized;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_signed;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_integer;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_exact;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::has_infinity;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::has_quiet_NaN;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::has_signaling_NaN;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::has_denorm;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::has_denorm_loss;
template <typename B, typename I, unsigned int F>
constexpr std::float_round_style numeric_limits<fpm::fixed<B,I,F>>::round_style;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_iec_559;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_bounded;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::is_modulo;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::digits;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::digits10;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::max_digits10;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::radix;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::min_exponent;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::min_exponent10;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::max_exponent;
template <typename B, typename I, unsigned int F>
constexpr int numeric_limits<fpm::fixed<B,I,F>>::max_exponent10;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::traps;
template <typename B, typename I, unsigned int F>
constexpr bool numeric_limits<fpm::fixed<B,I,F>>::tinyness_before;

}

#endif