// SPDX-FileCopyrightText: 2015 Evan Teran
// SPDX-License-Identifier: MIT
// From: https://github.com/eteran/cpp-utilities/blob/master/fixed/include/cpp-utilities/fixed.h
// See also: http://stackoverflow.com/questions/79677/whats-the-best-way-to-do-fixed-point-math
#pragma once
#if __cplusplus >= 201402L
#define CONSTEXPR14 constexpr
#else
#define CONSTEXPR14
#endif
#include <cstddef> // for size_t
#include <cstdint>
#include <exception>
#include <ostream>
#include <type_traits>
namespace Common {
template <size_t I, size_t F>
class FixedPoint;
namespace detail {
// helper templates to make magic with types :)
// these allow us to determine resonable types from
// a desired size, they also let us infer the next largest type
// from a type which is nice for the division op
template <size_t T>
struct type_from_size {
using value_type = void;
using unsigned_type = void;
using signed_type = void;
static constexpr bool is_specialized = false;
};
#if defined(__GNUC__) && defined(__x86_64__) && !defined(__STRICT_ANSI__)
template <>
struct type_from_size<128> {
static constexpr bool is_specialized = true;
static constexpr size_t size = 128;
using value_type = __int128;
using unsigned_type = unsigned __int128;
using signed_type = __int128;
using next_size = type_from_size<256>;
};
#endif
template <>
struct type_from_size<64> {
static constexpr bool is_specialized = true;
static constexpr size_t size = 64;
using value_type = int64_t;
using unsigned_type = std::make_unsigned<value_type>::type;
using signed_type = std::make_signed<value_type>::type;
using next_size = type_from_size<128>;
};
template <>
struct type_from_size<32> {
static constexpr bool is_specialized = true;
static constexpr size_t size = 32;
using value_type = int32_t;
using unsigned_type = std::make_unsigned<value_type>::type;
using signed_type = std::make_signed<value_type>::type;
using next_size = type_from_size<64>;
};
template <>
struct type_from_size<16> {
static constexpr bool is_specialized = true;
static constexpr size_t size = 16;
using value_type = int16_t;
using unsigned_type = std::make_unsigned<value_type>::type;
using signed_type = std::make_signed<value_type>::type;
using next_size = type_from_size<32>;
};
template <>
struct type_from_size<8> {
static constexpr bool is_specialized = true;
static constexpr size_t size = 8;
using value_type = int8_t;
using unsigned_type = std::make_unsigned<value_type>::type;
using signed_type = std::make_signed<value_type>::type;
using next_size = type_from_size<16>;
};
// this is to assist in adding support for non-native base
// types (for adding big-int support), this should be fine
// unless your bit-int class doesn't nicely support casting
template <class B, class N>
constexpr B next_to_base(N rhs) {
return static_cast<B>(rhs);
}
struct divide_by_zero : std::exception {};
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> divide(
FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
typename std::enable_if<type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
using next_type = typename FixedPoint<I, F>::next_type;
using base_type = typename FixedPoint<I, F>::base_type;
constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
next_type t(numerator.to_raw());
t <<= fractional_bits;
FixedPoint<I, F> quotient;
quotient = FixedPoint<I, F>::from_base(next_to_base<base_type>(t / denominator.to_raw()));
remainder = FixedPoint<I, F>::from_base(next_to_base<base_type>(t % denominator.to_raw()));
return quotient;
}
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> divide(
FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
typename std::enable_if<!type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
using unsigned_type = typename FixedPoint<I, F>::unsigned_type;
constexpr int bits = FixedPoint<I, F>::total_bits;
if (denominator == 0) {
throw divide_by_zero();
} else {
int sign = 0;
FixedPoint<I, F> quotient;
if (numerator < 0) {
sign ^= 1;
numerator = -numerator;
}
if (denominator < 0) {
sign ^= 1;
denominator = -denominator;
}
unsigned_type n = numerator.to_raw();
unsigned_type d = denominator.to_raw();
unsigned_type x = 1;
unsigned_type answer = 0;
// egyptian division algorithm
while ((n >= d) && (((d >> (bits - 1)) & 1) == 0)) {
x <<= 1;
d <<= 1;
}
while (x != 0) {
if (n >= d) {
n -= d;
answer += x;
}
x >>= 1;
d >>= 1;
}
unsigned_type l1 = n;
unsigned_type l2 = denominator.to_raw();
// calculate the lower bits (needs to be unsigned)
while (l1 >> (bits - F) > 0) {
l1 >>= 1;
l2 >>= 1;
}
const unsigned_type lo = (l1 << F) / l2;
quotient = FixedPoint<I, F>::from_base((answer << F) | lo);
remainder = n;
if (sign) {
quotient = -quotient;
}
return quotient;
}
}
// this is the usual implementation of multiplication
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> multiply(
FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
typename std::enable_if<type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
using next_type = typename FixedPoint<I, F>::next_type;
using base_type = typename FixedPoint<I, F>::base_type;
constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
next_type t(static_cast<next_type>(lhs.to_raw()) * static_cast<next_type>(rhs.to_raw()));
t >>= fractional_bits;
return FixedPoint<I, F>::from_base(next_to_base<base_type>(t));
}
// this is the fall back version we use when we don't have a next size
// it is slightly slower, but is more robust since it doesn't
// require and upgraded type
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> multiply(
FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
typename std::enable_if<!type_from_size<I + F>::next_size::is_specialized>::type* = nullptr) {
using base_type = typename FixedPoint<I, F>::base_type;
constexpr size_t fractional_bits = FixedPoint<I, F>::fractional_bits;
constexpr base_type integer_mask = FixedPoint<I, F>::integer_mask;
constexpr base_type fractional_mask = FixedPoint<I, F>::fractional_mask;
// more costly but doesn't need a larger type
const base_type a_hi = (lhs.to_raw() & integer_mask) >> fractional_bits;
const base_type b_hi = (rhs.to_raw() & integer_mask) >> fractional_bits;
const base_type a_lo = (lhs.to_raw() & fractional_mask);
const base_type b_lo = (rhs.to_raw() & fractional_mask);
const base_type x1 = a_hi * b_hi;
const base_type x2 = a_hi * b_lo;
const base_type x3 = a_lo * b_hi;
const base_type x4 = a_lo * b_lo;
return FixedPoint<I, F>::from_base((x1 << fractional_bits) + (x3 + x2) +
(x4 >> fractional_bits));
}
} // namespace detail
template <size_t I, size_t F>
class FixedPoint {
static_assert(detail::type_from_size<I + F>::is_specialized, "invalid combination of sizes");
public:
static constexpr size_t fractional_bits = F;
static constexpr size_t integer_bits = I;
static constexpr size_t total_bits = I + F;
using base_type_info = detail::type_from_size<total_bits>;
using base_type = typename base_type_info::value_type;
using next_type = typename base_type_info::next_size::value_type;
using unsigned_type = typename base_type_info::unsigned_type;
public:
#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Woverflow"
#endif
static constexpr base_type fractional_mask =
~(static_cast<unsigned_type>(~base_type(0)) << fractional_bits);
static constexpr base_type integer_mask = ~fractional_mask;
#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif
public:
static constexpr base_type one = base_type(1) << fractional_bits;
public: // constructors
FixedPoint() = default;
FixedPoint(const FixedPoint&) = default;
FixedPoint(FixedPoint&&) = default;
FixedPoint& operator=(const FixedPoint&) = default;
template <class Number>
constexpr FixedPoint(
Number n, typename std::enable_if<std::is_arithmetic<Number>::value>::type* = nullptr)
: data_(static_cast<base_type>(n * one)) {}
public: // conversion
template <size_t I2, size_t F2>
CONSTEXPR14 explicit FixedPoint(FixedPoint<I2, F2> other) {
static_assert(I2 <= I && F2 <= F, "Scaling conversion can only upgrade types");
using T = FixedPoint<I2, F2>;
const base_type fractional = (other.data_ & T::fractional_mask);
const base_type integer = (other.data_ & T::integer_mask) >> T::fractional_bits;
data_ =
(integer << fractional_bits) | (fractional << (fractional_bits - T::fractional_bits));
}
private:
// this makes it simpler to create a FixedPoint point object from
// a native type without scaling
// use "FixedPoint::from_base" in order to perform this.
struct NoScale {};
constexpr FixedPoint(base_type n, const NoScale&) : data_(n) {}
public:
static constexpr FixedPoint from_base(base_type n) {
return FixedPoint(n, NoScale());
}
public: // comparison operators
constexpr bool operator==(FixedPoint rhs) const {
return data_ == rhs.data_;
}
constexpr bool operator!=(FixedPoint rhs) const {
return data_ != rhs.data_;
}
constexpr bool operator<(FixedPoint rhs) const {
return data_ < rhs.data_;
}
constexpr bool operator>(FixedPoint rhs) const {
return data_ > rhs.data_;
}
constexpr bool operator<=(FixedPoint rhs) const {
return data_ <= rhs.data_;
}
constexpr bool operator>=(FixedPoint rhs) const {
return data_ >= rhs.data_;
}
public: // unary operators
constexpr bool operator!() const {
return !data_;
}
constexpr FixedPoint operator~() const {
// NOTE(eteran): this will often appear to "just negate" the value
// that is not an error, it is because -x == (~x+1)
// and that "+1" is adding an infinitesimally small fraction to the
// complimented value
return FixedPoint::from_base(~data_);
}
constexpr FixedPoint operator-() const {
return FixedPoint::from_base(-data_);
}
constexpr FixedPoint operator+() const {
return FixedPoint::from_base(+data_);
}
CONSTEXPR14 FixedPoint& operator++() {
data_ += one;
return *this;
}
CONSTEXPR14 FixedPoint& operator--() {
data_ -= one;
return *this;
}
CONSTEXPR14 FixedPoint operator++(int) {
FixedPoint tmp(*this);
data_ += one;
return tmp;
}
CONSTEXPR14 FixedPoint operator--(int) {
FixedPoint tmp(*this);
data_ -= one;
return tmp;
}
public: // basic math operators
CONSTEXPR14 FixedPoint& operator+=(FixedPoint n) {
data_ += n.data_;
return *this;
}
CONSTEXPR14 FixedPoint& operator-=(FixedPoint n) {
data_ -= n.data_;
return *this;
}
CONSTEXPR14 FixedPoint& operator*=(FixedPoint n) {
return assign(detail::multiply(*this, n));
}
CONSTEXPR14 FixedPoint& operator/=(FixedPoint n) {
FixedPoint temp;
return assign(detail::divide(*this, n, temp));
}
private:
CONSTEXPR14 FixedPoint& assign(FixedPoint rhs) {
data_ = rhs.data_;
return *this;
}
public: // binary math operators, effects underlying bit pattern since these
// don't really typically make sense for non-integer values
CONSTEXPR14 FixedPoint& operator&=(FixedPoint n) {
data_ &= n.data_;
return *this;
}
CONSTEXPR14 FixedPoint& operator|=(FixedPoint n) {
data_ |= n.data_;
return *this;
}
CONSTEXPR14 FixedPoint& operator^=(FixedPoint n) {
data_ ^= n.data_;
return *this;
}
template <class Integer,
class = typename std::enable_if<std::is_integral<Integer>::value>::type>
CONSTEXPR14 FixedPoint& operator>>=(Integer n) {
data_ >>= n;
return *this;
}
template <class Integer,
class = typename std::enable_if<std::is_integral<Integer>::value>::type>
CONSTEXPR14 FixedPoint& operator<<=(Integer n) {
data_ <<= n;
return *this;
}
public: // conversion to basic types
constexpr void round_up() {
data_ += (data_ & fractional_mask) >> 1;
}
constexpr int to_int() {
round_up();
return static_cast<int>((data_ & integer_mask) >> fractional_bits);
}
constexpr unsigned int to_uint() const {
round_up();
return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
}
constexpr int64_t to_long() {
round_up();
return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
}
constexpr int to_int_floor() const {
return static_cast<int>((data_ & integer_mask) >> fractional_bits);
}
constexpr int64_t to_long_floor() {
return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
}
constexpr unsigned int to_uint_floor() const {
return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
}
constexpr float to_float() const {
return static_cast<float>(data_) / FixedPoint::one;
}
constexpr double to_double() const {
return static_cast<double>(data_) / FixedPoint::one;
}
constexpr base_type to_raw() const {
return data_;
}
constexpr void clear_int() {
data_ &= fractional_mask;
}
constexpr base_type get_frac() const {
return data_ & fractional_mask;
}
public:
CONSTEXPR14 void swap(FixedPoint& rhs) {
using std::swap;
swap(data_, rhs.data_);
}
public:
base_type data_;
};
// if we have the same fractional portion, but differing integer portions, we trivially upgrade the
// smaller type
template <size_t I1, size_t I2, size_t F>
CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
operator+(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
const T l = T::from_base(lhs.to_raw());
const T r = T::from_base(rhs.to_raw());
return l + r;
}
template <size_t I1, size_t I2, size_t F>
CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
operator-(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
const T l = T::from_base(lhs.to_raw());
const T r = T::from_base(rhs.to_raw());
return l - r;
}
template <size_t I1, size_t I2, size_t F>
CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
operator*(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
const T l = T::from_base(lhs.to_raw());
const T r = T::from_base(rhs.to_raw());
return l * r;
}
template <size_t I1, size_t I2, size_t F>
CONSTEXPR14 typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type
operator/(FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = typename std::conditional<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>::type;
const T l = T::from_base(lhs.to_raw());
const T r = T::from_base(rhs.to_raw());
return l / r;
}
template <size_t I, size_t F>
std::ostream& operator<<(std::ostream& os, FixedPoint<I, F> f) {
os << f.to_double();
return os;
}
// basic math operators
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs += rhs;
return lhs;
}
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs -= rhs;
return lhs;
}
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs *= rhs;
return lhs;
}
template <size_t I, size_t F>
CONSTEXPR14 FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs /= rhs;
return lhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, Number rhs) {
lhs += FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, Number rhs) {
lhs -= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, Number rhs) {
lhs *= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, Number rhs) {
lhs /= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator+(Number lhs, FixedPoint<I, F> rhs) {
FixedPoint<I, F> tmp(lhs);
tmp += rhs;
return tmp;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator-(Number lhs, FixedPoint<I, F> rhs) {
FixedPoint<I, F> tmp(lhs);
tmp -= rhs;
return tmp;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator*(Number lhs, FixedPoint<I, F> rhs) {
FixedPoint<I, F> tmp(lhs);
tmp *= rhs;
return tmp;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator/(Number lhs, FixedPoint<I, F> rhs) {
FixedPoint<I, F> tmp(lhs);
tmp /= rhs;
return tmp;
}
// shift operators
template <size_t I, size_t F, class Integer,
class = typename std::enable_if<std::is_integral<Integer>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator<<(FixedPoint<I, F> lhs, Integer rhs) {
lhs <<= rhs;
return lhs;
}
template <size_t I, size_t F, class Integer,
class = typename std::enable_if<std::is_integral<Integer>::value>::type>
CONSTEXPR14 FixedPoint<I, F> operator>>(FixedPoint<I, F> lhs, Integer rhs) {
lhs >>= rhs;
return lhs;
}
// comparison operators
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator>(FixedPoint<I, F> lhs, Number rhs) {
return lhs > FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator<(FixedPoint<I, F> lhs, Number rhs) {
return lhs < FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator>=(FixedPoint<I, F> lhs, Number rhs) {
return lhs >= FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator<=(FixedPoint<I, F> lhs, Number rhs) {
return lhs <= FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator==(FixedPoint<I, F> lhs, Number rhs) {
return lhs == FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator!=(FixedPoint<I, F> lhs, Number rhs) {
return lhs != FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator>(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) > rhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator<(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) < rhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator>=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) >= rhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator<=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) <= rhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator==(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) == rhs;
}
template <size_t I, size_t F, class Number,
class = typename std::enable_if<std::is_arithmetic<Number>::value>::type>
constexpr bool operator!=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) != rhs;
}
} // namespace Common
#undef CONSTEXPR14