yuzu/src/common/fixed_point.h
Lioncash 6e1c6297a3 fixed_point: Mark default constructor as constexpr
Ensures that a fixed-point value is always initialized

This likely also fixes several cases of uninitialized values being
operated on, since we have multiple areas in the codebase where the
default constructor is being used like:

Common::FixedPoint<50, 14> current_sample{};

and is then followed up with an arithmetic operation like += or
something else, which operates directly on FixedPoint's internal data
member, which would previously be uninitialized.
2022-10-18 16:06:50 -04:00

652 lines
20 KiB
C++

// 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
#include <cstddef> // for size_t
#include <cstdint>
#include <exception>
#include <ostream>
#include <type_traits>
#include <common/concepts.h>
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_t<value_type>;
using signed_type = std::make_signed_t<value_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_t<value_type>;
using signed_type = std::make_signed_t<value_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_t<value_type>;
using signed_type = std::make_signed_t<value_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_t<value_type>;
using signed_type = std::make_signed_t<value_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>
constexpr FixedPoint<I, F> divide(
FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
std::enable_if_t<type_from_size<I + F>::next_size::is_specialized>* = 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>
constexpr FixedPoint<I, F> divide(
FixedPoint<I, F> numerator, FixedPoint<I, F> denominator, FixedPoint<I, F>& remainder,
std::enable_if_t<!type_from_size<I + F>::next_size::is_specialized>* = 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>
constexpr FixedPoint<I, F> multiply(
FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
std::enable_if_t<type_from_size<I + F>::next_size::is_specialized>* = 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>
constexpr FixedPoint<I, F> multiply(
FixedPoint<I, F> lhs, FixedPoint<I, F> rhs,
std::enable_if_t<!type_from_size<I + F>::next_size::is_specialized>* = 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
constexpr FixedPoint() = default;
constexpr FixedPoint(const FixedPoint&) = default;
constexpr FixedPoint& operator=(const FixedPoint&) = default;
constexpr FixedPoint(FixedPoint&&) noexcept = default;
constexpr FixedPoint& operator=(FixedPoint&&) noexcept = default;
template <IsArithmetic Number>
constexpr FixedPoint(Number n) : data_(static_cast<base_type>(n * one)) {}
public: // conversion
template <size_t I2, size_t F2>
constexpr 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
friend constexpr auto operator<=>(FixedPoint lhs, FixedPoint rhs) = default;
public: // unary operators
[[nodiscard]] constexpr bool operator!() const {
return !data_;
}
[[nodiscard]] 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_);
}
[[nodiscard]] constexpr FixedPoint operator-() const {
return FixedPoint::from_base(-data_);
}
[[nodiscard]] constexpr FixedPoint operator+() const {
return FixedPoint::from_base(+data_);
}
constexpr FixedPoint& operator++() {
data_ += one;
return *this;
}
constexpr FixedPoint& operator--() {
data_ -= one;
return *this;
}
constexpr FixedPoint operator++(int) {
FixedPoint tmp(*this);
data_ += one;
return tmp;
}
constexpr FixedPoint operator--(int) {
FixedPoint tmp(*this);
data_ -= one;
return tmp;
}
public: // basic math operators
constexpr FixedPoint& operator+=(FixedPoint n) {
data_ += n.data_;
return *this;
}
constexpr FixedPoint& operator-=(FixedPoint n) {
data_ -= n.data_;
return *this;
}
constexpr FixedPoint& operator*=(FixedPoint n) {
return assign(detail::multiply(*this, n));
}
constexpr FixedPoint& operator/=(FixedPoint n) {
FixedPoint temp;
return assign(detail::divide(*this, n, temp));
}
private:
constexpr 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
constexpr FixedPoint& operator&=(FixedPoint n) {
data_ &= n.data_;
return *this;
}
constexpr FixedPoint& operator|=(FixedPoint n) {
data_ |= n.data_;
return *this;
}
constexpr FixedPoint& operator^=(FixedPoint n) {
data_ ^= n.data_;
return *this;
}
template <IsIntegral Integer>
constexpr FixedPoint& operator>>=(Integer n) {
data_ >>= n;
return *this;
}
template <IsIntegral Integer>
constexpr FixedPoint& operator<<=(Integer n) {
data_ <<= n;
return *this;
}
public: // conversion to basic types
constexpr void round_up() {
data_ += (data_ & fractional_mask) >> 1;
}
[[nodiscard]] constexpr int to_int() {
round_up();
return static_cast<int>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr unsigned int to_uint() {
round_up();
return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr int64_t to_long() {
round_up();
return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr int to_int_floor() const {
return static_cast<int>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr int64_t to_long_floor() const {
return static_cast<int64_t>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr unsigned int to_uint_floor() const {
return static_cast<unsigned int>((data_ & integer_mask) >> fractional_bits);
}
[[nodiscard]] constexpr float to_float() const {
return static_cast<float>(data_) / FixedPoint::one;
}
[[nodiscard]] constexpr double to_double() const {
return static_cast<double>(data_) / FixedPoint::one;
}
[[nodiscard]] constexpr base_type to_raw() const {
return data_;
}
constexpr void clear_int() {
data_ &= fractional_mask;
}
[[nodiscard]] constexpr base_type get_frac() const {
return data_ & fractional_mask;
}
public:
constexpr void swap(FixedPoint& rhs) noexcept {
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>
constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator+(
FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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>
constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator-(
FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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>
constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator*(
FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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>
constexpr std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>> operator/(
FixedPoint<I1, F> lhs, FixedPoint<I2, F> rhs) {
using T = std::conditional_t<I1 >= I2, FixedPoint<I1, F>, FixedPoint<I2, F>>;
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>
constexpr FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs += rhs;
return lhs;
}
template <size_t I, size_t F>
constexpr FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs -= rhs;
return lhs;
}
template <size_t I, size_t F>
constexpr FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs *= rhs;
return lhs;
}
template <size_t I, size_t F>
constexpr FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, FixedPoint<I, F> rhs) {
lhs /= rhs;
return lhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr FixedPoint<I, F> operator+(FixedPoint<I, F> lhs, Number rhs) {
lhs += FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr FixedPoint<I, F> operator-(FixedPoint<I, F> lhs, Number rhs) {
lhs -= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr FixedPoint<I, F> operator*(FixedPoint<I, F> lhs, Number rhs) {
lhs *= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr FixedPoint<I, F> operator/(FixedPoint<I, F> lhs, Number rhs) {
lhs /= FixedPoint<I, F>(rhs);
return lhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr 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, IsArithmetic Number>
constexpr 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, IsArithmetic Number>
constexpr 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, IsArithmetic Number>
constexpr 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, IsIntegral Integer>
constexpr FixedPoint<I, F> operator<<(FixedPoint<I, F> lhs, Integer rhs) {
lhs <<= rhs;
return lhs;
}
template <size_t I, size_t F, IsIntegral Integer>
constexpr FixedPoint<I, F> operator>>(FixedPoint<I, F> lhs, Integer rhs) {
lhs >>= rhs;
return lhs;
}
// comparison operators
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator>(FixedPoint<I, F> lhs, Number rhs) {
return lhs > FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator<(FixedPoint<I, F> lhs, Number rhs) {
return lhs < FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator>=(FixedPoint<I, F> lhs, Number rhs) {
return lhs >= FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator<=(FixedPoint<I, F> lhs, Number rhs) {
return lhs <= FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator==(FixedPoint<I, F> lhs, Number rhs) {
return lhs == FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator!=(FixedPoint<I, F> lhs, Number rhs) {
return lhs != FixedPoint<I, F>(rhs);
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator>(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) > rhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator<(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) < rhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator>=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) >= rhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator<=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) <= rhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator==(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) == rhs;
}
template <size_t I, size_t F, IsArithmetic Number>
constexpr bool operator!=(Number lhs, FixedPoint<I, F> rhs) {
return FixedPoint<I, F>(lhs) != rhs;
}
} // namespace Common