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During a project at my work I needed a convenient way to store values taking up the smallest amount of bits necessary, not in memory but later when they're serialized into an array of unsigned short ints. For instance, a value that could be between 0 and 7 was only supposed to be 3 bits long. I ended up developing my own solution based on std::bitset with some additional code in order to make it work with signed values. Another goal was to make it work as close to a regular integer type as possible. This is the code (https://github.com/AndersHogqvist/custom_int):

#include <bitset>
#include <type_traits>

template<size_t Size>
class TypeBase 
public:
 size_t size() const 
 return data_.size();
 

 unsigned long to_ulong() const 
 return data_.to_ulong();
 

 unsigned long long to_ullong() const 
 return data_.to_ullong();
 

 std::bitset<Size> data() const 
 return data_;
 

 std::string to_string() const 
 return data_.to_string();
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator=(const T value) 
 data_ = std::bitset<Size>(value);
 return *this;
 

 bool operator==(const TypeBase<Size> &other) const 
 return data_ == other.data();
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator==(const T value) const 
 return data_.to_ullong() == value;
 

 bool operator!=(const TypeBase<Size> &other) const 
 return !(*this == other);
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator!=(const T value) const 
 return data_ != std::bitset<Size>(value);
 

 bool operator<(const TypeBase<Size> &other) const 
 if (data_ == other.data_) 
 return false;
 
 return less_than_(other.data_);
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator<(const T value) const 
 return less_than_(std::bitset<Size>(value));
 

 bool operator<=(const TypeBase<Size> &other) const 
 if (data_ == other.data_) 
 return true;
 
 return less_than_or_eq_(other.data_);
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator<=(const T value) const 
 return less_than_or_eq_(std::bitset<Size>(value));
 

 bool operator>(const TypeBase<Size> &other) const 
 if (data_ == other.data_) 
 return false;
 
 return greater_than_(other.data_);
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator>(const T value) const 
 return greater_than_(std::bitset<Size>(value));
 

 bool operator>=(const TypeBase<Size> &other) const 
 if (data_ == other.data_) 
 return true;
 
 return greater_than_or_eq_(other.data_);
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 bool operator>=(const T value) const 
 return greater_than_or_eq_(std::bitset<Size>(value));
 

 TypeBase<Size> &operator+(const TypeBase<Size> &other) 
 bool carry = false;
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other.data_[ix], carry);
 
 return *this;
 

 TypeBase<Size> &operator+(const std::bitset<Size> &other) 
 bool carry = false;
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other[ix], carry);
 
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator+(const T value) 
 bool carry = false;
 std::bitset<Size> other(value);
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other[ix], carry);
 
 return *this;
 

 TypeBase<Size> &operator+=(const TypeBase<Size> &other) 
 bool carry = false;
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other.data_[ix], carry);
 
 return *this;
 

 TypeBase<Size> &operator+=(const std::bitset<Size> &other) 
 bool carry = false;
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other[ix], carry);
 
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator+=(const T value) 
 bool carry = false;
 std::bitset<Size> other(value);
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other[ix], carry);
 
 return *this;
 

 TypeBase<Size> &operator++(int) 
 bool carry = false;
 std::bitset<Size> other(1);
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other[ix], carry);
 
 return *this;
 

 TypeBase<Size> &operator-(const TypeBase<Size> &other) 
 subtract_(other.data_);
 return *this;
 

 TypeBase<Size> &operator-(const std::bitset<Size> &other) 
 subtract_(other);
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator-(const T value) 
 subtract_(std::bitset<Size>(value));
 return *this;
 

 TypeBase<Size> &operator-=(const TypeBase<Size> &other) 
 subtract_(other.data_);
 return *this;
 

 TypeBase<Size> &operator-=(const std::bitset<Size> &other) 
 subtract_(other);
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator-=(const T value) 
 subtract_(std::bitset<Size>(value));
 return *this;
 

 TypeBase<Size> &operator--(int) 
 subtract_(std::bitset<Size>(1));
 return *this;
 

 TypeBase<Size> &operator*(const TypeBase<Size> &other) 
 multiply_(other.data_);
 return *this;
 

 TypeBase<Size> &operator*(const std::bitset<Size> &other) 
 multiply_(other);
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator*(const T value) 
 multiply_(std::bitset<Size>(value));
 return *this;
 

 TypeBase<Size> &operator*=(const TypeBase<Size> &other) 
 multiply_(other.data_);
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator*=(const T value) 
 multiply_(std::bitset<Size>(value));
 return *this;
 

 TypeBase<Size> &operator/(const TypeBase<Size> &other) 
 data_ = data_.to_ullong() / other.to_ullong();
 return *this;
 

 TypeBase<Size> &operator/(const std::bitset<Size> &other) 
 data_ = data_.to_ullong() / other.to_ullong();
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator/(const T value) 
 data_ = data_.to_ullong() / value;
 return *this;
 

 TypeBase<Size> &operator/=(const TypeBase<Size> &other) 
 data_ = data_.to_ullong() / other.to_ullong();
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 TypeBase<Size> &operator/=(const T value) 
 data_ = data_.to_ullong() / value;
 return *this;
 

 template<size_t S>
 friend std::ostream &operator <<(std::ostream &out, const TypeBase<S> &u);
protected:
 TypeBase() = default;
 ~TypeBase() = default;

 std::bitset<Size> data_;

 bool add_(bool b1, bool b2, bool &carry) 

 void subtract_(const std::bitset<Size> &other) 
 bool borrow = false;
 for (int i = 0; i < Size; i++) 
 if (borrow) 
 if (data_[i]) 
 data_[i] = other[i];
 borrow = other[i];
 
 else 
 data_[i] = !other[i];
 borrow = true;
 
 
 else 
 if (data_[i]) 
 data_[i] = !other[i];
 borrow = false;
 
 else 
 data_[i] = other[i];
 borrow = other[i];
 
 
 
 

 void multiply_(const std::bitset<Size> &other) 
 std::bitset<Size> tmp = data_;
 data_.reset();
 if (tmp.count() < other.count()) 
 for (int i = 0; i < Size; i++) 
 if (tmp[i]) 
 operator+=(other << i);
 
 
 
 else 
 for (int i = 0; i < Size; i++) 
 if (other[i]) 
 operator+=(tmp << i);
 
 
 
 

 bool less_than_or_eq_(const std::bitset<Size> &other) const 
 for (int i = Size - 1; i >= 0; i--) 
 if (data_[i] && !other[i]) 
 return false;
 
 if (!data_[i] && other[i]) 
 return true;
 
 
 return true;
 

 bool less_than_(const std::bitset<Size> &other) const 
 for (int i = Size - 1; i >= 0; i--) 
 if (data_[i] && !other[i]) 
 return false;
 
 if (!data_[i] && other[i]) 
 return true;
 
 
 return false;
 

 bool greater_than_or_eq_(const std::bitset<Size> &other) const 
 for (int i = Size - 1; i >= 0; i--) 
 if (data_[i] && !other[i]) 
 return true;
 
 if (!data_[i] && other[i]) 
 return false;
 
 
 return true;
 

 bool greater_than_(const std::bitset<Size> &other) const 
 for (int i = Size - 1; i >= 0; i--) 
 if (data_[i] && !other[i]) 
 return true;
 
 if (!data_[i] && other[i]) 
 return false;
 
 
 return false;
 
;

template<size_t Size>
class Int : public TypeBase<Size> 
public:
 Int() = default;

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 Int(const T value) 
 TypeBase<Size>::operator=(value);
 

 ~Int() = default;

 Int<Size> &operator=(const TypeBase<Size> &other) 
 if (this->data_ == other.data()) 
 return *this;
 
 this->data_ = other.data();
 return *this;
 

 long long to_int() const 
 if (this->data_[Size - 1]) 
 std::bitset<Size> tmp = this->data_;
 tmp.flip();
 return tmp.to_ullong() * -1 - 1;
 
 return this->data_.to_ullong();
 

 Int<Size> &operator/(const TypeBase<Size> &other) 
 this->data_ = to_int() / other.to_ullong();
 return *this;
 

 Int<Size> &operator/(const std::bitset<Size> &other) 
 this->data_ = to_int() / other.to_ullong();
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 Int<Size> &operator/(const T value) 
 this->data_ = to_int() / value;
 return *this;
 

 Int<Size> &operator/=(const TypeBase<Size> &other) 
 this->data_ = to_int() / other.to_ullong();
 return *this;
 

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 Int<Size> &operator/=(const T value) 
 this->data_ = to_int() / value;
 return *this;
 
;

template<size_t Size>
std::ostream &operator<<(std::ostream &out, const Int<Size> &u) 
 out << u.to_int();
 return out;


template<size_t Size>
class UInt : public TypeBase<Size> 
public:
 UInt() = default;

 template<typename T,
 typename std::enable_if<std::is_integral<T>::value, T>::type* = nullptr>
 UInt(const T value) 
 TypeBase<Size>::operator=(value);
 

 ~UInt() = default;

 UInt<Size> &operator=(const TypeBase<Size> &other) 
 if (this->data_ == other.data()) 
 return *this;
 
 this->data_ = other.data();
 return *this;
 

 unsigned long long to_int() const 
 return this->data_.to_ullong();
 
;

template<size_t Size>
std::ostream &operator<<(std::ostream &out, const UInt<Size> &u) 
 out << u.to_ullong();
 return out;

Here are some examples on how it's supposed to be used:

#include <iostream>

#include "custom_int.h"

using namespace std;

int main() 
 Int<13> test1 = 1;
 UInt<5> test2;

 cout << "test1: " << test1 << endl;
 cout << "test2: " << test2 << endl;

 test1++;
 cout << "test1: " << test1 << endl;

 test1--;
 cout << "test1: " << test1 << endl;

 test1 -= 10;
 cout << "test1: " << test1 << endl;

 auto test3 = test1;

 cout << "test3: " << test3 << endl;

 test3 /= 3;

 cout << "test3: " << test3 << endl;

 test2 += 20;

 cout << "test2: " << test2 << endl;

 test2 = test2 / 10;

 cout << "test2: " << test2 << endl;

I'm by no means a seasoned C++ developer, so even if I believe it's working the way it should I would love to have some input on what can be improved.

What I'm mostly concerned about is the performance (unnecessary copying etc). It's supposed to be used in a real time application so I need it to be as fast as possible.

A significant performance drain is bit-by-bit computation loops such as

 TypeBase<Size> &operator+=(const TypeBase<Size> &other) 
 bool carry = false;
 for (size_t ix = 0; ix < Size; ++ix) 
 data_[ix] = add_(data_[ix], other.data_[ix], carry);
 
 return *this;
 

Unfortunately, at this time such constructs are not recognized by major compilers, and probably also not by various embedded compilers (which if I recall correctly you mentioned earlier).

For small Size it could be implemented with plain old arithmetic operators,

 TypeBase<Size> &operator+=(const TypeBase<Size> &other) 
 data_ = std::bitset<Size>(to_ullong() + other.to_ullong());
 return *this;
 

Which unsurprisingly compiles to normal addition.

Larger Size is trickier to support efficiently this way.