# Safe Comparisons of Integrals with C++20

When you compare signed and unsigned integers, you may not get the result you expect. Thanks to the six `std::cmp_`* functions, there is a cure in C++20.

Maybe, you remember the rule “ES.100 Don’t mix signed and unsigned arithmetic” from the C++ Core Guidelines. I wrote a few words about it in my previous post on “Arithmetic Rules“. Today, I want to investigate this issue and compare signed and unsigned integers.

## Unsafe Comparison of Integrals

Of course, there is a reason for the program name `unsafeComparison.cpp`.

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```// unsafeComparison.cpp

#include <iostream>

int main() {

std::cout << std::endl;

std::cout << std::boolalpha;

int x = -3;                  // (1)
unsigned int y = 7;          // (2)

std::cout << "-3 < 7:  " << (x < y) << std::endl;
std::cout << "-3 <= 7: " << (x <= y) << std::endl;
std::cout << "-3 > 7:  " << (x > y) << std::endl;
std::cout << "-3 => 7: " << (x >= y) << std::endl;

std::cout << std::endl;

}
```

When I execute the program, the output may not meet your expectations.

When you read the program output, you recognize -3 should be bigger than 7. You presumably know the reason. I compared a `signed x` (line (1)) with an` unsigned y` (line (2)). What is happening under the hood? The following program provides the answer.

```// unsafeComparison2.cpp

int main() {
int x = -3;
unsigned int y = 7;

bool val = x < y;              // (1)
static_assert(static_cast<unsigned int>(-3) == 4'294'967'293);
}
```

In the example, I’m focusing on the less-than-operator. C++ Insights gives me the following output:

Here is what’s happening:

1. The compiler transforms the expression` x < y `(line 1) into `static_cast<unsigned int>(x) < y`. In particular, the `signed` `x` is converted to an unsigned int.
2. Due to the conversion,` -3 `becomes 4’294’967’293.
3. ` 4'294'967'293` is equal to (-3) modulo (2 to the power of 32).
4. 32 is the number of bits of an unsigned` int` on C++ Insights.

Thanks to C++20, we have a safe comparison of integrals.

## Safe Comparison of Integrals

C++20 supports the six comparison functions for integrals:

Thanks to the six comparison functions, I can easily transform the previous program` unsafeComparison.cpp` into the program `safeComparison.cpp. `The new comparison functions require the header `<utility`>.

```// safeComparison.cpp

#include <iostream>
#include <utility>

int main() {

std::cout << std::endl;

std::cout << std::boolalpha;

int x = -3;
unsigned int y = 7;

std::cout << "3 == 7:  " << std::cmp_equal(x, y) << std::endl;
std::cout << "3 != 7:  " << std::cmp_not_equal(x, y) << std::endl;
std::cout << "-3 < 7:  " << std::cmp_less(x, y) << std::endl;
std::cout << "-3 <= 7: " << std::cmp_less_equal(x, y) << std::endl;
std::cout << "-3 > 7:  " << std::cmp_greater(x, y) << std::endl;
std::cout << "-3 => 7: " << std::cmp_greater_equal(x, y) << std::endl;

std::cout << std::endl;

}
```

I also used in this program the equal and not equal operators.

Thanks to GCC 10, here is the expected result:

Invoking a comparison function with a non-integral value would cause a compile-time error.

```// safeComparison2.cpp

#include <iostream>
#include <utility>

int main() {

double x = -3.5;             // (1)
unsigned int y = 7;          // (2)

std::cout << "-3.5 < 7:  " << std::cmp_less(x, y) << std::endl;

}
```

Trying to compare a `double` (line (1)) and an `unsigned int` (line (2)) gives the GCC 10 compiler a lengthy error message. Here is the crucial line of the error message:

The internal type-traits  __is_standard_integer failed. I was curious about what that means and looked it up in the GCC type-traits implementation on GitHub. Here are the relevant lines from the header` type-traits:`

```// Check if a type is one of the signed or unsigned integer types.
template<typename _Tp>
using __is_standard_integer
= __or_<__is_signed_integer<_Tp>, __is_unsigned_integer<_Tp>>;

// Check if a type is one of the signed integer types.
template<typename _Tp>
using __is_signed_integer = __is_one_of<__remove_cv_t<_Tp>,
signed char, signed short, signed int, signed long,
signed long long

// Check if a type is one of the unsigned integer types.
template<typename _Tp>
using __is_unsigned_integer = __is_one_of<__remove_cv_t<_Tp>,
unsigned char, unsigned short, unsigned int, unsigned long,
unsigned long long
```

`__remove_cv_t` is the internal function of GCC to remove `const` or `volatile` from a type.

Maybe, you are now curious about what happens when you compare a `double` and an `unsigned int` the classical way.

Here is the modified program `safeComparison2.cpp.`

```// classicalComparison.cpp

int main() {

double x = -3.5;
unsigned int y = 7;

auto res = x < y;     // true

}
```

It works. The crucial `unsigned int` is floating-point promoted to `double`. C++ Insights shows the truth:

After so many comparisons, I want to end this post with our new mathematical constants with C++20.

## Mathematical Constants

First, the constants require the header `<numbers>` and the namespace `std::numbers`. The following tables give you the first overview.

The program `mathematicConstants.cpp` applies the mathematical constants.

```// mathematicConstants.cpp

#include <iomanip>
#include <iostream>
#include <numbers>

int main() {

std::cout << std::endl;

std::cout<< std::setprecision(10);

std::cout << "std::numbers::e: " <<  std::numbers::e << std::endl;
std::cout << "std::numbers::log2e: " <<  std::numbers::log2e << std::endl;
std::cout << "std::numbers::log10e: " <<  std::numbers::log10e << std::endl;
std::cout << "std::numbers::pi: " <<  std::numbers::pi << std::endl;
std::cout << "std::numbers::inv_pi: " <<  std::numbers::inv_pi << std::endl;
std::cout << "std::numbers::inv_sqrtpi: " <<  std::numbers::inv_sqrtpi << std::endl;
std::cout << "std::numbers::ln2: " <<  std::numbers::ln2 << std::endl;
std::cout << "std::numbers::sqrt2: " <<  std::numbers::sqrt2 << std::endl;
std::cout << "std::numbers::sqrt3: " <<  std::numbers::sqrt3 << std::endl;
std::cout << "std::numbers::inv_sqrt3: " <<  std::numbers::inv_sqrt3 << std::endl;
std::cout << "std::numbers::egamma: " <<  std::numbers::egamma << std::endl;
std::cout << "std::numbers::phi: " <<  std::numbers::phi << std::endl;

std::cout << std::endl;

}
```

Here is the output of the program with the MSVC compiler 19.27.

The mathematical constants are available for `float`, `double`, and `long double`. Per-default `double` is used, but you can also specify `float` (`std::numbers::pi_v<float>`) or` long double` (`std::numbers::pi_v<long double>`).

## What’s next?

C++20 offers more valuable utilities. For example, you can ask your compiler which C++ feature it supports, and can easily create functional objects with `std::bind_front, `or perform different actions in a function whether the function runs a compile-time or at runtime.

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