# Safe Comparisons of Integrals with C++20

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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 to "Arithmetic Rules". Today, I want to dig deeper into this issue and compare signed and unsigned integers.

## Unsafe Comparison of Integrals

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

```// 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 output of the program, 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.

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## 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 operator.

Thanks to GCC 10, here is the expected result: Invoking a comparison function a non-integral value would causes 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 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 the new mathematical constants we have 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 useful utilities. For example, you can ask your compiler which C++ feature it supports, 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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### Modernes C++, 0 #1 C 2020-11-30 21:49
‘Integrals’ DOES NOT mean the same as ‘Integers’.
0 #2 Rainer Grimm 2020-12-01 21:47
Quoting C:
‘Integrals’ DOES NOT mean the same as ‘Integers’.

This name is a big source of trouble. Let me quote the standard:

3.9.1 Fundamental types [basic.fundamental]

Types bool, char, char16_t, char32_t, wchar_t, and the signed and unsigned integer types are collectively called integral types. A synonym for integral type is integer type.[...]

By the way, I used the term Integral in my German translation of this post and got more than 20 complaints. This happens when you exactly use the names of the standard.
0 #3 Dave 2021-02-23 17:53
Quoting Rainer Grimm:
Quoting C:
‘Integrals’ DOES NOT mean the same as ‘Integers’.

This name is a big source of trouble. Let me quote the standard:

3.9.1 Fundamental types [basic.fundamental]

Types bool, char, char16_t, char32_t, wchar_t, and the signed and unsigned integer types are collectively called integral types. A synonym for integral type is integer type.[...]

By the way, I used the term Integral in my German translation of this post and got more than 20 complaints. This happens when you exactly use the names of the standard.

Ok, but then you should use the full definition - "integral types". Your title is very misleading to search engines and people :)

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