Safe Comparisons of Integrals with C++20

This is a cross-post from www.ModernesCpp.com.

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.

Let's start with an unsafe comparison.

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.

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 with 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 function 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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