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.
Let’s start with an unsafe comparison.
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:
- The compiler transforms the expression
x < y
(line 1) intostatic_cast<unsigned int>(x) < y
. In particular, thesigned
x
is converted to an unsigned int. - Due to the conversion,
-3
becomes 4’294’967’293. 4'294'967'293
is equal to (-3) modulo (2 to the power of 32).- 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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