std::sqrt,s...f,std::sqrtl(3)

🌸 NAME 🌸

std::sqrt, std::sqrtf, std::sqrtl — okay so the NAME line literally says std::sqrt,std::sqrtf,std::sqrtl - std::sqrt,std::sqrtf,std::sqrtl, and honestly? A squad so iconic they named it twice 💅.

This is the std::sqrt,s...f,std::sqrtl(3) page from the C++ Standard Libary (yes, the header spells it Libary, not me 💀), manual section 3. It's the square-root bestie manual, and we're getting into it.

✨ Synopsis ✨

Defined in header <cmath>, bestie. Here's the signature lineup, exactly as the page serves it:

Defined in header <cmath>

float       sqrt ( float num );

double      sqrt ( double num );                            (until C++23)

long double sqrt ( long double num );
/* floating-point-type */                                   (since C++23)
            sqrt ( /* floating-point-type */ num );
(constexpr since C++26)

float       sqrtf( float num );                     (1) (2) (since C++11)
(constexpr since C++26)

long double sqrtl( long double num );                   (3) (since C++11)
(constexpr since C++26)

Additional overloads (since C++11), also defined in header <cmath>:

Additional overloads (since C++11)

Defined in header <cmath>

template< class Integer >                               (A)
(constexpr since C++26)

double      sqrt ( Integer num );

Then the numbered tea:

• 1-3) Computes the square root of num.
• The library provides overloads of std::sqrt for all cv-unqualified floating-point types as the type of the parameter. (since C++23)
• A) Additional overloads are provided for all integer types, which are treated as double. (since C++11)

🍓 Parameters 🍓

• num — floating-point or integer value.

🌈 Return value 🌈

If no errors occur, the square root of num is returned — the page writes it all fancy as ({\small \sqrt{num} }), aka √num. Iconic math behavior, no cap 💖.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

🦋 Error handling 🦋

Errors are reported as specified in math_errhandling.

Domain error occurs if num is less than zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559), then:

• If the argument is less than -0, FE_INVALID is raised and NaN is returned.
• If the argument is +∞ or ±0, it is returned, unmodified.
• If the argument is NaN, NaN is returned.

💅 Notes 💅

std::sqrt is required by the IEEE standard to be correctly rounded from the infinitely precise result. In particular, the exact result is produced if it can be represented in the floating-point type. The only other operations which require this are the arithmetic operators and the function std::fma. Other functions, including std::pow, are not so constrained. So yeah — std::sqrt is in the correctly rounded excellence club, and std::pow is not invited to that specific meeting. Periodt.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sqrt(num) has the same effect as std::sqrt(static_cast<double>(num)).

🎀 Example 🎀

The original page has a // Run this code line, and then this exact code:

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
// #pragma STDC FENV_ACCESS ON

int main()
{
    // normal use
    std::cout << "sqrt(100) = " << std::sqrt(100) << '\n'
              << "sqrt(2) = " << std::sqrt(2) << '\n'
              << "golden ratio = " << (1 + std::sqrt(5)) / 2 << '\n';

    // special values
    std::cout << "sqrt(-0) = " << std::sqrt(-0.0) << '\n';

    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);

    std::cout << "sqrt(-1.0) = " << std::sqrt(-1) << '\n';
    if (errno == EDOM)
        std::cout << "    errno = EDOM " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

🌸 Possible output 🌸

sqrt(100) = 10
sqrt(2) = 1.41421
golden ratio = 1.61803
sqrt(-0) = -0
sqrt(-1.0) = -nan
    errno = EDOM Numerical argument out of domain
    FE_INVALID raised

👑 See also 👑

• pow — raises a number to the given power ((x^y)) (function).
• powf (C++11), powl (C++11) — raises a number to the given power ((x^y)) (function).
• cbrt, cbrtf (C++11), cbrtl (C++11) — computes cube root ((\sqrt[3]{x}), aka 3√x) (function).
• hypot, hypotf (C++11), hypotl (C++11) — computes square root of the sum of the squares of two or three (since C++17) given numbers ((\sqrt{x^2+y^2}), (\sqrt{x^2+y^2+z^2})) (function).
• sqrt(std::complex) — complex square root in the range of the right half-plane (function template).
• sqrt(std::valarray) — applies the function std::sqrt to each element of valarray (function template).
• C documentation for sqrt.

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Okay that's the whole vibe 💖 — footer source/version and date, folded in cute: http://cppreference.com, 2024.06.10, page std::sqrt,s...f,std::sqrtl(3). Bye bestie, go compute some roots! 🫶✨