std::comp_e...p_ellint_1l(3)

💖 std::comp_ellint_1, std::comp_ellint_1f, std::comp_ellint_1l 💖

okay so bestie, welcome to the <cmath> corner of the C++ Standard Libary manual — yes, “Libary” is exactly how the page header spells it, no cap. The page title is std::comp_e...p_ellint_1l(3) (that ellipsis is the page’s own abbreviation, not me being shady). We’re talking about the complete elliptic integral of the first kind, and honestly? kinda iconic. 🎀

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🌸 NAME 🌸

std::comp_ellint_1, std::comp_ellint_1f, std::comp_ellint_1l — the whole trio, together, slaying in <cmath>. ✨

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✨ Synopsis ✨

Here’s the signature lineup, verbatim so nobody gets lost:

double      comp_ellint_1( double arg );

double      comp_ellint_1( float arg );
double      comp_ellint_1( long double arg );  (1)
float       comp_ellint_1f( float arg );

long double comp_ellint_1l( long double arg );
double      comp_ellint_1( IntegralType arg ); (2)

1. Computes the complete elliptic integral of the first kind of arg.
2. A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

⚠️ Important vibe check: as all special functions, comp_ellint_1 is only guaranteed to be available in <cmath> if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.

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🫶 Parameters 🫶

• arg — value of a floating-point or integral type.

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🎀 Return value 🎀

If no errors occur, the value of the complete elliptic integral of the first kind of arg, that is ellint_1(arg, π/2), is returned. 💅

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🦋 Error handling 🦋

Errors may be reported as specified in math_errhandling.

• If the argument is NaN, NaN is returned and domain error is not reported.
• If |arg| > 1, a domain error may occur.

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🌈 Notes 🌈

Implementations that do not support TR 29124 but support TR 19768 provide this function in the header tr1/cmath and namespace std::tr1.

An implementation of this function is also available in boost.math.

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🧪 Example 🧪

The page says it works as shown with gcc 6.0, and it cues the snippet with // Run this code — so go off, bestie:

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>

int main()
{
    double hpi = std::acos(-1) / 2;
    std::cout << "K(0) = " << std::comp_ellint_1(0) << '\n'
              << "π/2 = " << hpi << '\n'
              << "K(0.5) = " << std::comp_ellint_1(0.5) << '\n'
              << "F(0.5, π/2) = " << std::ellint_1(0.5, hpi) << '\n';
}

Output

K(0) = 1.5708
π/2 = 1.5708
K(0.5) = 1.68575
F(0.5, π/2) = 1.68575

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🔗 External links 🔗

Weisstein, Eric W. "Complete Elliptic Integral of the First Kind." From MathWorld--A Wolfram Web Resource.

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👀 See also 👀

• ellint_1 (incomplete) elliptic integral of the first kind
• ellint_1f (function)
• ellint_1l

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okay that’s the whole page, bestie. source/version: http://cppreference.com · date: 2024.06.10 · title vibe: std::comp_e...p_ellint_1l(3) — mwah 💋✨