std::ellint...d::ellint_1l(3)

🎀 NAME 🎀

okay so welcome to the C++ Standard Library manual, bestie 💖 — this page has main character energy for std::ellint_1, std::ellint_1f, and std::ellint_1l. No cap, it’s giving elliptic integrals, and we’re gonna get through every lil detail together. 🫶

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🌸 Synopsis 🌸

Here’s the receipts, bestie 🧾 — signatures exactly as printed, no edits, no cap:

Defined in header <cmath>.

float       ellint_1 ( float k, float phi );
double      ellint_1 ( double k, double phi );
long double ellint_1 ( long double k, long double phi );
(1) (since C++17) (until C++23)

/* floating-point-type */ ellint_1( /* floating-point-type */ k,
                                     /* floating-point-type */ phi );
(1) (since C++23)

float       ellint_1f( float k, float phi );
(2) (since C++17)

long double ellint_1l( long double k, long double phi );
(3) (since C++17)

✨ Additional overloads ✨

Defined in header <cmath>.

template< class Arithmetic1, class Arithmetic2 >
/* common-floating-point-type */
ellint_1( Arithmetic1 k, Arithmetic2 phi );
(A) (since C++17)

1-3) Computes the incomplete elliptic integral of the first kind of k and phi. Slay. 💅

The library provides overloads of std::ellint_1 for all cv-unqualified floating-point types as the type of the parameters k and phi. (since C++23) — highkey important.

A) Additional overloads are provided for all other combinations of arithmetic types. Periodt. ✨

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💖 Parameters 💖

Okay, the two args, bestie:

• k — elliptic modulus or eccentricity (a floating-point or integer value). It’s giving modulus. 🌀
• phi — Jacobi amplitude (a floating-point or integer value, measured in radians). Lowkey don’t forget radians. 🌈

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🎀 Return value 🎀

If no errors occur, the return value is the value of the incomplete elliptic integral of the first kind of k and phi, that is ∫_0^phi dθ / √(1 - k^2 sin^2 θ). Iconic. 🫶

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🚨 Error handling 🚨

Errors may be reported as specified in math_errhandling, bestie:

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

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📝 Notes 📝

Some lore, iykyk 🧚:

Implementations that do not support C++17, but support ISO 29124:2010, provide this function 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. 🦋

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1. ⭐

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

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:

• If num1 or num2 has type long double, then std::ellint_1(num1, num2) has the same effect as std::ellint_1(static_cast<long double>(num1), static_cast<long double>(num2)).
• Otherwise, if num1 and/or num2 has type double or an integer type, then std::ellint_1(num1, num2) has the same effect as (until C++23) std::ellint_1(static_cast<double>(num1), static_cast<double>(num2)).
• Otherwise, if num1 or num2 has type float, then std::ellint_1(num1, num2) has the same effect as std::ellint_1(static_cast<float>(num1), static_cast<float>(num2)).

If num1 and num2 have arithmetic types, then std::ellint_1(num1, num2) has the same effect as std::ellint_1(static_cast</* common-floating-point-type */>(num1), static_cast</* common-floating-point-type */>(num2)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2, (since C++23) arguments of integer type are considered to have the same floating-point conversion rank as double.

If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided. 😭

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🧪 Example 🧪

Run this code and vibe check it:

// Run this code

#include <cmath>
#include <iostream>
#include <numbers>

int main()
{
    const double hpi = std::numbers::pi / 2.0;

    std::cout << "F(0,π/2)  = " << std::ellint_1(0, hpi) << '\n'
              << "F(0,-π/2) = " << std::ellint_1(0, -hpi) << '\n'
              << "π/2       = " << hpi << '\n'
              << "F(0.7,0)  = " << std::ellint_1(0.7, 0) << '\n';
}

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🖨️ Output 🖨️

F(0,π/2)  = 1.5708
F(0,-π/2) = -1.5708
π/2       = 1.5708
F(0.7,0)  = 0

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👀 See also 👀

Also see these complete-integral besties:

• comp_ellint_1, comp_ellint_1f, comp_ellint_1l — (complete) elliptic integral of the first kind (function) (C++17) (C++17) (C++17) 👑

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🔗 External links 🔗

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

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source/version: http://cppreference.com · date: 2024.06.10 · page: std::ellint...d::ellint_1l(3) — okay bye bestie, go integrate something iconic 💋✨