std::atanh,...std::atanhl(3)

okay bestie, welcome to the C++ Standard Library manual page for std::atanh,...std::atanhl — it’s the inverse hyperbolic tangent family and it’s lowkey iconic. 🦋💖

💖 NAME 💖

std::atanh,std::atanhf,std::atanhl — std::atanh,std::atanhf,std::atanhl. Periodt. 💅

🌸 Synopsis 🌸

Defined in header <cmath>

float       atanh ( float num );

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

long double atanh ( long double num );
/* floating-point-type */                                    (since C++23)
                atanh ( /* floating-point-type */ num );
                                                                (constexpr since C++26)
float       atanhf( float num );                     (1) (2) (since C++11)
                                                                (constexpr since C++26)
long double atanhl( long double num );                   (3) (since C++11)
                                                                (constexpr since C++26)

Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >                                (A) (constexpr since C++26)
double      atanh ( Integer num );

1-3) Computes the inverse hyperbolic tangent of num. 🧮✨

The library provides overloads of std::atanh 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. That’s the input, bestie. 🫶

✨ Return value ✨

If no errors occur, the inverse hyperbolic tangent of num (tanh-1 (num), or artanh(num)), is returned. 💖

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

If a pole error occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned (with the correct sign). 🔥

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.

If the argument is not on the interval [-1, +1], a range error occurs.

If the argument is ±1, a pole error occurs.

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

• if the argument is ±0, it is returned unmodified.
• if the argument is ±1, ±∞ is returned and FE_DIVBYZERO is raised.
• if |num|>1, NaN is returned and FE_INVALID is raised.
• if the argument is NaN, NaN is returned.

🦋 Notes 🦋

Although the C standard (to which C++ refers for this function) names this function "arc hyperbolic tangent", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic tangent" (used by POSIX) or "area hyperbolic tangent". 🧚💜

POSIX specifies that in case of underflow, num is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

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::atanh(num) has the same effect as std::atanh(static_cast<double>(num)). 👑

🍓 Example 🍓

// Run this code

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

int main()
{
    std::cout << "atanh(0) = " << std::atanh(0) << '\n'
              << "atanh(-0) = " << std::atanh(-0.0) << '\n'
              << "atanh(0.9) = " << std::atanh(0.9) << '\n';

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

    std::cout << "atanh(-1) = " << std::atanh(-1) << '\n';

    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";
}

🌈 Possible output 🌈

atanh(0) = 0
atanh(-0) = -0
atanh(0.9) = 1.47222
atanh(-1) = -inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised

👑 See also 👑

• asinh, asinhf, asinhl (C++11) (C++11) (C++11) — computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)
• acosh, acoshf, acoshl (C++11) (C++11) (C++11) — computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)
• tanh, tanhf, tanhl (C++11) (C++11) — computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)
• atanh(std::complex) (C++11) — computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z}}\)artanh(z)) (function template)
• C documentation for atanh

⭐ External links ⭐

• Weisstein, Eric W. "Inverse Hyperbolic Tangent." From MathWorld — A Wolfram Web Resource.

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mwah 💋 this page’s source/version is http://cppreference.com, stamped 2024.06.10, and the manual tag is std::atanh,...std::atanhl(3). Bye bestie, go compute some area hyperbolic tangent! 🫶💖