# std::tanh, std::tanhf, std::tanhl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float tanh ( float num ); double tanh ( double num ); long double tanh ( long double num ); |  | (until C++23)
/*floating-point-type*/ tanh ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float tanhf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double tanhl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> tanh ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double tanh ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the hyperbolic tangent of num. The library provides overloads of `std::tanh` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::tanh` on v_num.

    (See `math-floating-point` and `deduced-simd-t` for their definitions.)

(since C++26)

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 hyperbolic tangent of num (tanh(num), or

enum -e-num
enum +e-num

) is returned.

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

- if the argument is ±0, ±0 is returned.
- if the argument is ±∞, ±1 is returned.
- if the argument is NaN, NaN is returned.

### Notes

POSIX specifies that in case of underflow, num is returned unmodified, and if that is not supported, and 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::tanh(num) has the same effect as std::tanh(static_cast<double>(num)).

### Example

Run this code

    #include <cmath>
    #include <iostream>
    #include <random>

    double get_random_between(double min, double max)
    {
        std::random_device rd;
        std::mt19937 gen(rd());
        return std::uniform_real_distribution<>(min, max)(gen);
    }

    int main()
    {
        const double x = get_random_between(-1.0, 1.0);

        std::cout << std::showpos
                  << "tanh(+1) = " << std::tanh(+1) << '\n'
                  << "tanh(-1) = " << std::tanh(-1) << '\n'
                  << "tanh(x)*sinh(2*x)-cosh(2*x) = "
                  << std::tanh(x) * std::sinh(2 * x) - std::cosh(2 * x) << '\n'
                  // special values:
                  << "tanh(+0) = " << std::tanh(+0.0) << '\n'
                  << "tanh(-0) = " << std::tanh(-0.0) << '\n';
    }

Output:

    tanh(+1) = +0.761594
    tanh(-1) = -0.761594
    tanh(x)*sinh(2*x)-cosh(2*x) = -1
    tanh(+0) = +0
    tanh(-0) = -0

### See also

sinhsinhfsinhl (C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x)) (function)
coshcoshfcoshl (C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)artanh(x)) (function)
tanh(std::complex) | computes hyperbolic tangent of a complex number (\({\small\tanh{z}}\)tanh(z)) (function template)
tanh(std::valarray) | applies the function std::tanh to each element of valarray (function template)
C documentation for tanh

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