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Difference between revisions of "cpp/numeric/math/tanh"

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< cpp‎ | numeric‎ | math
m (1 revision: import content)
m (Example fix.)
 
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{{cpp/title|tanh}}
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{{cpp/title|tanh|tanhf|tanhl}}
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{{cpp/numeric/math/sidebar}}
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{{cpp/numeric/math/navbar}}
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{{ddcl list begin}}
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{{cpp/numeric/math/declarations
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{{ddcl list header | cmath}}
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|family=tanh
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{{ddcl list item |
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|param1=num
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float      tanh( float arg );
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|constexpr_since=26
 +
|desc=Computes the hyperbolic tangent of {{c|num}}.
 
}}
 
}}
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{{ddcl list item |
 
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double      tanh( double arg );
 
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}}
 
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{{ddcl list item |
 
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long double tanh( long double arg );
 
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}}
 
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{{ddcl list end}}
 
  
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Computes hyperbolic tangent of {{tt|arg}}
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===Parameters===
 +
{{par begin}}
 +
{{par|num|floating-point or integer value}}
 +
{{par end}}
  
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<!-- ======== -->
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===Return value===
−
{{params}}
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If no errors occur, the hyperbolic tangent of {{c|num}} ({{math|tanh(num)}}, or {{math|{{mfrac|e{{su|p=num}}-e{{su|p=-num}}|e{{su|p=num}}+e{{su|p=-num}}}}}}) is returned.
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{{param list begin}}
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{{param list item | arg | floating point value}}
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{{param list end}}
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<!-- ======== -->
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If a range error occurs due to underflow, the correct result (after rounding) is returned.
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{{returns}}
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hyperbolic tangent of {{tt|arg}}
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===Error handling===
 +
Errors are reported as specified in {{lc|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===
 +
[https://pubs.opengroup.org/onlinepubs/9699919799/functions/tanh.html POSIX specifies] that in case of underflow, {{c|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.
 +
 
 +
{{cpp/numeric/math/additional integer overload note|tanh}}
 +
 
 +
===Example===
 +
{{example
 +
|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
 +
}}
  
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<!-- ======== -->
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===See also===
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{{see also}}
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{{dsc begin}}
 +
{{dsc inc|cpp/numeric/math/dsc sinh}}
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{{dsc inc|cpp/numeric/math/dsc cosh}}
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{{dsc inc|cpp/numeric/math/dsc atanh}}
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{{dsc inc|cpp/numeric/complex/dsc tanh}}
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{{dsc inc|cpp/numeric/valarray/dsc tanh}}
 +
{{dsc see c|c/numeric/math/tanh}}
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{{dsc end}}
  
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{{dcl list begin}}
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{{langlinks|de|es|fr|it|ja|pl|pt|ru|zh}}
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{{dcl list template | cpp/numeric/math/dcl list sinh}}
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{{dcl list template | cpp/numeric/math/dcl list cosh}}
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{{dcl list template | cpp/numeric/math/dcl list atanh}}
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{{dcl list end}}
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Latest revision as of 22:03, 20 August 2024

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
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tanh
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Macro constants
 
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)
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)
A) Additional overloads are provided for all integer types, which are treated as double.
 (since C++11)

Contents

[edit] Parameters

num - floating-point or integer value

[edit] 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.

[edit] 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.

[edit] 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)).

[edit] 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

[edit] See also

(C++11)(C++11)
 computes hyperbolic sine (sinh(x))
(function) [edit]
(C++11)(C++11)
 computes hyperbolic cosine (cosh(x))
(function) [edit]
(C++11)(C++11)(C++11)
 computes the inverse hyperbolic tangent (artanh(x))
(function) [edit]
computes hyperbolic tangent of a complex number (tanh(z))
(function template) [edit]
applies the function std::tanh to each element of valarray
(function template) [edit]
C documentation for tanh
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