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

From cppreference.com
< cpp‎ | numeric‎ | math
m (std::)
m (Example fix.)
 
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{{cpp/title|tanh}}
+
{{cpp/title|tanh|tanhf|tanhl}}
 
{{cpp/numeric/math/navbar}}
 
{{cpp/numeric/math/navbar}}
−
{{dcl begin}}
+
{{cpp/numeric/math/declarations
−
{{dcl header | cmath}}
+
|family=tanh
−
{{dcl |num=1|
+
|param1=num
−
float      tanh( float arg );
+
|constexpr_since=26
 +
|desc=Computes the hyperbolic tangent of {{c|num}}.
 
}}
 
}}
−
{{dcl |num=2|
 
−
double      tanh( double arg );
 
−
}}
 
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{{dcl |num=3|
 
−
long double tanh( long double arg );
 
−
}}
 
−
{{dcl | since=c++11 |num=4|
 
−
double      tanh( Integral arg );
 
−
}}
 
−
{{dcl end}}
 
−
 
−
Computes the hyperbolic tangent of {{tt|arg}}
 
−
@4@ A set of overloads or a function template accepting an argument of any [[cpp/types/is_integral|integral type]]. Equivalent to 2) (the argument is cast to {{c|double}}).
 
  
 
===Parameters===
 
===Parameters===
 
{{par begin}}
 
{{par begin}}
−
{{par | arg | value of a floating-point or [[cpp/types/is_integral|Integral type]]}}
+
{{par|num|floating-point or integer value}}
 
{{par end}}
 
{{par end}}
  
 
===Return value===
 
===Return value===
−
If no errors occur, the hyperbolic tangent of {{tt|arg}} ({{math|tanh(arg)}}, or {{math|{{mfrac|e{{su|p=arg}}-e{{su|p=-arg}}|e{{su|p=arg}}+e{{su|p=-arg}}}}}}) is returned.
+
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.
  
 
If a range error occurs due to underflow, the correct result (after rounding) is returned.
 
If a range error occurs due to underflow, the correct result (after rounding) is returned.
  
 
===Error handling===
 
===Error handling===
−
Errors are reported as specified in [[cpp/numeric/math/math_errhandling|math_errhandling]]
+
Errors are reported as specified in {{lc|math_errhandling}}.
  
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
−
* if the argument is ±0, ±0 is returned
+
* if the argument is ±0, ±0 is returned.
−
* If the argument is ±∞, ±1 is returned
+
* if the argument is ±∞, ±1 is returned.
−
* if the argument is NaN, NaN is returned
+
* if the argument is NaN, NaN is returned.
  
 
===Notes===
 
===Notes===
−
[http://pubs.opengroup.org/onlinepubs/9699919799/functions/tanh.html POSIX specifies] that in case of underflow, {{tt|arg}} 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.
+
[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.
  
−
===Examples===
+
{{cpp/numeric/math/additional integer overload note|tanh}}
−
{{example|
+
 
−
|code=#include <iostream>
+
===Example===
 +
{{example
 +
|code=
 
#include <cmath>
 
#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()
 
int main()
 
{
 
{
−
     std::cout << "tanh(1) = " << std::tanh(1) << '\n'
+
    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(-1) = " << std::tanh(-1) << '\n'
−
               << "tanh(0.1)*sinh(0.2)-cosh(0.2) = "
+
               << "tanh(x)*sinh(2*x)-cosh(2*x) = "
−
               << std::tanh(0.1) * std::sinh(0.2) - std::cosh(0.2) << '\n';
+
               << std::tanh(x) * std::sinh(2 * x) - std::cosh(2 * x) << '\n'
−
    // special values
+
              // special values:
−
    std::cout << "tanh(+0) = " << std::tanh(+0.0) << '\n'
+
              << "tanh(+0) = " << std::tanh(+0.0) << '\n'
−
               << "tanh(-0) = " << std::tanh(-0.0) << '\n';
+
               << "tanh(-0) = " << std::tanh(-0.0) << '\n';
 
}
 
}
 
|output=
 
|output=
−
tanh(1) = 0.761594
+
tanh(+1) = +0.761594
 
tanh(-1) = -0.761594
 
tanh(-1) = -0.761594
−
tanh(0.1)*sinh(0.2)-cosh(0.2) = -1
+
tanh(x)*sinh(2*x)-cosh(2*x) = -1
−
tanh(+0) = 0
+
tanh(+0) = +0
 
tanh(-0) = -0
 
tanh(-0) = -0
 
}}
 
}}
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===See also===
 
===See also===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/numeric/math/dsc sinh}}
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{{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 cosh}}
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{{dsc inc | cpp/numeric/math/dsc atanh}}
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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/complex/dsc tanh}}
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{{dsc inc | cpp/numeric/valarray/dsc tanh}}
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{{dsc inc|cpp/numeric/valarray/dsc tanh}}
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{{dsc see c | c/numeric/math/tanh}}
+
{{dsc see c|c/numeric/math/tanh}}
 
{{dsc end}}
 
{{dsc end}}
  
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[[de:cpp/numeric/math/tanh]]
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{{langlinks|de|es|fr|it|ja|pl|pt|ru|zh}}
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[[es:cpp/numeric/math/tanh]]
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[[fr:cpp/numeric/math/tanh]]
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[[it:cpp/numeric/math/tanh]]
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[[ja:cpp/numeric/math/tanh]]
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[[pl:cpp/numeric/math/tanh]]
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[[pt:cpp/numeric/math/tanh]]
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[[ru:cpp/numeric/math/tanh]]
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[[zh:cpp/numeric/math/tanh]]
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Latest revision as of 22:03, 20 August 2024

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
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Basic linear algebra algorithms (C++26)
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(C++11)
(C++11)
Power functions
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(C++11)
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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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