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

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< cpp‎ | numeric‎ | math
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{{cpp/title|cos}}
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{{cpp/title|cos|cosf|cosl}}
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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=cos
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{{ddcl list item |
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|param1=num
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float      cos( float arg );
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|constexpr_since=26
 +
|desc=Computes the cosine of {{c|num}} (measured in radians).
 
}}
 
}}
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{{ddcl list item |
+
 
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double      cos( double arg );
+
===Parameters===
 +
{{par begin}}
 +
{{par|num|floating-point or integer value representing angle in radians}}
 +
{{par end}}
 +
 
 +
===Return value===
 +
If no errors occur, the cosine of {{c|num}} ({{math|cos(num)}}) in the range {{closed range|-1.0|+1.0}}, is returned.
 +
 
 +
{{rrev|until=c++11|
 +
The result may have little or no significance if the magnitude of {{c|num}} is large.
 
}}
 
}}
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{{ddcl list item |
 
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long double cos( long double arg );
 
−
}}
 
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{{ddcl list end}}
 
  
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Computes cosine of {{tt|arg}}
+
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
  
−
<!-- ======== -->
+
If a range error occurs due to underflow, the correct result (after rounding) is returned.
−
{{params}}
+
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{{param list begin}}
+
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{{param list item | arg | floating point value representing angle in radians}}
+
−
{{param list end}}
+
  
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<!-- ======== -->
+
===Error handling===
−
{{returns}}
+
Errors are reported as specified in {{lc|math_errhandling}}.
  
−
cosine of {{tt|arg}} in the range {{tt|[-1.0 ; 1.0]}}.  
+
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 +
* if the argument is ±0, the result is {{c|1.0}}.
 +
* if the argument is ±∞, NaN is returned and {{lc|FE_INVALID}} is raised.
 +
* if the argument is NaN, NaN is returned.
  
−
Domain error occurs if {{tt|arg}} is infinite. {{cpp|NAN}} is returned in that case.
+
===Notes===
 +
The case where the argument is infinite is not specified to be a domain error in C, but it is defined as a [https://pubs.opengroup.org/onlinepubs/9699919799/functions/cos.html domain error in POSIX].
 +
 
 +
{{cpp/numeric/math/additional integer overload note|cos}}
 +
 
 +
===Example===
 +
{{example
 +
|code=
 +
#include <cerrno>
 +
#include <cfenv>
 +
#include <cmath>
 +
#include <iomanip>
 +
#include <iostream>
 +
#include <numbers>
 +
 
 +
// #pragma STDC FENV_ACCESS ON
 +
 
 +
constexpr double pi = std::numbers::pi; // or std::acos(-1) before C++20
 +
 
 +
constexpr double your_cos(double x)
 +
{
 +
    double cos{1}, pow{x};
 +
    for (auto fac{1ull}, n{1ull}; n != 19; fac *= ++n, pow *= x)
 +
        if ((n & 1) == 0)
 +
            cos += (n & 2 ? -pow : pow) / fac;
 +
    return cos;
 +
}
 +
 
 +
int main()
 +
{
 +
    std::cout << std::setprecision(10) << std::showpos
 +
              << "Typical usage:\n"
 +
              << "std::cos(pi/3) = " << std::cos(pi / 3) << '\n'
 +
              << "your cos(pi/3) = " << your_cos(pi / 3) << '\n'
 +
              << "std::cos(pi/2) = " << std::cos(pi / 2) << '\n'
 +
              << "your cos(pi/2) = " << your_cos(pi / 2) << '\n'
 +
              << "std::cos(-3*pi/4) = " << std::cos(-3 * pi / 4) << '\n'
 +
              << "your cos(-3*pi/4) = " << your_cos(-3 * pi / 4) << '\n'
 +
              << "Special values:\n"
 +
              << "std::cos(+0) = " << std::cos(0.0) << '\n'
 +
              << "std::cos(-0) = " << std::cos(-0.0) << '\n';
 +
 
 +
    // error handling
 +
    std::feclearexcept(FE_ALL_EXCEPT);
 +
 
 +
    std::cout << "cos(INFINITY) = " << std::cos(INFINITY) << '\n';
 +
    if (std::fetestexcept(FE_INVALID))
 +
        std::cout << "    FE_INVALID raised\n";
 +
}
 +
|p=true
 +
|output=
 +
Typical usage:
 +
std::cos(pi/3) = +0.5
 +
your cos(pi/3) = +0.5
 +
std::cos(pi/2) = +6.123233996e-17
 +
your cos(pi/2) = -3.373452105e-15
 +
std::cos(-3*pi/4) = -0.7071067812
 +
your cos(-3*pi/4) = -0.7071067812
 +
Special values:
 +
std::cos(+0) = +1
 +
std::cos(-0) = +1
 +
cos(INFINITY) = -nan
 +
    FE_INVALID raised
 +
}}
  
−
<!-- ======== -->
+
===See also===
−
{{see also}}
+
{{dsc begin}}
 +
{{dsc inc|cpp/numeric/math/dsc sin}}
 +
{{dsc inc|cpp/numeric/math/dsc tan}}
 +
{{dsc inc|cpp/numeric/math/dsc acos}}
 +
{{dsc inc|cpp/numeric/complex/dsc cos}}
 +
{{dsc inc|cpp/numeric/valarray/dsc cos}}
 +
{{dsc see c|c/numeric/math/cos}}
 +
{{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 sin}}
+
−
{{dcl list template | cpp/numeric/math/dcl list tan}}
+
−
{{dcl list template | cpp/numeric/math/dcl list acos}}
+
−
{{dcl list end}}
+

Latest revision as of 08:47, 13 November 2023

 
C++
 
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Defined in header <cmath>
(1)
float       cos ( float num );

double      cos ( double num );

long double cos ( long double num );
 (until C++23)
/* floating-point-type */
            cos ( /* floating-point-type */ num );
 (since C++23)
(constexpr since C++26)
float       cosf( float num );
 (2) (since C++11)
(constexpr since C++26)
long double cosl( long double num );
 (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >
double      cos ( Integer num );
 (A) (constexpr since C++26)
1-3) Computes the cosine of num (measured in radians). The library provides overloads of std::cos 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 representing angle in radians

[edit] Return value

If no errors occur, the cosine of num (cos(num)) in the range [-1.0, +1.0], is returned.

The result may have little or no significance if the magnitude of num is large.

(until C++11)

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

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, the result is 1.0.
  • if the argument is ±∞, NaN is returned and FE_INVALID is raised.
  • if the argument is NaN, NaN is returned.

[edit] Notes

The case where the argument is infinite is not specified to be a domain error in C, but it is defined as a domain error in POSIX.

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

[edit] Example

Run this code
#include <cerrno>
#include <cfenv>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <numbers>
 
// #pragma STDC FENV_ACCESS ON
 
constexpr double pi = std::numbers::pi; // or std::acos(-1) before C++20
 
constexpr double your_cos(double x)
{
    double cos{1}, pow{x};
    for (auto fac{1ull}, n{1ull}; n != 19; fac *= ++n, pow *= x)
        if ((n & 1) == 0)
            cos += (n & 2 ? -pow : pow) / fac;
    return cos;
}
 
int main()
{
    std::cout << std::setprecision(10) << std::showpos
              << "Typical usage:\n"
              << "std::cos(pi/3) = " << std::cos(pi / 3) << '\n'
              << "your cos(pi/3) = " << your_cos(pi / 3) << '\n'
              << "std::cos(pi/2) = " << std::cos(pi / 2) << '\n'
              << "your cos(pi/2) = " << your_cos(pi / 2) << '\n'
              << "std::cos(-3*pi/4) = " << std::cos(-3 * pi / 4) << '\n'
              << "your cos(-3*pi/4) = " << your_cos(-3 * pi / 4) << '\n'
              << "Special values:\n"
              << "std::cos(+0) = " << std::cos(0.0) << '\n'
              << "std::cos(-0) = " << std::cos(-0.0) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "cos(INFINITY) = " << std::cos(INFINITY) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

Possible output: 

Typical usage:
std::cos(pi/3) = +0.5
your cos(pi/3) = +0.5
std::cos(pi/2) = +6.123233996e-17
your cos(pi/2) = -3.373452105e-15
std::cos(-3*pi/4) = -0.7071067812
your cos(-3*pi/4) = -0.7071067812
Special values:
std::cos(+0) = +1
std::cos(-0) = +1
cos(INFINITY) = -nan
    FE_INVALID raised

[edit] See also

(C++11)(C++11)
 computes sine (sin(x))
(function) [edit]
(C++11)(C++11)
 computes tangent (tan(x))
(function) [edit]
(C++11)(C++11)
 computes arc cosine (arccos(x))
(function) [edit]
computes cosine of a complex number (cos(z))
(function template) [edit]
applies the function std::cos to each element of valarray
(function template) [edit]
C documentation for cos
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