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

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< cpp‎ | numeric‎ | math
m (correct link)
m ({{closed range}}.)
 
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−
{{cpp/title|sin}}
+
{{cpp/title|sin|sinf|sinl}}
 
{{cpp/numeric/math/navbar}}
 
{{cpp/numeric/math/navbar}}
−
{{dcl begin}}
+
{{cpp/numeric/math/declarations
−
{{dcl header | cmath}}
+
|family=sin
−
{{dcl |num=1|
+
|param1=num
−
float      sin( float arg );
+
|constexpr_since=26
 +
|desc=Computes the sine of {{c|num}} (measured in radians).
 
}}
 
}}
−
{{dcl |num=2|
 
−
double      sin( double arg );
 
−
}}
 
−
{{dcl |num=3|
 
−
long double sin( long double arg );
 
−
}}
 
−
{{dcl |num=4| since=c++11 |
 
−
double      sin( Integral arg );
 
−
}}
 
−
{{dcl end}}
 
−
 
−
Computes the sine of {{tt|arg}} (measured in radians).
 
−
@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 representing angle in radians, of a floating-point or [[cpp/types/is_integral|Integral type]]}}
+
{{par|num|floating-point or integer value representing angle in radians}}
 
{{par end}}
 
{{par end}}
  
 
===Return value===
 
===Return value===
−
If no errors occur, the sine of {{tt|arg}} ({{math|sin(arg)}}) in the range {{math|[-1 ; +1]}}, is returned.
+
If no errors occur, the sine of {{c|num}} ({{math|sin(num)}}) in the range {{closed range|-1|+1}}, is returned.
  
−
{{rev begin}}
+
{{rrev|until=c++11|
−
{{rev|until=c++11|
+
The result may have little or no significance if the magnitude of {{c|num}} is large.
−
The result may have little or no significance if the magnitude of {{tt|arg}} is large
+
 
}}
 
}}
−
{{rev end}}
 
  
−
If a domain error occurs, an implementation-defined value is returned (NaN where supported)
+
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.
 
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, it is returned unmodified
+
* if the argument is ±0, it is returned unmodified.
−
* if the argument is ±∞, NaN is returned and {{lc|FE_INVALID}} is raised <!-- not defined as a domain error in C or C++, although defined as a domain error in POSIX -->
+
* if the argument is ±∞, NaN is returned and {{lc|FE_INVALID}} is raised.<!--not defined as a domain error in C or C++, although defined as a domain error in POSIX-->
−
* if the argument is NaN, NaN is returned
+
* if the argument is NaN, NaN is returned.
  
 
===Notes===
 
===Notes===
−
The case where the argument is infinite is not specified to be a domain error in C (to which C++ defers), but it is defined as a [http://pubs.opengroup.org/onlinepubs/9699919799/functions/sin.html domain error in POSIX]
+
The case where the argument is infinite is not specified to be a domain error in C (to which C++ defers), but it is defined as a [https://pubs.opengroup.org/onlinepubs/9699919799/functions/sin.html domain error in POSIX].
  
−
POSIX also specifies that in case of underflow, {{tt|arg}} 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.
+
POSIX also specifies that in case of underflow, {{c|num}} is returned unmodified, and if that is not supported, an implementation-defined value no greater than {{lc|DBL_MIN}}, {{lc|FLT_MIN}}, and {{lc|LDBL_MIN}} is returned.
 +
 
 +
{{cpp/numeric/math/additional integer overload note|sin}}
  
 
===Example===
 
===Example===
−
{{example|code=
+
{{example
−
#include <iostream>
+
|code=
−
#include <cmath>
+
 
#include <cerrno>
 
#include <cerrno>
 
#include <cfenv>
 
#include <cfenv>
 +
#include <cmath>
 +
#include <iomanip>
 +
#include <iostream>
 +
 +
// #pragma STDC FENV_ACCESS ON
 +
 +
const double pi = std::acos(-1); // or std::numbers::pi since C++20
 +
 +
constexpr double your_sin(double x)
 +
{
 +
    double sin{0}, pow{x};
 +
    for (auto fac{1LLU}, n{1ULL}; n != 20; fac *= ++n, pow *= x)
 +
        if (n & 1)
 +
            sin += (n & 2 ? -pow : pow) / fac;
 +
    return sin;
 +
}
  
−
#pragma STDC FENV_ACCESS ON
 
−
const double pi = std::acos(-1);
 
 
int main()
 
int main()
 
{
 
{
−
    // typical usage
+
     std::cout << std::setprecision(10) << std::showpos
−
     std::cout << "sin(pi/6) = " << std::sin(pi/6) << '\n'
+
              << "Typical usage:\n"
−
               << "sin(pi/2) = " << std::sin(pi/2) << '\n'
+
              << "std::sin(pi/6) = " << std::sin(pi / 6) << '\n'
−
               << "sin(-3*pi/4) = " << std::sin(-3*pi/4) << '\n';
+
               << "your sin(pi/6) = " << your_sin(pi / 6) << '\n'
−
    // special values
+
              << "std::sin(pi/2) = " << std::sin(pi / 2) << '\n'
−
    std::cout << "sin(+0) = " << std::sin(0.0) << '\n'
+
               << "your sin(pi/2) = " << your_sin(pi / 2) << '\n'
−
               << "sin(-0) = " << std::sin(-0.0) << '\n';
+
              << "std::sin(-3*pi/4) = " << std::sin(-3 * pi / 4) << '\n'
−
     // error handling  
+
              << "your sin(-3*pi/4) = " << your_sin(-3 * pi / 4) << '\n'
 +
              << "Special values:\n"
 +
              << "std::sin(+0) = " << std::sin(0.0) << '\n'
 +
               << "std::sin(-0) = " << std::sin(-0.0) << '\n';
 +
 
 +
     // error handling
 
     std::feclearexcept(FE_ALL_EXCEPT);
 
     std::feclearexcept(FE_ALL_EXCEPT);
−
     std::cout << "sin(INFINITY) = " << std::sin(INFINITY) << '\n';
+
 
−
     if(std::fetestexcept(FE_INVALID)) std::cout << "    FE_INVALID raised\n";
+
     std::cout << "std::sin(INFINITY) = " << std::sin(INFINITY) << '\n';
 +
     if (std::fetestexcept(FE_INVALID))
 +
        std::cout << "    FE_INVALID raised\n";
 
}
 
}
 
|p=true
 
|p=true
 
|output=
 
|output=
−
sin(pi/6) = 0.5
+
Typical usage:
−
sin(pi/2) = 1
+
std::sin(pi/6) = +0.5
−
sin(-3*pi/4) = -0.707107
+
your sin(pi/6) = +0.5
−
sin(+0) = 0
+
std::sin(pi/2) = +1
−
sin(-0) = -0
+
your sin(pi/2) = +1
−
sin(INFINITY) = -nan
+
std::sin(-3*pi/4) = -0.7071067812
 +
your sin(-3*pi/4) = -0.7071067812
 +
Special values:
 +
std::sin(+0) = +0
 +
std::sin(-0) = -0
 +
std::sin(INFINITY) = -nan
 
     FE_INVALID raised
 
     FE_INVALID raised
 
}}
 
}}
Line 87: Line 100:
 
===See also===
 
===See also===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/numeric/math/dsc cos}}
+
{{dsc inc|cpp/numeric/math/dsc cos}}
−
{{dsc inc | cpp/numeric/math/dsc tan}}
+
{{dsc inc|cpp/numeric/math/dsc tan}}
−
{{dsc inc | cpp/numeric/math/dsc asin}}
+
{{dsc inc|cpp/numeric/math/dsc asin}}
−
{{dsc inc | cpp/numeric/complex/dsc sin}}
+
{{dsc inc|cpp/numeric/complex/dsc sin}}
−
{{dsc inc | cpp/numeric/valarray/dsc sin}}
+
{{dsc inc|cpp/numeric/valarray/dsc sin}}
−
{{dsc see c | c/numeric/math/sin}}
+
{{dsc see c|c/numeric/math/sin}}
 
{{dsc end}}
 
{{dsc end}}
  
 
{{langlinks|de|es|fr|it|ja|pl|pt|ru|zh}}
 
{{langlinks|de|es|fr|it|ja|pl|pt|ru|zh}}

Latest revision as of 08:45, 13 November 2023

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Common mathematical functions
Functions
Basic operations
(C++11)  
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)(C++11)(C++11)
Exponential functions
(C++11)
(C++11)

(C++11)
(C++11)
Power functions
(C++11)
(C++11)
Trigonometric and
hyperbolic functions
(C++11)
(C++11)
(C++11)

Error and gamma functions
(C++11)
(C++11)
(C++11)
(C++11)
Nearest integer floating point operations
(C++11)(C++11)(C++11)
(C++11)
(C++11)
(C++11)(C++11)(C++11)
Floating point manipulation functions
(C++11)(C++11)
(C++11)
(C++11)
(C++11)(C++11)
(C++11)
Classification and comparison
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
Types
(C++11)
(C++11)
(C++11)
Macro constants
 
Defined in header <cmath>
(1)
float       sin ( float num );

double      sin ( double num );

long double sin ( long double num );
 (until C++23)
/* floating-point-type */
            sin ( /* floating-point-type */ num );
 (since C++23)
(constexpr since C++26)
float       sinf( float num );
 (2) (since C++11)
(constexpr since C++26)
long double sinl( long double num );
 (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >
double      sin ( Integer num );
 (A) (constexpr since C++26)
1-3) Computes the sine of num (measured in radians). The library provides overloads of std::sin 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 sine of num (sin(num)) in the range [-1, +1], 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, it is returned unmodified.
  • 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 (to which C++ defers), but it is defined as a domain error in POSIX.

POSIX also 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::sin(num) has the same effect as std::sin(static_cast<double>(num)).

[edit] Example

Run this code
#include <cerrno>
#include <cfenv>
#include <cmath>
#include <iomanip>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
const double pi = std::acos(-1); // or std::numbers::pi since C++20
 
constexpr double your_sin(double x)
{
    double sin{0}, pow{x};
    for (auto fac{1LLU}, n{1ULL}; n != 20; fac *= ++n, pow *= x)
        if (n & 1)
            sin += (n & 2 ? -pow : pow) / fac;
    return sin;
}
 
int main()
{
    std::cout << std::setprecision(10) << std::showpos
              << "Typical usage:\n"
              << "std::sin(pi/6) = " << std::sin(pi / 6) << '\n'
              << "your sin(pi/6) = " << your_sin(pi / 6) << '\n'
              << "std::sin(pi/2) = " << std::sin(pi / 2) << '\n'
              << "your sin(pi/2) = " << your_sin(pi / 2) << '\n'
              << "std::sin(-3*pi/4) = " << std::sin(-3 * pi / 4) << '\n'
              << "your sin(-3*pi/4) = " << your_sin(-3 * pi / 4) << '\n'
              << "Special values:\n"
              << "std::sin(+0) = " << std::sin(0.0) << '\n'
              << "std::sin(-0) = " << std::sin(-0.0) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "std::sin(INFINITY) = " << std::sin(INFINITY) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

Possible output: 

Typical usage:
std::sin(pi/6) = +0.5
your sin(pi/6) = +0.5
std::sin(pi/2) = +1
your sin(pi/2) = +1
std::sin(-3*pi/4) = -0.7071067812
your sin(-3*pi/4) = -0.7071067812
Special values:
std::sin(+0) = +0
std::sin(-0) = -0
std::sin(INFINITY) = -nan
    FE_INVALID raised

[edit] See also

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