Trigonometric functions¶

`acos` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> acos(const T1 &x)

Returns the arc cosine of x. The returned angle is in the range 0 through \(\pi\).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_INTRINSIC flt_type<T1> acos(const T1& x)
{
    return intrinsics::acos(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/asin_acos.hpp#L56

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::acos, E1> acos(E1 &&x)

Returns template expression that returns the arc cosine of x.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_INTRINSIC internal::expression_function<fn::acos, E1> acos(E1&& x)
{
    return { fn::acos(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/asin_acos.hpp#L65

`asin` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> asin(const T1 &x)

Returns the arc sine of x. The returned angle is in the range \(-\pi/2\) through \(\pi/2\).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_INTRINSIC flt_type<T1> asin(const T1& x)
{
    return intrinsics::asin(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/asin_acos.hpp#L39

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::asin, E1> asin(E1 &&x)

Returns template expression that returns the arc sine of x.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_INTRINSIC internal::expression_function<fn::asin, E1> asin(E1&& x)
{
    return { fn::asin(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/asin_acos.hpp#L48

`atan` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> atan(const T1 &x)

Returns the arc tangent of x. The returned angle is in the range \(-\pi/2\) through \(\pi/2\).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> atan(const T1& x)
{
    return intrinsics::atan(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L40

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::atan, E1> atan(E1 &&x)

Returns template expression that returns the arc tangent of x.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::atan, E1> atan(E1&& x)
{
    return { fn::atan(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L49

`atan2` function¶

template <typename T1, typename T2,
          KFR_ENABLE_IF(is_numeric_args<T1, T2>)>
common_type<T1, T2> atan2(const T1 &x, const T2 &y)

Returns the arc tangent of y/x using the signs of arguments to determine the correct quadrant.

Source code

template <typename T1, typename T2, KFR_ENABLE_IF(is_numeric_args<T1, T2>)>
KFR_FUNCTION common_type<T1, T2> atan2(const T1& x, const T2& y)
{
    return intrinsics::atan2(x, y);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L77

template <typename E1, typename E2,
          KFR_ENABLE_IF(is_input_expressions<E1, E2>)>
internal::expression_function<fn::atan2, E1, E2>
atan2(E1 &&x, E2 &&y)

Returns template expression that returns the arc tangent of y/x.

Source code

template <typename E1, typename E2, KFR_ENABLE_IF(is_input_expressions<E1, E2>)>
KFR_FUNCTION internal::expression_function<fn::atan2, E1, E2> atan2(E1&& x, E2&& y)
{
    return { fn::atan2(), std::forward<E1>(x), std::forward<E2>(y) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L86

`atan2deg` function¶

template <typename T1, typename T2,
          KFR_ENABLE_IF(is_numeric_args<T1, T2>)>
common_type<T1, T2> atan2deg(const T1 &x, const T2 &y)

Returns the arc tangent of y/x (expressed in degrees) using the signs of arguments to determine the correct quadrant.

Source code

template <typename T1, typename T2, KFR_ENABLE_IF(is_numeric_args<T1, T2>)>
KFR_FUNCTION common_type<T1, T2> atan2deg(const T1& x, const T2& y)
{
    return intrinsics::atan2deg(x, y);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L96

template <typename E1, typename E2,
          KFR_ENABLE_IF(is_input_expressions<E1, E2>)>
internal::expression_function<fn::atan2deg, E1, E2>
atan2deg(E1 &&x, E2 &&y)

Returns template expression that returns the arc tangent of y/x (expressed in degrees).

Source code

template <typename E1, typename E2, KFR_ENABLE_IF(is_input_expressions<E1, E2>)>
KFR_FUNCTION internal::expression_function<fn::atan2deg, E1, E2> atan2deg(E1&& x, E2&& y)
{
    return { fn::atan2deg(), std::forward<E1>(x), std::forward<E2>(y) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L105

`atandeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> atandeg(const T1 &x)

Returns the arc tangent of the x, expressed in degrees. The returned angle is in the range -90 through 90.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> atandeg(const T1& x)
{
    return intrinsics::atandeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L59

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::atandeg, E1>
atandeg(E1 &&x)

Returns template expression that returns the arc tangent of the x, expressed in degrees.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::atandeg, E1> atandeg(E1&& x)
{
    return { fn::atandeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/atan.hpp#L68

`cos` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> cos(const T1 &x)

Returns the trigonometric cosine of x.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> cos(const T1& x)
{
    return intrinsics::cos(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L57

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::cos, E1> cos(E1 &&x)

Returns the trigonometric cosine of x. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::cos, E1> cos(E1&& x)
{
    return { fn::cos(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L66

`cos2x` function¶

template <typename T> T cos2x(const T &sinx, const T &cosx)

Returns the trigonometric cosine of the angle 2x using already computed sin(x) and cos(x).

Source code

template <typename T>
KFR_INTRINSIC T cos2x(const T& sinx, const T& cosx)
{
    return sqr(cosx) - sqr(sinx);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L304

`cos3x` function¶

template <typename T> T cos3x(const T &sinx, const T &cosx)

Returns the trigonometric cosine of the angle 3x using already computed sin(x) and cos(x).

Source code

template <typename T>
KFR_INTRINSIC T cos3x(const T& sinx, const T& cosx)
{
    return cosx * (1 - 4 * sqr(sinx));
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L313

`cosdeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> cosdeg(const T1 &x)

Returns the trigonometric cosine of the x (expressed in degrees).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> cosdeg(const T1& x)
{
    return intrinsics::cosdeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L169

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::cosdeg, E1> cosdeg(E1 &&x)

Returns the trigonometric cosine of the x (expressed in degrees). Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::cosdeg, E1> cosdeg(E1&& x)
{
    return { fn::cosdeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L178

`cossin` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> cossin(const T1 &x)

Returns the trigonometric cosine of the even elements of the x and sine of the odd elements. x must be a vector.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> cossin(const T1& x)
{
    return intrinsics::cossin(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L132

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::cossin, E1> cossin(E1 &&x)

Returns the trigonometric cosine of the even elements of the x and sine of the odd elements. x must be a vector. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::cossin, E1> cossin(E1&& x)
{
    return { fn::cossin(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L142

`cossindeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> cossindeg(const T1 &x)

Returns the trigonometric cosine of the even elements of the x and sine of the odd elements. x must be a vector and expressed in degrees.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> cossindeg(const T1& x)
{
    return intrinsics::cossindeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L246

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::cossindeg, E1>
cossindeg(E1 &&x)

Returns the trigonometric cosine of the even elements of the x and sine of the odd elements. x must be expressed in degrees. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::cossindeg, E1> cossindeg(E1&& x)
{
    return { fn::cossindeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L256

`fastcos` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> fastcos(const T1 &x)

Returns an approximation of the trigonometric cosine of x.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> fastcos(const T1& x)
{
    return intrinsics::fastcos(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L93

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::fastcos, E1>
fastcos(E1 &&x)

Returns an approximation of the trigonometric cosine of x. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::fastcos, E1> fastcos(E1&& x)
{
    return { fn::fastcos(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L102

`fastcosdeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> fastcosdeg(const T1 &x)

Returns an approximation of the trigonometric cosine of the x (expressed in degrees).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> fastcosdeg(const T1& x)
{
    return intrinsics::fastcosdeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L206

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::fastcosdeg, E1>
fastcosdeg(E1 &&x)

Returns an approximation of the trigonometric cosine of the x (expressed in degrees). Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::fastcosdeg, E1> fastcosdeg(E1&& x)
{
    return { fn::fastcosdeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L216

`fastsin` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> fastsin(const T1 &x)

Returns an approximation of the trigonometric sine of x.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> fastsin(const T1& x)
{
    return intrinsics::fastsin(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L75

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::fastsin, E1>
fastsin(E1 &&x)

Returns an approximation of the trigonometric sine of x. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::fastsin, E1> fastsin(E1&& x)
{
    return { fn::fastsin(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L84

`fastsindeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> fastsindeg(const T1 &x)

Returns an approximation of the trigonometric sine of the x (expressed in degrees).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> fastsindeg(const T1& x)
{
    return intrinsics::fastsindeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L187

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::fastsindeg, E1>
fastsindeg(E1 &&x)

Returns an approximation of the trigonometric sine of the x (expressed in degrees). Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::fastsindeg, E1> fastsindeg(E1&& x)
{
    return { fn::fastsindeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L197

`sin` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> sin(const T1 &x)

Returns the trigonometric sine of x.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> sin(const T1& x)
{
    return intrinsics::sin(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L39

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::sin, E1> sin(E1 &&x)

Returns the trigonometric sine of x. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::sin, E1> sin(E1&& x)
{
    return { fn::sin(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L48

`sin2x` function¶

template <typename T> T sin2x(const T &sinx, const T &cosx)

Returns the trigonometric sine of the angle 2x using sin(x) and cos(x).

Source code

template <typename T>
KFR_INTRINSIC T sin2x(const T& sinx, const T& cosx)
{
    return 2 * sinx * cosx;
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L286

`sin3x` function¶

template <typename T> T sin3x(const T &sinx, const T &cosx)

Returns the trigonometric sine of the angle 3x using already computed sin(x) and cos(x).

Source code

template <typename T>
KFR_INTRINSIC T sin3x(const T& sinx, const T& cosx)
{
    return sinx * (-1 + 4 * sqr(cosx));
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L295

`sinc` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> sinc(const T1 &x)

Returns the sinc function of x.

\[ sinc(x) = \frac{sin(x)}{x} \]

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> sinc(const T1& x)
{
    return intrinsics::sinc(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L268

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::sinc, E1> sinc(E1 &&x)

Returns the sinc function of x. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::sinc, E1> sinc(E1&& x)
{
    return { fn::sinc(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L277

`sincos` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> sincos(const T1 &x)

Returns the trigonometric sine of the even elements of the x and cosine of the odd elements. x must be a vector.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> sincos(const T1& x)
{
    return intrinsics::sincos(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L112

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::sincos, E1> sincos(E1 &&x)

Returns the trigonometric sine of the even elements of the x and cosine of the odd elements. x must be a vector. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::sincos, E1> sincos(E1&& x)
{
    return { fn::sincos(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L122

`sincosdeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> sincosdeg(const T1 &x)

Returns the trigonometric sine of the even elements of the x and cosine of the odd elements. x must be a vector and expressed in degrees.

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> sincosdeg(const T1& x)
{
    return intrinsics::sincosdeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L226

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::sincosdeg, E1>
sincosdeg(E1 &&x)

Returns the trigonometric sine of the even elements of the x and cosine of the odd elements. x must be expressed in degrees. Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::sincosdeg, E1> sincosdeg(E1&& x)
{
    return { fn::sincosdeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L236

`sindeg` function¶

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
flt_type<T1> sindeg(const T1 &x)

Returns the trigonometric sine of the x (expressed in degrees).

Source code

template <typename T1, KFR_ENABLE_IF(is_numeric<T1>)>
KFR_FUNCTION flt_type<T1> sindeg(const T1& x)
{
    return intrinsics::sindeg(x);
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L151

template <typename E1,
          KFR_ENABLE_IF(is_input_expression<E1>)>
internal::expression_function<fn::sindeg, E1> sindeg(E1 &&x)

Returns the trigonometric sine of the x (expressed in degrees). Accepts and returns expressions.

Source code

template <typename E1, KFR_ENABLE_IF(is_input_expression<E1>)>
KFR_FUNCTION internal::expression_function<fn::sindeg, E1> sindeg(E1&& x)
{
    return { fn::sindeg(), std::forward<E1>(x) };
}

https://github.com/kfrlib/kfr/blob//include/kfr/math/sin_cos.hpp#L160

Auto-generated from sources, Revision , https://github.com/kfrlib/kfr/blob//include/kfr/

Trigonometric functions¶

acos function¶

asin function¶

atan function¶

atan2 function¶

atan2deg function¶

atandeg function¶

cos function¶

cos2x function¶

cos3x function¶

cosdeg function¶

cossin function¶

cossindeg function¶

fastcos function¶

fastcosdeg function¶

fastsin function¶

fastsindeg function¶

sin function¶

sin2x function¶

sin3x function¶

sinc function¶

sincos function¶

sincosdeg function¶

sindeg function¶

`acos` function¶

`asin` function¶

`atan` function¶

`atan2` function¶

`atan2deg` function¶

`atandeg` function¶

`cos` function¶

`cos2x` function¶

`cos3x` function¶

`cosdeg` function¶

`cossin` function¶

`cossindeg` function¶

`fastcos` function¶

`fastcosdeg` function¶

`fastsin` function¶

`fastsindeg` function¶

`sin` function¶

`sin2x` function¶

`sin3x` function¶

`sinc` function¶

`sincos` function¶

`sincosdeg` function¶

`sindeg` function¶