Detailed Description

Functions that implement math functions. Take care that some of the implementations will return results with less precision than what the FPU calculates.

Functions
template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >	sin (const Vector< T, Abi > &x)
	Returns the sine of all input values in `x`.

template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >	cos (const Vector< T, Abi > &x)
	Returns the cosine of all input values in `x`.

template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >	asin (const Vector< T, Abi > &x)
	Returns the arcsine of all input values in `x`.

template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >	atan (const Vector< T, Abi > &x)
	Returns the arctangent of all input values in `x`.

template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >	atan2 (const Vector< T, Abi > &y, const Vector< T, Abi > &x)
	Returns the arctangent of all input values in `x` and `y`.

template<typename T , typename Abi >
void	sincos (const Vector< T, Abi > &x, Vector< T, detail::not_fixed_size_abi< Abi > > sin, Vector< T, Abi > cos)

template<typename T , typename Abi , typename = enable_if<std::is_floating_point<T>::value && !detail::is_fixed_size_abi<Abi>::value>>
Vector< T, Abi >	copysign (Vector< T, Abi > magnitude, Vector< T, Abi > sign)
	Copies the sign(s) of `sign` to the value(s) in `magnitude` and returns the resulting vector.

template<typename T , typename Abi , typename = enable_if<std::is_floating_point<T>::value && !detail::is_fixed_size_abi<Abi>::value>>
Vector< T, Abi >	exponent (Vector< T, Abi > x)
	Extracts the exponent of each floating-point vector component.

template<typename T , typename Abi >
Vector< T, detail::not_fixed_size_abi< Abi > >::MaskType	isnegative (Vector< T, Abi > x)
	Returns for each vector component whether it stores a negative value.

Function Documentation

◆ sin()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > > sin ( const Vector< T, Abi > & x )

inline

Returns the sine of all input values in x.

Parameters

x	The values to apply the sine function on.

Returns: the sine of x.

Note

The single-precision implementation has a precision of max. 2 ulp (mean 0.17 ulp) in the range [-8192, 8192]. (testSin< float_v> with a maximal distance of 2 to the reference (mean: 0.310741))

The double-precision implementation has a precision of max. 3 ulp (mean 1040 ulp) in the range [-8192, 8192]. (testSin<double_v> with a maximal distance of 1 to the reference (mean: 0.170621))

The precision and execution latency depends on:

Abi (e.g. Scalar uses the <cmath> implementation
whether Vc_HAVE_LIBMVEC is defined
for the <cmath> fallback, the implementations differ (e.g. MacOS vs. Linux vs. Windows; fpmath=sse vs. fpmath=387)

Vc versions before 1.4 had different precision.

Definition at line 134 of file trigonometric.h.

◆ cos()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > > cos ( const Vector< T, Abi > & x )

inline

Returns the cosine of all input values in x.

Parameters

x	The values to apply the cosine function on.

Returns: the cosine of x.

Note: The single-precision implementation has a precision of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].; The double-precision implementation has a precision of max. 3 ulp (mean 1160 ulp) in the range [-8192, 8192].; Vc versions before 1.4 had different precision.

Definition at line 151 of file trigonometric.h.

◆ asin()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > > asin ( const Vector< T, Abi > & x )

inline

Returns the arcsine of all input values in x.

Parameters

x	The values to apply the arcsine function on.

Returns: the arcsine of x.

Note: The single-precision implementation has an error of max. 2 ulp (mean 0.3 ulp).; The double-precision implementation has an error of max. 36 ulp (mean 0.4 ulp).

Definition at line 168 of file trigonometric.h.

◆ atan()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > > atan ( const Vector< T, Abi > & x )

inline

Returns the arctangent of all input values in x.

Parameters

x	The values to apply the arctangent function on.

Returns: the arctangent of x.

Note: The single-precision implementation has an error of max. 3 ulp (mean 0.4 ulp) in the range [-8192, 8192].; The double-precision implementation has an error of max. 2 ulp (mean 0.1 ulp) in the range [-8192, 8192].

Definition at line 183 of file trigonometric.h.

◆ atan2()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > > atan2	(	const Vector< T, Abi > &	y,
		const Vector< T, Abi > &	x )

inline

Returns the arctangent of all input values in x and y.

Calculates the angle given the lengths of the opposite and adjacent legs in a right triangle.

Parameters

y	The opposite leg.
x	The adjacent leg.

Returns: the arctangent of y / x.

Definition at line 199 of file trigonometric.h.

◆ sincos()

template<typename T , typename Abi >

void sincos	(	const Vector< T, Abi > &	x,
		Vector< T, detail::not_fixed_size_abi< Abi > > *	sin,
		Vector< T, Abi > *	cos )

inline

Parameters

x	Input value to both sine and cosine.
sin	A non-null pointer to a potentially uninitialized object of type Vector. When `sincos` returns, `*sin` contains the result of `sin(x)`.
cos	A non-null pointer to a potentially uninitialized object of type Vector. When `sincos` returns, `*cos` contains the result of `cos(x)`.

See also: sin, cos

Definition at line 217 of file trigonometric.h.

◆ copysign()

template<typename T , typename Abi , typename = enable_if<std::is_floating_point<T>::value && !detail::is_fixed_size_abi<Abi>::value>>

Vector< T, Abi > copysign	(	Vector< T, Abi >	magnitude,
		Vector< T, Abi >	sign )

inline

Copies the sign(s) of sign to the value(s) in magnitude and returns the resulting vector.

Parameters

magnitude	This vector's magnitude will be used in the return vector.
sign	This vector's sign bit will be used in the return vector.

Returns: a value where the sign of the value equals the sign of sign. I.e. sign(copysign(v, r)) == sign(r).

◆ exponent()

template<typename T , typename Abi , typename = enable_if<std::is_floating_point<T>::value && !detail::is_fixed_size_abi<Abi>::value>>

Vector< T, Abi > exponent ( Vector< T, Abi > x )

inline

Extracts the exponent of each floating-point vector component.

Parameters

x	The vector of values to check for the sign.

Returns: the exponent to base 2.

This function provides efficient access to the exponent of the floating point number. The returned value is a fast approximation to the logarithm of base 2. The absolute error of that approximation is between [0, 1[.

Examples:

 value | exponent | log2
=======|==========|=======
   1.0 |        0 | 0
   2.0 |        1 | 1
   3.0 |        1 | 1.585
   3.9 |        1 | 1.963
   4.0 |        2 | 2
   4.1 |        2 | 2.036

Warning: This function assumes a positive value (non-zero). If the value is negative the sign bit will modify the returned value. An input value of zero will return the bias of the floating-point representation. If you compile with Vc runtime checks, the function will assert values greater than or equal to zero.

You may use abs to apply this function to negative values:

exponent(abs(v))

Vc::abs

fixed_size_simd< T, N > abs(const SimdArray< T, N, V, M > &x)

Applies the std::abs function component-wise and concurrently.

Definition simdarray.h:1806

Vc::exponent

fixed_size_simd< T, N > exponent(const SimdArray< T, N, V, M > &x)

Applies the std::exponent function component-wise and concurrently.

Definition simdarray.h:1814

◆ isnegative()

template<typename T , typename Abi >

Vector< T, detail::not_fixed_size_abi< Abi > >::MaskType isnegative ( Vector< T, Abi > x )

inline

Returns for each vector component whether it stores a negative value.

Parameters

x	The vector of values to check for the sign.

Returns: a mask which is true only in those components that are negative in x.

Definition at line 106 of file vector.h.