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
Vc::Vector< T >	sqrt (const Vc::Vector< T > &v)
	Returns the square root of `v`.
Vc::Vector< T >	rsqrt (const Vc::Vector< T > &v)
	Returns the reciprocal square root of `v`.
Vc::Vector< T >	reciprocal (const Vc::Vector< T > &v)
	Returns the reciprocal of `v`.
Vc::Vector< T >	abs (const Vc::Vector< T > &v)
	Returns the absolute value of `v`.
Vc::Vector< T >	round (const Vc::Vector< T > &v)
	Returns the closest integer to `v`; 0.5 is rounded to even.
Vc::Vector< T >	log (const Vc::Vector< T > &v)
Vc::Vector< T >	log2 (const Vc::Vector< T > &v)
Vc::Vector< T >	log10 (const Vc::Vector< T > &v)
Vc::Vector< T >	exp (const Vc::Vector< T > &v)
Vc::Vector< T >	min (const Vc::Vector< T > &x, const Vc::Vector< T > &y)
Vc::Vector< T >	max (const Vc::Vector< T > &x, const Vc::Vector< T > &y)
Vc::Vector< T >	frexp (const Vc::Vector< T > &x, Vc::SimdArray< int, size()> *e)
	Convert floating-point number to fractional and integral components.
Vc::Vector< T >	ldexp (Vc::Vector< T > x, Vc::SimdArray< int, size()> e)
	Multiply floating-point number by integral power of 2.
Vc::Mask< T >	isfinite (const Vc::Vector< T > &x)
Vc::Mask< T >	isnan (const Vc::Vector< T > &x)
Vc::Vector< T >	fma (Vc::Vector< T > a, Vc::Vector< T > b, Vc::Vector< T > c)
	Multiplies `a` with `b` and then adds `c`, without rounding between the multiplication and the addition.
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

◆ log()

Vc::Vector< T > log ( const Vc::Vector< T > & v )

Parameters

v	The values to apply the logarithm on.

Returns: the natural logarithm of v.

Note: The single-precision implementation has an error of max. 1 ulp (mean 0.020 ulp) in the range ]0, 1000] (including denormals).; The double-precision implementation has an error of max. 1 ulp (mean 0.020 ulp) in the range ]0, 1000] (including denormals).

Referenced by log().

◆ log2()

Vc::Vector< T > log2 ( const Vc::Vector< T > & v )

Parameters

v	The values to apply the logarithm on.

Returns: the base-2 logarithm of v.

Note: The single-precision implementation has an error of max. 1 ulp (mean 0.016 ulp) in the range ]0, 1000] (including denormals).; The double-precision implementation has an error of max. 1 ulp (mean 0.016 ulp) in the range ]0, 1000] (including denormals).

Referenced by log2().

◆ log10()

Vc::Vector< T > log10 ( const Vc::Vector< T > & v )

Parameters

v	The values to apply the logarithm on.

Returns: the base-10 logarithm of v.

Note: The single-precision implementation has an error of max. 2 ulp (mean 0.31 ulp) in the range ]0, 1000] (including denormals).; The double-precision implementation has an error of max. 2 ulp (mean 0.26 ulp) in the range ]0, 1000] (including denormals).

Referenced by log10().

◆ exp()

Vc::Vector< T > exp ( const Vc::Vector< T > & v )

Parameters

v	The values to apply the exponential function on.

Returns: the exponential of v.

Referenced by exp().

◆ min()

Vc::Vector< T > min	(	const Vc::Vector< T > &	x,
		const Vc::Vector< T > &	y )

Parameters

x	\VSize{T} values to compare component-wise against `y`.
y	\VSize{T} values to compare component-wise against `x`.

Returns: the minimum of x and y.

Referenced by min(), and SimdArray< T, N, V, VN >::min().

◆ max()

Vc::Vector< T > max	(	const Vc::Vector< T > &	x,
		const Vc::Vector< T > &	y )

Parameters

x	\VSize{T} values to compare component-wise against `y`.
y	\VSize{T} values to compare component-wise against `x`.

Returns: the maximum of x and y.

Referenced by max(), and SimdArray< T, N, V, VN >::max().

◆ frexp()

Vc::Vector< T > frexp	(	const Vc::Vector< T > &	x,
		Vc::SimdArray< int, size()> *	e )

Convert floating-point number to fractional and integral components.

Parameters

x	value to be split into normalized fraction and exponent
e	the exponent to base 2 of `x`

Returns: the normalized fraction. If x is non-zero, the return value is x times a power of two, and its absolute value is always in the range [0.5,1).; If x is zero, then the normalized fraction is zero and zero is stored in e.; If x is a NaN, a NaN is returned, and the value of *e is unspecified.; If x is positive infinity (negative infinity), positive infinity (nega‐ tive infinity) is returned, and the value of *e is unspecified.

◆ ldexp()

Vc::Vector< T > ldexp	(	Vc::Vector< T >	x,
		Vc::SimdArray< int, size()>	e )

Multiply floating-point number by integral power of 2.

Parameters

x	value to be multiplied by 2 ^ `e`
e	exponent

Returns: x * 2 ^ e

◆ isfinite()

Vc::Mask< T > isfinite ( const Vc::Vector< T > & x )

Parameters

x	The \VSize{T} values to check for finite values.

Returns: a mask that tells whether the values in the vector are finite (i.e. not NaN or +/-inf).

Referenced by isfinite().

◆ isnan()

Vc::Mask< T > isnan ( const Vc::Vector< T > & x )

Parameters

x	The \VSize{T} values to check for NaN values.

Returns: a mask that tells whether the values in the vector are NaN.

Referenced by isnan().

◆ fma()

Vc::Vector< T > fma	(	Vc::Vector< T >	a,
		Vc::Vector< T >	b,
		Vc::Vector< T >	c )

Multiplies a with b and then adds c, without rounding between the multiplication and the addition.

Parameters

a	First multiplication factor.
b	Second multiplication factor.
c	Summand that will be added after multiplication.

Returns: The \VSize{T} values of a * b + c with higher precision due to no rounding between multiplication and addition.

Note: This operation may have explicit hardware support, in which case it is normally faster to use the FMA instead of separate multiply and add instructions.; If the target hardware does not have FMA support this function will be considerably slower than a normal a * b + c. This is due to the increased precision fusedMultiplyAdd provides.; The compiler normally detects opportunities for using the hardware FMA instructions from normal multiplication and addition/subtraction operators. Use this function only if you require the additional precision.

◆ 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

Vc::Vector< T > abs(const Vc::Vector< T > &v)

Returns the absolute value of v.

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.