Math

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
float_v	sqrt (const float_v &v)
	Returns the square root of v.
float_v	rsqrt (const float_v &v)
	Returns the reciprocal square root of v.
float_v	reciprocal (const float_v &v)
	Returns the reciprocal of v.
float_v	abs (const float_v &v)
	Returns the absolute value of v.
float_v	round (const float_v &v)
	Returns the closest integer to v; 0.5 is rounded to even.
float_v	log (const float_v &v)
	Returns the natural logarithm of v.
float_v	log2 (const float_v &v)
	Returns the base-2 logarithm of v.
float_v	log10 (const float_v &v)
	Returns the base-10 logarithm of v.
float_v	exp (const float_v &v)
	Returns the exponential of v.
float_v	sin (const float_v &v)
	Returns the sine of v.
float_v	cos (const float_v &v)
	Returns the cosine of v.
void	sincos (const float_v &v, float_v *sin, float_v *cos)
	Calculates the sine and cosine of v.
float_v	asin (const float_v &v)
	Returns the arcsine of v.
float_v	atan (const float_v &v)
	Returns the arctangent of v.
float_v	atan2 (const float_v &x, const float_v &y)
	Returns the arctangent of x / y.
float_v	min (const float_v &x, const float_v &y)
	Returns the minimum of x and y.
float_v	max (const float_v &x, const float_v &y)
	Returns the maximum of x and y.
float_v	frexp (const float_v &x, int_v *e)
	Convert floating-point number to fractional and integral components.
float_v	ldexp (float_v x, int_v e)
	Multiply floating-point number by integral power of 2.
float_m	isfinite (const float_v &x)
	Returns a mask that tells whether the values in the vector are finite (i.e. not NaN or +/-inf).
float_m	isnan (const float_v &x)
	Returns a mask that tells whether the values in the vector are NaN.
double_v	sqrt (const double_v &v)
	Returns the square root of v.
double_v	rsqrt (const double_v &v)
	Returns the reciprocal square root of v.
double_v	reciprocal (const double_v &v)
	Returns the reciprocal of v.
double_v	abs (const double_v &v)
	Returns the absolute value of v.
double_v	round (const double_v &v)
	Returns the closest integer to v; 0.5 is rounded to even.
double_v	log (const double_v &v)
	Returns the natural logarithm of v.
double_v	log2 (const double_v &v)
	Returns the base-2 logarithm of v.
double_v	log10 (const double_v &v)
	Returns the base-10 logarithm of v.
double_v	exp (const double_v &v)
	Returns the exponential of v.
double_v	sin (const double_v &v)
	Returns the sine of v.
double_v	cos (const double_v &v)
	Returns the cosine of v.
void	sincos (const double_v &v, double_v *sin, double_v *cos)
	Calculates the sine and cosine of v.
double_v	asin (const double_v &v)
	Returns the arcsine of v.
double_v	atan (const double_v &v)
	Returns the arctangent of v.
double_v	atan2 (const double_v &x, const double_v &y)
	Returns the arctangent of x / y.
double_v	min (const double_v &x, const double_v &y)
	Returns the minimum of x and y.
double_v	max (const double_v &x, const double_v &y)
	Returns the maximum of x and y.
double_v	frexp (const double_v &x, int_v *e)
	Convert floating-point number to fractional and integral components.
double_v	ldexp (double_v x, int_v e)
	Multiply floating-point number by integral power of 2.
double_m	isfinite (const double_v &x)
	Returns a mask that tells whether the values in the vector are finite (i.e. not NaN or +/-inf).
double_m	isnan (const double_v &x)
	Returns a mask that tells whether the values in the vector are NaN.
sfloat_v	sqrt (const sfloat_v &v)
	Returns the square root of v.
sfloat_v	rsqrt (const sfloat_v &v)
	Returns the reciprocal square root of v.
sfloat_v	reciprocal (const sfloat_v &v)
	Returns the reciprocal of v.
sfloat_v	abs (const sfloat_v &v)
	Returns the absolute value of v.
sfloat_v	round (const sfloat_v &v)
	Returns the closest integer to v; 0.5 is rounded to even.
sfloat_v	log (const sfloat_v &v)
	Returns the natural logarithm of v.
sfloat_v	log2 (const sfloat_v &v)
	Returns the base-2 logarithm of v.
sfloat_v	log10 (const sfloat_v &v)
	Returns the base-10 logarithm of v.
sfloat_v	exp (const sfloat_v &v)
	Returns the exponential of v.
sfloat_v	sin (const sfloat_v &v)
	Returns the sine of v.
sfloat_v	cos (const sfloat_v &v)
	Returns the cosine of v.
void	sincos (const sfloat_v &v, sfloat_v *sin, sfloat_v *cos)
	Calculates the sine and cosine of v.
sfloat_v	asin (const sfloat_v &v)
	Returns the arcsine of v.
sfloat_v	atan (const sfloat_v &v)
	Returns the arctangent of v.
sfloat_v	atan2 (const sfloat_v &x, const sfloat_v &y)
	Returns the arctangent of x / y.
sfloat_v	min (const sfloat_v &x, const sfloat_v &y)
	Returns the minimum of x and y.
sfloat_v	max (const sfloat_v &x, const sfloat_v &y)
	Returns the maximum of x and y.
sfloat_v	frexp (const sfloat_v &x, short_v *e)
	Convert floating-point number to fractional and integral components.
sfloat_v	ldexp (sfloat_v x, short_v e)
	Multiply floating-point number by integral power of 2.
sfloat_m	isfinite (const sfloat_v &x)
	Returns a mask that tells whether the values in the vector are finite (i.e. not NaN or +/-inf).
sfloat_m	isnan (const sfloat_v &x)
	Returns a mask that tells whether the values in the vector are NaN.

Function Documentation

float_v Vc::log

(

const float_v &

v

)

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).

float_v Vc::log2

(

const float_v &

v

)

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).

float_v Vc::log10

(

const float_v &

v

)

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).

float_v Vc::sin

(

const float_v &

v

)

Returns the sine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.17 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1040 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

float_v Vc::cos

(

const float_v &

v

)

Returns the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

void Vc::sincos	(	const float_v &	v,
		float_v *	sin,
		float_v *	cos
	)

Calculates the sine and cosine of v.

The values are returned in the sin and cos parameters.

Parameters

[in]	v	input value to sin and cos
[out]	sin	Needs to be a non-null pointer which will be set to the sine of v.
[out]	cos	Needs to be a non-null pointer which will be set to the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

float_v Vc::asin

(

const float_v &

v

)

Returns the arcsine of v.

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).

float_v Vc::atan

(

const float_v &

v

)

Returns the arctangent of v.

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].

float_v Vc::frexp	(	const float_v &	x,
		int_v *	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.

float_v Vc::ldexp	(	float_v	x,
		int_v	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

double_v Vc::log

(

const double_v &

v

)

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).

double_v Vc::log2

(

const double_v &

v

)

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).

double_v Vc::log10

(

const double_v &

v

)

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).

double_v Vc::sin

(

const double_v &

v

)

Returns the sine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.17 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1040 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

double_v Vc::cos

(

const double_v &

v

)

Returns the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

void Vc::sincos	(	const double_v &	v,
		double_v *	sin,
		double_v *	cos
	)

Calculates the sine and cosine of v.

The values are returned in the sin and cos parameters.

Parameters

[in]	v	input value to sin and cos
[out]	sin	Needs to be a non-null pointer which will be set to the sine of v.
[out]	cos	Needs to be a non-null pointer which will be set to the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

double_v Vc::asin

(

const double_v &

v

)

Returns the arcsine of v.

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).

double_v Vc::atan

(

const double_v &

v

)

Returns the arctangent of v.

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].

double_v frexp	(	const double_v &	x,
		int_v *	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.

Note

Often int_v::Size == double_v::Size * 2, then only every second value in *e is defined.

double_v ldexp	(	double_v	x,
		int_v	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

Note

Often int_v::Size == double_v::Size * 2, then only every second value in *e is defined.

sfloat_v Vc::log

(

const sfloat_v &

v

)

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).

sfloat_v Vc::log2

(

const sfloat_v &

v

)

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).

sfloat_v Vc::log10

(

const sfloat_v &

v

)

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).

sfloat_v Vc::sin

(

const sfloat_v &

v

)

Returns the sine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.17 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1040 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

sfloat_v Vc::cos

(

const sfloat_v &

v

)

Returns the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

void Vc::sincos	(	const sfloat_v &	v,
		sfloat_v *	sin,
		sfloat_v *	cos
	)

Calculates the sine and cosine of v.

The values are returned in the sin and cos parameters.

Parameters

[in]	v	input value to sin and cos
[out]	sin	Needs to be a non-null pointer which will be set to the sine of v.
[out]	cos	Needs to be a non-null pointer which will be set to the cosine of v.

Note

The single-precision implementation has an error of max. 2 ulp (mean 0.18 ulp) in the range [-8192, 8192].

The double-precision implementation has an error of max. 8e6 ulp (mean 1160 ulp) in the range [-8192, 8192].

Vc versions before 0.7 had much larger errors.

sfloat_v Vc::asin

(

const sfloat_v &

v

)

Returns the arcsine of v.

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).

sfloat_v Vc::atan

(

const sfloat_v &

v

)

Returns the arctangent of v.

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].

sfloat_v Vc::frexp	(	const sfloat_v &	x,
		short_v *	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.

sfloat_v Vc::ldexp	(	sfloat_v	x,
		short_v	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