Represents an arbitrary precision floating point value. More...

#include <arithmetic-gmp.hpp>

Classes
struct	PrecisionInit

Public Types
typedef RealContext	Context
	The context type.

Public Member Functions
long	getApproxExponent () const PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Returns approximate `e` such that \|x\| is approximately . More...

Real &	operator= (const Real &r)
	Assigns the given floating point number `r` to this floating point number. More...

template<class A , template< typename, typename > class O>
Real &	operator= (const expressions::Expression< RealContext, A, O > &E)
	Assigns the floating point expression `E` to this floating point number. More...

unsigned long	precision () const PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Retrieves the precision of this floating point number. More...

	Real ()
	Creates a new floating point number. More...

	Real (const RealContext &rc)
	Creates a real with the precision given by the context. More...

	Real (const Real &r, bool clone=true)
	Creates a copy of the given floating point number. More...

	Real (const Real &r, const RealContext &rc)
	Creates a copy of the given floating point number with the given context's precision. More...

	Real (long i)
	Creates a new floating point number from the given native integer. More...

	Real (long i, const RealContext &rc)
	Creates a new floating point number from the given native integer with the given context's precision. More...

	Real (unsigned long i)
	Creates a new floating point number from the given native integer. More...

	Real (unsigned long i, const RealContext &rc)
	Creates a new floating point number from the given native integer with the given context's precision. More...

	Real (long long i)
	Creates a new floating point number from the given native integer. More...

	Real (long long i, const RealContext &rc)
	Creates a new floating point number from the given native integer with the given context's precision. More...

	Real (double d)
	Creates a new floating point number from the given native floating point number. More...

	Real (double d, const RealContext &rc)
	Creates a new floating point number from the given native floating point number with the given context's precision. More...

	Real (long double d)
	Creates a new floating point number from the given native floating point number. More...

	Real (long double d, const RealContext &rc)
	Creates a new floating point number from the given native floating point number with the given context's precision. More...

	Real (const Integer &i)
	Creates a new floating point number from the given arbitrary precision integer. More...

	Real (const Integer &i, const RealContext &rc)
	Creates a new floating point number from the given arbitrary precision integer with the given context's precision. More...

template<class A , template< typename, typename > class O>
	Real (const expressions::Expression< RealContext, A, O > &E)
	Creates a floating point number from the given floating point expression. More...

template<class A , template< typename, typename > class O>
	Real (const expressions::Expression< RealContext, A, O > &E, const RealContext &rc)
	Creates a floating point number from the given floating point expression and Real context. More...

void	setContext (const RealContext &rc)
	Adjusts the precision of this floating point number to the given context's precision. More...

	~Real () PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Releases the memory used by the arbitrary precision floating point number.

Friends
void	abs (Real &r, const Real &a)
	Takes the absolute value of `a` and stores the result in `r`. More...

void	acos (Real &res, const Real &a)
	Computes the arccosine of `a` and stores the result in `res`. More...

void	add (Real &r, const Real &a, const Real &b)
	Adds `a` and `b` and stores the result in `r`. More...

void	addmul (Real &r, const Real &a, const Real &b)
	Multiplies `a` and `b` and adds the result to `r`. More...

void	asin (Real &res, const Real &a)
	Computes the arcsine of `a` and stores the result in `res`. More...

void	atan (Real &res, const Real &a)
	Computes the arctangent of `a` and stores the result in `res`. More...

void	atan2 (Real &res, const Real &y, const Real &x)
	Computes the arctangent of $\tfrac{y}{x}$ `and stores the result in`res`. The signs of`x`and`y` are used to determine the quadrant and yield a result in $[-\pi, \pi]$ . More...

int	compare (const Real &a, const Real &b)
	Compares the two floating point numbers. More...

int	compareAbsValues (const Real &a, const Real &b)
	Compares the two floating point numbers in absolute value. More...

void	cos (Real &res, const Real &a)
	Computes the cosine of `a` and stores the result in `res`. More...

void	decrement (Real &r, const Real &a)
	Decrements `a` by one and stores the result in `r`. More...

void	div (Real &r, const Real &a, const Real &b)
	Divides `a` by `b` and stores the result in `r`. More...

void	divmod (Real &q, Real &r, const Real &a, const Real &b)
	Stores quotient and remainder of the division of `a` by `b` in `q` respectively `r`. More...

void	exp (Real &res, const Real &a)
	Computes the exponential function at `a` and stores the result in `res`. More...

void	gamma (Real &res, const Real &a)
	Computes the Gamma function at `a` and stores the result in `res`. More...

void	increment (Real &r, const Real &a)
	Increments `a` by one and stores the result in `r`. More...

bool	isNegative (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being strictly negative. More...

bool	isNonNegative (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being positive or zero. More...

bool	isNonPositive (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being negative or zero. More...

bool	isOne (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being one. More...

bool	isPositive (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being strictly positive. More...

bool	isZero (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Tests the given `plll::arithmetic::Real` object for being zero. More...

void	lgamma (Real &res, const Real &a)
	Computes the logarithm of the absolute value of the Gamma function at `a` and stores the result in `res`. More...

void	lgamma (Real &res, int &sign, const Real &a)
	Computes the logarithm of the absolute value of the Gamma function at `a` and stores the result in `res`. The sign of the Gamma function at `a` is stored in `sign`. More...

void	log (Real &res, const Real &a)
	Computes the natural logarithm of `a` and stores the result in `res`. More...

void	log10 (Real &res, const Real &a)
	Computes the logarithm of `a` to base 10 and stores the result in `res`. More...

void	log2 (Real &res, const Real &a)
	Computes the logarithm of `a` to base 2 and stores the result in `res`. More...

void	makeAbs (Real &a) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Makes the operand non-negative. More...

void	mod (Real &r, const Real &a, const Real &b)
	Takes the remainder of the division of `a` by `b` and stores it in `r`. More...

void	mul (Real &r, const Real &a, const Real &b)
	Multiplies `a` with `b` and stores the result in `r`. More...

void	neg (Real &r, const Real &a)
	Negates `a` and stores the result in `r`. More...

bool	operator!= (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b` for inequality. More...

bool	operator< (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b`. More...

std::ostream &	operator<< (std::ostream &s, const Real &r)
	Outputs the floating point number on the given output stream.

bool	operator<= (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b`. More...

bool	operator== (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b` for equality. More...

bool	operator> (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b`. More...

bool	operator>= (const Real &a, const Real &b)
	Compares the two floating point numbers `a` and `b`. More...

std::istream &	operator>> (std::istream &s, Real &r)
	Reads the floating point number from the given input stream.

void	power (Real &res, const Real &a, const Integer &b)
	Raises `a` to the power `b` and stores the result in `res`. More...

void	power (Real &res, const Real &a, const Real &b)
	Raises `a` to the power `b` and stores the result in `res`. More...

void	setInfinity (Real &r, bool sign)
	Sets the given floating point number to $\pm \infty$ . More...

void	setNaN (Real &r)
	Sets the given floating point number to `Not a Number`.

void	setOne (Real &r)
	Sets the given floating point number to one.

void	setZero (Real &r, bool sign)
	Sets the given floating point number to $\pm 0$ . More...

void	shl (Real &r, const Real &a, const Real &b)
	Multiplies `a` by and stores the result in `r`. More...

void	shl (Real &r, const Real &a, long b)
	Multiplies `a` by and stores the result in `r`. More...

void	shr (Real &r, const Real &a, const Real &b)
	Multiplies `a` by $2^{-b}$ and stores the result in `r`. More...

void	shr (Real &r, const Real &a, long b)
	Multiplies `a` by $2^{-b}$ and stores the result in `r`. More...

int	sign (const Real &r) PLLL_INTERNAL_NOTHROW_POSTFIX_INLINE
	Returns the sign of the given floating point number. More...

void	sin (Real &res, const Real &a)
	Computes the sine of `a` and stores the result in `res`. More...

void	sqrt (Real &res, const Real &a)
	Computes the square root of `a` and stores the result in `res`. More...

void	square (Real &r, const Real &a)
	Computes the square of `a` and stores the result in `r`. More...

void	sub (Real &r, const Real &a, const Real &b)
	Subtracts `b` from `a` and stores the result in `r`. More...

void	submul (Real &r, const Real &a, const Real &b)
	Multiplies `a` and `b` and subtracts the result from `r`. More...

void	tan (Real &res, const Real &a)
	Computes the tangent of `a` and stores the result in `res`. More...

Detailed Description

Represents an arbitrary precision floating point value.

Definition at line 2036 of file arithmetic-gmp.hpp.

Constructor & Destructor Documentation

plll::arithmetic::Real::Real ( )

inline

Creates a new floating point number.

Warning: Default value is NaN and not zero!

Definition at line 2093 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( const RealContext & rc )

inlineexplicit

Creates a real with the precision given by the context.

Parameters

rc	A context.

Definition at line 2140 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	const Real &	r,
		bool	clone = `true`
	)

inline

Creates a copy of the given floating point number.

Parameters

r	The floating point number to copy.
clone	If `true`, creates a copy with the same precision. If `false`, creates a copy of the default precision.

Definition at line 2152 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	const Real &	r,
		const RealContext &	rc
	)

inlineexplicit

Creates a copy of the given floating point number with the given context's precision.

Parameters

r	The floating point number to copy.
rc	The context whose precision to use for the result.

Definition at line 2170 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( long i )

inlineexplicit

Creates a new floating point number from the given native integer.

Parameters

i	The native integer whose value to take.

Definition at line 2209 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	long	i,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given native integer with the given context's precision.

Parameters

i	The native integer whose value to take.
rc	The context whose precision to take.

Definition at line 2221 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( unsigned long i )

inlineexplicit

Creates a new floating point number from the given native integer.

Parameters

i	The native integer whose value to take.

Definition at line 2232 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	unsigned long	i,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given native integer with the given context's precision.

Parameters

i	The native integer whose value to take.
rc	The context whose precision to take.

Definition at line 2244 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( long long i )

inlineexplicit

Creates a new floating point number from the given native integer.

Parameters

i	The native integer whose value to take.

Definition at line 2255 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	long long	i,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given native integer with the given context's precision.

Parameters

i	The native integer whose value to take.
rc	The context whose precision to take.

Definition at line 2268 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( double d )

inlineexplicit

Creates a new floating point number from the given native floating point number.

Parameters

d	The native floating point number whose value to take.

Definition at line 2280 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	double	d,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given native floating point number with the given context's precision.

Parameters

d	The native floating point number whose value to take.
rc	The context whose precision to take.

Definition at line 2292 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( long double d )

inlineexplicit

Creates a new floating point number from the given native floating point number.

Parameters

d	The native floating point number whose value to take.

Definition at line 2304 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	long double	d,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given native floating point number with the given context's precision.

Parameters

d	The native floating point number whose value to take.
rc	The context whose precision to take.

Definition at line 2316 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real ( const Integer & i )

inlineexplicit

Creates a new floating point number from the given arbitrary precision integer.

Parameters

i	The arbitrary precision integer whose value to take.

Definition at line 2328 of file arithmetic-gmp.hpp.

plll::arithmetic::Real::Real	(	const Integer &	i,
		const RealContext &	rc
	)

inlineexplicit

Creates a new floating point number from the given arbitrary precision integer with the given context's precision.

Parameters

i	The arbitrary precision integer whose value to take.
rc	The context whose precision to take.

Definition at line 2340 of file arithmetic-gmp.hpp.

template<class A , template< typename, typename > class O>

plll::arithmetic::Real::Real ( const expressions::Expression< RealContext, A, O > & E )

inline

Creates a floating point number from the given floating point expression.

Parameters

E	The expression used to create this floating point number.

Definition at line 2352 of file arithmetic-gmp.hpp.

template<class A , template< typename, typename > class O>

plll::arithmetic::Real::Real	(	const expressions::Expression< RealContext, A, O > &	E,
		const RealContext &	rc
	)

inline

Creates a floating point number from the given floating point expression and Real context.

Parameters

E	The expression used to create this floating point number.
rc	The context whose precision to take.

Definition at line 2366 of file arithmetic-gmp.hpp.

Member Function Documentation

long plll::arithmetic::Real::getApproxExponent ( ) const

inline

Returns approximate e such that |x| is approximately $2^e$ .

The value of e should be OK up to +-2.

Returns: $\approx \log_2 |x|$ .

Definition at line 3215 of file arithmetic-gmp.hpp.

Real& plll::arithmetic::Real::operator= ( const Real & r )

inline

Assigns the given floating point number r to this floating point number.

Parameters

r	The floating point number to assign to this floating point number.

Returns: A reference to this floating point number.

Definition at line 2378 of file arithmetic-gmp.hpp.

template<class A , template< typename, typename > class O>

Real& plll::arithmetic::Real::operator= ( const expressions::Expression< RealContext, A, O > & E )

inline

Assigns the floating point expression E to this floating point number.

Parameters

E	The floating point expression.

Returns: A reference to this floating point number.

Definition at line 2395 of file arithmetic-gmp.hpp.

unsigned long plll::arithmetic::Real::precision ( ) const

inline

Retrieves the precision of this floating point number.

Returns: The precision in mantissa bits of the current floating point number.

Definition at line 2181 of file arithmetic-gmp.hpp.

void plll::arithmetic::Real::setContext ( const RealContext & rc )

inline

Adjusts the precision of this floating point number to the given context's precision.

Parameters

rc	A context whose precision to use.

Definition at line 2192 of file arithmetic-gmp.hpp.

Friends And Related Function Documentation

void abs	(	Real &	r,
		const Real &	a
	)

friend

Takes the absolute value of a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 2902 of file arithmetic-gmp.hpp.

void acos	(	Real &	res,
		const Real &	a
	)

friend

Computes the arccosine of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3064 of file arithmetic-gmp.hpp.

void add	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Adds a and b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2444 of file arithmetic-gmp.hpp.

void addmul	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Multiplies a and b and adds the result to r.

Parameters

r	The accumulator.
a	The first operand.
b	The second operand.

Definition at line 2588 of file arithmetic-gmp.hpp.

void asin	(	Real &	res,
		const Real &	a
	)

friend

Computes the arcsine of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3055 of file arithmetic-gmp.hpp.

void atan	(	Real &	res,
		const Real &	a
	)

friend

Computes the arctangent of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3073 of file arithmetic-gmp.hpp.

void atan2	(	Real &	res,
		const Real &	y,
		const Real &	x
	)

friend

Computes the arctangent of $\tfrac{y}{x}$ and stores the result inres. The signs ofxandy` are used to determine the quadrant and yield a result in $[-\pi, \pi]$ .

Parameters

res	The result.
y	The numerator of the fraction the function is evaluated at.
x	The denominator of the fraction the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3082 of file arithmetic-gmp.hpp.

int compare	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers.

Parameters

a	The first operand.
b	The second operand.

Returns: Returns a negative number if , zero if and a positive number if .

Definition at line 2950 of file arithmetic-gmp.hpp.

int compareAbsValues	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers in absolute value.

Parameters

a	The first operand.
b	The second operand.

Returns: Returns a negative number if , zero if and a positive number if .

Definition at line 3002 of file arithmetic-gmp.hpp.

void cos	(	Real &	res,
		const Real &	a
	)

friend

Computes the cosine of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3037 of file arithmetic-gmp.hpp.

void decrement	(	Real &	r,
		const Real &	a
	)

friend

Decrements a by one and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 2884 of file arithmetic-gmp.hpp.

void div	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Divides a by b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2693 of file arithmetic-gmp.hpp.

void divmod	(	Real &	q,
		Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Stores quotient and remainder of the division of a by b in q respectively r.

Parameters

q	The quotient.
r	The remainder.
a	The first operand.
b	The second operand.

Definition at line 2787 of file arithmetic-gmp.hpp.

void exp	(	Real &	res,
		const Real &	a
	)

friend

Computes the exponential function at a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3094 of file arithmetic-gmp.hpp.

void gamma	(	Real &	res,
		const Real &	a
	)

friend

Computes the Gamma function at a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Square Roots and Full Powers

Definition at line 3139 of file arithmetic-gmp.hpp.

void increment	(	Real &	r,
		const Real &	a
	)

friend

Increments a by one and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 2875 of file arithmetic-gmp.hpp.

bool isNegative ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being strictly negative.

Returns: Returns true if and only if the argument is strictly negative.

See also: Predicates

Definition at line 2432 of file arithmetic-gmp.hpp.

bool isNonNegative ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being positive or zero.

Returns: Returns true if and only if the argument is positive or zero.

See also: Predicates

Definition at line 2426 of file arithmetic-gmp.hpp.

bool isNonPositive ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being negative or zero.

Returns: Returns true if and only if the argument is negative or zero.

See also: Predicates

Definition at line 2438 of file arithmetic-gmp.hpp.

bool isOne ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being one.

Returns: Returns true if and only if the argument is one.

See also: Predicates

Definition at line 2414 of file arithmetic-gmp.hpp.

bool isPositive ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being strictly positive.

Returns: Returns true if and only if the argument is strictly positive.

See also: Predicates

Definition at line 2420 of file arithmetic-gmp.hpp.

bool isZero ( const Real & r )

friend

Tests the given plll::arithmetic::Real object for being zero.

Returns: Returns true if and only if the argument is zero.

See also: Predicates

Definition at line 2408 of file arithmetic-gmp.hpp.

void lgamma	(	Real &	res,
		const Real &	a
	)

friend

Computes the logarithm of the absolute value of the Gamma function at a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Special Functions

Definition at line 3148 of file arithmetic-gmp.hpp.

void lgamma	(	Real &	res,
		int &	sign,
		const Real &	a
	)

friend

Computes the logarithm of the absolute value of the Gamma function at a and stores the result in res. The sign of the Gamma function at a is stored in sign.

Parameters

res	The result.
sign	Will be set to 1 if $\Gamma(a) \ge 0$ and -1 otherwise.

See also: Special Functions

Parameters

a	The value the function is evaluated at.

Definition at line 3158 of file arithmetic-gmp.hpp.

void log	(	Real &	res,
		const Real &	a
	)

friend

Computes the natural logarithm of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

Definition at line 3103 of file arithmetic-gmp.hpp.

void log10	(	Real &	res,
		const Real &	a
	)

friend

Computes the logarithm of a to base 10 and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

Definition at line 3121 of file arithmetic-gmp.hpp.

void log2	(	Real &	res,
		const Real &	a
	)

friend

Computes the logarithm of a to base 2 and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

Definition at line 3112 of file arithmetic-gmp.hpp.

void makeAbs ( Real & a )

friend

Makes the operand non-negative.

Parameters

a	The operand.

Definition at line 2911 of file arithmetic-gmp.hpp.

void mod	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Takes the remainder of the division of a by b and stores it in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2775 of file arithmetic-gmp.hpp.

void mul	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Multiplies a with b and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2641 of file arithmetic-gmp.hpp.

void neg	(	Real &	r,
		const Real &	a
	)

friend

Negates a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 2893 of file arithmetic-gmp.hpp.

bool operator!=	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b for inequality.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a does not equal b.

Definition at line 944 of file arithmetic-gmp-rops.hpp.

bool operator<	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a is less than b.

Definition at line 980 of file arithmetic-gmp-rops.hpp.

bool operator<=	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a is less than or equal to b.

Definition at line 956 of file arithmetic-gmp-rops.hpp.

bool operator==	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b for equality.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a equals b.

Definition at line 932 of file arithmetic-gmp-rops.hpp.

bool operator>	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a is greater than b.

Definition at line 992 of file arithmetic-gmp-rops.hpp.

bool operator>=	(	const Real &	a,
		const Real &	b
	)

friend

Compares the two floating point numbers a and b.

Parameters

a	The first operand.
b	The second operand.

Returns: true if and only if a is greater than or equal to b.

Definition at line 968 of file arithmetic-gmp-rops.hpp.

void power	(	Real &	res,
		const Real &	a,
		const Integer &	b
	)

friend

Raises a to the power b and stores the result in res.

Parameters

res	The result.
a	The base.
b	The exponent.

Definition at line 3185 of file arithmetic-gmp.hpp.

void power	(	Real &	res,
		const Real &	a,
		const Real &	b
	)

friend

Raises a to the power b and stores the result in res.

Parameters

res	The result.
a	The base.
b	The exponent.

See also: Square Roots and Full Powers

Definition at line 3194 of file arithmetic-gmp.hpp.

void setInfinity	(	Real &	r,
		bool	sign
	)

friend

Sets the given floating point number to $\pm \infty$ .

Parameters

r	The floating point variable to set to infinity.
sign	If `true`, the number is set to $+\infty$ , and otherwise to $-\infty$ . The default value is `true`.

Definition at line 2927 of file arithmetic-gmp.hpp.

void setZero	(	Real &	r,
		bool	sign
	)

friend

Sets the given floating point number to $\pm 0$ .

Parameters

r	The floating point variable to set to zero.
sign	If `true`, the number is set to , and otherwise to . The default value is `true`.

Definition at line 2932 of file arithmetic-gmp.hpp.

void shl	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Multiplies a by $2^b$ and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2825 of file arithmetic-gmp.hpp.

void shl	(	Real &	r,
		const Real &	a,
		long	b
	)

friend

Multiplies a by $2^b$ and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

See also: Square Roots and Full Powers

Definition at line 2857 of file arithmetic-gmp.hpp.

void shr	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Multiplies a by $2^{-b}$ and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

See also: Square Roots and Full Powers

Definition at line 2841 of file arithmetic-gmp.hpp.

void shr	(	Real &	r,
		const Real &	a,
		long	b
	)

friend

Multiplies a by $2^{-b}$ and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2866 of file arithmetic-gmp.hpp.

int sign ( const Real & r )

friend

Returns the sign of the given floating point number.

Returns: Returns a negative value if the value is negative, 0 if it is zero, and a positive value if it is positive.

See also: Predicates

Definition at line 3013 of file arithmetic-gmp.hpp.

void sin	(	Real &	res,
		const Real &	a
	)

friend

Computes the sine of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3028 of file arithmetic-gmp.hpp.

void sqrt	(	Real &	res,
		const Real &	a
	)

friend

Computes the square root of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

Definition at line 3130 of file arithmetic-gmp.hpp.

void square	(	Real &	r,
		const Real &	a
	)

friend

Computes the square of a and stores the result in r.

Parameters

r	The result.
a	The operand.

Definition at line 3019 of file arithmetic-gmp.hpp.

void sub	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Subtracts b from a and stores the result in r.

Parameters

r	The result.
a	The first operand.
b	The second operand.

Definition at line 2496 of file arithmetic-gmp.hpp.

void submul	(	Real &	r,
		const Real &	a,
		const Real &	b
	)

friend

Multiplies a and b and subtracts the result from r.

Parameters

r	The accumulator.
a	The first operand.
b	The second operand.

Definition at line 2614 of file arithmetic-gmp.hpp.

void tan	(	Real &	res,
		const Real &	a
	)

friend

Computes the tangent of a and stores the result in res.

Parameters

res	The result.
a	The value the function is evaluated at.

See also: Trigonometric Functions

Definition at line 3046 of file arithmetic-gmp.hpp.

The documentation for this class was generated from the following file:

/home/felix/projects/code/plll/plll/plll/include/plll/arithmetic-gmp.hpp

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