Nat Class Reference

#include <pk.h>

---

Detailed Description

Data type used to represent elements of various algebraic objects.

Public Types
typedef Nat const &	cNat
	const reference to a Nat
Public Member Functions
Inspectors
int	bit (int k) const
	Get k-th bit of this object.
int	degree () const
	Get length of this object in bits.
int	length () const
	Get length of this object in nwords.
Arithmetic and Logical Operations
void	add1 (cnat y)
	Add number to this one.
void	sub1 (cnat y)
	Subtract number from this one.
void	subr (cnwordp a)
	Subtract this object from another.
void	extend (int n)
	Extend length of this object by specified number of nwords.
void	shiftright (int k=1)
	Right shift this object by a specified number of bits.
void	shiftleft (int k=1)
	Left shift this object by a specified number of bits.
void	xorshift (int k, cnat a)
	Left shift number and XOR into this object.
Assignment and Arithmetic Operators
Nat &	operator= (nword x)
	Assignment operator.
Nat &	operator= (const Nat &x)
	Assignment operator.
void	operator+= (cnat y)
	Increment this object by a specified amount.
void	operator-= (cnat y)
	Decrement this object by a specified amount.
Predicates
bool	isOdd () const
	Predicate to test oddness.
bool	isEven () const
	Predicate to test evenness.
bool	operator== (nword n) const
	Predicate to test equality of natural numbers.
bool	operator!= (nword n) const
	Predicate to test inequality of natural numbers.
bool	operator== (cNat x) const
	Predicate to test equality of Nat objects.
bool	operator!= (cNat x) const
	Predicate to test inequality of Nat objects.
bool	operator<= (cNat x) const
	Predicate to test "less than or equal to" relation between Nat objects.
bool	operator>= (cNat x) const
	Predicate to test "greater than or equal to" relation between Nat objects.
bool	operator< (cNat x) const
	Predicate to test "less than" relation between Nat objects.
bool	operator> (cNat x) const
	Predicate to test "greater than" relation between Nat objects.

---

Member Function Documentation

void add1

(

cnat

y

)

Add number to this one.

Parameters:

y

object to add to this object

int bit

(

int

k

)

const

Get k-th bit of this object.

Parameters:

k

index of bit to return

Returns:

k-th bit of the natural number represented by this object

int degree

(

)

const

Get length of this object in bits.

Returns:

log2(x)

void extend

(

int

n

)

Extend length of this object by specified number of nwords.

Parameters:

n

new size of object in nwords.

Remarks:

Modifies: w is padded with zeros so len >= n

bool isEven

(

)

const [inline]

Predicate to test evenness.

Returns:

true, if the number stored in this object is even
false otherwise

bool isOdd

(

)

const [inline]

Predicate to test oddness.

Returns:

true, if the number stored in this object is odd
false, otherwise.

int length

(

)

const [inline]

Get length of this object in nwords.

Returns:

len (i.e., number of nwords are used by this object)

bool operator!=

(

cNat

x

)

const [inline]

Predicate to test inequality of Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x != this
false, if x == this

bool operator!=

(

nword

n

)

const [inline]

Predicate to test inequality of natural numbers.

Parameters:

n

nword to compare with this object.

Returns:

true, if this object does not equal n
false, if they are equal

void operator+=

(

cnat

y

)

Increment this object by a specified amount.

Parameters:

y

the number to add to this object

void operator-=

(

cnat

y

)

[inline]

Decrement this object by a specified amount.

Parameters:

y

number to be sutracted from this object

bool operator<

(

cNat

x

)

const [inline]

Predicate to test "less than" relation between Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x < this
false, otherwise

bool operator<=

(

cNat

x

)

const [inline]

Predicate to test "less than or equal to" relation between Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x <= this
false, otherwise

Nat& operator=

(

const Nat &

x

)

Assignment operator.

Parameters:

x

Nat to assign to this object

Returns:

a reference to this object

Remarks:

Modifies: w (x.w is copied into this.w).

Warning: this.len *must* be >= x.len

Nat& operator=

(

nword

x

)

Assignment operator.

Parameters:

x

nword to assign to this object

Returns:

a reference to this object

Remarks:

Modifies: w (this object becomes a Nat with len = 1)

bool operator==

(

cNat

x

)

const [inline]

Predicate to test equality of Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x == this
false, if x != this

bool operator==

(

nword

n

)

const

Predicate to test equality of natural numbers.

Parameters:

n

nword to compare with this object.

Returns:

true, if this object equals n
false, if they are unequal

bool operator>

(

cNat

x

)

const [inline]

Predicate to test "greater than" relation between Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x > this
false, otherwise

bool operator>=

(

cNat

x

)

const [inline]

Predicate to test "greater than or equal to" relation between Nat objects.

Parameters:

x

Nat object to which this one is to be compared

Returns:

true, if x >= this
false otherwise

void shiftleft

(

int

k = 1

)

Left shift this object by a specified number of bits.

Parameters:

k

number of bits to left shift this object.

void shiftright

(

int

k = 1

)

Right shift this object by a specified number of bits.

Parameters:

k

number of bits to right shift this object.

void sub1

(

cnat

y

)

Subtract number from this one.

Parameters:

y

object to subtract from this object

void subr

(

cnwordp

a

)

Subtract this object from another.

Parameters:

a

object from which to subtract this object

Remarks:

Modifies: w = a - this.w

void xorshift	(	int	k,
		cnat	a
	)

Left shift number and XOR into this object.

Parameters:

	k	number of bits to leftshift a
	a	number to XOR with this Modifies: w (this gets the result of this XOR'd with a left shifted k bits).

---

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

• pk.h

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