Regina Calculation Engine
|
Represents an arbitrary precision integer. More...
#include <maths/nlargeinteger.h>
Public Member Functions | |
NLargeInteger () | |
Initialises this integer to zero. More... | |
NLargeInteger (int value) | |
Initialises this integer to the given value. More... | |
NLargeInteger (unsigned value) | |
Initialises this integer to the given value. More... | |
NLargeInteger (long value) | |
Initialises this integer to the given value. More... | |
NLargeInteger (unsigned long value) | |
Initialises this integer to the given value. More... | |
NLargeInteger (const NLargeInteger &value) | |
Initialises this integer to the given value. More... | |
NLargeInteger (const char *value, int base=10, bool *valid=0) | |
Initialises this integer to the given value which is represented as a string of digits in a given base. More... | |
NLargeInteger (const std::string &value, int base=10, bool *valid=0) | |
Initialises this integer to the given value which is represented as a string of digits in a given base. More... | |
virtual | ~NLargeInteger () |
Destroys this integer. More... | |
bool | isInfinite () const |
Determines if this large integer is infinity. More... | |
long | longValue () const |
Returns the value of this integer as a long. More... | |
std::string | stringValue (int base=10) const |
Returns the value of this integer as a string in the given base. More... | |
NLargeInteger & | operator= (const NLargeInteger &value) |
Sets this integer to the given value. More... | |
NLargeInteger & | operator= (int value) |
Sets this integer to the given value. More... | |
NLargeInteger & | operator= (unsigned value) |
Sets this integer to the given value. More... | |
NLargeInteger & | operator= (long value) |
Sets this integer to the given value. More... | |
NLargeInteger & | operator= (unsigned long value) |
Sets this integer to the given value. More... | |
NLargeInteger & | operator= (const char *value) |
Sets this integer to the given value which is represented as a string of digits in base 10. More... | |
NLargeInteger & | operator= (const std::string &value) |
Sets this integer to the given value which is represented as a string of digits in base 10. More... | |
void | swap (NLargeInteger &other) |
Swaps the values of this and the given integer. More... | |
bool | operator== (const NLargeInteger &compareTo) const |
Determines if this is equal to the given integer. More... | |
bool | operator== (long compareTo) const |
Determines if this is equal to the given integer. More... | |
bool | operator!= (const NLargeInteger &compareTo) const |
Determines if this is not equal to the given integer. More... | |
bool | operator!= (long compareTo) const |
Determines if this is not equal to the given integer. More... | |
bool | operator< (const NLargeInteger &compareTo) const |
Determines if this is less than the given integer. More... | |
bool | operator< (long compareTo) const |
Determines if this is less than the given integer. More... | |
bool | operator> (const NLargeInteger &compareTo) const |
Determines if this is greater than the given integer. More... | |
bool | operator> (long compareTo) const |
Determines if this is greater than the given integer. More... | |
bool | operator<= (const NLargeInteger &compareTo) const |
Determines if this is less than or equal to the given integer. More... | |
bool | operator<= (long compareTo) const |
Determines if this is less than or equal to the given integer. More... | |
bool | operator>= (const NLargeInteger &compareTo) const |
Determines if this is greater than or equal to the given integer. More... | |
bool | operator>= (long compareTo) const |
Determines if this is greater than or equal to the given integer. More... | |
NLargeInteger & | operator++ () |
The preincrement operator. More... | |
NLargeInteger | operator++ (int) |
The postincrement operator. More... | |
NLargeInteger & | operator-- () |
The predecrement operator. More... | |
NLargeInteger | operator-- (int) |
The postdecrement operator. More... | |
NLargeInteger | operator+ (const NLargeInteger &other) const |
Adds this to the given integer and returns the result. More... | |
NLargeInteger | operator- (const NLargeInteger &other) const |
Subtracts the given integer from this and returns the result. More... | |
NLargeInteger | operator* (const NLargeInteger &other) const |
Multiplies this by the given integer and returns the result. More... | |
NLargeInteger | operator/ (const NLargeInteger &other) const |
Divides this by the given integer and returns the result. More... | |
NLargeInteger | divExact (const NLargeInteger &other) const |
Divides this by the given integer and returns the result. More... | |
NLargeInteger | operator% (const NLargeInteger &other) const |
Determines the remainder when this integer is divided by the given integer. More... | |
NLargeInteger | divisionAlg (const NLargeInteger &divisor, NLargeInteger &remainder) const |
Uses the division algorithm to obtain a quotient and remainder when dividing by the given integer. More... | |
NLargeInteger | operator- () const |
Determines the negative of this integer. More... | |
NLargeInteger & | operator+= (const NLargeInteger &other) |
Adds the given integer to this. More... | |
NLargeInteger & | operator+= (long other) |
Adds the given integer to this. More... | |
NLargeInteger & | operator-= (const NLargeInteger &other) |
Subtracts the given integer from this. More... | |
NLargeInteger & | operator-= (long other) |
Subtracts the given integer from this. More... | |
NLargeInteger & | operator*= (const NLargeInteger &other) |
Multiplies the given integer by this. More... | |
NLargeInteger & | operator/= (const NLargeInteger &other) |
Divides this by the given integer. More... | |
NLargeInteger & | divByExact (const NLargeInteger &other) |
Divides this by the given integer. More... | |
NLargeInteger & | operator%= (const NLargeInteger &other) |
Reduces this integer modulo the given integer. More... | |
void | negate () |
Negates this integer. More... | |
void | raiseToPower (unsigned long exp) |
Raises this integer to the power of the given exponent. More... | |
NLargeInteger | abs () const |
Determines the absolute value of this integer. More... | |
NLargeInteger | gcd (const NLargeInteger &other) const |
Determines the greatest common divisor of this and the given integer. More... | |
NLargeInteger | lcm (const NLargeInteger &other) const |
Determines the lowest common multiple of this and the given integer. More... | |
NLargeInteger | gcdWithCoeffs (const NLargeInteger &other, NLargeInteger &u, NLargeInteger &v) const |
Determines the greatest common divisor of this and the given integer and finds the smallest coefficients with which these integers combine to give their gcd. More... | |
int | legendre (const NLargeInteger &p) const |
Returns the Legendre symbol (a/p), where a is this integer and p is an odd prime. More... | |
NLargeInteger | randomBoundedByThis () |
Generate a pseudo-random NLargeInteger that is uniformly distributed in the interval [0,*this) More... | |
void | setRaw (mpz_srcptr fromData) |
Set this large integer to a copy of the given raw GMP integer. More... | |
mpz_srcptr | rawData () const |
Returns the raw GMP data that describes this integer. More... | |
Static Public Member Functions | |
static NLargeInteger | randomBinary (unsigned long n) |
Generate a pseudo-random NLargeInteger that is uniformly distributed in the interval [0,2^n). More... | |
static NLargeInteger | randomCornerBinary (unsigned long n) |
Generate a pseudo-random NLargeInteger that is distributed in the interval [0,2^n), with a tendency to have long strings of 0s and 1s in its binary expansion. More... | |
Static Public Attributes | |
static const NLargeInteger | zero |
Globally available zero. More... | |
static const NLargeInteger | one |
Globally available one. More... | |
static const NLargeInteger | infinity |
Globally available infinity. More... | |
Friends | |
class | NPrimes |
Allow access to private members. More... | |
class | NRational |
Allow access to private members. More... | |
std::ostream & | operator<< (std::ostream &out, const NLargeInteger &large) |
Writes the given integer to the given output stream. More... | |
Represents an arbitrary precision integer.
Calculations will be exact no matter how large the integers become. Current algorithms and representations use the GNU multiple precision arithmetic library.
Infinity is catered for. For comparison operations, infinity is considered larger than any other integer but equal to itself.
All routines in this class, including random number generation, are thread-safe.
|
inline |
Initialises this integer to zero.
|
inline |
Initialises this integer to the given value.
value | the new value of this integer. |
|
inline |
Initialises this integer to the given value.
value | the new value of this integer. |
|
inline |
Initialises this integer to the given value.
value | the new value of this integer. |
|
inline |
Initialises this integer to the given value.
value | the new value of this integer. |
|
inline |
Initialises this integer to the given value.
value | the new value of this integer. |
|
inline |
Initialises this integer to the given value which is represented as a string of digits in a given base.
If not specified, the base defaults to 10. If the given base is zero, the base will be automatically determined. If the given string begins with 0x
or 0X
, the base will be assumed to be 16. Otherwise, if the string begins with 0
, the base will be assumed to be 8. Otherwise it will be taken as base 10.
Whitespace may be present in the given string and will simply be ignored.
Error detection is possible by passing a non-null boolean pointer as the third parameter to this constructor.
value | the new value of this integer, represented as a string of digits in base base. |
base | the base in which value is given. |
valid | if this pointer is not null, the boolean referenced will be set to true if the entire given string was a valid large integer representation and false otherwise. |
|
inline |
Initialises this integer to the given value which is represented as a string of digits in a given base.
If not specified, the base defaults to 10. If the given base is zero, the base will be automatically determined. If the given string begins with 0x
or 0X
, the base will be assumed to be 16. Otherwise, if the string begins with 0
, the base will be assumed to be 8. Otherwise it will be taken as base 10.
Whitespace may be present in the given string and will simply be ignored.
Error detection is possible by passing a non-null boolean pointer as the third parameter to this constructor.
value | the new value of this integer, represented as a string of digits in base base. |
base | the base in which value is given. |
valid | if this pointer is not null, the boolean referenced will be set to true if the entire given string was a valid large integer representation and false otherwise. |
|
inlinevirtual |
Destroys this integer.
|
inline |
Determines the absolute value of this integer.
This integer is not changed.
|
inline |
Divides this by the given integer.
This can only be used when the given integer divides into this exactly, and is much faster than ordinary division. This integer is changed to reflect the result.
other | the integer to divide this by. |
|
inline |
Divides this by the given integer and returns the result.
This can only be used when the given integer divides into this exactly, and is much faster than ordinary division. This integer is not changed.
other | the integer to divide this by. |
NLargeInteger regina::NLargeInteger::divisionAlg | ( | const NLargeInteger & | divisor, |
NLargeInteger & | remainder | ||
) | const |
Uses the division algorithm to obtain a quotient and remainder when dividing by the given integer.
Suppose this integer is n and we pass the divisor d. The division algorithm describes the result of dividing n by d; in particular, it expresses n = qd + r
, where q is the quotient and r is the remainder.
The division algorithm is precise about which values of q and r are chosen; in particular it chooses the unique r in the range 0 <= r < |d|
.
Note that this differs from other division routines in this class, in that it always rounds to give a non-negative remainder. Thus NLargeInteger(-7).divisionAlg(3) gives quotient -3 and remainder 2, whereas (-7)/3 gives quotient -2 and (-7)%3 gives remainder -1.
The two results are passed back to the caller as follows: The quotient q is passed back as the return value of the function, and the remainder r is stored in the reference argument r.
In the special case where the given divisor is 0 (not allowed by the usual division algorithm), this routine selects quotient 0 and remainder n.
divisor | the divisor d. |
remainder | used to store the remainder r when the functon returns. The initial value of this argument is ignored. |
|
inline |
Determines the greatest common divisor of this and the given integer.
This integer is not changed.
Note that the result might possibly be negative. As a special case, gcd(0,0) is considered to be zero.
other | the integer whose greatest common divisor with this will be found. |
NLargeInteger regina::NLargeInteger::gcdWithCoeffs | ( | const NLargeInteger & | other, |
NLargeInteger & | u, | ||
NLargeInteger & | v | ||
) | const |
Determines the greatest common divisor of this and the given integer and finds the smallest coefficients with which these integers combine to give their gcd.
Note that the given integers need not be non-negative. However, the gcd returned is guaranteed to be non-negative.
If d is the gcd of this and other, the values placed into u and v will be those for which u*this + v*other = d
, -abs(this)/d < v*sign(other) <= 0
and 1 <= u*sign(this) <= abs(other)/d
. These equations are not satisfied when either of this or other are zero, but in this case u and v are both 0, 1 or -1, using as many zeros as possible.
other | the integer whose greatest common divisor with this will be found. |
u | a variable into which the final coefficient of this will be placed. |
v | a variable into which the final coefficient of other will be placed. |
|
inline |
Determines if this large integer is infinity.
true
if and only if this large integer is infinity.
|
inline |
Determines the lowest common multiple of this and the given integer.
This integer is not changed.
Note that the result might possibly be negative.
other | the integer whose lowest common multiple with this will be found. |
|
inline |
Returns the Legendre symbol (a/p), where a is this integer and p is an odd prime.
The Legendre symbol is equal to 0 if this integer is divisible by p, 1 if this integer is congruent to a square mod p (but not divisible by p), and -1 otherwise.
p | the given odd prime. |
|
inline |
Returns the value of this integer as a long.
If this integer is outside the range of a long, the result is unpredictable.
|
inline |
Negates this integer.
This integer is changed to reflect the result.
Negating infinity will result in infinity.
|
inline |
Determines if this is not equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this and the given integer are not equal.
|
inline |
Determines if this is not equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this and the given integer are not equal.
|
inline |
Determines the remainder when this integer is divided by the given integer.
If non-zero, the result will have the same sign as this integer. This integer is not changed.
For a division routine that always returns a non-negative remainder, see divisionAlg().
other | the integer to divide this by. |
|
inline |
Reduces this integer modulo the given integer.
If non-zero, the result will have the same sign as the original value of this integer. This integer is changed to reflect the result.
For a mod routine that always returns a non-negative remainder, see divisionAlg().
other | the integer modulo which this integer will be reduced. |
|
inline |
Multiplies this by the given integer and returns the result.
This integer is not changed.
If either factor of the product is infinite, the result will be infinity.
other | the integer to multiply by this integer. |
|
inline |
Multiplies the given integer by this.
This integer is changed to reflect the result.
If either factor of the product is infinite, the result will be infinity.
other | the integer to multiply with this integer. |
|
inline |
Adds this to the given integer and returns the result.
This integer is not changed.
If either term of the sum is infinite, the result will be infinity.
other | the integer to add to this integer. |
|
inline |
The preincrement operator.
This operator increments this integer by one, and returns a reference to the integer after the increment.
|
inline |
The postincrement operator.
This operator increments this integer by one, and returns a copy of the integer before the increment.
|
inline |
Adds the given integer to this.
This integer is changed to reflect the result.
If either term of the sum is infinite, the result will be infinity.
other | the integer to add to this integer. |
|
inline |
Adds the given integer to this.
This integer is changed to reflect the result.
If either term of the sum is infinite, the result will be infinity.
other | the integer to add to this integer. |
|
inline |
Subtracts the given integer from this and returns the result.
This integer is not changed.
If either term of the difference is infinite, the result will be infinity.
other | the integer to subtract from this integer. |
|
inline |
Determines the negative of this integer.
This integer is not changed.
Negating infinity will return infinity.
|
inline |
The predecrement operator.
This operator decrements this integer by one, and returns a reference to the integer after the decrement.
|
inline |
The postdecrement operator.
This operator decrements this integer by one, and returns a copy of the integer before the decrement.
|
inline |
Subtracts the given integer from this.
This integer is changed to reflect the result.
If either term of the difference is infinite, the result will be infinity.
other | the integer to subtract from this integer. |
|
inline |
Subtracts the given integer from this.
This integer is changed to reflect the result.
If either term of the difference is infinite, the result will be infinity.
other | the integer to subtract from this integer. |
|
inline |
Divides this by the given integer and returns the result.
The result will be truncated to an integer, i.e. rounded towards zero. This integer is not changed.
If other is known to divide this integer exactly, divExact() should be used instead.
Infinity divided by anything will return infinity; anything finite divided by infinity will return zero; anything finite divided by zero will return infinity.
For a division routine that always rounds down, see divisionAlg().
other | the integer to divide this by. |
|
inline |
Divides this by the given integer.
The result will be truncated to an integer, i.e. rounded towards zero. This integer is changed to reflect the result.
If other is known to divide this integer exactly, divByExact() should be used instead.
Infinity divided by anything will return infinity; anything finite divided by infinity will return zero; anything finite divided by zero will return infinity.
For a division routine that always rounds down, see divisionAlg().
other | the integer to divide this by. |
|
inline |
Determines if this is less than the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is less than the given integer.
|
inline |
Determines if this is less than the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is less than the given integer.
|
inline |
Determines if this is less than or equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is less than or equal to the given integer.
|
inline |
Determines if this is less than or equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is less than or equal to the given integer.
|
inline |
Sets this integer to the given value.
value | the new value of this integer. |
|
inline |
Sets this integer to the given value.
value | the new value of this integer. |
|
inline |
Sets this integer to the given value.
value | the new value of this integer. |
|
inline |
Sets this integer to the given value.
value | the new value of this integer. |
|
inline |
Sets this integer to the given value.
value | the new value of this integer. |
|
inline |
Sets this integer to the given value which is represented as a string of digits in base 10.
Whitespace may be present in the given string and will simply be ignored.
value | the new value of this integer, represented as a string of digits in base 10. |
|
inline |
Sets this integer to the given value which is represented as a string of digits in base 10.
Whitespace may be present in the given string and will simply be ignored.
value | the new value of this integer, represented as a string of digits in base 10. |
|
inline |
Determines if this is equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this and the given integer are equal.
|
inline |
Determines if this is equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this and the given integer are equal.
|
inline |
Determines if this is greater than the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is greater than the given integer.
|
inline |
Determines if this is greater than the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is greater than the given integer.
|
inline |
Determines if this is greater than or equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is greater than or equal to the given integer.
|
inline |
Determines if this is greater than or equal to the given integer.
compareTo | the integer with which this will be compared. |
true
if and only if this is greater than or equal to the given integer.
|
inline |
Raises this integer to the power of the given exponent.
This integer is changed to reflect the result.
Note that 0 to the power of 0 will be 1, infinity to the power of 0 will be 1, and infinity to the power of anything else will be infinity.
exp | the power to which this integer will be raised. |
|
static |
Generate a pseudo-random NLargeInteger that is uniformly distributed in the interval [0,2^n).
n | the maximum number of bits in the pseudo-random integer. |
NLargeInteger regina::NLargeInteger::randomBoundedByThis | ( | ) |
Generate a pseudo-random NLargeInteger that is uniformly distributed in the interval [0,*this)
|
static |
Generate a pseudo-random NLargeInteger that is distributed in the interval [0,2^n), with a tendency to have long strings of 0s and 1s in its binary expansion.
n | the maximum number of bits in the pseudo-random integer. |
|
inline |
Returns the raw GMP data that describes this integer.
This routine allows NLargeInteger to interact directly with libgmp and libgmpxx if necessary.
|
inline |
Set this large integer to a copy of the given raw GMP integer.
This routine allows NLargeInteger to interact directly with libgmp and libgmpxx if necessary.
fromData | the raw GMP integer to clone. |
std::string regina::NLargeInteger::stringValue | ( | int | base = 10 ) | const |
Returns the value of this integer as a string in the given base.
If not specified, the base defaults to 10.
If this integer is infinity, the string returned will be inf
.
|
inline |
Swaps the values of this and the given integer.
other | the integer whose value will be swapped with this. |
|
friend |
Allow access to private members.
|
friend |
Allow access to private members.
|
friend |
Writes the given integer to the given output stream.
out | the output stream to which to write. |
large | the integer to write. |
|
static |
Globally available infinity.
|
static |
Globally available one.
|
static |
Globally available zero.