Regina Calculation Engine
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Represents an arbitrary precision integer. More...
#include <maths/ninteger.h>
Public Member Functions | |
NIntegerBase () | |
Initialises this integer to zero. More... | |
NIntegerBase (int value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (unsigned value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (long value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (unsigned long value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (const NIntegerBase< supportInfinity > &value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (const NIntegerBase<!supportInfinity > &value) | |
Initialises this integer to the given value. More... | |
template<int bytes> | |
NIntegerBase (const NNativeInteger< bytes > &value) | |
Initialises this integer to the given value. More... | |
NIntegerBase (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... | |
NIntegerBase (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... | |
~NIntegerBase () | |
Destroys this integer. More... | |
bool | isNative () const |
Returns whether we are currently working with a native C/C++ long, or whether we have switched to GMP large integer arithmetic for this integer. More... | |
bool | isZero () const |
Returns whether or not this integer is zero. More... | |
int | sign () const |
Returns the sign of this integer. More... | |
bool | isInfinite () const |
Returns whether this integer is infinity. More... | |
void | makeInfinite () |
Sets this integer to be infinity. More... | |
long | longValue () const |
Returns the value of this integer as a long. More... | |
template<int bytes> | |
IntOfSize< bytes >::type | nativeValue () const |
Returns the value of this integer as a native integer of some fixed byte length. More... | |
std::string | stringValue (int base=10) const |
Returns the value of this integer as a string in the given base. More... | |
NIntegerBase & | operator= (const NIntegerBase &value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (const NIntegerBase<!supportInfinity > &value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (int value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (unsigned value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (long value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (unsigned long value) |
Sets this integer to the given value. More... | |
NIntegerBase & | operator= (const char *value) |
Sets this integer to the given value which is represented as a string of digits in base 10. More... | |
NIntegerBase & | 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 (NIntegerBase &other) |
Swaps the values of this and the given integer. More... | |
bool | operator== (const NIntegerBase &rhs) const |
Determines if this is equal to the given integer. More... | |
bool | operator== (const NIntegerBase<!supportInfinity > &rhs) const |
Determines if this is equal to the given integer. More... | |
bool | operator== (long rhs) const |
Determines if this is equal to the given integer. More... | |
bool | operator!= (const NIntegerBase &rhs) const |
Determines if this is not equal to the given integer. More... | |
bool | operator!= (const NIntegerBase<!supportInfinity > &rhs) const |
Determines if this is not equal to the given integer. More... | |
bool | operator!= (long rhs) const |
Determines if this is not equal to the given integer. More... | |
bool | operator< (const NIntegerBase &rhs) const |
Determines if this is less than the given integer. More... | |
bool | operator< (long rhs) const |
Determines if this is less than the given integer. More... | |
bool | operator> (const NIntegerBase &rhs) const |
Determines if this is greater than the given integer. More... | |
bool | operator> (long rhs) const |
Determines if this is greater than the given integer. More... | |
bool | operator<= (const NIntegerBase &rhs) const |
Determines if this is less than or equal to the given integer. More... | |
bool | operator<= (long rhs) const |
Determines if this is less than or equal to the given integer. More... | |
bool | operator>= (const NIntegerBase &rhs) const |
Determines if this is greater than or equal to the given integer. More... | |
bool | operator>= (long rhs) const |
Determines if this is greater than or equal to the given integer. More... | |
NIntegerBase & | operator++ () |
The preincrement operator. More... | |
NIntegerBase | operator++ (int) |
The postincrement operator. More... | |
NIntegerBase & | operator-- () |
The predecrement operator. More... | |
NIntegerBase | operator-- (int) |
The postdecrement operator. More... | |
NIntegerBase | operator+ (const NIntegerBase &other) const |
Adds this to the given integer and returns the result. More... | |
NIntegerBase | operator+ (long other) const |
Adds this to the given integer and returns the result. More... | |
NIntegerBase | operator- (const NIntegerBase &other) const |
Subtracts the given integer from this and returns the result. More... | |
NIntegerBase | operator- (long other) const |
Subtracts the given integer from this and returns the result. More... | |
NIntegerBase | operator* (const NIntegerBase &other) const |
Multiplies this by the given integer and returns the result. More... | |
NIntegerBase | operator* (long other) const |
Multiplies this by the given integer and returns the result. More... | |
NIntegerBase | operator/ (const NIntegerBase &other) const |
Divides this by the given integer and returns the result. More... | |
NIntegerBase | operator/ (long other) const |
Divides this by the given integer and returns the result. More... | |
NIntegerBase | divExact (const NIntegerBase &other) const |
Divides this by the given integer and returns the result. More... | |
NIntegerBase | divExact (long other) const |
Divides this by the given integer and returns the result. More... | |
NIntegerBase | operator% (const NIntegerBase &other) const |
Determines the remainder when this integer is divided by the given integer. More... | |
NIntegerBase | operator% (long other) const |
Determines the remainder when this integer is divided by the given integer. More... | |
NIntegerBase< supportInfinity > | divisionAlg (const NIntegerBase< supportInfinity > &divisor, NIntegerBase< supportInfinity > &remainder) const |
Uses the division algorithm to obtain a quotient and remainder when dividing by the given integer. More... | |
NIntegerBase | operator- () const |
Determines the negative of this integer. More... | |
NIntegerBase & | operator+= (const NIntegerBase &other) |
Adds the given integer to this. More... | |
NIntegerBase & | operator+= (long other) |
Adds the given integer to this. More... | |
NIntegerBase & | operator-= (const NIntegerBase &other) |
Subtracts the given integer from this. More... | |
NIntegerBase & | operator-= (long other) |
Subtracts the given integer from this. More... | |
NIntegerBase & | operator*= (const NIntegerBase &other) |
Multiplies the given integer by this. More... | |
NIntegerBase & | operator*= (long other) |
Multiplies the given integer by this. More... | |
NIntegerBase & | operator/= (const NIntegerBase &other) |
Divides this by the given integer. More... | |
NIntegerBase & | operator/= (long other) |
Divides this by the given integer. More... | |
NIntegerBase & | divByExact (const NIntegerBase &other) |
Divides this by the given integer. More... | |
NIntegerBase & | divByExact (long other) |
Divides this by the given integer. More... | |
NIntegerBase & | operator%= (const NIntegerBase &other) |
Reduces this integer modulo the given integer. More... | |
NIntegerBase & | operator%= (long 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... | |
NIntegerBase | abs () const |
Determines the absolute value of this integer. More... | |
void | gcdWith (const NIntegerBase &other) |
Sets this integer to be the greatest common divisor of this and the given integer. More... | |
NIntegerBase | gcd (const NIntegerBase &other) const |
Determines the greatest common divisor of this and the given integer. More... | |
void | lcmWith (const NIntegerBase &other) |
Sets this integer to be the lowest common multiple of this and the given integer. More... | |
NIntegerBase | lcm (const NIntegerBase &other) const |
Determines the lowest common multiple of this and the given integer. More... | |
NIntegerBase< supportInfinity > | gcdWithCoeffs (const NIntegerBase< supportInfinity > &other, NIntegerBase< supportInfinity > &u, NIntegerBase< supportInfinity > &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 NIntegerBase< supportInfinity > &p) const |
Returns the Legendre symbol (a/p), where a is this integer and p is an odd prime. More... | |
NIntegerBase< supportInfinity > | randomBoundedByThis () const |
Generate a pseudo-random integer that is uniformly distributed in the interval [0,*this). More... | |
void | setRaw (mpz_srcptr fromData) |
Set this to a copy of the given raw GMP integer. More... | |
mpz_srcptr | rawData () const |
Returns the raw GMP data that describes this integer. More... | |
mpz_ptr | rawData () |
Returns the raw GMP data that describes this integer. More... | |
void | makeLarge () |
Converts this integer to use a GMP large integer representation, regardless of whether this is actually necessary. More... | |
void | tryReduce () |
Converts this integer to use a native C/C++ long representation, if this is possible. More... | |
template<int bytes> | |
IntOfSize< bytes >::type | nativeValue () const |
template<> | |
bool | isInfinite () const |
template<> | |
bool | isInfinite () const |
template<> | |
void | makeInfinite () |
template<> | |
void | makeInfinite () |
template<> | |
void | swap (NIntegerBase< true > &other) |
template<> | |
void | swap (NIntegerBase< false > &other) |
template<> | |
NIntegerBase (bool, bool) | |
Static Public Member Functions | |
static NIntegerBase < supportInfinity > | randomBinary (unsigned long n) |
Generate a pseudo-random integer that is uniformly distributed in the interval [0,2^n). More... | |
static NIntegerBase < supportInfinity > | randomCornerBinary (unsigned long n) |
Generate a pseudo-random integer 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 NIntegerBase < supportInfinity > | zero |
Globally available zero. More... | |
static const NIntegerBase < supportInfinity > | one |
Globally available one. More... | |
static const NIntegerBase < supportInfinity > | infinity |
Globally available infinity. More... | |
Friends | |
class | NIntegerBase<!supportInfinity > |
template<int bytes> | |
class | NNativeInteger |
template<bool supportInfinity_> | |
std::ostream & | operator<< (std::ostream &out, const NIntegerBase< supportInfinity_ > &large) |
Represents an arbitrary precision integer.
Calculations are always guaranteed to be exact, regardless of how large the integers become.
The current implementation uses fast native integer arithmetic wherever possible, whilst always testing for potential overflow. If a potential overflow is detected, this class switches to using the GNU multiple precision arithmetic library (libgmp) instead.
This class takes a single boolean argument supportInfinity. If this is true
, then this class will support infinity as an allowed value. If this is false
(the default), then infinity is not supported, and any attempt to work with infinity will lead to undefined behaviour. Supporting infinity is more flexible, but also comes with a slight performance cost (very roughly estimated at around 10%-20%).
For the purposes of comparison, infinity is considered larger than any other integer but equal to itself.
All routines in this class, including random number generation, are thread-safe.
The opportunistic use of native arithmetic where possible was inspired by the (much more complex and powerful) lazy exact arithmetic in CGAL. Thanks to Menelaos Karavelas for encouraging me to take another look at these ideas.
false
(the default), simply use NIntegerBase. For supportInfinity = true
, use NLargeInteger.
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Initialises this integer to zero.
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Initialises this integer to the given value.
value | the new value of this integer. |
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Initialises this integer to the given value.
value | the new value of this integer. |
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Initialises this integer to the given value.
value | the new value of this integer. |
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Initialises this integer to the given value.
value | the new value of this integer. |
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Initialises this integer to the given value.
value | the new value of this integer. |
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Initialises this integer to the given value.
This constructor is marked as explicit in the hope of avoiding accidental (and unintentional) mixing of template parameters.
value | the new value of this integer. |
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Initialises this integer to the given value.
This constructor is marked as explicit in the hope of avoiding accidental (and unintentional) mixing of integer classes.
value | the new value of this integer. |
regina::NIntegerBase< supportInfinity >::NIntegerBase | ( | const char * | value, |
int | base = 10 , |
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bool * | valid = 0 |
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) |
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 at the beginning or the end of 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.
For finer details on how the string parsing works, see strtol() from the standard C library (on which this method is based).
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. |
regina::NIntegerBase< supportInfinity >::NIntegerBase | ( | const std::string & | value, |
int | base = 10 , |
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bool * | valid = 0 |
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) |
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 at the beginning or the end of 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.
For finer details on how the string parsing works, see strtol() from the standard C library (on which this method is based).
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. |
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Destroys this integer.
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Determines the absolute value of this integer.
This integer is not changed.
NIntegerBase& regina::NIntegerBase< supportInfinity >::divByExact | ( | const NIntegerBase< supportInfinity > & | other | ) |
Divides this by the given integer.
This can only be used when the given integer divides into this exactly, and for large integers this is much faster than ordinary division. This integer is changed to reflect the result.
other | the integer to divide this by. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::divByExact | ( | long | other | ) |
Divides this by the given integer.
This can only be used when the given integer divides into this exactly, and for large integers this is much faster than ordinary division. This integer is changed to reflect the result.
other | the integer to divide this by. |
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Divides this by the given integer and returns the result.
This can only be used when the given integer divides into this exactly, and for large integers can be much faster than ordinary division. This integer is not changed.
other | the integer to divide this by. |
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Divides this by the given integer and returns the result.
This can only be used when the given integer divides into this exactly, and for large integers can be much faster than ordinary division. This integer is not changed.
other | the integer to divide this by. |
NIntegerBase<supportInfinity> regina::NIntegerBase< supportInfinity >::divisionAlg | ( | const NIntegerBase< supportInfinity > & | divisor, |
NIntegerBase< supportInfinity > & | 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 NIntegerBase(-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. |
NIntegerBase< supportInfinity > regina::NIntegerBase< supportInfinity >::gcd | ( | const NIntegerBase< supportInfinity > & | other | ) | const |
Determines the greatest common divisor of this and the given integer.
This integer is not changed.
The result is guaranteed to be non-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. |
void regina::NIntegerBase< supportInfinity >::gcdWith | ( | const NIntegerBase< supportInfinity > & | other | ) |
Sets this integer to be the greatest common divisor of this and the given integer.
The result is guaranteed to be non-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. |
NIntegerBase<supportInfinity> regina::NIntegerBase< supportInfinity >::gcdWithCoeffs | ( | const NIntegerBase< supportInfinity > & | other, |
NIntegerBase< supportInfinity > & | u, | ||
NIntegerBase< supportInfinity > & | 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. |
bool regina::NIntegerBase< supportInfinity >::isInfinite | ( | ) | const |
Returns whether this integer is infinity.
true
if and only if this integer is infinity.
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Returns whether we are currently working with a native C/C++ long, or whether we have switched to GMP large integer arithmetic for this integer.
If this integer is infinite, this routine will return false
.
true
if and only if we are still using a native C/C++ long.
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Returns whether or not this integer is zero.
This is micro-optimised to be faster than simply testing whether (*this) == 0.
true
if and only if this integer is zero. NIntegerBase< supportInfinity > regina::NIntegerBase< supportInfinity >::lcm | ( | const NIntegerBase< supportInfinity > & | other | ) | const |
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. |
void regina::NIntegerBase< supportInfinity >::lcmWith | ( | const NIntegerBase< supportInfinity > & | other | ) |
Sets this integer to be the lowest common multiple of this and the given integer.
Note that the result might possibly be negative.
other | the integer whose lowest common multiple with this will be found. |
int regina::NIntegerBase< supportInfinity >::legendre | ( | const NIntegerBase< supportInfinity > & | p | ) | const |
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. |
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Returns the value of this integer as a long.
It is the programmer's reponsibility to ensure that this integer is within the required range. If this integer is too large or small to fit into a long, then the result will be undefined.
Note that, assuming the value is within the required range, this routine will give correct results regardless of whether the underlying representation is a native or large integer.
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Sets this integer to be infinity.
If the template parameter supportInfinity is false
, this routine safely does nothing.
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Converts this integer to use a GMP large integer representation, regardless of whether this is actually necessary.
The contents of this integer will be preserved.
It does not matter which kind of representation this integer is currently using.
IntOfSize<bytes>::type regina::NIntegerBase< supportInfinity >::nativeValue | ( | ) | const |
Returns the value of this integer as a native integer of some fixed byte length.
It is the programmer's reponsibility to ensure that this integer is within the required range. If this integer is too large or small to fit into the return type, then the result will be undefined.
Note that, assuming the value is within the required range, this routine will give correct results regardless of whether the underlying representation is a native or large integer.
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Negates this integer.
This integer is changed to reflect the result.
Negating infinity will result in infinity.
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Determines if this is not equal to the given integer.
rhs | the integer with which this will be compared. |
true
if and only if this and the given integer are not equal.
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Determines if this is not equal to the given integer.
rhs | the integer with which this will be compared. |
true
if and only if this and the given integer are not equal.
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Determines if this is not equal to the given integer.
rhs | the integer with which this will be compared. |
true
if and only if this and the given integer are not equal.
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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. |
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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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator%= | ( | const NIntegerBase< supportInfinity > & | other | ) |
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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator%= | ( | long | other | ) |
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. |
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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. |
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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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator*= | ( | const NIntegerBase< supportInfinity > & | other | ) |
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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator*= | ( | long | other | ) |
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. |
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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. |
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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. |
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The preincrement operator.
This operator increments this integer by one, and returns a reference to the integer after the increment.
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The postincrement operator.
This operator increments this integer by one, and returns a copy of the integer before the increment.
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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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator+= | ( | long | other | ) |
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. |
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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. |
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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. |
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Determines the negative of this integer.
This integer is not changed.
Negative infinity will return infinity.
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The predecrement operator.
This operator decrements this integer by one, and returns a reference to the integer after the decrement.
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The postdecrement operator.
This operator decrements this integer by one, and returns a copy of the integer before the decrement.
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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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator-= | ( | long | other | ) |
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. |
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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 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 zero will return infinity.
For a division routine that always rounds down, see divisionAlg().
other | the integer to divide this by. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator/= | ( | const NIntegerBase< supportInfinity > & | other | ) |
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. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator/= | ( | long | other | ) |
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 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.
rhs | 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.
rhs | 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.
rhs | 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.
rhs | 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.
value | the new value of this integer. |
NIntegerBase& regina::NIntegerBase< supportInfinity >::operator= | ( | const char * | value | ) |
Sets this integer to the given value which is represented as a string of digits in base 10.
Whitespace may be present at the beginning or end of 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 at the beginning or end of 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.
rhs | 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.
rhs | 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.
rhs | 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.
rhs | 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.
rhs | 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.
rhs | 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.
rhs | the integer with which this will be compared. |
true
if and only if this is greater than or equal to the given integer. void regina::NIntegerBase< supportInfinity >::raiseToPower | ( | unsigned long | exp | ) |
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 integer that is uniformly distributed in the interval [0,2^n).
n | the maximum number of bits in the pseudo-random integer. |
NIntegerBase<supportInfinity> regina::NIntegerBase< supportInfinity >::randomBoundedByThis | ( | ) | const |
Generate a pseudo-random integer that is uniformly distributed in the interval [0,*this).
|
static |
Generate a pseudo-random integer 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 NIntegerBase to interact directly with libgmp and libgmpxx if necessary.
false
.
|
inline |
Returns the raw GMP data that describes this integer.
This routine allows NIntegerBase to interact directly with libgmp and libgmpxx if necessary.
false
.
|
inline |
Set this to a copy of the given raw GMP integer.
This routine allows NIntegerBase to interact directly with libgmp and libgmpxx if necessary.
fromData | the raw GMP integer to clone. |
|
inline |
Returns the sign of this integer.
In this routine, infinity is considered to have sign +1.
std::string regina::NIntegerBase< supportInfinity >::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
.
void regina::NIntegerBase< supportInfinity >::swap | ( | NIntegerBase< supportInfinity > & | other | ) |
Swaps the values of this and the given integer.
other | the integer whose value will be swapped with this. |
|
inline |
Converts this integer to use a native C/C++ long representation, if this is possible.
However, if this integer is outside the range of a C/C++ long, then it will remain as a GMP large integer instead (i.e., nothing will change). Whatever happens, the contents of this integer will be preserved.
It does not matter which kind of representation this integer is currently using.
|
static |
Globally available infinity.
This is only defined if supportInfinity is true
. Any attempt to use it when supportInfinity is false
should generate a linker error.
|
static |
Globally available one.
|
static |
Globally available zero.