Givaro
Data Structures | Typedefs | Functions
Givaro Namespace Reference

Arithmetic on GF(p^k), with p a prime number less than 2^15. More...

Data Structures

class  ArrayAllocatort
 ArrayAllocator: class for allocation of arrays. More...
class  Array0Tag
struct  __giv_map_less_ith< T, UNARYOP, 0 >
struct  __giv_map_less_ith< T, UNARYOP, ith >
struct  __giv_map_less_ith_const< T, UNARYOP, 0 >
struct  __giv_map_less_ith_const< T, UNARYOP, ith >
class  Bits
struct  ElemRef
struct  ElemConstRef
struct  Pair
class  Key
 The class Key. More...
class  HashTable
class  List0
class  Stack
class  Integer
 This is the Integer class. More...
class  IntegerDom
class  IntFactorDom
class  IntNumTheoDom
class  FermatDom
class  IntPrimeDom
class  IntRNSsystem
class  IntRSADom
class  IntSqrtModDom
class  GivMMInfo
class  BlocFreeList
class  GivMMFreeList
class  GivMMRefCount
class  GivaroMM
class  RefCountPtr
class  RefCounter
struct  ieee
class  Rational
class  RationalDom
class  Neutral
class  givNoInit
class  givNoCopy
class  givWithCopy
class  GivError
class  GivMathError
class  GivBadFormat
class  GivMathDivZero
struct  __givdom_trait_name
class  BaseDomain
class  GivaroMain
class  GivaroAppli
class  GivaroNoInit
class  InitAfter
class  GivModule
class  ObjectInit
class  GivRandom
class  BaseTimer
 base for class RealTimer; class SysTimer; class UserTimer; More...
class  RealTimer
class  UserTimer
class  SysTimer
class  Timer
class  GIV_randIter
 Random field Element generator. More...
struct  ChineseRemainder
struct  ChineseRemainder< Ring, Domain, false >
class  Extension
class  GIV_ExtensionrandIter
class  GFqDom
class  GFqExtFast
class  GFqExt
struct  GFqKronecker
class  Montgomery< Std32 >
 This class implements the standard arithmetic with Modulo Elements. More...
class  Primes16
class  RNSsystem
 class RNSsystem. More...
class  RNSsystemFixed
 NO DOC. More...
class  AdicSize
class  ZpzDom< Std16 >
 This class implement the standard arithmetic with Modulo Elements. More...
class  ZpzDom< Log16 >
 This class implement the standard arithmetic with Modulo Elements. More...
class  ZpzDom< Std32 >
 This class implement the standard arithmetic with Modulo Elements. More...
class  ZpzDom< Unsigned32 >
 This class implement the standard arithmetic with Modulo Elements. More...
class  ZpzDom< Std64 >
 This class implement the standard arithmetic with Modulo Elements. More...
class  ZpzDom< Integer >
 This class implement the standard arithmetic with Modulo Elements. More...
struct  Std16
struct  Std32
struct  Unsigned32
struct  Log16
struct  Std64
class  StaticElement
class  MatrixDom< Domain, Dense >
class  MatrixDom
class  MatrixDom< Domain, Sparse >
struct  RetMatrixStorage
struct  RetMatrix2Storage
struct  RetMatrixStorage< T, Dense >
struct  RetMatrixStorage< T, Sparse >
class  Degree
class  Indeter
struct  Interpolation
struct  NewtonInterpGeomMultip
struct  NewtonInterpGeom
class  Poly1CRT
class  givvector
class  Poly1Dom< Domain, Dense >
class  Poly1FactorDom
class  Poly1PadicDom< Domain, Dense >
struct  KSpace
class  Undefined
struct  IsEqual
struct  IsEqual< A, A >
struct  IsNotEqual
class  Sporadic
class  Dense
class  Sparse
struct  Sparsity_Trait
class  DefaultFormat
struct  StructFormat
class  FixedTruncDom
struct  Frac
struct  FracDom
struct  HighOrder
class  isUndefinedIterator
class  isForwardIterator
class  isBidirectionalIterator
class  isRandomIterator
struct  IteratorTraits
struct  IteratorInterface
struct  BaseOP
struct  CopyOp
struct  MulOp
struct  DivOp
struct  ModOp
struct  AddOp
struct  SubOp
struct  NegOp
struct  MulAddOp
struct  Curried1
struct  Curried2
struct  QuotientDom
class  TruncDom
struct  RetVectorStorage
struct  RetVector2Storage
struct  RetVectorStorage< T, Dense >
class  VectorDom
 VectorDom<Domain,StorageTag> More...
class  VectorDom< Domain, Sparse >

Typedefs

typedef BaseDomain< char > CharDom
typedef BaseDomain< short > ShortDom
typedef BaseDomain< int > IntDom
typedef BaseDomain< long > LongDom
typedef BaseDomain< float > FloatDom
typedef BaseDomain< double > DoubleDom

Functions

template<class T >
class Array0 GIVARO_PERF_INEHERIT (Array0, T)
template<class T , size_t SIZE>
class ArrayFixed GIVARO_PERF_INEHERIT (ArrayFixed, T)
std::ostream & operator<< (std::ostream &o, const Bits &a)
template<class T1 , class T2 >
ostream & operator<< (ostream &o, const Pair< T1, T2 > &p)
template<class T1 , class T2 >
istream & operator>> (istream &fin, Pair< T1, T2 > &p)
int compare (const Integer &a, const Integer &b)
int absCompare (const Integer &a, const Integer &b)
Integerinv (Integer &u, const Integer &a, const Integer &b)
Integerinvin (Integer &u, const Integer &b)
Integer gcd (const Integer &a, const Integer &b)
Integer gcd (const Integer &a, const Integer &b, Integer &u, Integer &v)
Integergcd (Integer &g, const Integer &a, const Integer &b)
Integergcd (Integer &g, const Integer &a, const Integer &b, Integer &u, Integer &v)
Integer pp (const Integer &P, const Integer &Q)
Integerlcm (Integer &g, const Integer &a, const Integer &b)
Integer lcm (const Integer &a, const Integer &b)
Integerpow (Integer &Res, const Integer &n, const long l)
Integerpow (Integer &Res, const unsigned long n, const unsigned long l)
Integerpow (Integer &Res, const Integer &n, const unsigned long l)
Integerpow (Integer &Res, const Integer &n, const int l)
Integerpow (Integer &Res, const Integer &n, const unsigned int l)
Integer pow (const Integer &n, const long l)
Integer pow (const Integer &n, const unsigned long l)
Integer pow (const Integer &n, const int l)
Integer pow (const Integer &n, const unsigned int l)
Integerpowmod (Integer &Res, const Integer &n, const unsigned long e, const Integer &m)
Integerpowmod (Integer &Res, const Integer &n, const long e, const Integer &m)
Integerpowmod (Integer &Res, const Integer &n, const unsigned int e, const Integer &m)
Integerpowmod (Integer &Res, const Integer &n, const int e, const Integer &m)
Integerpowmod (Integer &Res, const Integer &n, const Integer &e, const Integer &m)
Integer powmod (const Integer &n, const unsigned long e, const Integer &m)
Integer powmod (const Integer &n, const long e, const Integer &m)
Integer powmod (const Integer &n, const unsigned int e, const Integer &m)
Integer powmod (const Integer &n, const int e, const Integer &m)
Integer powmod (const Integer &n, const Integer &e, const Integer &m)
Integer fact (unsigned long l)
Integer sqrt (const Integer &p)
Integer sqrtrem (const Integer &p, Integer &rem)
Integersqrt (Integer &r, const Integer &p)
Integersqrtrem (Integer &r, const Integer &p, Integer &rem)
bool root (Integer &q, const Integer &, unsigned int n)
long logp (const Integer &a, const Integer &p)
double logtwo (const Integer &a)
double naturallog (const Integer &a)
void swap (Integer &, Integer &)
int sign (const Integer &a)
int isZero (const Integer &a)
int isOne (const Integer &a)
int isperfectpower (const Integer &)
Integer abs (const Integer &n)
Integerprevprime (Integer &, const Integer &p)
Integernextprime (Integer &, const Integer &p)
int probab_prime (const Integer &p)
int probab_prime (const Integer &p, int r)
int jacobi (const Integer &u, const Integer &v)
int legendre (const Integer &u, const Integer &v)
unsigned long length (const Integer &a)
std::istream & operator>> (std::istream &i, Integer &n)
std::ostream & operator<< (std::ostream &o, const Integer &n)
std::ostream & absOutput (std::ostream &o, const Integer &n)
void importWords (Integer &, size_t, int, int, int, size_t, const void *)
int operator!= (const Integer &a, const Integer &b)
int operator!= (int l, const Integer &n)
int operator!= (long l, const Integer &n)
int operator!= (unsigned long l, const Integer &n)
int operator== (const Integer &a, const Integer &b)
int operator== (int l, const Integer &n)
int operator== (long l, const Integer &n)
int operator== (unsigned long l, const Integer &n)
int operator== (const Integer &n, unsigned long l)
int operator== (const Integer &n, int l)
int operator== (const Integer &n, long l)
int operator< (const Integer &a, const Integer &b)
int operator< (const int l, const Integer &n)
int operator< (const long l, const Integer &n)
int operator< (const unsigned long l, const Integer &n)
int operator<= (const Integer &n, unsigned long l)
int operator<= (unsigned long l, const Integer &n)
int operator>= (unsigned long l, const Integer &n)
int operator>= (const Integer &n, unsigned long l)
int operator> (int l, const Integer &n)
int operator> (long l, const Integer &n)
int operator> (unsigned long l, const Integer &n)
int operator> (const Integer &a, const Integer &b)
int operator<= (const Integer &a, const Integer &b)
int operator<= (const Integer &n, int l)
int operator<= (const Integer &n, long l)
int operator<= (int l, const Integer &n)
int operator<= (long l, const Integer &n)
int operator>= (const Integer &a, const Integer &b)
int operator>= (int l, const Integer &n)
int operator>= (long l, const Integer &n)
int operator>= (const Integer &n, int l)
int operator>= (const Integer &n, long l)
Integer operator+ (const int l, const Integer &n)
Integer operator+ (const unsigned int l, const Integer &n)
Integer operator+ (const long l, const Integer &n)
Integer operator+ (const unsigned long l, const Integer &n)
Integer operator+ (const Integer &n, const int l)
Integer operator+ (const Integer &n, const unsigned int l)
Integeroperator+= (Integer &n, const int l)
Integeroperator+= (Integer &n, const unsigned int l)
Integer operator- (const int l, const Integer &n)
Integer operator- (const unsigned int l, const Integer &n)
Integer operator- (const long l, const Integer &n)
Integer operator- (const unsigned long l, const Integer &n)
Integer operator- (const Integer &n, const int l)
Integer operator- (const Integer &n, const unsigned int l)
Integeroperator-= (Integer &n, const int l)
Integeroperator-= (Integer &n, const unsigned int l)
Integer operator* (const int l, const Integer &n)
Integer operator* (const unsigned int l, const Integer &n)
Integer operator* (const long l, const Integer &n)
Integer operator* (const unsigned long l, const Integer &n)
Integer operator* (const Integer &n, const int l)
Integer operator* (const Integer &n, const unsigned int l)
Integeroperator*= (Integer &n, const int l)
Integeroperator*= (Integer &n, const unsigned int l)
Integer operator/ (const int l, const Integer &n)
Integer operator/ (const long l, const Integer &n)
Integer operator/ (const Integer &n, const int l)
Integer operator/ (const Integer &n, const unsigned int l)
Integeroperator/= (Integer &n, const int l)
Integeroperator/= (Integer &n, const long l)
Integeroperator/= (Integer &n, const unsigned int l)
Integer operator% (const int l, const Integer &n)
Integer operator% (const long l, const Integer &n)
Integer operator% (const Integer &n, const int l)
Integer operator% (const Integer &n, const unsigned int l)
Integeroperator%= (Integer &n, const int l)
Integeroperator%= (Integer &n, const unsigned int l)
int isZero (const short int a)
int isZero (const int a)
int isZero (const long a)
int isZero (const unsigned short int a)
int isZero (const unsigned int a)
int isZero (const unsigned long a)
void Add_Curve (const Integer &n, const Integer A, const Integer &ax, const Integer &az, Integer &cx, Integer &cz)
void one_Mul_Curve (const Integer &n, const Integer A, const Integer &mm, const Integer &nn, const Integer &px, const Integer &pz, Integer &ax, Integer &az)
void one_Mul_Curve2 (const Integer &n, const Integer A, const Integer &mm, const Integer &nn, const Integer &px, const Integer &pz, Integer &aax, Integer &aaz)
void Mul_Curve (const Integer &n, Integer &Ai, const Integer &mm, const Integer &nn, const Integer &B1, Integer &Xi, Integer &Zi)
Integerppin (Integer &res, const Integer &prime)
std::ostream & operator<< (std::ostream &o, const GivMMInfo &T)
int compare (const Rational &a, const Rational &b)
int absCompare (const Rational &a, const Rational &b)
template double power (double x, unsigned int p)
std::istream & operator>> (std::istream &in, Rational &r)
const Rational pow (const Rational &r, const long l)
const Integer floor (const Rational &r)
const Integer ceil (const Rational &r)
const Integer round (const Rational &r)
const Integer trunc (const Rational &r)
const Rational abs (const Rational &r)
const Rational pow (const Rational &n, unsigned int l)
const Rational pow (const Rational &n, unsigned long l)
unsigned long length (const Rational &r)
int sign (const Rational &r)
int isZero (const Rational &r)
int isOne (const Rational &r)
int isInteger (const Rational &r)
int operator!= (const Rational &a, const Rational &b)
int operator== (const Rational &a, const Rational &b)
int operator< (const Rational &a, const Rational &b)
int operator> (const Rational &a, const Rational &b)
int operator<= (const Rational &a, const Rational &b)
int operator>= (const Rational &a, const Rational &b)
const Rational operator+ (const Rational &r, const int i)
const Rational operator- (const Rational &r, const int i)
const Rational operator* (const Rational &r, const int i)
const Rational operator/ (const Rational &r, const int i)
const Rational operator+ (const int i, const Rational &r)
const Rational operator- (const int i, const Rational &r)
const Rational operator* (const int i, const Rational &r)
const Rational operator/ (const int i, const Rational &r)
std::ostream & operator<< (std::ostream &o, const Rational &a)
std::ostream & operator<< (std::ostream &o, const GivError &E)
template<typename T >
unsigned GIVINTLOG (const T &a)
template<class TT , class UU >
TT power (const TT n, const UU l)
template<class D , class TT >
TT & dom_power (TT &res, const TT &n, long l, const D &F)
std::ostream & operator<< (std::ostream &o, const BaseTimer &BT)
std::ostream & operator<< (std::ostream &o, const Timer &T)
template<class Rt >
Rt FF_EXPONENT_MAX (const Rt p, const Rt e=1)
template<typename Field >
unsigned long Exponent_Trait (const Field &F)
template<>
unsigned long Exponent_Trait (const GFqDom< long > &F)
template<typename BaseField >
unsigned long Exponent_Trait (const Extension< BaseField > &F)
long value (const Degree &d)
std::ostream & operator<< (std::ostream &o, const Indeter &X)
std::istream & operator>> (std::istream &s_in, Indeter &X)
int operator== (const Indeter &i1, const Indeter &i2)
int operator!= (const Indeter &i1, const Indeter &i2)
int operator<= (const Indeter &i1, const Indeter &i2)
int operator< (const Indeter &i1, const Indeter &i2)
int operator>= (const Indeter &i1, const Indeter &i2)
int operator> (const Indeter &i1, const Indeter &i2)
template<class T >
const Poly1< T > Karatsuba (const Poly1< T > &P, const Poly1< T > &Q)
template<class Domain >
KSpace< Domainoperator* (const typename KSpace< Domain >::Scalar_t &v, const KSpace< Domain > &U)
template<class Domain >
void dotprod (typename Domain::Scalar_t &dot, const KSpace< Domain > &U, const KSpace< Domain > &V)
template<class Domain >
ostream & operator<< (ostream &sout, const KSpace< Domain > &U)
template<class Domain >
istream & operator>> (istream &sin, KSpace< Domain > &U)
template<class T , class Tag >
StructFormat< T, Tag > Formatted (const T &val, Tag xx)

Detailed Description

Arithmetic on GF(p^k), with p a prime number less than 2^15.

Specialized for fast conversions to floating point numbers. Main difference in interface is init/convert.

Bibliography:
[JG Dumas, Q-adic Transform Revisited, ISSAC 2008]
Warning:
k strictly greater than 1
Todo:
use NTL if available ?

Typedef Documentation

typedef BaseDomain<char> CharDom
typedef BaseDomain<short> ShortDom
typedef BaseDomain<int> IntDom
typedef BaseDomain<long> LongDom
typedef BaseDomain<float> FloatDom
typedef BaseDomain<double> DoubleDom

Function Documentation

class Array0 Givaro::GIVARO_PERF_INEHERIT ( Array0  ,
 
)
class ArrayFixed Givaro::GIVARO_PERF_INEHERIT ( ArrayFixed  ,
 
)
std::ostream& Givaro::operator<< ( std::ostream &  o,
const Bits &  a 
) [inline]
ostream& Givaro::operator<< ( ostream &  o,
const Pair< T1, T2 > &  p 
)
istream& Givaro::operator>> ( istream &  fin,
Pair< T1, T2 > &  p 
)
int compare ( const Integer &  a,
const Integer &  b 
)
int absCompare ( const Integer &  a,
const Integer &  b 
)
Integer & inv ( Integer &  u,
const Integer &  a,
const Integer &  b 
)
Integer & invin ( Integer &  u,
const Integer &  b 
)
Integer gcd ( const Integer &  a,
const Integer &  b 
)
Integer gcd ( const Integer &  a,
const Integer &  b,
Integer &  u,
Integer &  v 
)
Integer & gcd ( Integer &  g,
const Integer &  a,
const Integer &  b 
)
Integer & gcd ( Integer &  g,
const Integer &  a,
const Integer &  b,
Integer &  u,
Integer &  v 
)
Integer pp ( const Integer &  P,
const Integer &  Q 
)
Integer & lcm ( Integer &  g,
const Integer &  a,
const Integer &  b 
)
Integer lcm ( const Integer &  a,
const Integer &  b 
)
Integer & pow ( Integer &  Res,
const Integer &  n,
const long  l 
)
Integer & pow ( Integer &  Res,
const unsigned long  n,
const unsigned long  l 
)
Integer & pow ( Integer &  Res,
const Integer &  n,
const unsigned long  l 
)
Integer& Givaro::pow ( Integer &  Res,
const Integer &  n,
const int  l 
)
Integer& Givaro::pow ( Integer &  Res,
const Integer &  n,
const unsigned int  l 
)
Integer pow ( const Integer &  n,
const long  l 
)
Integer pow ( const Integer &  n,
const unsigned long  l 
)
Integer Givaro::pow ( const Integer &  n,
const int  l 
)
Integer Givaro::pow ( const Integer &  n,
const unsigned int  l 
)
Integer & powmod ( Integer &  Res,
const Integer &  n,
const unsigned long  e,
const Integer &  m 
)
Integer & powmod ( Integer &  Res,
const Integer &  n,
const long  e,
const Integer &  m 
)
Integer& Givaro::powmod ( Integer &  Res,
const Integer &  n,
const unsigned int  e,
const Integer &  m 
)
Integer& Givaro::powmod ( Integer &  Res,
const Integer &  n,
const int  e,
const Integer &  m 
)
Integer & powmod ( Integer &  Res,
const Integer &  n,
const Integer &  e,
const Integer &  m 
)
Integer powmod ( const Integer &  n,
const unsigned long  e,
const Integer &  m 
)
Integer powmod ( const Integer &  n,
const long  e,
const Integer &  m 
)
Integer Givaro::powmod ( const Integer &  n,
const unsigned int  e,
const Integer &  m 
)
Integer Givaro::powmod ( const Integer &  n,
const int  e,
const Integer &  m 
)
Integer powmod ( const Integer &  n,
const Integer &  e,
const Integer &  m 
)
Integer fact ( unsigned long  l)
Integer sqrt ( const Integer &  p)
Integer sqrtrem ( const Integer &  p,
Integer &  rem 
)
Integer & sqrt ( Integer &  r,
const Integer &  p 
)
Integer & sqrtrem ( Integer &  r,
const Integer &  p,
Integer &  rem 
)
bool root ( Integer &  q,
const Integer &  a,
unsigned int  n 
)
long logp ( const Integer &  a,
const Integer &  p 
)
double logtwo ( const Integer &  a)
double naturallog ( const Integer &  a)
void swap ( Integer &  a,
Integer &  b 
)
int sign ( const Integer &  a) [inline]
int isZero ( const Integer &  a) [inline]
int isOne ( const Integer &  a) [inline]
int isperfectpower ( const Integer &  n)
Integer abs ( const Integer &  n) [inline]
Integer & prevprime ( Integer &  r,
const Integer &  p 
)
Integer & nextprime ( Integer &  r,
const Integer &  p 
)
int probab_prime ( const Integer &  p)
int probab_prime ( const Integer &  p,
int  r 
)
int jacobi ( const Integer &  u,
const Integer &  v 
)
int legendre ( const Integer &  u,
const Integer &  v 
)
unsigned long length ( const Integer &  a) [inline]
std::istream & operator>> ( std::istream &  i,
Integer &  n 
)
std::ostream & operator<< ( std::ostream &  o,
const Integer &  n 
) [inline]
std::ostream & absOutput ( std::ostream &  o,
const Integer &  n 
)
void importWords ( Integer &  x,
size_t  count,
int  order,
int  size,
int  endian,
size_t  nails,
const void *  op 
)
int Givaro::operator!= ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator!= ( int  l,
const Integer &  n 
) [inline]
int Givaro::operator!= ( long  l,
const Integer &  n 
) [inline]
int Givaro::operator!= ( unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator== ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator== ( int  l,
const Integer &  n 
) [inline]
int Givaro::operator== ( long  l,
const Integer &  n 
) [inline]
int Givaro::operator== ( unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator== ( const Integer &  n,
unsigned long  l 
) [inline]
int Givaro::operator== ( const Integer &  n,
int  l 
) [inline]
int Givaro::operator== ( const Integer &  n,
long  l 
) [inline]
int Givaro::operator< ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator< ( const int  l,
const Integer &  n 
) [inline]
int Givaro::operator< ( const long  l,
const Integer &  n 
) [inline]
int Givaro::operator< ( const unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator<= ( const Integer &  n,
unsigned long  l 
) [inline]
int Givaro::operator<= ( unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator>= ( unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator>= ( const Integer &  n,
unsigned long  l 
) [inline]
int Givaro::operator> ( int  l,
const Integer &  n 
) [inline]
int Givaro::operator> ( long  l,
const Integer &  n 
) [inline]
int Givaro::operator> ( unsigned long  l,
const Integer &  n 
) [inline]
int Givaro::operator> ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator<= ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator<= ( const Integer &  n,
int  l 
) [inline]
int Givaro::operator<= ( const Integer &  n,
long  l 
) [inline]
int Givaro::operator<= ( int  l,
const Integer &  n 
) [inline]
int Givaro::operator<= ( long  l,
const Integer &  n 
) [inline]
int Givaro::operator>= ( const Integer &  a,
const Integer &  b 
) [inline]
int Givaro::operator>= ( int  l,
const Integer &  n 
) [inline]
int Givaro::operator>= ( long  l,
const Integer &  n 
) [inline]
int Givaro::operator>= ( const Integer &  n,
int  l 
) [inline]
int Givaro::operator>= ( const Integer &  n,
long  l 
) [inline]
Integer Givaro::operator+ ( const int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator+ ( const unsigned int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator+ ( const long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator+ ( const unsigned long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator+ ( const Integer &  n,
const int  l 
) [inline]
Integer Givaro::operator+ ( const Integer &  n,
const unsigned int  l 
) [inline]
Integer& Givaro::operator+= ( Integer &  n,
const int  l 
) [inline]
Integer& Givaro::operator+= ( Integer &  n,
const unsigned int  l 
) [inline]
Integer Givaro::operator- ( const int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator- ( const unsigned int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator- ( const long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator- ( const unsigned long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator- ( const Integer &  n,
const int  l 
) [inline]
Integer Givaro::operator- ( const Integer &  n,
const unsigned int  l 
) [inline]
Integer& Givaro::operator-= ( Integer &  n,
const int  l 
) [inline]
Integer& Givaro::operator-= ( Integer &  n,
const unsigned int  l 
) [inline]
Integer Givaro::operator* ( const int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator* ( const unsigned int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator* ( const long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator* ( const unsigned long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator* ( const Integer &  n,
const int  l 
) [inline]
Integer Givaro::operator* ( const Integer &  n,
const unsigned int  l 
) [inline]
Integer& Givaro::operator*= ( Integer &  n,
const int  l 
) [inline]
Integer& Givaro::operator*= ( Integer &  n,
const unsigned int  l 
) [inline]
Integer Givaro::operator/ ( const int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator/ ( const long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator/ ( const Integer &  n,
const int  l 
) [inline]
Integer Givaro::operator/ ( const Integer &  n,
const unsigned int  l 
) [inline]
Integer& Givaro::operator/= ( Integer &  n,
const int  l 
) [inline]
Integer& Givaro::operator/= ( Integer &  n,
const long  l 
) [inline]
Integer& Givaro::operator/= ( Integer &  n,
const unsigned int  l 
) [inline]
Integer Givaro::operator% ( const int  l,
const Integer &  n 
) [inline]
Integer Givaro::operator% ( const long  l,
const Integer &  n 
) [inline]
Integer Givaro::operator% ( const Integer &  n,
const int  l 
) [inline]
Integer Givaro::operator% ( const Integer &  n,
const unsigned int  l 
) [inline]
Integer& Givaro::operator%= ( Integer &  n,
const int  l 
) [inline]
Integer& Givaro::operator%= ( Integer &  n,
const unsigned int  l 
) [inline]
int Givaro::isZero ( const short int  a) [inline]
int Givaro::isZero ( const int  a) [inline]
int Givaro::isZero ( const long  a) [inline]
int Givaro::isZero ( const unsigned short int  a) [inline]
int Givaro::isZero ( const unsigned int  a) [inline]
int Givaro::isZero ( const unsigned long  a) [inline]
void Givaro::Add_Curve ( const Integer &  n,
const Integer  A,
const Integer &  ax,
const Integer &  az,
Integer &  cx,
Integer &  cz 
) [inline]
void Givaro::one_Mul_Curve ( const Integer &  n,
const Integer  A,
const Integer &  mm,
const Integer &  nn,
const Integer &  px,
const Integer &  pz,
Integer &  ax,
Integer &  az 
) [inline]
void Givaro::one_Mul_Curve2 ( const Integer &  n,
const Integer  A,
const Integer &  mm,
const Integer &  nn,
const Integer &  px,
const Integer &  pz,
Integer &  aax,
Integer &  aaz 
) [inline]
void Givaro::Mul_Curve ( const Integer &  n,
Integer &  Ai,
const Integer &  mm,
const Integer &  nn,
const Integer &  B1,
Integer &  Xi,
Integer &  Zi 
) [inline]
Integer& Givaro::ppin ( Integer &  res,
const Integer &  prime 
) [inline]
std::ostream& Givaro::operator<< ( std::ostream &  o,
const GivMMInfo &  T 
) [inline]
int compare ( const Rational &  a,
const Rational &  b 
)
int absCompare ( const Rational &  a,
const Rational &  b 
)
template double Givaro::power ( double  x,
unsigned int  p 
)
std::istream & operator>> ( std::istream &  in,
Rational &  r 
)
const Rational pow ( const Rational &  r,
const long  l 
)
const Integer floor ( const Rational &  r)
const Integer ceil ( const Rational &  r)
const Integer round ( const Rational &  r)
const Integer trunc ( const Rational &  r)
const Rational abs ( const Rational &  r) [inline]
const Rational Givaro::pow ( const Rational &  n,
unsigned int  l 
)
const Rational Givaro::pow ( const Rational &  n,
unsigned long  l 
)
unsigned long length ( const Rational &  r) [inline]
int sign ( const Rational &  r) [inline]
int isZero ( const Rational &  r) [inline]
int isOne ( const Rational &  r) [inline]
int isInteger ( const Rational &  r) [inline]
int Givaro::operator!= ( const Rational &  a,
const Rational &  b 
) [inline]
int Givaro::operator== ( const Rational &  a,
const Rational &  b 
) [inline]
int Givaro::operator< ( const Rational &  a,
const Rational &  b 
) [inline]
int Givaro::operator> ( const Rational &  a,
const Rational &  b 
) [inline]
int Givaro::operator<= ( const Rational &  a,
const Rational &  b 
) [inline]
int Givaro::operator>= ( const Rational &  a,
const Rational &  b 
) [inline]
const Rational Givaro::operator+ ( const Rational &  r,
const int  i 
) [inline]
const Rational Givaro::operator- ( const Rational &  r,
const int  i 
) [inline]
const Rational Givaro::operator* ( const Rational &  r,
const int  i 
) [inline]
const Rational Givaro::operator/ ( const Rational &  r,
const int  i 
) [inline]
const Rational Givaro::operator+ ( const int  i,
const Rational &  r 
) [inline]
const Rational Givaro::operator- ( const int  i,
const Rational &  r 
) [inline]
const Rational Givaro::operator* ( const int  i,
const Rational &  r 
) [inline]
const Rational Givaro::operator/ ( const int  i,
const Rational &  r 
) [inline]
std::ostream& Givaro::operator<< ( std::ostream &  o,
const Rational &  a 
) [inline]
std::ostream& Givaro::operator<< ( std::ostream &  o,
const GivError &  E 
)
unsigned Givaro::GIVINTLOG ( const T &  a) [inline]
TT Givaro::power ( const TT  n,
const UU  l 
)
TT& Givaro::dom_power ( TT &  res,
const TT &  n,
long  l,
const D &  F 
)
std::ostream& Givaro::operator<< ( std::ostream &  o,
const BaseTimer &  BT 
) [inline]
std::ostream& Givaro::operator<< ( std::ostream &  o,
const Timer &  T 
) [inline]
Rt Givaro::FF_EXPONENT_MAX ( const Rt  p,
const Rt  e = 1 
)
unsigned long Givaro::Exponent_Trait ( const Field F)
unsigned long Givaro::Exponent_Trait ( const GFqDom< long > &  F)
unsigned long Givaro::Exponent_Trait ( const Extension< BaseField > &  F)
long Givaro::value ( const Degree &  d) [inline]
std::ostream& Givaro::operator<< ( std::ostream &  o,
const Indeter &  X 
)
std::istream& Givaro::operator>> ( std::istream &  s_in,
Indeter &  X 
)
int Givaro::operator== ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
int Givaro::operator!= ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
int Givaro::operator<= ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
int Givaro::operator< ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
int Givaro::operator>= ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
int Givaro::operator> ( const Indeter &  i1,
const Indeter &  i2 
) [inline]
const Poly1<T> Givaro::Karatsuba ( const Poly1< T > &  P,
const Poly1< T > &  Q 
)
KSpace<Domain> Givaro::operator* ( const typename KSpace< Domain >::Scalar_t &  v,
const KSpace< Domain > &  U 
)
void Givaro::dotprod ( typename Domain::Scalar_t &  dot,
const KSpace< Domain > &  U,
const KSpace< Domain > &  V 
) [inline]
ostream& Givaro::operator<< ( ostream &  sout,
const KSpace< Domain > &  U 
) [inline]
istream& Givaro::operator>> ( istream &  sin,
KSpace< Domain > &  U 
) [inline]
StructFormat<T,Tag> Givaro::Formatted ( const T &  val,
Tag  xx 
)