fast_Ring< TNum, kdefs > Class Template Reference
[Algebra objects, Fields and Rings]

Implements some fast basic operations for elemens of a ring F_q[epsilon] or field F_q with small characteristic;
For all operations the user must be sure that the operators are regular represantants of ring elements, in doubt by calling the Convert() function. Currently all represantant values must lie between 0 and (characteristic-1). Allowed 'eps' precisions are 0 (is a field) and 1 (is a ring)
Parametrized with element Type (TNum) and characteristic of the field the ring is based on during compile time. More...

#include <fast_Ring.h>

Collaboration diagram for fast_Ring< TNum, kdefs >:
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List of all members.

Classes

struct  sqrtInf

Public Types

typedef struct fast_Ring::sqrtInf sqrtInf_t
typedef TNum ElementType
typedef fast_Ring< TNum, kdefs > FieldType
typedef FieldType::ElementType ScalarType

Public Member Functions

bool wellDefined ()
const FieldType * getField () const
const FieldType & getFieldRef () const
Constructors / Destructors

 fast_Ring (unsigned short _characteristic, unsigned short epsPrec)
 ~fast_Ring ()
properties

unsigned short getCharacteristic () const
const unsigned short & getCharacteristicRef () const
unsigned short getEpsPrecision () const
void setEpsPrecision (int epsPrecision) const
safety

bool isValid (TNum a) const
add

TNum add (const TNum a, const TNum b) const
TNum addRef (const TNum &a, const TNum &b) const
add in place

void addInPlace (TNum &a, const TNum b) const
void addInPlaceRef (TNum &a, const TNum &b) const
additive inverse

TNum addInv (const TNum a) const
TNum addInvRef (const TNum &a) const
void addInvInPlace (TNum &a) const
accMult

void accMult (TNum &a, const TNum b, const TNum c) const
void accMultRef (TNum &a, const TNum &b, const TNum &c) const
void accMult (TNum *a, const TNum b, const TNum c) const
void accMultAddr (TNum *a, const TNum *b, const TNum *c) const
 accMult assumes, that b is not zero, and
void accMultSpec (TNum *const a, const TNum b, const TNum *const c) const
multiplication

TNum multiply (const TNum a, const TNum b) const
TNum multiplyRef (const TNum &a, const TNum &b) const
 multipliziert zwei Zahlen
multiply in place

void multiplyInPlace (TNum &a, const TNum b) const
void multiplyInPlaceRef (TNum &a, const TNum &b) const
scalar multiplication

TNum scalarMultiply (const FieldType::ElementType a, const TNum b) const
TNum scalarMultiplyRef (const FieldType::ElementType &a, const TNum &b) const
 multipliziert zwei Zahlen
scalar multiply in place

void scalarMultiplyInPlace (const FieldType::ElementType a, TNum &b) const
void scalarMultiplyInPlaceRef (const FieldType::ElementType &a, TNum &b) const
multiplication by Exponents

TNum const multByExp (const TNum a, const TNum b) const
TNum const multByExpRef (const TNum &a, const TNum &b) const
void multByExpInPlace (TNum &a, const TNum b) const
void multByExpInPlaceRef (TNum &a, const TNum &b) const
multiplicative inverse

TNum multInv (const TNum a) const
TNum multInvRef (const TNum &a) const
void multInvInPlace (TNum &a) const
power

TNum pow (TNum const a, unsigned int exp) const
void powInPlace (TNum &a, unsigned int exp) const
sqrd

sqrtInf sqrt (const TNum a) const
sqrtInf sqrtRef (const TNum &a) const
Conversion

FieldType::ElementType lookupModuloTable (int convertee) const
int getLookupModuloTableSize () const
template<class TConvNum >
TNum Convert (const TConvNum a) const
TNum Convert (const double a) const
 Convert eventuell umbenennen ConvertScalarToRingElement
TNum Convert (const int a) const
 Convert eventuell umbenennen ConvertScalarToRingElement
template<class TConvNum >
void ConvertInPlace (TConvNum &a) const
int ConvertScalar (const int a) const
 einfuehren ConvertScalarToFieldElement
int ConvertScalarSpec (const int a) const
 convert a integer to Ring element. Assumption: a >=0
int FastConvertScalar (const int a) const
 convert a integer to Ring Elemen. Assumption: a >=-getCharacteristic() /
Table index computation

size_t getMaxSingleIndex () const
size_t getMaxPairIndex () const
size_t getSingleIndex (const TNum z1) const
size_t getSingleIndexByRef (const TNum &z1) const
size_t getPairIndexByRef (const TNum &z1, const TNum &z2) const
size_t getPairIndex (const TNum z1, const TNum z2) const

Protected Member Functions

void init ()
TNum * createAdditionTable ()
 only for the case, that table pointers are static
TNum * createMultiplicationTable ()
 creates multiplication table
TNum * createSubtractionTable ()
TNum * createAdditiveInverseTable ()
TNum * createMultiplicativeInverseTable ()

TNum getGenerator ()
 Returns a generator of the Ring0} if exists, otherwise TNum::Zero.
TNum * initElementsToExponentsTab (TNum erzeuger)
TNum * initExponentsToElementTab (TNum erzeuger)
TNum * createFastAdditionTable ()
 only for epsilon==0
FieldType::ElementType * createModuloTable ()
sqrtInf_t * createSqrtTable ()

Private Attributes

const unsigned short characteristic
long moduloTableSize_m
const unsigned short epsilon
const TNum generator
const TNum * elementsToExponentsTab
const TNum * exponentsToElementTab
const TNum * additiveInverseTable
const TNum * multiplicationTable
const TNum * additionTable
const TNum * multiplicativeInverseTable
const TNum * fastAdditionTable
const ScalarType * moduloTable
const sqrtInf_t * sqrtTable

Detailed Description

template<class TNum, class kdefs>
class fast_Ring< TNum, kdefs >

Main idea: table lookup instead of computation. For big characteristics this method costs performance, because the operation lookup tables does not fit in L1 or L2 cache But for small characteristics it works very well.

To avoid copying data, functions with reference parameters were implemented, because it is impossible to enforce inlining. But that costs implementation overhead and is dangerous, because is is possible to pass a reference to a temporary variable. and woult result in an error.

Die Schnelligkeit der Berechnungen beruht auf Verwendung von Operationstabellen und von der Annahme, dass alle Funktionsaufrufe mit gültigen Parametern ausgeführt werden. Die Operationstabellen sind so ausgelegt, dass mit Hilfe von Bit Shift Operationen das Ergebnis einer Rechenoperation abgelesen werden kann: statt

ArrayIndex(a,b)=a*charakteristik+b

ArrayIndex(a,b)=a*Zweierpotenz+b benutzt wird.; Zweierpotenz>=charakteristik, Somit kann die Indexfunktion mit Bit Schifts und bitweisem 'OR' berechnet werden Der Nachteil ist, dass mehr Speicherplatz, als benötigt belegt wird.

Die Berechnungen werden wieder langsamer, wenn die Tabellen nicht in den Cache passen. Bei Charakteristik 29 und dem Zahlentype 'number_eps1' beträgt der Speicherplatzbedarf 29^4*2 Bytes * 2 Tabellen (Multiplikation, Addition) = 4 MByte und bei Charakteristik 23 1119364 = 1 MByte

Note:
Komisch, dass die 23-er Berechnung nicht wesentlich schneller ist - wieso sollte sie? es gibt nur 1 strudelgroesse weniger!
in the optimized and error-free version it is not tested, if an operation result is really a legal ring/field representative. Moreover, in a correct frommer algorithm implementation this test is not neccessary.
Todo:
multiplyOnCPU einfuehren bzw multiplyByHand
Todo:
Idee: shift index bei generischer Version - hätte vielleicht Vorteile, da schneller addiert werden kann. Hm, warum wird die Optimierte Version ohne Addition nicht schneller? Schliesslich wird der Platz für den Pointer auf die Additionstabelle frei.
Todo:
ueberpruefen, ob man nicht ohne die funktionen mit parametern 'passed by reference' auskommen kann, d.h. ob dies nicht wesentlich die performance verschlechtert, und wie man bei 'pass by value'-parametern und Rückgabewerten unnötiges Kopieren verhindern kann.

Definition at line 92 of file fast_Ring.h.

Member Typedef Documentation

template<class TNum, class kdefs>
typedef TNum fast_Ring< TNum, kdefs >::ElementType

Definition at line 108 of file fast_Ring.h.

template<class TNum, class kdefs>
typedef fast_Ring< TNum,kdefs > fast_Ring< TNum, kdefs >::FieldType

Definition at line 110 of file fast_Ring.h.

template<class TNum, class kdefs>
typedef FieldType::ElementType fast_Ring< TNum, kdefs >::ScalarType

Definition at line 112 of file fast_Ring.h.

template<class TNum, class kdefs>
typedef struct fast_Ring::sqrtInf fast_Ring< TNum, kdefs >::sqrtInf_t

Constructor & Destructor Documentation

template<class TNum , class kdefs >
fast_Ring< TNum, kdefs >::fast_Ring ( unsigned short  _char,
unsigned short  _epsPrec 
) [inline]
Todo:
hier pruefen, ob tNum gross genug ausgelegt ist

Definition at line 13 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::characteristic, fast_Ring< TNum, kdefs >::epsilon, fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::wellDefined().

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template<class TNum , class kdefs >
fast_Ring< TNum, kdefs >::~fast_Ring (  )  [inline]

Definition at line 95 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::additiveInverseTable, fast_Ring< TNum, kdefs >::elementsToExponentsTab, fast_Ring< TNum, kdefs >::exponentsToElementTab, fast_Ring< TNum, kdefs >::fastAdditionTable, fast_Ring< TNum, kdefs >::moduloTable, fast_Ring< TNum, kdefs >::multiplicationTable, fast_Ring< TNum, kdefs >::multiplicativeInverseTable, and fast_Ring< TNum, kdefs >::sqrtTable.

Member Function Documentation

template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::accMult ( TNum *  a,
const TNum  b,
const TNum  c 
) const [inline]

Definition at line 656 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::accMult ( TNum &  a,
const TNum  b,
const TNum  c 
) const [inline]

Definition at line 641 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::accMultAddr ( TNum *  a,
const TNum *  b,
const TNum *  c 
) const [inline]

Definition at line 763 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::accMultRef ( TNum &  a,
const TNum &  b,
const TNum &  c 
) const [inline]

Definition at line 673 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::accMultSpec ( TNum *const   a,
const TNum  b,
const TNum *const   c 
) const [inline]

Optimierung : Eigenen Überlegungen nach sollte die Multiplikation an dieser Stelle per Tabelle und die Addition auf der CPU erledigt werden, weil ein Multiplikator fest ist und nur der andere variiert ( characteristic*characteristic mögliche Werte) Dagegen variieren bei der Addition beide Zahlen, was zu erheblichen Cache misses führen müsste. Allerdings ist die Laufzeit auf einem Intel-Rechner katastrophal, wenn man die Addition auf der CPU durchführt. Es gab mal eine Konfiguration, wo die Addition auf der CPU schneller war, jetzt ist die Laufzeit in etwa gleich, oder schlechter mit der Addition auf der CPU

Definition at line 698 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::add ( const TNum  a,
const TNum  b 
) const [inline]

Definition at line 290 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getPairIndex().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::addInPlace ( TNum &  a,
const TNum  b 
) const [inline]

Definition at line 319 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getPairIndex().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::addInPlaceRef ( TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 334 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getPairIndexByRef().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::addInv ( const TNum  a  )  const [inline]

Definition at line 352 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additiveInverseTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getSingleIndex().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::addInvInPlace ( TNum &  a  )  const [inline]

Definition at line 375 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additiveInverseTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getSingleIndexByRef().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::addInvRef ( const TNum &  a  )  const [inline]

Definition at line 364 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additiveInverseTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getSingleIndexByRef().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::addRef ( const TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 303 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::getPairIndexByRef().

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template<class TNum , class kdefs >
TNum fast_Ring< TNum, kdefs >::Convert ( const int  a  )  const [inline]

Definition at line 180 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::ConvertScalar(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

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template<class TNum , class kdefs >
TNum fast_Ring< TNum, kdefs >::Convert ( const double  a  )  const [inline]

Definition at line 166 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::ConvertScalar(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

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template<class TNum , class kdefs >
template<class TConvNum >
TNum fast_Ring< TNum, kdefs >::Convert ( const TConvNum  src  )  const [inline]
Parameters:
src TConvNum object src must implement getX() and getEps() -Interface . In general this can be replaced by getValue(epsPrecision)-Interface, but is not neccessary in this specialized class

Definition at line 142 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::ConvertScalar(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

Referenced by fast_Ring< TNum, kdefs >::accMult(), fast_Ring< TNum, kdefs >::accMultAddr(), fast_Ring< TNum, kdefs >::accMultRef(), fast_Ring< TNum, kdefs >::accMultSpec(), fast_Ring< TNum, kdefs >::add(), fast_Ring< TNum, kdefs >::addInPlace(), fast_Ring< TNum, kdefs >::addInPlaceRef(), fast_Ring< TNum, kdefs >::addInv(), fast_Ring< TNum, kdefs >::addInvInPlace(), fast_Ring< TNum, kdefs >::addInvRef(), fast_Ring< TNum, kdefs >::addRef(), fast_Ring< TNum, kdefs >::isValid(), fast_Ring< TNum, kdefs >::multInv(), fast_Ring< TNum, kdefs >::multInvInPlace(), fast_Ring< TNum, kdefs >::multInvRef(), fast_Ring< TNum, kdefs >::multiply(), fast_Ring< TNum, kdefs >::multiplyInPlace(), fast_Ring< TNum, kdefs >::multiplyInPlaceRef(), fast_Ring< TNum, kdefs >::multiplyRef(), fast_Ring< TNum, kdefs >::scalarMultiply(), fast_Ring< TNum, kdefs >::scalarMultiplyInPlace(), fast_Ring< TNum, kdefs >::scalarMultiplyInPlaceRef(), fast_Ring< TNum, kdefs >::scalarMultiplyRef(), fast_Ring< TNum, kdefs >::sqrt(), and fast_Ring< TNum, kdefs >::sqrtRef().

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template<class TNum , class kdefs >
template<class TConvNum >
void fast_Ring< TNum, kdefs >::ConvertInPlace ( TConvNum &  a  )  const [inline]

riscy in some cases? does currently ignore the case where TConvNum.getEpsPrecision > 1. assert( getEpsPrecision()<=1 ); gehoert in den Konstruktor dieser Klasse, da sie offenbar nicht mit EPSPrecision >1 arbeiten kann und muss. An anderen Stellen kann diese Abfrage entfernt werden.

Definition at line 218 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::ConvertScalar(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

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template<class TNum , class kdefs >
int fast_Ring< TNum, kdefs >::ConvertScalar ( const int  a  )  const [inline]
Todo:
TNum::scalarType zurueckgeben oder bei int bleiben?

Definition at line 239 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

Referenced by fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::ConvertInPlace(), and fast_Ring< TNum, kdefs >::lookupModuloTable().

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template<class TNum , class kdefs >
int fast_Ring< TNum, kdefs >::ConvertScalarSpec ( const int  a  )  const [inline]

Definition at line 261 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum , class kdefs >
TNum * fast_Ring< TNum, kdefs >::createAdditionTable (  )  [inline, protected]

create addition table

Initialisiert die Additionstabelle . Es gibt zwei Faelle: epsPrecision==0 und epsPrecision==1 Bei epsPrecision =0 sind die Eintraege eindimensional (x) und fuer epsPrecision==1 zweidimensional (x,eps).

Optimierungsmoeglichkeit: steht wenig cache zur Verfuegung, so kann der Cache-Bedarf um die Haelfte reduziert werden, wenn die Additionstabelle nur Eindimensional angelegt wird und die add-Funktionen bei epsPrecision==1 (x1,eps1)+(x2,eps2) simulieren.

Definition at line 842 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getEpsPrecision(), fast_Ring< TNum, kdefs >::getMaxPairIndex(), and fast_Ring< TNum, kdefs >::getPairIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum , class kdefs >
TNum * fast_Ring< TNum, kdefs >::createAdditiveInverseTable (  )  [inline, protected]
Todo:
modulo % getCharacteristic() in initAddInv() unnoetig

Definition at line 903 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getEpsPrecision(), fast_Ring< TNum, kdefs >::getMaxSingleIndex(), and fast_Ring< TNum, kdefs >::getSingleIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum , class kdefs >
TNum * fast_Ring< TNum, kdefs >::createFastAdditionTable (  )  [inline, protected]

Definition at line 879 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum , class kdefs >
fast_Ring< TNum, kdefs >::FieldType::ElementType * fast_Ring< TNum, kdefs >::createModuloTable (  )  [inline, protected]

Definition at line 1110 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::characteristic, and fast_Ring< TNum, kdefs >::moduloTableSize_m.

Referenced by fast_Ring< TNum, kdefs >::init().

template<class TNum , class kdefs >
TNum * fast_Ring< TNum, kdefs >::createMultiplicationTable (  )  [inline, protected]

Definition at line 932 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getEpsPrecision(), fast_Ring< TNum, kdefs >::getMaxPairIndex(), and fast_Ring< TNum, kdefs >::getPairIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum , class kdefs >
TNum * fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable (  )  [inline, protected]

creates multiplicative inverse table

Todo:

in den Initialisierungsfunktionen die Convert-Funktion nutzen!

initInv überarbeiten!

Definition at line 998 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getEpsPrecision(), fast_Ring< TNum, kdefs >::getMaxSingleIndex(), and fast_Ring< TNum, kdefs >::getSingleIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum , class kdefs >
fast_Ring< TNum, kdefs >::sqrtInf_t * fast_Ring< TNum, kdefs >::createSqrtTable (  )  [inline, protected]

Definition at line 1160 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getMaxSingleIndex(), fast_Ring< TNum, kdefs >::sqrtInf::solutions, fast_Ring< TNum, kdefs >::sqrt(), and fast_Ring< TNum, kdefs >::sqrtInf::sqrt.

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum, class kdefs>
TNum* fast_Ring< TNum, kdefs >::createSubtractionTable (  )  [protected]
template<class TNum , class kdefs >
int fast_Ring< TNum, kdefs >::FastConvertScalar ( const int  a  )  const [inline]
Precondition:
assumption: a >=-getCharacteristic()

Definition at line 275 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum, class kdefs>
unsigned short fast_Ring< TNum, kdefs >::getCharacteristic (  )  const [inline]

Definition at line 172 of file fast_Ring.h.

References fast_Ring< TNum, kdefs >::characteristic.

Referenced by fast_Ring< TNum, kdefs >::ConvertScalar(), fast_Ring< TNum, kdefs >::ConvertScalarSpec(), fast_Ring< TNum, kdefs >::createAdditionTable(), fast_Ring< TNum, kdefs >::createAdditiveInverseTable(), fast_Ring< TNum, kdefs >::createFastAdditionTable(), fast_Ring< TNum, kdefs >::createMultiplicationTable(), fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable(), fast_Ring< TNum, kdefs >::createSqrtTable(), fast_Ring< TNum, kdefs >::FastConvertScalar(), fast_Ring< TNum, kdefs >::getGenerator(), fast_Ring< TNum, kdefs >::getMaxPairIndex(), fast_Ring< TNum, kdefs >::getMaxSingleIndex(), fast_Ring< TNum, kdefs >::getPairIndex(), fast_Ring< TNum, kdefs >::getSingleIndex(), fast_Ring< TNum, kdefs >::initElementsToExponentsTab(), fast_Ring< TNum, kdefs >::initExponentsToElementTab(), fast_Ring< TNum, kdefs >::multByExp(), fast_Ring< TNum, kdefs >::multByExpInPlace(), fast_Ring< TNum, kdefs >::multByExpInPlaceRef(), and fast_Ring< TNum, kdefs >::multByExpRef().

template<class TNum, class kdefs>
const unsigned short& fast_Ring< TNum, kdefs >::getCharacteristicRef (  )  const [inline]

Definition at line 173 of file fast_Ring.h.

References fast_Ring< TNum, kdefs >::characteristic.

Referenced by fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::getSingleIndexByRef().

template<class TNum, class kdefs>
unsigned short fast_Ring< TNum, kdefs >::getEpsPrecision (  )  const [inline]

Definition at line 175 of file fast_Ring.h.

References fast_Ring< TNum, kdefs >::epsilon.

Referenced by fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::ConvertInPlace(), fast_Ring< TNum, kdefs >::createAdditionTable(), fast_Ring< TNum, kdefs >::createAdditiveInverseTable(), fast_Ring< TNum, kdefs >::createFastAdditionTable(), fast_Ring< TNum, kdefs >::createMultiplicationTable(), fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable(), and fast_Ring< TNum, kdefs >::getGenerator().

template<class TNum, class kdefs>
const FieldType* fast_Ring< TNum, kdefs >::getField (  )  const [inline]
Todo:
alternativ Field asls const Membervariable.

Definition at line 151 of file fast_Ring.h.

template<class TNum, class kdefs>
const FieldType& fast_Ring< TNum, kdefs >::getFieldRef (  )  const [inline]

Definition at line 156 of file fast_Ring.h.

template<class TNum , class kdefs >
TNum fast_Ring< TNum, kdefs >::getGenerator (  )  [inline, protected]
Todo:

herausfinden, welchen Datentyp wir nach der -Operation haben und ob es Probleme bei unsigned Datentypen gibt.

vernuenftige Loesung fuer epsPrecision>0.

testen , ob angegebene Charakteristik eine Primzahl ist - Merkt man das nicht spaetestens wenn es keinen Erzeuger gibt?

Definition at line 781 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), and fast_Ring< TNum, kdefs >::getEpsPrecision().

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template<class TNum , class kdefs >
int fast_Ring< TNum, kdefs >::getLookupModuloTableSize (  )  const [inline]

Definition at line 1136 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::moduloTableSize_m.

template<class TNum , class kdefs >
size_t fast_Ring< TNum, kdefs >::getMaxPairIndex (  )  const [inline]

Definition at line 1267 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

Referenced by fast_Ring< TNum, kdefs >::createAdditionTable(), and fast_Ring< TNum, kdefs >::createMultiplicationTable().

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template<class TNum , class kdefs >
size_t fast_Ring< TNum, kdefs >::getMaxSingleIndex (  )  const [inline]

Definition at line 1259 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

Referenced by fast_Ring< TNum, kdefs >::createAdditiveInverseTable(), fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable(), fast_Ring< TNum, kdefs >::createSqrtTable(), fast_Ring< TNum, kdefs >::initElementsToExponentsTab(), and fast_Ring< TNum, kdefs >::initExponentsToElementTab().

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template<class TNum, class kdefs >
size_t fast_Ring< TNum, kdefs >::getPairIndex ( const TNum  z1,
const TNum  z2 
) const [inline]

Definition at line 1289 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

Referenced by fast_Ring< TNum, kdefs >::accMult(), fast_Ring< TNum, kdefs >::accMultAddr(), fast_Ring< TNum, kdefs >::accMultRef(), fast_Ring< TNum, kdefs >::accMultSpec(), fast_Ring< TNum, kdefs >::add(), fast_Ring< TNum, kdefs >::addInPlace(), fast_Ring< TNum, kdefs >::createAdditionTable(), fast_Ring< TNum, kdefs >::createMultiplicationTable(), fast_Ring< TNum, kdefs >::multiply(), fast_Ring< TNum, kdefs >::multiplyInPlace(), fast_Ring< TNum, kdefs >::scalarMultiply(), and fast_Ring< TNum, kdefs >::scalarMultiplyInPlace().

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template<class TNum, class kdefs >
size_t fast_Ring< TNum, kdefs >::getPairIndexByRef ( const TNum &  z1,
const TNum &  z2 
) const [inline]

Definition at line 1296 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristicRef().

Referenced by fast_Ring< TNum, kdefs >::accMultRef(), fast_Ring< TNum, kdefs >::addInPlaceRef(), fast_Ring< TNum, kdefs >::addRef(), fast_Ring< TNum, kdefs >::multiplyInPlaceRef(), fast_Ring< TNum, kdefs >::multiplyRef(), fast_Ring< TNum, kdefs >::scalarMultiplyInPlaceRef(), and fast_Ring< TNum, kdefs >::scalarMultiplyRef().

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template<class TNum, class kdefs >
size_t fast_Ring< TNum, kdefs >::getSingleIndex ( const TNum  z1  )  const [inline]

Definition at line 1275 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

Referenced by fast_Ring< TNum, kdefs >::addInv(), fast_Ring< TNum, kdefs >::createAdditiveInverseTable(), fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable(), fast_Ring< TNum, kdefs >::multInv(), and fast_Ring< TNum, kdefs >::multInvInPlace().

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template<class TNum, class kdefs >
size_t fast_Ring< TNum, kdefs >::getSingleIndexByRef ( const TNum &  z1  )  const [inline]

Definition at line 1283 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristicRef().

Referenced by fast_Ring< TNum, kdefs >::addInvInPlace(), fast_Ring< TNum, kdefs >::addInvRef(), and fast_Ring< TNum, kdefs >::multInvRef().

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template<class TNum , class kdefs >
void fast_Ring< TNum, kdefs >::init (  )  [inline, protected]
Todo:
warum dieser Init-Kram ? gibt sowieso nur einen Konstruktor, aber nun gut...

Definition at line 35 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::additionTable, fast_Ring< TNum, kdefs >::additiveInverseTable, fast_Ring< TNum, kdefs >::createAdditionTable(), fast_Ring< TNum, kdefs >::createAdditiveInverseTable(), fast_Ring< TNum, kdefs >::createFastAdditionTable(), fast_Ring< TNum, kdefs >::createModuloTable(), fast_Ring< TNum, kdefs >::createMultiplicationTable(), fast_Ring< TNum, kdefs >::createMultiplicativeInverseTable(), fast_Ring< TNum, kdefs >::createSqrtTable(), fast_Ring< TNum, kdefs >::elementsToExponentsTab, fast_Ring< TNum, kdefs >::exponentsToElementTab, fast_Ring< TNum, kdefs >::fastAdditionTable, fast_Ring< TNum, kdefs >::generator, fast_Ring< TNum, kdefs >::initElementsToExponentsTab(), fast_Ring< TNum, kdefs >::initExponentsToElementTab(), fast_Ring< TNum, kdefs >::moduloTable, fast_Ring< TNum, kdefs >::multiplicationTable, fast_Ring< TNum, kdefs >::multiplicativeInverseTable, and fast_Ring< TNum, kdefs >::sqrtTable.

Referenced by fast_Ring< TNum, kdefs >::fast_Ring().

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template<class TNum, class kdefs >
TNum * fast_Ring< TNum, kdefs >::initElementsToExponentsTab ( TNum  erzeuger  )  [inline, protected]
Todo:
is only correct for epsPrecision==0 and does not really belong in fast_Ring class!

Definition at line 1045 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), and fast_Ring< TNum, kdefs >::getMaxSingleIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum, class kdefs >
TNum * fast_Ring< TNum, kdefs >::initExponentsToElementTab ( TNum  erzeuger  )  [inline, protected]
Note:
exponentsToElementTab koennte PerformanceProbleme bereiten, wenn intern die Indizierungsfunktnion verwendet wuerde

Definition at line 1083 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic(), and fast_Ring< TNum, kdefs >::getMaxSingleIndex().

Referenced by fast_Ring< TNum, kdefs >::init().

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template<class TNum, class kdefs>
bool fast_Ring< TNum, kdefs >::isValid ( TNum  a  )  const [inline]

Definition at line 190 of file fast_Ring.h.

References fast_Ring< TNum, kdefs >::Convert().

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template<class TNum , class kdefs >
fast_Ring< TNum, kdefs >::FieldType::ElementType fast_Ring< TNum, kdefs >::lookupModuloTable ( int  convertee  )  const [inline]

Definition at line 1143 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::ConvertScalar(), fast_Ring< TNum, kdefs >::moduloTable, and fast_Ring< TNum, kdefs >::moduloTableSize_m.

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template<class TNum, class kdefs >
TNum const fast_Ring< TNum, kdefs >::multByExp ( const TNum  a,
const TNum  b 
) const [inline]

Definition at line 516 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::multByExpInPlace ( TNum &  a,
const TNum  b 
) const [inline]

Definition at line 544 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::multByExpInPlaceRef ( TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 558 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum, class kdefs >
TNum const fast_Ring< TNum, kdefs >::multByExpRef ( const TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 530 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::getCharacteristic().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::multInv ( const TNum  a  )  const [inline]

Definition at line 573 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getSingleIndex(), and fast_Ring< TNum, kdefs >::multiplicativeInverseTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::multInvInPlace ( TNum &  a  )  const [inline]

Definition at line 617 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getSingleIndex(), and fast_Ring< TNum, kdefs >::multiplicativeInverseTable.

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::multInvRef ( const TNum &  a  )  const [inline]

Definition at line 592 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getSingleIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicativeInverseTable.

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::multiply ( const TNum  a,
const TNum  b 
) const [inline]

Definition at line 396 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::multiplyInPlace ( TNum &  a,
const TNum  b 
) const [inline]

Definition at line 428 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::multiplyInPlaceRef ( TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 439 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicationTable.

Referenced by fast_Ring< TNum, kdefs >::pow(), and fast_Ring< TNum, kdefs >::powInPlace().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::multiplyRef ( const TNum &  a,
const TNum &  b 
) const [inline]

Definition at line 411 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::pow ( TNum const  a,
unsigned int  exp 
) const [inline]

Definition at line 1211 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::multiplyInPlaceRef().

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::powInPlace ( TNum &  a,
unsigned int  exp 
) const [inline]

Definition at line 1235 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::multiplyInPlaceRef().

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::scalarMultiply ( const FieldType::ElementType  a,
const TNum  b 
) const [inline]

Definition at line 456 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::scalarMultiplyInPlace ( const FieldType::ElementType  a,
TNum &  b 
) const [inline]

Definition at line 489 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndex(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
void fast_Ring< TNum, kdefs >::scalarMultiplyInPlaceRef ( const FieldType::ElementType &  a,
TNum &  b 
) const [inline]

Definition at line 502 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs >
TNum fast_Ring< TNum, kdefs >::scalarMultiplyRef ( const FieldType::ElementType &  a,
const TNum &  b 
) const [inline]

Definition at line 472 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), fast_Ring< TNum, kdefs >::getPairIndexByRef(), and fast_Ring< TNum, kdefs >::multiplicationTable.

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template<class TNum, class kdefs>
void fast_Ring< TNum, kdefs >::setEpsPrecision ( int  epsPrecision  )  const [inline]

Definition at line 177 of file fast_Ring.h.

References fast_Ring< TNum, kdefs >::epsilon.

template<class TNum, class kdefs >
fast_Ring< TNum, kdefs >::sqrtInf_t fast_Ring< TNum, kdefs >::sqrt ( const TNum  a  )  const [inline]

Definition at line 740 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::sqrtTable.

Referenced by fast_Ring< TNum, kdefs >::createSqrtTable().

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template<class TNum, class kdefs >
fast_Ring< TNum, kdefs >::sqrtInf_t fast_Ring< TNum, kdefs >::sqrtRef ( const TNum &  a  )  const [inline]

Definition at line 751 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::Convert(), and fast_Ring< TNum, kdefs >::sqrtTable.

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template<class TNum , class kdefs >
bool fast_Ring< TNum, kdefs >::wellDefined (  )  [inline]

Definition at line 26 of file fast_Ring.cpp.

References fast_Ring< TNum, kdefs >::characteristic.

Referenced by fast_Ring< TNum, kdefs >::fast_Ring().

Member Data Documentation

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::additionTable [private]

Definition at line 132 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::accMult(), fast_Ring< TNum, kdefs >::accMultAddr(), fast_Ring< TNum, kdefs >::accMultRef(), fast_Ring< TNum, kdefs >::accMultSpec(), fast_Ring< TNum, kdefs >::add(), fast_Ring< TNum, kdefs >::addInPlace(), fast_Ring< TNum, kdefs >::addInPlaceRef(), fast_Ring< TNum, kdefs >::addRef(), fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::additiveInverseTable [private]

Definition at line 130 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::addInv(), fast_Ring< TNum, kdefs >::addInvInPlace(), fast_Ring< TNum, kdefs >::addInvRef(), fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const unsigned short fast_Ring< TNum, kdefs >::characteristic [private]

Definition at line 118 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::createModuloTable(), fast_Ring< TNum, kdefs >::fast_Ring(), fast_Ring< TNum, kdefs >::getCharacteristic(), fast_Ring< TNum, kdefs >::getCharacteristicRef(), and fast_Ring< TNum, kdefs >::wellDefined().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::elementsToExponentsTab [private]

Definition at line 127 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const unsigned short fast_Ring< TNum, kdefs >::epsilon [private]
Todo:
Variable umbenenen in epsPrecision.

Definition at line 123 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::fast_Ring(), fast_Ring< TNum, kdefs >::getEpsPrecision(), and fast_Ring< TNum, kdefs >::setEpsPrecision().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::exponentsToElementTab [private]

Definition at line 128 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::fastAdditionTable [private]

Definition at line 134 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const TNum fast_Ring< TNum, kdefs >::generator [private]

Definition at line 126 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init().

template<class TNum, class kdefs>
const ScalarType* fast_Ring< TNum, kdefs >::moduloTable [private]

Definition at line 136 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), fast_Ring< TNum, kdefs >::lookupModuloTable(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
long fast_Ring< TNum, kdefs >::moduloTableSize_m [private]

Definition at line 120 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::createModuloTable(), fast_Ring< TNum, kdefs >::getLookupModuloTableSize(), and fast_Ring< TNum, kdefs >::lookupModuloTable().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::multiplicationTable [private]

Definition at line 131 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::accMult(), fast_Ring< TNum, kdefs >::accMultAddr(), fast_Ring< TNum, kdefs >::accMultRef(), fast_Ring< TNum, kdefs >::accMultSpec(), fast_Ring< TNum, kdefs >::init(), fast_Ring< TNum, kdefs >::multiply(), fast_Ring< TNum, kdefs >::multiplyInPlace(), fast_Ring< TNum, kdefs >::multiplyInPlaceRef(), fast_Ring< TNum, kdefs >::multiplyRef(), fast_Ring< TNum, kdefs >::scalarMultiply(), fast_Ring< TNum, kdefs >::scalarMultiplyInPlace(), fast_Ring< TNum, kdefs >::scalarMultiplyInPlaceRef(), fast_Ring< TNum, kdefs >::scalarMultiplyRef(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const TNum* fast_Ring< TNum, kdefs >::multiplicativeInverseTable [private]

Definition at line 133 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), fast_Ring< TNum, kdefs >::multInv(), fast_Ring< TNum, kdefs >::multInvInPlace(), fast_Ring< TNum, kdefs >::multInvRef(), and fast_Ring< TNum, kdefs >::~fast_Ring().

template<class TNum, class kdefs>
const sqrtInf_t* fast_Ring< TNum, kdefs >::sqrtTable [private]

Definition at line 137 of file fast_Ring.h.

Referenced by fast_Ring< TNum, kdefs >::init(), fast_Ring< TNum, kdefs >::sqrt(), fast_Ring< TNum, kdefs >::sqrtRef(), and fast_Ring< TNum, kdefs >::~fast_Ring().

The documentation for this class was generated from the following files:
Generated on Tue Nov 23 13:10:53 2010 for centerfocus by  doxygen 1.6.3