include/numerix/modular_int.hpp File Reference

#include <basix/operators.hpp>
#include <basix/int.hpp>
#include <numerix/rational.hpp>
#include <numerix/modular.hpp>

Go to the source code of this file.

Classes

struct modulus_maximum_size_int< size >
struct _helper< C, is_signed >
struct _helper< C, false >
struct maximum_size_helper< C >
struct maximum_value_helper< C >
struct modulus_normalization_int_naive< V >
struct modulus_reduction_int_naive< V >
struct modulus_add_int_naive< V >
struct add_mod_helper< C, b >
struct add_mod_helper< C, false >
struct modulus_mul_int_naive< V >
struct mul_mod_helper< C, D >
struct mul_mod_helper< C, void >
struct modulus_inv_int_naive< V >
struct modulus_div_int_naive< V >
struct modulus_encoding_int_naive< V >
struct modulus_int_naive< size >
struct modulus_mul_int_preinverse< V >
struct _dynamic_inverse_helper< C, D >
struct _dynamic_inverse_helper< C, void >
struct auxiliaries_helper< C, p >
Compute the auxiliary quantities attached to the modulus p. More...
struct _inverse_helper< D, Dummy >
struct _inverse_helper< void, Dummy >
struct mul_mod_helper< C, D, m >
struct mul_mod_helper< C, void, m >
struct modulus_int_preinverse< m >
class modulus< C, modulus_int_preinverse< m > >
struct modulus_variant_helper< unsigned char >
struct modulus_variant_helper< short unsigned int >
struct modulus_variant_helper< unsigned int >
struct modulus_variant_helper< long unsigned int >
struct modulus_variant_helper< long long unsigned int >
struct modulus_variant_helper< char >
struct modulus_variant_helper< signed char >
struct modulus_variant_helper< short int >
struct modulus_variant_helper< int >
struct modulus_variant_helper< long int >
struct modulus_variant_helper< long long int >
struct lift_helper< modular< modulus< unsigned char, V >, W > >
struct project_helper< unsigned char >
struct lift_helper< modular< modulus< signed char, V >, W > >
struct project_helper< signed char >
struct lift_helper< modular< modulus< unsigned short int, V >, W > >
struct project_helper< unsigned short int >
struct lift_helper< modular< modulus< signed short int, V >, W > >
struct project_helper< signed short int >
struct lift_helper< modular< modulus< unsigned int, V >, W > >
struct project_helper< unsigned int >
struct lift_helper< modular< modulus< int, V >, W > >
struct project_helper< int >
struct lift_helper< modular< modulus< unsigned long int, V >, W > >
struct project_helper< unsigned long int >
struct lift_helper< modular< modulus< long int, V >, W > >
struct project_helper< long int >
struct lift_helper< modular< modulus< unsigned long long int, V >, W > >
struct project_helper< unsigned long long int >
struct lift_helper< modular< modulus< long long int, V >, W > >
struct project_helper< long long int >
struct as_helper< modular< modulus< unsigned char, V >, W >, rational >
struct as_helper< modular< modulus< signed char, V >, W >, rational >
struct as_helper< modular< modulus< unsigned short int, V >, W >, rational >
struct as_helper< modular< modulus< signed short int, V >, W >, rational >
struct as_helper< modular< modulus< unsigned int, V >, W >, rational >
struct as_helper< modular< modulus< int, V >, W >, rational >
struct as_helper< modular< modulus< unsigned long int, V >, W >, rational >
struct as_helper< modular< modulus< long int, V >, W >, rational >
struct as_helper< modular< modulus< unsigned long long int, V >, W >, rational >
struct as_helper< modular< modulus< long long int, V >, W >, rational >

Namespaces

namespace mmx

Defines

#define TMPL template<typename C, typename M>
#define TMPL template<typename C>
#define Variant modulus_int_preinverse
#define TMPLVW template<typename V, typename W>
#define Modular(I) modular<modulus<I,V>,W>
#define DECLARE_HELPER(I)
#define DECLARE_HELPER(I)
#define DECLARE_HELPER(I)

Functions

UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< unsigned char, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, unsigned char, modular< modulus< unsigned char > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< signed char, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, signed char, modular< modulus< signed char > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< unsigned short int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, unsigned short int, modular< modulus< unsigned short int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< signed short int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, signed short int, modular< modulus< signed short int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< unsigned int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, unsigned int, modular< modulus< unsigned int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, int, modular< modulus< int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< unsigned long int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, unsigned long int, modular< modulus< unsigned long int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< long int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, long int, modular< modulus< long int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< unsigned long long int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, unsigned long long int, modular< modulus< unsigned long long int > >)
UNARY_RETURN_TYPE (template< typename V, typename W >, lift_op, modular< modulus< long long int, V >, W >, integer)
UNARY_RETURN_TYPE (STMPL, project_op, long long int, modular< modulus< long long int > >)
template<typename V , typename W > rational reconstruct (const modular< modulus< signed char, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< signed char, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< signed short int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< signed short int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< long int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< long int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< long long int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< long long int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< unsigned char, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< unsigned char, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< unsigned short int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< unsigned short int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< unsigned int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< unsigned int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< unsigned long int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< unsigned long int, V >, W > &x, rational &r)
template<typename V , typename W > rational reconstruct (const modular< modulus< unsigned long long int, V >, W > &x)
template<typename V , typename W > bool is_reconstructible (const modular< modulus< unsigned long long int, V >, W > &x, rational &r)

Define Documentation

#define DECLARE_HELPER ( I )

Value:

template<typename V, typename W>                                \
  rational reconstruct (const modular<modulus<I,V>,W>& x) {     \
    typedef signed_of_helper<I>::type J;                        \
    J n, d;                                                     \
    bool b= reconstruct (n, d, *x, *get_modulus (x));           \
    if (b) return rational (n) / rational (d);                  \
    ERROR ("rational reconstruction failed"); }                 \
  template<typename V, typename W>                              \
  bool is_reconstructible (const modular<modulus<I,V>,W>& x,    \
                           rational& r) {                       \
    typedef signed_of_helper<I>::type J;                        \
    J n, d;                                                     \
    bool b= reconstruct (n, d, *x, *get_modulus (x));           \
    if (!b) return false;                                       \
    r= rational (n) / rational (d);                             \
    return true; }

Definition at line 1135 of file modular_int.hpp.

#define DECLARE_HELPER ( I )

Value:

template<typename V, typename W>                        \
  struct as_helper<modular<modulus<I,V>,W>, rational> {         \
    static inline modular<modulus<I,V>,W>                       \
    cv (const rational& a) {                                    \
      return as<modular<modulus<I,V>,W> > (numerator (a))       \
           / as<modular<modulus<I,V>,W> > (denominator (a)); }  \
  };

Definition at line 1135 of file modular_int.hpp.

#define DECLARE_HELPER ( I )

Value:

UNARY_RETURN_TYPE(TMPLVW,lift_op,Modular(I),integer);                   \
  UNARY_RETURN_TYPE(STMPL,project_op,I,modular<modulus<I> >);           \
  TMPLVW                                                                \
  struct lift_helper<Modular(I)> {                                      \
    template<typename R> static inline void                             \
    set_op (R&y, const Modular(I)& x) {                                 \
      set_as (y, *x); }                                                 \
    static inline integer                                               \
    op (const Modular(I)& x) {                                          \
      return as<integer> (*x); }                                        \
  };                                                                    \
  STMPL                                                                 \
  struct project_helper<I> {                                            \
    TMPLVW static inline void                                           \
    set_op (Modular(I)& y, const I& x) {                                \
      y= Modular(I) (x); }                                              \
    static inline modular<modulus<I> >                                  \
    op (const I& x) {                                                   \
      return modular<modulus<I> > (x); }                                \
  };

Definition at line 1135 of file modular_int.hpp.

#define Modular ( I ) modular<modulus<I,V>,W>

Definition at line 1069 of file modular_int.hpp.

#define TMPL template<typename C>

Hereafter C must be a genuine C/C++ int type, signed or not. If C has bit-size k and if m <= k is the maximum number of bits allowed for the modulus then the modulus 0 actually stands for 2^m.

Definition at line 527 of file modular_int.hpp.

#define TMPL template<typename C, typename M>

Hereafter C must be a genuine C/C++ int type, signed or not. If C has bit-size k and if m <= k is the maximum number of bits allowed for the modulus then the modulus 0 actually stands for 2^m.

Definition at line 527 of file modular_int.hpp.

#define TMPLVW template<typename V, typename W>

Definition at line 1068 of file modular_int.hpp.

#define Variant modulus_int_preinverse

Definition at line 1016 of file modular_int.hpp.