/usr/include/cln/numtheory.h is in libcln-dev 1.3.3-1ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | // Number theoretic operations.
#ifndef _CL_NUMTHEORY_H
#define _CL_NUMTHEORY_H
#include "cln/number.h"
#include "cln/integer.h"
#include "cln/modinteger.h"
#include "cln/condition.h"
namespace cln {
// jacobi(a,b) returns the Jacobi symbol
// ( a )
// ( --- )
// ( b )
// a, b must be integers, b > 0, b odd. The result is 0 iff gcd(a,b) > 1.
extern int jacobi (sintV a, sintV b);
extern int jacobi (const cl_I& a, const cl_I& b);
// isprobprime(n), n integer > 0,
// returns true when n is probably prime.
// This is pretty quick, but no caching is done.
extern bool isprobprime (const cl_I& n);
// nextprobprime(x) returns the smallest probable prime >= x.
extern const cl_I nextprobprime (const cl_R& x);
#if 0
// primitive_root(R) of R = Z/pZ, with p a probable prime,
// returns
// either a generator of (Z/pZ)^*, assuming p is prime, or
// a proof that p is not prime, maybe even a non-trivial factor of p.
struct primitive_root_t {
cl_composite_condition* condition;
cl_MI gen;
// Constructors.
primitive_root_t (cl_composite_condition* c) : condition (c) {}
primitive_root_t (const cl_MI& g) : condition (NULL), gen (g) {}
};
extern const primitive_root_t primitive_root (const cl_modint_ring& R);
#endif
// sqrt_mod_p(R,x) where x is an element of R = Z/pZ, with p a probable prime,
// returns
// either the square roots of x in R, assuming p is prime, or
// a proof that p is not prime, maybe even a non-trivial factor of p.
struct sqrt_mod_p_t {
cl_composite_condition* condition;
// If no condition:
int solutions; // 0,1,2
cl_I factor; // zero or non-trivial factor of p
cl_MI solution[2]; // max. 2 solutions
// Constructors.
sqrt_mod_p_t () {}
sqrt_mod_p_t (cl_composite_condition* c) : condition (c) {}
sqrt_mod_p_t (int s) : condition (NULL), solutions (s) {}
sqrt_mod_p_t (int s, const cl_MI& x0) : condition (NULL), solutions (s)
{ solution[0] = x0; }
sqrt_mod_p_t (int s, const cl_MI& x0, const cl_MI& x1) : condition (NULL), solutions (s)
{ solution[0] = x0; solution[1] = x1; }
};
extern const sqrt_mod_p_t sqrt_mod_p (const cl_modint_ring& R, const cl_MI& x);
// cornacchia1(d,p) solves x^2 + d*y^2 = p.
// cornacchia4(d,p) solves x^2 + d*y^2 = 4*p.
// d is an integer > 0, p is a probable prime.
// It returns
// either a nonnegative solution (x,y), if it exists, assuming p is prime, or
// a proof that p is not prime, maybe even a non-trivial factor of p.
struct cornacchia_t {
cl_composite_condition* condition;
// If no condition:
int solutions; // 0,1
// If solutions=1 and d > 4 (d > 64 for cornacchia4):
// All solutions are (x,y), (-x,y), (x,-y), (-x,-y).
cl_I solution_x; // x >= 0
cl_I solution_y; // y >= 0
// Constructors.
cornacchia_t () {}
cornacchia_t (cl_composite_condition* c) : condition (c) {}
cornacchia_t (int s) : condition (NULL), solutions (s) {}
cornacchia_t (int s, const cl_I& x, const cl_I& y) : condition (NULL), solutions (s), solution_x (x), solution_y (y) {}
};
extern const cornacchia_t cornacchia1 (const cl_I& d, const cl_I& p);
extern const cornacchia_t cornacchia4 (const cl_I& d, const cl_I& p);
} // namespace cln
#endif /* _CL_NUMTHEORY_H */
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