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B.9 Number-Theoretic Member Functions

const unsigned int
ld (void) const;

return ⌊log2(a)⌋ 

const int
iseven (void) const;

test a for divisibility by 2: true if a even

 

const int
isodd (void) const;

test a for divisibility by 2: true if a odd

 

const LINT
issqr (void) const;

test a for being square

 

const int
isprime (void) const;

test a for primality

 

const LINT
gcd (const LINT& b);

return gcd of a and b 

const LINT
xgcd (const LINT& b,
    LINT& u, int& sign_u,
    LINT& v, int& sign_v)
const;

extended Euclidean algorithm with return of gcd of a and b, u and v contain the absolute values of the factors of the linear combination g = sign_u*u*a + sign_v*v*b 

const LINT
inv (const LINT& b) const;

return the multiplicative inverse of a mod b 

const LINT
lcm (const LINT& b) const;

return the least common multiple of a and b 

const int
jacobi (const LINT& b) const;

return the Jacobi symbol ()

 

const LINT
root (void) const;

return the integer part of the square root of a 

const LINT
root (const LINT& p) const;

return the square root of a modulo an odd prime p 

const LINT
root (const LINT& p,
    const LINT& q) const;

return the square root of a modulo p*q, where p and q are odd primes

 

const int
twofact (LINT& odd) const;

return the even part of a, odd contains the odd part of a 

const LINT
chinrem (const LINT& m,
     const LINT& b,
     const LINT& n) const;

return a solution x of the system of simultaneous congruences x ≡ a mod m and x ≡ b mod n, if a solution exists
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