/*
    multiprecision.h by Noam HACHE

    This file contains the type definition of lentier, representing an integer of over 64bits,
    and functions related to the addition, substraction, multiplication, division and comparaison of this lentier type.
*/


// Type definition of a "long int"
typedef struct {
    unsigned int *p;
    unsigned int size;
} lentier;

/*
    Add 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the addition of the 2 operands
*/
struct lentier Add_lentier(struct lentier a, struct lentier b);

/*
    Substract 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the substraction of the 2 operands
*/
struct lentier Sub_lentier(struct lentier a, struct lentier b);

/*
    Compare 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        a char, 0 if the operands are identical
                1 if a is greater than b
                -1 if a is lower than b
*/
char Cmp_lentier(struct lentier a, struct lentier b);

/*
    Multiply 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the multiplication of the 2 operands
*/
struct lentier Mult_classique(struct lentier a, struct lentier b);

/*
    Euclidean division of 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the rest of the euclidean division of the 2 operands
*/
struct lentier Div_eucl(struct lentier a, struct lentier b);

/*
    Modular multiplication of 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the modular multiplication of the 2 operands
*/
struct lentier Mul_mod(struct lentier a, struct lentier b);

/*
    Modular exponentiation of 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the modular exponentiation of the 2 operands
*/
struct lentier Exp_mod(struct lentier a, struct lentier x, struct lentier N);

/*
    Modular exponentiation of 2 lentier

    Args: 
        a (lentier): the first operand
        b (lentier): the second operand
    
    Returns:
        an lentier, the modular exponentiation of the 2 operands
*/