euclidean_algorithm_extended.c File Reference

Program to perform the extended Euclidean algorithm More...

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>

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Data Structures
struct	euclidean_result
	for tests More...

Functions
static void	single_test (int a, int b, int gcd, int x, int y)
	perform one single check on the result of the algorithm with provided parameters and expected output
static void	test ()
	Perform tests on known results.
int	main ()
	Main Function.
typedef struct euclidean_result	euclidean_result_t
	for tests
static void	xy_push (int arr[2], int newval)
	gives queue-like behavior to an array of two ints, pushing an element onto the end and pushing one off the front
static void	calculate_next_xy (int quotient, int prev[2])
	calculates the value of x or y and push those into the small 'queues'
euclidean_result_t	extended_euclidean_algorithm (int a, int b)
	performs the extended Euclidean algorithm on integer inputs a and b

Detailed Description

Program to perform the extended Euclidean algorithm

The extended Euclidean algorithm, on top of finding the GCD (greatest common divisor) of two integers a and b, also finds the values x and y such that ax+by = gcd(a, b)

Typedef Documentation

euclidean_result_t

typedef struct euclidean_result euclidean_result_t

for tests

for IO for div function and corresponding div_t struct

a structure holding the values resulting from the extended Euclidean algorithm

Function Documentation

calculate_next_xy()

static void calculate_next_xy ( int  quotient, int  prev[2]  )

inlinestatic

calculates the value of x or y and push those into the small 'queues'

Both x and y are found by taking their value from 2 iterations ago minus the product of their value from 1 iteration ago and the most recent quotient.

Parameters

quotient	the quotient from the latest iteration of the Euclidean algorithm
prev	the 'queue' holding the values of the two previous iterations

Returns

void

{
    int next = prev[1] - (prev[0] * quotient);
    xy_push(prev, next);
}

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extended_euclidean_algorithm()

euclidean_result_t extended_euclidean_algorithm	(	int	a,
		int	b
	)

performs the extended Euclidean algorithm on integer inputs a and b

Parameters

a	first integer input
b	second integer input

Returns

euclidean_result_t containing the gcd, and values x and y such that ax + by = gcd

{
    int previous_remainder = 1;
    int previous_x_values[2] = {0, 1};
    int previous_y_values[2] = {1, 0};
    div_t div_result;
    euclidean_result_t result;
 
    /* swap values of a and b */
    if (abs(a) < abs(b))
    {
        a ^= b;
        b ^= a;
        a ^= b;
    }
 
    div_result.rem = b;
 
    while (div_result.rem > 0)
    {
        div_result = div(a, b);
 
        previous_remainder = b;
 
        a = b;
        b = div_result.rem;
 
        calculate_next_xy(div_result.quot, previous_x_values);
        calculate_next_xy(div_result.quot, previous_y_values);
    }
 
    result.gcd = previous_remainder;
    result.x = previous_x_values[1];
    result.y = previous_y_values[1];
 
    return result;
}

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main()

int main

(

void

)

Main Function.

Returns

0 upon successful program exit

{
    test();  // run self-test implementations
    return 0;
}

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single_test()

static void single_test ( int  a, int  b, int  gcd, int  x, int  y  )

inlinestatic

perform one single check on the result of the algorithm with provided parameters and expected output

Parameters

a	first paramater for Euclidean algorithm
b	second parameter for Euclidean algorithm
gcd	expected value of result.gcd
x	expected value of result.x
y	expected value of result.y

Returns

void

{
    euclidean_result_t result;
 
    result = extended_euclidean_algorithm(a, b);
    assert(result.gcd == gcd);
    assert(result.x == x);
    assert(result.y == y);
}

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test()

static void test ( void  )

static

Perform tests on known results.

Returns

void

{
    single_test(40, 27, 1, -2, 3);
    single_test(71, 41, 1, -15, 26);
    single_test(48, 18, 6, -1, 3);
    single_test(99, 303, 3, -16, 49);
    single_test(14005, 3507, 1, -305, 1218);
 
    printf("All tests have successfully passed!\n");
}

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xy_push()

static void xy_push ( int  arr[2], int  newval  )

inlinestatic

gives queue-like behavior to an array of two ints, pushing an element onto the end and pushing one off the front

Parameters

arr	an array of ints acting as a queue
newval	the value being pushed into arr

Returns

void

{
    arr[1] = arr[0];
    arr[0] = newval;
}