sol2.c File Reference

Problem 23 solution - optimization using look-up array More...

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

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Functions
char	get_perfect_number (unsigned long N)
char	is_abundant (unsigned long N)
unsigned long	get_next_abundant (unsigned long N)
char	is_sum_of_abundant (unsigned long N)
int	main (int argc, char **argv)

Variables
long	MAX_N = 28123
char *	abundant_flags = NULL

Detailed Description

Problem 23 solution - optimization using look-up array

Author

Krishna Vedala

Optimization applied - compute & store abundant numbers once into a look-up array.

Function Documentation

get_next_abundant()

unsigned long get_next_abundant

(

unsigned long

N

)

Find the next abundant number after N and not including N

{
    unsigned long i;
    /* keep checking successive numbers till an abundant number is found */
    for (i = N + 1; !is_abundant(i); ++i)
        ;
    return i;
}

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get_perfect_number()

char get_perfect_number

(

unsigned long

N

)

Returns

-1 if N is deficient

1 if N is abundant

0 if N is perfect

{
    unsigned long sum = 1;
    char ret = 0;
 
    for (unsigned long i = 2; i * i <= N; i++)
    {
        if (N % i == 0)
        {
            sum += i;
            unsigned long tmp = N / i;
            if (tmp != i)
                sum += tmp;
        }
    }
 
    ret = sum == N ? 0 : (sum > N ? 1 : -1);
#ifdef DEBUG
    printf("%5lu: %5lu : %d\n", N, sum, ret);
#endif
    return ret;
}

is_abundant()

char is_abundant

(

unsigned long

N

)

Is the given number an abundant number (1) or not (0)

{
    // return abundant_flags[N >> 3] & (1 << N % 8) ? 1 : 0;
    return abundant_flags[N >> 3] & (1 << (N & 7))
               ? 1
               : 0; /* optimized modulo operation */
}

is_sum_of_abundant()

char is_sum_of_abundant

(

unsigned long

N

)

check if a given number can be represented as a sum of two abundant numbers.

Returns

1 - if yes

0 - if not

optimized logic: i + j = N where both i and j should be abundant hence we can simply check for j = N - i as we loop through i

{
    /** optimized logic:
     * i + j = N   where both i and j should be abundant
     * hence we can simply check for j = N - i as we loop through i
     **/
    for (unsigned long i = get_next_abundant(1); i <= (N >> 1);
         i = get_next_abundant(i))
        if (is_abundant(N - i))
        {
#ifdef DEBUG
            printf("\t%4lu + %4lu = %4lu\n", i, N - i, N);
#endif
            return 1;
        }
    return 0;
}

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main()

int main	(	int	argc,
		char **	argv
	)

Main function

byte array to store flags to identify abundant numbers the flags are identified by bits

{
    unsigned long sum = 0;
    if (argc == 2)
        MAX_N = strtoul(argv[1], NULL, 10);
 
    /** byte array to store flags to identify abundant numbers
     * the flags are identified by bits
     **/
    abundant_flags = (char *)calloc(MAX_N >> 3, 1);
    if (!abundant_flags)
    {
        perror("Unable to allocate memoey!");
        return -1;
    }
 
#ifdef _OPENMP
    printf("Using OpenMP parallleization with %d threads\n",
           omp_get_max_threads());
#else
    printf("Not using parallleization!\n");
#endif
 
    clock_t start_time = clock();
 
    /* Loop to set abundant flags */
    long N;
#ifdef _OPENMP
#pragma omp for schedule(runtime)
#endif
    for (N = 1; N <= MAX_N; N++)
    {
        char ret = get_perfect_number(N);
        if (ret == 1)
        {
            // int byte_offset = N % 8, index = N >> 3;
            int byte_offset = N & 7, index = N >> 3;
#ifdef _OPENMP
#pragma omp critical
#endif
            abundant_flags[index] |= ret << byte_offset;
        }
        // if (i % 100 == 0)
        //     printf("... %5lu: %8lu\r", i, sum);
    }
 
    clock_t end_time = clock();
    double t1 = 1e3 * (end_time - start_time) / CLOCKS_PER_SEC;
    printf("Time taken to get abundant numbers: %.4g ms\n", t1);
 
    clock_t t2 = 0;
    long i;
#ifdef _OPENMP
#pragma omp parallel for schedule(runtime) reduction(+ : sum)
#endif
    for (i = 1; i < MAX_N; i++)
    {
        clock_t start_time1 = clock();
        if (!is_sum_of_abundant(i))
            // #ifdef _OPENMP
            // #pragma omp critical
            // #endif
            sum += i;
        clock_t end_time1 = clock();
#ifdef _OPENMP
#pragma omp critical
#endif
        t2 += end_time1 - start_time1;
 
        printf("... %5lu: %8lu\r", i, sum);
        if (i % 100 == 0)
            fflush(stdout);
    }
 
#ifdef DEBUG
    putchar('\n');
#endif
    double t22 = 1e3 * t2 / CLOCKS_PER_SEC;
    printf("Time taken for final sum: %.4g ms\nTotal Time taken: %.4g ms\n",
           t22, t1 + t22);
    printf("Memory used: %lu bytes\n", MAX_N >> 3);
    printf("Sum of numbers that cannot be represented as sum of two abundant "
           "numbers : %lu\n",
           sum);
 
    free(abundant_flags);
 
    return 0;
}

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Variable Documentation

abundant_flags

char* abundant_flags = NULL

This is the global array to be used to store a flag to identify if a particular number is abundant (1) or not (0). Using a whole byte to store a binary info would be redundant. We will use each byte to represent 8 numbers by relying on bits. This saves memory required by 1/8

MAX_N

long MAX_N = 28123

Limit of numbers to check