Ulam's spiral generator for number enthusiasts

// ----------------------------------------------------------------------------
// "THE BEER-WARE LICENSE" (Revision 43):
// <[email protected]> wrote this file. As long as you retain this notice you
// can do whatever you want with this stuff. If we meet some day, and you think
// this stuff is worth it, you can buy me a beer in return Aaron R. Yool
// ----------------------------------------------------------------------------


#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

typedef enum{false, true = !false} bool;

usage(const char *name)
{
    printf("Usage: %s <grid size> <origin > 0>\n", name);
    exit(-1);
}

cursor(unsigned int x, unsigned int y)
{
    printf("\033[%i;%iH", y, x);
}

color(unsigned int quality, unsigned int color)
{
    printf("\033[%i;%im", quality, color);
}

clear_screen()
{
    printf("\033[1;1H\033[2J");
}

int digits_needed(long double n)
{
    int i=0, c;
    for(c=n;c>0;c=c/10)i++;
    return i;
}

// corners work like this where o = 1 and n = 10:
//
// f(n) = n^2-n+o
// 1, 3, 7, 13, 21, 31, 43, 57, 73, 91
// R  L  R   L   R   L   R   L   R   L
//
// f(n) = n^2+o
// 2, 5, 10, 17, 26, 37, 50, 65, 82, 101
// U  D   U   D   U   D   U   D   U    D

#define RIGHT 0x1
#define LEFT 0x2

#define UP 0x3
#define DOWN 0x4

bool crf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)-3*n+o;
        if(x == f) return true;
        n++;
    }
    return false;
}

bool clf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)+n+o;
        if(x == f) return true;
        n++;
    }
    return false;
}

bool cuf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)-n+o;
        if(x == f) return true;
        n++;
    }
    return false;
}

bool cdf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)+3*n+o;
        if(x == f) return true;
        n++;
    }
    return false;
}


char crdf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = powl(n,2)-n+o;
        if(x == f) return fmod(n, 2) ? RIGHT : LEFT;
        n++;
    }
    return 0;
}


char cldf(long double n, long double o, long double x)
{
    long double f, i = n; n = 1;
    for(i;i > 0;--i)
    {
        f = powl(n,2)+o;
        if(x == f) return fmod(n, 2) ? UP : DOWN;
        n++;
    }
    return 0;
}

bool prime(long double x)
{
    long double i;
    if(x == 2) return true;
    else if(x < 2 || fmod(x, 2) == 0) return false;
    for(i=3;i<=sqrtl(x);i++)
    {
        if(fmod(x, i) == 0) return false;
    }
    return true;
}

generate_grid(long double n, long double o)
{
    long double direction, i, c, cld, crd, x = fmod(n, 2) ? n/2 : n/2-1, y=n/2, digits = digits_needed(n*n+o);
    clear_screen();

    for(c=0;c<n;c++)
    for(i=0;i<=n;i++)
    {
        cursor((i*(digits+1))+1,c+3);
        putchar('|');
    }

    for(i=o;i<=n*n+o-1;i++)
    {
        crd = crdf(n, o, i);
        cld = cldf(n, o, i);
        if(prime(i)) color(4,31);
        if(crd){direction = crd;color(1,102);}
        else if(cld){direction = cld;color(1,43);}
        else if(crf(n, o, i))color(1,44);
        else if(clf(n, o, i))color(1,45);
        else if(cuf(n, o, i))color(1,46);
        else if(cdf(n, o, i))color(1,42);

        cursor((x*(digits+1))+2,3+y);

        for(c=digits-digits_needed(i);c>0;c--)
            putchar('0');
        printf("%i",i);
        color(0,0);

        switch((int)direction)
        {
            case RIGHT: x++;break;
            case LEFT: x--;break;
            case UP: y--;break;
            case DOWN: y++;break;
            default: break;
        }
    }

    cursor(0,n+3);
}

main(unsigned int count, const char **args)
{
    long double i = 0, f, n = 0, o = 0;

    if(count == 3 ? (args[1][0] >= '0' && args[1][0] <= '9') : false)
        n = atoll(args[1]);
    else
        usage(args[0]);

    if(args[2][0] >= '0' && args[2][0] <= '9')
        o = atoll(args[2]);
    else
        usage(args[0]);

    if(o<1) usage(args[0]);

    generate_grid(n,o);
    printf("\n\no = %.0LF\n", o);

    // right diagonal from origin
    color(1,32);
    printf("f1(n) = n^2-n+o\n");
    i = n+100;n = 1;
    for(i;i > 0;--i)
    {
        f = powl(n,2)-n+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
        color(0,0);
    }
    color(0,0);

    // left diagonal from origin
    color(1,33);
    printf("f2(n) = n^2+o\n");
    i = n-2;n = 1;
    for(i;i > 0;--i)
    {
        f = powl(n,2)+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
    }
    color(0,0);

    // right of origin
    color(1,34);
    printf("f3(n) = 4n^2-3n+o\n");
    i = n/2;n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)-3*n+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
    }
    color(0,0);

    // down from origin
    color(0,32);
    printf("f4(n) = 4n^2+3n+o\n");
    i = n-2;n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)+3*n+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
    }
    color(0,0);

    // up from origin
    color(1,36);
    printf("f5(n) = 4n^2-n+o\n");
    i = n;n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)-n+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
    }
    color(0,0);

    // to the left of origin
    color(1,35);
    printf("f6(n) = 4n^2+n+o\n");
    i = n-2;n = 1;
    for(i;i > 0;--i)
    {
        f = 4*powl(n,2)+n+o;
        color(0,0);
        if(prime(f)) color(1,31);
        i > 1 ? printf("%.0LF, ", f) : printf("%.0LF\n\n", f);
        n++;
    }
    color(0,0);

    return;
}