sine

// apple xcode
// paulogp

/* sine */
/* computes sine using very simple floating arithmetic. */

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

static char *float_2_ascii (float the_num);
float fix_float (float the_num);
float factorial (float the_num);

static char *float_2_ascii (float the_num)
{
    static char the_result[15]; // place to put the number

    sprintf(the_result, "%8.3E", the_num);

    return (the_result);
}

float fix_float (float the_num)
{
    float the_result; // result of the conversion
    char the_ascii[15]; // ascii version of number

    sprintf(the_ascii, "%8.4e", the_num);
    sscanf(the_ascii, "%e", &the_result);

    return (the_result);
}

float factorial (float the_num)
{
    if (the_num <= 1.0)
    {
        return (the_num);
    }
    else
    {
        return (the_num *factorial(the_num - 1.0));
    }
}

int main (int argc, const char * argv[])
{
    float the_test_value = 1.4;

    float the_total; // total of series so far
    float new_total; // newer version of total
    float term_top; // top part of term
    float term_bottom; // bottom of current term
    float the_term; // current term
    float the_exp; // exponent of current term
    float the_sign; // +1 or -1 (changes on each term)
    float the_value; // value of the argument to sin
    int the_index; // index for countin terms

    printf("calculating...\n\n");

    the_value = fix_float(the_test_value);

    the_total = 0.0;
    the_exp = 1.0;
    the_sign = 1.0;

    for (the_index = 0;; ++the_index)
    {
        term_top = fix_float(pow(the_value, the_exp));
        term_bottom = fix_float(factorial(the_exp));
        the_term = fix_float(term_top / term_bottom);

        printf("x++%d   %s\n", (int)exp, float_2_ascii(term_top));
        printf("%d!     %s\n", (int)exp, float_2_ascii(term_bottom));
        printf("x**%d/%d! %s\n", (int)exp, (int)exp, float_2_ascii(the_term));
        printf("\n");

        new_total = fix_float(the_total + the_sign * the_term);

        if (new_total == the_total)
        {
            break;
        }

        the_total = new_total;
        the_sign = -the_sign;
        the_exp = the_exp + 2.0;

        printf(" total = %s\n", float_2_ascii(the_total));
        printf("\n");
    }

    printf("%d term computed\n", the_index + 1);
    printf("rad sin(%s) = %s\n", float_2_ascii(the_value), float_2_ascii(the_total));
    printf("Actual sin(%G) = %G\n", the_test_value, sin(the_test_value));

    return 0;
}