// 1-15-C.c

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

/* Function declarations */
int main();
double my_sin( double x );

/* Function definitions */

/* int main()
 *
 * Compare our implementation of sin(x) using its
 * Taylor series with the implementation provided
 * by the C standard library.
 */
int main() {
    double x = 3.2;

    /* Print floating-point numbers with 16 digits
     * after the decimal point.
     */
    printf( "my_sin(x): %.16f\n", my_sin( x ) );
    printf( "sin(x):    %.16f\n",    sin( x ) );
    printf( "reference: %.16f\n", -0.058374143427579909137 );

    return 0;
}

/* double my_sin( double x )
 *
 * Approximate sin(x) using the Taylor series
 *
 *                 x^3   x^5   x^7
 *     sin(x) = x - --- + --- - --- + ...
 *                  3!    5!    7!
 *
 * Rather than calculating each power and factorial
 * separately, calculate each term from the previous
 * term:
 *
 *                    x^2
 *     next = -term -----------,
 *                  n(n + 1)
 *
 * where n takes the values 2, 4, 6, ...
 */
double my_sin( double x ) {
    if ( !isfinite( x ) ) {
        return NAN;
    }

    double result = x;
    double term   = x;
    double n;

    /* Since C99, variables may be declared in the
     * initialization expression of a for loop:
     *
     *     for ( double n = 2.0; ... )
     *
     * Declaring 'n' separately also allows this
     * code to compile using older versions of C.
     */
    for ( n = 2.0; ; n += 2.0 ) {
        term *= -(x/n)*(x/(n + 1.0));

        if ( fabs( term ) < 1e-16 ) {
            break;
        }

        result += term;
    }

    return result;
}
```
```c
#include <stdio.h>
#include <math.h>

/* Function declarations */
int main();
double my_sin( double x );

/* Function definitions */

/* int main()
 *
 * Compare our implementation of sin(x) using its
 * Taylor series with the implementation provided
 * by the C standard library.
 */
int main() {
    double x = 3.2;

    /* Print floating-point numbers with 16 digits
     * after the decimal point.
     */
    printf( "my_sin(x): %.16f\n", my_sin( x ) );
    printf( "sin(x):    %.16f\n",    sin( x ) );
    printf( "reference: %.16f\n", -0.058374143427579909137 );

    return 0;
}

/* double my_sin( double x )
 *
 * Approximate sin(x) using the Taylor series
 *
 *                 x^3   x^5   x^7
 *     sin(x) = x - --- + --- - --- + ...
 *                  3!    5!    7!
 *
 * Rather than calculating each power and factorial
 * separately, calculate each term from the previous
 * term:
 *
 *                    x^2
 *     next = -term -----------,
 *                  n(n + 1)
 *
 * where n takes the values 2, 4, 6, ...
 */
double my_sin( double x ) {
    if ( !isfinite( x ) ) {
        return NAN;
    }

    double result = x;
    double term   = x;
    double n;

    /* Since C99, variables may be declared in the
     * initialization expression of a for loop:
     *
     *     for ( double n = 2.0; ... )
     *
     * Declaring 'n' separately also allows this
     * code to compile using older versions of C.
     */
    for ( n = 2.0; ; n += 2.0 ) {
        term *= -(x/n)*(x/(n + 1.0));

        if ( fabs( term ) < 1e-16 ) {
            break;
        }

        result += term;
    }

    return result;
}
```
```c
#include <stdio.h>
#include <math.h>

/* Function declarations */
int main();
double my_sin( double x );

/* Function definitions */

/* int main()
 *
 * Compare our implementation of sin(x) using its
 * Taylor series with the implementation provided
 * by the C standard library.
 */
int main() {
    double x = 3.2;

    /* Print floating-point numbers with 16 digits
     * after the decimal point.
     */
    printf( "my_sin(x): %.16f\n", my_sin( x ) );
    printf( "sin(x):    %.16f\n",    sin( x ) );
    printf( "reference: %.16f\n", -0.058374143427579909137 );

    return 0;
}

/* double my_sin( double x )
 *
 * Approximate sin(x) using the Taylor series
 *
 *                 x^3   x^5   x^7
 *     sin(x) = x - --- + --- - --- + ...
 *                  3!    5!    7!
 *
 * Rather than calculating each power and factorial
 * separately, calculate each term from the previous
 * term:
 *
 *                    x^2
 *     next = -term -----------,
 *                  n(n + 1)
 *
 * where n takes the values 2, 4, 6, ...
 */
double my_sin( double x ) {
    if ( !isfinite( x ) ) {
        return NAN;
    }

    double result = x;
    double term   = x;
    double n;

    /* Since C99, variables may be declared in the
     * initialization expression of a for loop:
     *
     *     for ( double n = 2.0; ... )
     *
     * Declaring 'n' separately also allows this
     * code to compile using older versions of C.
     */
    for ( n = 2.0; ; n += 2.0 ) {
        term *= -(x/n)*(x/(n + 1.0));

        if ( fabs( term ) < 1e-16 ) {
            break;
        }

        result += term;
    }

    return result;
}