```/* nag_numdiff_fwd (d04aac) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

#ifdef __cplusplus
extern "C"
{
#endif
static double NAG_CALL f(double x, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void)
{
/* Scalars */
Integer   exit_status = 0;
Integer   i, k, l, step, nder;
double    hbase, h_init, h_reduce, xval;
/* Arrays */
double    der[14], erest[14], ruser[1];
/* Nag Types */
Nag_Comm  comm;
NagError  fail;

INIT_FAIL(fail);

printf("nag_numdiff_fwd (d04aac) Example Program Results\n");

/* For communication with user-supplied functions: */
ruser[0] = -1.0;
comm.user = ruser;

/* abs(nder) is largest order derivative required. */
nder = -7;
l = abs(nder);
/* nder < 0 and nder is even means only even derivatives,
* and nder < 0 and nder is odd, only odd derivatives.
*/
if (nder < 0) {
step = 2;
} else {
step = 1;
}
/* Initial step size. */
h_init = 0.5;
hbase = h_init;
/* Reduction factor applied to successive step sizes. */
h_reduce = 0.1;
/* Derivatives will be evaluated at x = xval. */
xval = 0.5;

printf("\nFour separate runs to calculate the first four odd order "
"derivatives of\n"
"   f(x) = 0.5*exp(2.0*x-1.0) at x = 0.5.\n"
"The exact results are 1, 4, 16 and 64\n\n"
"Input parameters common to all four runs\n"
"  xval = %f     nder = %" NAG_IFMT "\n", xval, nder);

for (k = 0; k < 4; k++) {
/* nag_numdiff_fwd (d04aac).
* Numerical differentiation, derivatives up to order 14,
* function of one real variable.
*/
nag_numdiff_fwd(xval, nder, hbase, der, erest, f, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_numdiff_fwd (d04aac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("\n"
"with step length %8.4f  the results are\n"
"Order        Derivative       Questionable?\n", hbase);

for (i = 0; i < l; i += step)
if (erest[i]<0.0) {
printf("%2" NAG_IFMT " %21s %13s\n", i + 1, "---------", "Yes");
} else {
printf("%2" NAG_IFMT " %21.3e %13s\n", i + 1, der[i], "No");
}

hbase = hbase * h_reduce;
}

END:
return exit_status;
}

static double NAG_CALL f(double x, Nag_Comm *comm)
{
if (comm->user[0] == -1.0) {
printf("(User-supplied callback f, first invocation.)\n");
comm->user[0] = 0.0;
}
return 0.5 * exp(2.0 * x - 1.0);
}
```