2

```
// Continued Fraction Expansion yields seven transcendental
// values from one function.
// Original Turbo C, modified and tested with Pelles C vegaseat 8oct2004
#include <stdio.h> // in/out functions
#include <math.h> // math functions
#define SIN 1
#define COS 2
#define TAN 3
#define EXP 4
#define SINH 5
#define COSH 6
#define TANH 7
#define PI 3.1415926536 // or use atan(1)*4.0
double trigfunc(int p, int n, double x);
//
// test trigfunc() against compiler functions
//
int main()
{
double x;
x = 30 * PI/180; // convert 30 degrees to radians
puts("Continued Fraction Expansion can yield seven transcendental values ... \n");
printf("x = 30 degrees = %11.10f radians \n\n",x);
printf("compiler sin(x) = %11.10f \n",sin(x));
printf("trigfunc(SIN,2,x) = %11.10f \n",trigfunc(SIN,2,x));
printf("trigfunc(SIN,3,x) = %11.10f \n\n",trigfunc(SIN,3,x));
printf("compiler cos(x) = %11.10f \n",cos(x));
printf("trigfunc(COS,3,x) = %11.10f \n\n",trigfunc(COS,3,x));
printf("compiler tan(x) = %11.10f \n",tan(x));
printf("trigfunc(TAN,3,x) = %11.10f \n\n",trigfunc(TAN,3,x));
printf("compiler exp(x) = %11.10f \n",exp(x));
printf("trigfunc(EXP,3,x) = %11.10f \n\n",trigfunc(EXP,3,x));
printf("compiler sinh(x) = %11.10f \n",sinh(x));
printf("trigfunc(SINH,3,x) = %11.10f \n\n",trigfunc(SINH,3,x));
printf("compiler cosh(x) = %11.10f \n",cosh(x));
printf("trigfunc(COSH,3,x) = %11.10f \n\n",trigfunc(COSH,3,x));
printf("compiler tanh(x) = %11.10f \n",tanh(x));
printf("trigfunc(TANH,3,x) = %11.10f \n\n",trigfunc(TANH,3,x));
getchar();
return 0;
}
//
// generate 7 transcendental values with one function
// p = function selector, #define the following:
// SIN 1 COS 2 TAN 3 EXP 4 SINH 5 COSH 6 TANH 7
// n = convergence cutoff, n = 3 is typical,
// higher n gives higher precision, but slower execution
//
double trigfunc(int p, int n, double x)
{
int k;
double r, s, t;
if (p <= 3)
{
r = - x * x; // trig
}
else
{
r = x * x; // hyperbolic
}
s = 4 * n + 2;
for (k = n; k > 0; k--)
{
s = 4 * k - 2 + r/s;
}
switch (p % 4)
{
case 0 : t = (s + x)/(s - x); // exp
break;
case 1 : t = 2 * x * s/(s * s - r); // sin, sinh
break;
case 2 : t = (s * s + r)/(s * s - r); // cos, cosh
break;
case 3 : t = 2 * x * s/(s * s + r); // tan, tanh
break;
}
return (t);
}
```

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