#include "library.h"

const double pom[] = { 0.0, +1.0, 0.0, -1.0 };

/* This calculates the sine of x (radians) using the Taylor
   series only as far as the term in X to-the-power-of MaxN */

double sine(const double x,
            const    int N,
            const    int MaxN,
            const double xpn,
            const double fac)
{
  if (N > MaxN)
    return 0.0;

  const double thisterm   = pom[N%4] * xpn / fac;
  const double otherterms = sine(x, 
                                 N+1, 
                                 MaxN,
                                 xpn * x, 
                                 fac * (N+1));

  return thisterm + otherterms;
}

double sine(const double x, const int MaxN)
{ return sine(x, 1, MaxN, x, 1); }

const double pi = acos(-1.0);

/* This plots the Nth approximation to sine, for angles
   between 0 and just over 360 degrees */

void one_test_sine(const double x, const int N)
{ if (x > 8)
    return;
  if (x == 0.0)
    move_to(x*100, 400-sine(x, N)*200);
  else
    draw_to(x*100, 400-sine(x, N)*200);
  one_test_sine(x+0.005, N); }

/* This does the same, but for the real library sine function */

void real_sine(const double x)
{ if (x > 8)
    return;
  if (x == 0.0)
    move_to(x*100, 400-sin(x)*200);
  else
    draw_to(x*100, 400-sin(x)*200);
  real_sine(x+0.002); }

/* This plots all the sine approximations, one by one,
   in different colours ranging from red to blue via green */

void testsine(int N, int MaxN)
{ if (N <= MaxN)
  { set_pen_color_hls(N*0.7/MaxN, 0.5, 1);
    one_test_sine(0.0, N);
    testsine(N+2, MaxN); } }

/* This plots the real sine in black, then all the approximations
   in various colours */

void main()
{ make_window(800, 600);
  set_pen_width(2);
  set_pen_color(color::black);
  real_sine(0.0);
  testsine(1, 51); }