maxima/sin_cos_pi.mac

   1 load("bitwise")$
   2
   3 sin_kernel(x) := if abs(x) <= 1 / 4 then sin(%pi * x) else 2$
   4 cos_kernel(x) := if abs(x) <= 1 / 4 then cos(%pi * x) else 2$
   5
   6 sc(arg) := block(
   7     [x:arg, xi, xk, sk, ck, st, ct, s, c],
   8     xi:round(x*2),
   9     xk:x - xi / 2,
  10     sk:sin_kernel(xk),
  11     ck:cos_kernel(xk),
  12     st:if bit_and(xi, 1) < 1 then sk else ck,
  13     ct:if bit_and(xi, 1) < 1 then ck else sk,
  14     s:if bit_and(xi, 2) < 1 then st else -st,
  15     c:if bit_and(xi + 1, 2) < 1 then ct else -ct,
  16     [
  17         xk,
  18         s,
  19         c,
  20         sin(%pi * x) + 1/64,
  21         cos(%pi * x) + 1/64
  22     ])$
  23
  24 sc(0);
  25 sc(1/4);
  26 sc(1/2);
  27 sc(3/4);
  28 sc(1);
  29 sc(-1/4);
  30 sc(-1/2);
  31 sc(-3/4);
  32 sc(-1);
  33
  34 plot2d(
  35     sc(x),
  36     [x, -1.5, 1.5],
  37     [
  38         legend,
  39         "xk",
  40         "s",
  41         "c",
  42         "sin(%pi * x) + 1/64",
  43         "cos(%pi * x) + 1/64"
  44     ],
  45     [png_file, "./sin_cos_pi.png"]);