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## -*- texinfo -*-
## @deftypefn {} {@var{y} =} cospi (@var{x})
## Compute cosine (@var{x} * pi) for each element of @var{x} accurately.
##
## The ordinary @code{cos} function uses IEEE floating point numbers and may
## produce results that are very close (within a few eps) of the correct
## value, but which are not exact.  The @code{cospi} function is more accurate
## and returns 0 exactly for half-integer values of @var{x} (e.g., @dots{},
## -3/2, -1/2, 1/2, 3/2, @dots{}), and +1/-1 for integer values.
##
## Example @*
## comparison of @code{cos} and @code{cospi} for half-integer values of @var{x}
##
## @example
## @group
## cos ([-3/2, -1/2, 1/2, 3/2] * pi)
## @result{}
##      -1.8370e-16   6.1232e-17   6.1232e-17  -1.8370e-16
##
## cospi ([-3/2, -1/2, 1/2, 3/2])
## @result{}
##        0   0   0   0
## @end group
## @end example
##
## @seealso{sinpi, cos}
## @end deftypefn

function y = cospi (x)

  if (nargin < 1)
    print_usage ();
  endif

  ## Advance phase by pi/2 so that algorithm from sinpi can be used.
  ## Unwrap integer multiples so that new domain is [0, 2).
  x = mod (x + 0.5, 2);

  ## Integer multiples of pi must be exactly zero.
  x(x == 1) = 0;

  y = sin (x * pi);

endfunction


%!assert (cospi ([-3/2, -1/2, 1/2, 3/2]) == 0)
%!assert (cospi ([-2, -1, 0, 1, 2]), [1, -1, 1, -1, 1])
%!assert (cospi (100 + [0.1:0.1:0.9]), cos ([0.1:0.1:0.9]*pi), 2*eps (100))

%!error <Invalid call> cospi ()