-- peval.adb Horners method for evaluating a polynomial
--           eval is the function that computes Horners method

with Ada.Text_IO; use Ada.Text_IO;

procedure peval is
  y : long_float;
  type vector is array(integer range <>) of long_float;
  c, r : vector(0..11);

  function eval(n : integer; x : long_float; c : vector) return long_float is
    -- Horners method for evaluating a polynomial
    -- an nth order polynomial has n+1 coefficients
    -- stored in c(0) through c(n)
    -- y := c(0) + c(1)*x + c(2)*x^2 +...+ c(n)*x^n
    y : long_float;
  begin
    if n<=0 then return c(0); end if;
    y := c(n)*x;
    for i in reverse 1..n-1 loop  -- do i:=n-1, 1, -1
      y := (c(i)+y)*x;
    end loop;
    y := y+c(0);
    return y;
  end eval;

begin
  put_line("peval.adb running");
  -- test peval by generation roots of a polynomial,
  -- then generating the polynomial, then evaluating
  for n in 3..10 loop  -- do n:=3,10  -- n is degree of polynomial
    new_line;
    put_line("y := c(0) + c(1)*x + c(2)*x^2 +...+ c(n)*x^n, for n=" &
               integer'image(n));
    put_line("roots are:");
    r(0) := 0.1;
    put_line("r(0)=" & long_float'image(r(0)));
    r(1) := 2.5;
    put_line("r(1)=" & long_float'image(r(1)));
    for i in 2..n-1 loop  -- do i:=2,n-1
      r(i) := r(i-1)+r(i-2);
      put_line("r("&integer'image(i)&")="&long_float'image(r(i)));
    end loop;
    -- generate polynomial coefficients
    c(0) := r(0)*r(1);
    c(1) := -(r(0)+r(1));
    c(2) := 1.0;
    for j in 2..n-1 loop  -- do j:=2,n-1
      for i in reverse 1..j+1 loop  -- do i:=j+1,1,-1
        c(i) := c(i-1);
      end loop;
      c(0) := 0.0;
      for i in 0..j loop  -- do i:=0,j
        c(i) := c(i) - r(j)*c(i+1);
      end loop;
    end loop;
    put_line("polynomial coefficients are:");
    for i in 0..n loop  -- do i:=0,n
      put_line("c("&integer'image(i)&")="&long_float'image(c(i)));
    end loop;
    put_line("polynomial evaluated at each root:");
    for i in 0..n-1 loop  -- do i:=0, n-1
      y := eval(n, r(i), c);
      put_line("r("&integer'image(i)&")="&long_float'image(r(i))&
               ", eval("&integer'image(n)&",r("&integer'image(i)&"),c)="&
               long_float'image(y));
    end loop;
  end loop;
end peval;