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Finding roots of polynomials as well as finding polynomials given roots. A polynomial of order 5131 is exemplified


This example works on FinSim 10_07_15 and subsequent versions.

This example shows how to find the roots of a polynomial and how to find the polynomial given the roots. Note that the polynomial is not sparse, as all its coefficients are non-zero, which make the problem more difficult. Also note that the coefficients are in a close range: -6 to 15, which makes the problem easier.

This example run on a laptop with core i7 at 2.4GHz in 13.89 seconds.

module top;
parameter size = 5131;
   real d, p[0:size-1], p1[0:size-1];
   VpFCartesian r[0:size-2];

   initial begin
      /* set the values of the coefficients of the polynomial p */
      $InitM(p, 1.5);
      p[0] = 15;
      p[1000] = 2;
      p [size-2] = 3;
      p [size-1] = -6;
      /* compute the roots r of polynomial p */
      r = $Roots(p);
      $PrintM(r, "%e");
      /* compute the polynomial p1 corresponding to the roots r */
      p1 = $Poly(r);
      /* denormalize the polynomial so that the coefficient of the highest order is not one but the same as in polynomial p */
      p1 = p1*p[0];
      $PrintM(p1, "%e");
      /* compare p and p1 */
      d = $VpDistAbsMax(p, p1);
      $display("distance = %e\n", d);
   end
endmodule // top


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