(* File: count-zeros by Hongyou Wu on 2006/08/27 *)
(*                                               *)
(* Input: aaZZ, bbZZ, efZZ[t_]                   *)
(*                                               *)
(* Optional input: inpZZ                         *)
(*                                               *)
(* Output: npointsZZ, nzerosZZ                   *)


Clear[iZZ,jZZ,npointsZZ,stepZZ,valueZZ,oonZZ,onZZ,nzerosZZ,osZZ,signZZ,ovalueZZ];


(* inp: initial number of points  oon: old old number                     *)
(* on: old number                 nzeros: number of zeros inside interval *)
(* os: old sign                                                           *)

If[ValueQ[inpZZ]==False || inpZZ<8, inpZZ=8];

npointsZZ=inpZZ; stepZZ=(bbZZ-aaZZ)/npointsZZ;

Do[valueZZ[jZZ]=efZZ[aaZZ+(jZZ-1)*stepZZ]//N, {jZZ,1,npointsZZ}];

oonZZ=-2; onZZ=-1; nzerosZZ=0; osZZ=Sign[ valueZZ[1] ];

Do[{signZZ=Sign[ valueZZ[jZZ] ];

    If[(osZZ!=0 && signZZ==0) || osZZ*signZZ<0, nzerosZZ=nzerosZZ+1];

    osZZ=signZZ; },

   {jZZ,2,npointsZZ} ];


(* ov: old value *)

iZZ=2;

While[iZZ<100 && (oonZZ!=nzerosZZ || onZZ!=nzerosZZ),

Do[ovZZ[jZZ]=valueZZ[jZZ], {jZZ,1,npointsZZ}];

stepZZ=stepZZ/2;

Do[{valueZZ[2*jZZ-1]=ovZZ[jZZ]; valueZZ[2*jZZ]=efZZ[aaZZ+(2*jZZ-1)*stepZZ]//N;},

   {jZZ,1,npointsZZ} ];

npointsZZ=2*npointsZZ;

oonZZ=onZZ; onZZ=nzerosZZ; nzerosZZ=0; osZZ=Sign[ valueZZ[1] ];

Do[{signZZ=Sign[ valueZZ[jZZ] ];

    If[(osZZ!=0 && signZZ==0) || osZZ*signZZ<0, nzerosZZ=nzerosZZ+1];

    osZZ=signZZ; },

   {jZZ,2,npointsZZ} ];

iZZ=iZZ+1;

];


If[oonZZ!=nzerosZZ || onZZ!=nzerosZZ, Print["Failed to count zeros!"]];


Clear[aaZZ,bbZZ,efZZ,inpZZ,iZZ,jZZ,stepZZ,valueZZ,oonZZ,onZZ,osZZ,signZZ,ovZZ];