/////////////////////////////////////
// DLLFormula01.cpp
// 
// stephen c. ferguson
// created 3/29/98
// http://www.HiWAAY.com/~stephenf/
//
/////////////////////////////////////

#define STRICT
#define WIN32_LEAN_AND_MEAN
#include <windows.h>

#include "fll01.h"

int Formula_Total();

#define FORMULA_TOTAL 20

typedef struct
{   // export pointer to address DLL
	int count;    // number of formulas in DLL
} TOTAL;

TOTAL Total;

int APIENTRY LibMain(HANDLE hInst, DWORD fdwReason, LPVOID lpReserved)
{	
	if (fdwReason == DLL_PROCESS_ATTACH)
	{
		wsprintf (cstr, "LibMain(): DLL loaded");

		Total.count = FORMULA_TOTAL;
	}
  else if (fdwReason == DLL_PROCESS_DETACH)
		wsprintf (cstr, "LibMain(): DLL unloaded");

	return TRUE;
}

////////////////////////////////////////////
void post00					(CDATA *v);

void formula41			(CDATA *v);
void formula42			(CDATA *v);
void formula43			(CDATA *v);
void formula44			(CDATA *v);
void formula45			(CDATA *v);
void formula46			(CDATA *v);
void formula47			(CDATA *v);
void formula48			(CDATA *v);
void formula49			(CDATA *v);
void formula50			(CDATA *v);
void formula51			(CDATA *v);
void formula52			(CDATA *v);
void formula53			(CDATA *v);
void formula54			(CDATA *v);
void formula55			(CDATA *v);
void formula56			(CDATA *v);
void formula57			(CDATA *v);
void formula58			(CDATA *v);
void formula59			(CDATA *v);
void formula60			(CDATA *v);

void initimage00		(CDATA *v);

void initpixel41		(CDATA *v);
void initpixel42		(CDATA *v);
void initpixel43		(CDATA *v);
void initpixel44		(CDATA *v);
void initpixel45		(CDATA *v);
void initpixel46		(CDATA *v);
void initpixel47		(CDATA *v);
void initpixel48		(CDATA *v);
void initpixel49		(CDATA *v);
void initpixel50		(CDATA *v);
void initpixel51		(CDATA *v);
void initpixel52		(CDATA *v);
void initpixel53		(CDATA *v);
void initpixel54		(CDATA *v);
void initpixel55		(CDATA *v);
void initpixel56		(CDATA *v);
void initpixel57		(CDATA *v);
void initpixel58		(CDATA *v);
void initpixel59		(CDATA *v);
void initpixel60		(CDATA *v);

////////////////////////////////////////////

typedef struct
{    // info structure
  void (*initimage)		(CDATA *v);   // image initialize
  void (*initpixel)		(CDATA *v);   // pixel initialize
  void (*action)			(CDATA *v);		// action iteration
  char *title;											// for selection purposes
  char *description;								// identification string(allocated by dll)
}INFO;

INFO Info[FORMULA_TOTAL] = 
{
	initimage00,initpixel41,formula41,"41 z=z-(z*z2*c-z-1)/(3*z2*c-z);"," ",
	initimage00,initpixel42,formula42,"42 z=z-(z*z2*c-z*c-1)/(3*z2*c-z);"," ",
	initimage00,initpixel43,formula43,"43 z=z-(z*z2*c-z2-1)/(3*z2*c-3*z2-3*z);"," ",
	initimage00,initpixel44,formula44,"44 z=z-(z*z2*c-z2*c-1)/(3*z2*c-z*c-z);"," ",
	initimage00,initpixel45,formula45,"45 z=(z-(z*z2-z)/(3*z2-1)); z=z*z*c;"," ",
	initimage00,initpixel46,formula46,"46 z=cos(z*c)*c;"," ",
	initimage00,initpixel47,formula47,"47 test"," ",
	initimage00,initpixel48,formula48,"48 z=log(sin(z*z))+c "," ",
	initimage00,initpixel49,formula49,"49 z=z*z*sin(__real__ z)+c*z*cos(__imag__ z)+c;  "," ",
	initimage00,initpixel50,formula50,"50 init c=cos_c(); iterate z=sin(z)*c; "," ",
	initimage00,initpixel51,formula51,"51 z=c*sin(z*z*z*z); "," ",
	initimage00,initpixel52,formula52,"52 6th order NMSet, init z=-(3*z)/4; iterate z=z-(z4*z4+z4*z2*z1*c-z)/(8*z4*z2*z1+7*z4*z2*c - 1); "," ",
	initimage00,initpixel53,formula53,"53 6th order NMSet, init z=-(2*z)/3, iterate z=z-(z4*z2+z4*z*c-1)/(6*z4*z+5*z2*z2*c); "," ",
	initimage00,initpixel54,formula54,"54 15th order NMSet, init z = -(13*z)/15; iterate z=z-(z12*z2*z+z12*z2*c-z)/(15*z12*z2+14*z12*z*c-1);"," ",
	initimage00,initpixel55,formula55,"55 Newtons apple, init z = 1/(4*z); iterate z=z-(4*z2*z*c-3*z2-2*z)/(12*z2*c-6*z-2);"," ",
	initimage00,initpixel56,formula56,"56 25th order NMSet, init z = -(23*z)/25; iterate z=z-(z24*z+z24*c-z)/(25*z24+24*z12*z8*z2*z*c-1);"," ",
	initimage00,initpixel57,formula57,"57 38th order NMSet, init z = -(18*z)/19; iterate z=z-(z36*z2+z36*z*c-z)/(38*z36*z+37*z36*c-1); "," ",
	initimage00,initpixel58,formula58,"58 50th order NMSet, init z = -(24*z)/25; iterate z=z-(z48*z2+z48*z*c-z)/(50*z48*z+49*z48*c-1);"," ",
	initimage00,initpixel59,formula59,"59 6th order NMSet, init z = -1/(2*z); iterate z=z-(6*z4*z*c+5*z4-1)/(30*z4*c+20*z2*z);"," ",
	initimage00,initpixel60,formula60,"60 19th order NMSet, init z = -4896/(5814*z); iterate z=z-(19*z16*z2*c+18*z16*z-z)/(342*z16*z*c + 306*z16-1);"," "
} ;

int Formula_Total() { return FORMULA_TOTAL; }

void post00 (CDATA *v) { } // does nothing in the formula DLL

void initimage00 (CDATA *v) 
{
}

void initpixel41 (CDATA *v) 
{ 
  //z = 1;
  c = v->c;
  c = csin_c();
  //v->z = z;
}

//MessageBox(NULL, "step 1", "bug", MB_OK);

////////////////////////////////////
void formula41(CDATA *v)  
{
  //MessageBox(NULL, "step 1", "bug", MB_OK);
  z = v->z;

  z2 = z*z;
  z = z - (z*z2 - 1 - csin_z())/(3*z2*c - ccos_z());

  v->z = z;
}

/////////////////////////////
void initpixel42 (CDATA *v) 
{ 
  c = v->c;
  //z = ctan_c() + 1;
}

void formula42(CDATA *v) 
{
  z = v->z;

  z2 = z*z;
  z=z-(z*z2*c-z*c-1+csin_z())/(3*z2*c-z-ccos_z());

  v->z = z;
}

////////////////////////////////////
void initpixel43 (CDATA *v) 
{ 
  c = v->c;
  c = csin_c();
}

void formula43(CDATA *v) 
{
  z = v->z;

  z2 = z*z;
  z=z-(z*z2*c-z2 + csin_z())/(3*z2*c-3*z2-3*z + ccos_z());

  v->z = z;
}

////////////////////////////////////
void initpixel44 (CDATA *v) 
{ 
  c = v->c;
  c = ccos_c();
}

void formula44(CDATA *v)  
{
  z = v->z;

  z2 = z*z;
  z = z-(z*z2*c-z2*c + csin_z())/(3*z2* c - z * c-z + ccos_z());

  v->z = z;
}

////////////////////////////////////
void initpixel45 (CDATA *v) 
{ 
  c = v->c;
}

void formula45(CDATA *v)  
{
  z = v->z;

  z2=z*z;
  z=(z-(z*z2-z-csin_z())/(3*z2-1-ccos_z()));
  z=z*z*c;

  v->z = z;
}

////////////////////////////////////
void initpixel46 (CDATA *v) 
{ 
  c = v->c;
}

void formula46(CDATA *v)  
{
  z = v->z;
  z2 = z*z;
  z3 = z2*z;
  z4 = z2*z2;
  z5 = z4*z;

  sine_cosine();

  z = z-(z5*zsin-z4*zsin-zsin*z*c-z)/(5*z4*zcos-z4*zcos-zcos*z*c-1);        
	
  v->z = z;
}

////////////////////////////////////
void initpixel47 (CDATA *v) 
{ 
  //c = v->c;
  c = v->c;
  //c = c*cexp_c();
  z = v->z;
  //v->z += 1;
  //c2 = csin_z();
}

void formula47(CDATA *v)  
{
  //				z2	= z;
  //				z1	= ((z*z).csin())*z/2;
  //				z		= z1*z1 + c;
	
  z = v->z;

  zexp = cexp_z();
  sine_cosine();

  z2 = z*z;
  //z3 = z2*z;
  //z4 = z2*z2;
  
  //v->z = z - (zsin - zsin*c)/(zcos - c);
  //v->z = z - (z*zsin-zsin)/(z*zcos-zcos-c);
  //v->z = z - (z*z - c - zsin)/(2*z*z*zcos);  
  //v->z = z - (zsin + c + clog_z())/(zcos + 1/z);
  //z = z - ((z3+z2+z*zsin)/(2*z2+2*z+zcos) + c);
  //v->z = z-(z4-zsin*cexp_z())/(4*z2-zcos)+c;    	
  //v->z = z-(z4-z3+zsin*cexp_z()+c)/(4*z-3*z2+zcos*cexp_z());    	  
  //v->z = z-((z4-z*zexp+z)/(4*z3-zexp*zcos)+c);
  //v->z = z - (zexp-zsin-c)/(zexp-zcos-1); // fltz4171-07-16-21.bmp	

  //zexp += (c*z); // fltz4171-07-18-04.bmp (1)
  //v->z = z - (zexp+zsin+c)/(zexp+zcos);  // fltz4171-07-18-04.bmp (2)

  //zexp += c;  // fltz4171-07-18-06.bmp (1)
  //zsin += c;
  //zcos += c;
  //v->z = z - (zsin-zexp-clog_z())/(zcos-zexp); // fltz4171-07-18-06.bmp (4)

  //zexp += c;  // fltz4171-07-18-06.bmp (1)
  //zsin += c;
  //zcos += c;
  //v->z = z - (zsin-zexp + z + c)/(zcos-zexp + z); // fltz4171-07-18-06.bmp (4)

  //zexp; 
  //zsin += z;
  //zcos += z;
  v->z = z - (zsin - zexp - c)/(zcos-zexp-1); 

  //zexp += zexp; 
  //zsin += zsin;
  //zcos += zcos;

  //v->z = z - (z-zexp-zsin)/(zexp-zcos-z); 
	
  //v->z = z;
	
}

////////////////////////////////////
void initpixel48 (CDATA *v) 
{ 
  c = v->c;
}

void formula48(CDATA *v)  
{
  z = v->z;

  z=z*z;
  z=csin_z();
  z=clog_z();
  z=z+c;

  v->z = z;
}

////////////////////////////////////
void initpixel49 (CDATA *v) 
{ 
  c = v->c;
}

void formula49(CDATA *v)  
{
  z = v->z;
	
  z = z*z*sin(__real__ z) + c*z*cos(__imag__ z) + c; 
	
  v->z = z;
}

////////////////////////////////////
void initpixel50 (CDATA *v) 
{ 
  c = v->c;
  c=ccos_c();
}

void formula50 (CDATA *v)  
{
  z = v->z;

  //  z=csin(z)*ccos(c);
  z=csin_z();
  z=z*c;

  v->z = z;
}

////////////////////////////////////
void initpixel51 (CDATA *v) 
{ 
  c = v->c;
}

void formula51 (CDATA *v)  
{
  z = v->z;

  //  z=c*csin(z*z*z*z);
  z=z*z;
  z=z*z;
  z=csin_z();
  z=z*c;

  v->z = z;
}

////////////////////////////////////
void initpixel52 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  z^8        + z^7*c - z;        // the function
  z'  =  8*z^7      + 7*(z^6)*c - 1;        // 1st derivative
  z'' =  7*8*(z^6)  + 7*6*(z^5)*c;       // 2nd derivative

  7*8*(z^6) = -7*6*(z^5)*c;
  z            = -(6*(z^5)*c)/(8*(z^5));
  z            = -(6*c)/8;
  z            = -(3*c)/4;

  */

  z = v->z;
  v->z = -(3*z)/4;
  c = z;
}

void formula52 (CDATA *v)  
{
  z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z  = z-(z4*z4 + z4*z2*z1 - 1 - csin_z())/(8*z4*z2*z1 + 7*z4*z2*c - ccos_z());

  v->z = z;
}

////////////////////////////////////
void initpixel53 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z			=  (z^6)       + (z^5)*c - 1;        // the function
  z'		=  6*(z^5)     + 5*(z^4)*c;    // 1st derivative
  z''		=  30*(z^4)    + 20*(z^3)*c;							// 2nd derivative

  30*(z^3)	  = -20*(z^3)*c;
	z						= -20*c/30;
	z						= -2*c/3;

  */

  c = v->c;

  z = v->z;
  z = -(2*z)/3;
  z = z;
}

void formula53 (CDATA *v)  
{
  z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z = z-(z4*z2 + z4*z*c + csin_z())/(6*z4*z + 5*z2*z2*c + ccos_z());

  v->z = z;
}

////////////////////////////////////
void initpixel54 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  z^15        + z^14*c - z;        // the function
  z'  =  15*z^14      + 14*(z^13)*c - 1;        // 1st derivative
  z'' =  15*14*(z^13)  + 14*13*(z^12)*c;       // 2nd derivative

  15*14*(z^13) = -14*13*(z^12)*c;
  z            = -(13*(z^12)*c)/(15*(z^12));
  z            = -(13*c)/15;
  z            = -(13*c)/15;

  */

  c = v->c;

  z = v->z;
  z = -(13*z)/15;
  v->z = z;

}

void formula54 (CDATA *v)  
{
	z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z8 = z4*z4;
  z12= z8*z4;
  z  = z-(z12*z2*z + z12*z2*c - z)/(15*z12*z2 + 14*z12*z*c - 1);

	v->z = z;
}

////////////////////////////////////
void initpixel55 (CDATA *v) 
{ 
  /*
	// A derivation of Newtons apple
  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  (z^4)*c        - z^3 - z^2;        // the function
  z'  =  4*(z^3)*c      - 3*(z^2) - 2*z;		// 1st derivative
  z'' =  12*(z^2)*c     - 6*z - 2;					// 2nd derivative
	z'' =  24*z*c - 6;												// 3rd derivative

  24*z*c = 6;
  z      = 6/24*c   
  z      = 1/(4*c)

  */
		
	z = v->z;
  z = 1/(4*z);
	v->z = z;
	
	c = v->c;
}

void formula55 (CDATA *v)  
{
	// A derivation of Newtons apple
	z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z  = z-(4*z2*z*c - 3*z2 - 2*z)/(12*z2*c - 6*z - 2);

	v->z = z;
}

////////////////////////////////////
void initpixel56 (CDATA *v) 
{ 
  /*
  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  z^25        + z^24*c - z;        // the function
  z'  =  25*z^24      + 24*(z^23)*c - 1;        // 1st derivative
  z'' =  25*24*(z^23)  + 24*23*(z^22)*c;       // 2nd derivative

  25*24*(z^23) = -24*23*(z^22)*c;
  z            = -(23*(z^22)*c)/(25*(z^22));
  z            = -(23*c)/25;
  z            = -(23*c)/25;

  */
	
	z = v->z;
  z = -(23*z)/25;
	v->z = z;

	c = v->c;
}

void formula56 (CDATA *v)  
{
	z = v->z;

	z2 = z*z;
  z4 = z2*z2;
  z8 = z4*z4;
  z12 = z8*z4;
	z24 = z12*z12;
  z  = z-(z24*z + z24*c - z)/(25*z24 + 24*z12*z8*z2*z*c - 1);

	v->z = z;
}

////////////////////////////////////
void initpixel57 (CDATA *v) 
{ 
  /*
  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  z^38        + z^37*c - z;        // the function
  z'  =  38*z^37      + 37*(z^36)*c - 1;        // 1st derivative
  z'' =  38*37*(z^36)  + 37*36*(z^35)*c;       // 2nd derivative

  38*37*(z^36) = -37*36*(z^35)*c;
  z            = -(36*(z^35)*c)/(38*(z^35));
  z            = -(36*c)/38;
  z            = -(18*c)/19;

  */
	
	z = v->z;
  z = -(18*z)/19;
	v->z = z;

	c = v->c;
}

void formula57 (CDATA *v)  
{
	z = v->z;
  
	z2 = z*z;
  z4 = z2*z2;
  z8 = z4*z4;
  z12 = z8*z4;
	z24 = z12*z12;
	z36 = z24*z12;
  z  = z-(z36*z2 + z36*z*c - z)/(38*z36*z + 37*z36*c - 1);

	v->z = z;
}

////////////////////////////////////
void initpixel58 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z   =  z^50        + z^49*c - z;        // the function
  z'  =  50*z^49      + 49*(z^48)*c - 1;        // 1st derivative
  z'' =  50*49*(z^48)  + 49*48*(z^47)*c;       // 2nd derivative

  50*49*(z^48) = -49*48*(z^47)*c;
  z            = -(48*(z^47)*c)/(50*(z^47));
  z            = -(48*c)/50;
  z            = -(24*c)/25;

  */

	z = v->z;
  z = -(24*z)/25;
	v->z = z;
	c = v->c;
}

void formula58 (CDATA *v)  
{
	z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z8 = z4*z4;
  z12 = z8*z4;
	z24 = z12*z12;
	//z36 = z24*z12;
	z48 = z24*z24;
  z  = z-(z48*z2 + z48*z*c - z)/(50*z48*z + 49*z48*c - 1);

	v->z = z;
}

////////////////////////////////////
void initpixel59 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z'    =  6*(z^5)*c      + 5*(z^4) - 1;
  z''   =  30*(z^4)*c     + 20*(z^3);
	z''   =  120*(z^3)*c    + 60*(z^2);

  120*(z^3)*c = -60*(z^2);
  z       = -60/120*c   
  z       = -1/(2*c)

  */
	
	z = v->z;
  z = -1/(2*z);
	v->z = z;

	c = v->c;
}

void formula59 (CDATA *v)  
{
	z = v->z;

  z2 = z*z;
  z4 = z2*z2;
  z  = z-(6*z4*z*c + 5*z4 - 1)/(30*z4*c + 20*z2*z);

	v->z = z;
}

////////////////////////////////////
void initpixel60 (CDATA *v) 
{ 
  /*

  Solve the roots of the function.
  Initialize z to one of the roots.
  Apply Newton's method for solving roots.
  z = z - f(z)/f(z')

  z'    =  19*(z^18)*c      + 18*(z^17);
  z''   =  342*(z^17)*c     + 306*(z^16);
	z''   =  5814*(z^16)*c    + 4896*(z^15);

  5814*(z^16)*c = -4896*(z^15);
  z             = -4896/(5814*c);   

  */

	z = v->z;
  z = -4896/(5814*z);
	v->z = z;

	c = v->c;
}

void formula60 (CDATA *v)  
{
	z = v->z;

  z2  = z*z;
  z4  = z2*z2;
  z8  = z4*z4;
	z16 = z8*z8; 
  z  = z-(19*z16*z2*c + 18*z16*z - z)/(342*z16*z*c + 306*z16 - 1);

	v->z = z;
}