/* TO EXERCISE & DISPLAY THE SIGMOID FUNCTION TO BE USED IN NEURAL NETWORKS
   Author Robert John Morton YE572246C December 1997 tab = 3 spaces */


#include <sys\types.h>
#include <sys\timeb.h>
#include <stdio.h>
#include <graph.h>
#include <math.h>

long	PlotErr[9];

// THE FOLLOWING TWO FUNCTIONS ARE TO BE EXERCISED

short	SigTab[1025];

#define	R		32767
#define	RR		65556	// 65534 + 22

void SigGen(void) {
   int   i;
   for (i = 0; i < 1024; i++)
      SigTab[i] = (double)(RR / (1 + exp(-((double)(((long)(i)) << 8))/R)) - R);
   SigTab[1024] = R;
}

int Sigmoid(int x) {
   int s, y, j;
   if ((s = x) < 0) x = -x;
   y = *(SigTab + (j = x >> 5));
   y += ((*(SigTab + j + 1) - y) * (x & 0x1F)) >> 5;
   if (s < 0) y = -y;
   return( y );
}

int Gaussian(int x) {
   #define D 9000
   double yy, xx = x;
   xx /= D;
   yy = exp( -(xx * xx) );
   return(R * yy);
}

// BELOW IS THE EXERCISER FOR THE TWO FUNCTIONS ABOVE

#define	XYscale	8       //right shift scaling factor
#define	Yorg 174	//origin displacement from top left
#define	Xorg 171	//origin displacement from top left

void ShowScale( short x1, short y1, short x2, short y2 ) {
   _moveto((x1 >> XYscale) + Xorg, (y1 >> XYscale) + Yorg);
   _lineto((x2 >> XYscale) + Xorg, (y2 >> XYscale) + Yorg);
}

main() {
   #define k   8
   int x, y, X, Y, pe = 1000;
   long e, o;
   char far *s;
   float slope;
   _setvideomode(_VRES16COLOR);
   _settextposition( 3,19); printf("+32767");
   _settextposition(20,19); printf("-32767");
   _settextposition(11, 3); printf("-32767");
   _settextposition(12,35); printf("+32767");
   _settextposition(1, 1);
   _setcolor(7);
   ShowScale(0, -32767, 0, +32767);
   ShowScale(-32767, 0, +32767, 0);
   printf("THE SIGMOID FUNCTION'S FIRST DERIVATIVE FOR USE IN THE MLP LEARNING ALGORITHM\n");
   _settextposition( 4,46); printf("The SIGMOID formula is:");
   _settextposition( 6,46); printf("f(x) = (2R+d)/(1+exp(-kx)) - R");
   _settextposition( 8,46); printf("Where R = 32767 and");
   _settextposition( 9,46); printf("-32767 <= x <= +32767");
   _settextposition(11,46); printf("`k' determines how step-like the");
   _settextposition(12,46); printf("function becomes. In this test");
   _settextposition(13,46); printf("k = 8. `k' can conveniently be a");
   _settextposition(14,46); printf("multiple of 2: 2,4,8,16,32,64...");
   _settextposition(16,46); printf("`d' is a small adjusting factor");
   _settextposition(17,46); printf("to make f(x) hit 32767 at exactly");
   _settextposition(18,46); printf("the point at which x hits 32767.");
   _settextposition(20,46); printf("The blue shadow curve behind the");
   _settextposition(21,46); printf("green is the pure Gaussian curve");
   _settextposition(22,46); printf("y = exp(-(x*x)) commonly used in");
   _settextposition(23,46); printf("radial basis function networks. ");
   _settextposition(23,3); printf("   x  =");
   _settextposition(24,3); printf(" f(x) =        (blue)");
   _settextposition(25,3); 
   printf("f'(x) = +0.000 (green)  f'(x) = (k/2)*(R + f(x))*(R - f(x))/(R*R)");
   _settextposition(27,3); 
   printf("f'(x) is plotted above as 32767 * (2 / k) times its actual value.");
   SigGen();
   x = -32767;		     // Draw the sigmoid curve
A: y = Sigmoid(x);
   _settextposition(23,11);	printf("%+6d",x);
   _settextposition(24,11);	printf("%+6d",y);
   _setcolor(9);
   _setpixel(Xorg + (x >> XYscale), Yorg - (y >> XYscale));
   o = y;
   y = Gaussian(x);
   _setpixel(Xorg + (x >> XYscale), Yorg - (y >> XYscale));
   e = (((R + o) * (R - o)) >> 15);
   y = e;
   _setcolor(10);
   _setpixel(Xorg + (x >> XYscale), Yorg - (y >> XYscale));
   e = (e * pe) >> 13;
   slope = e;
   slope /= 1000;
   _settextposition(25,11);	printf("%+5.3f",slope);
   if (x < 32751 && !kbhit()) { x += 16; goto A; }
   _settextposition(29,3);
   printf("FINISHED. HIT `RETURN' TO EXIT.\07");
   _settextposition(29,1);
   getchar();
   _setvideomode(_DEFAULTMODE);
}