_UNRAVELING OPTIMIZATION IN MICROSOFT C 6.0_
by Bruce D. Schatzman

[LISTING ONE]

#include <stdio.h>
long area[3];
void compute_areas(void);

main()
{
	int i;
	extern long area[3];
	compute_areas();
	for(i = 0; i <= 2; i++) printf("The approximate area of function %d is %ld\n", i, area[i]);
}

void compute_areas(void)
{	long temp, y0[100], y1[100], y2[100];
	extern long area[3];
	int i, k, a, b, c, d, n, m, j;

	a = 2; b = 5; c = 1; d = 3;
	area[0] = area[1] = area[2] = temp = 0;

       /*  compute 100 initial y values for all functions and approximate area under curves. Do this 100 times. */
	for (i = 0; i <= 99; i++) {
		for (j = 0; j <= 99; j++) {
			n = j-1;
			m = j+1;
			y0[j] = a*j*n + 48*j - (c+d);
			y1[j] = d*(j+10) + a*b;
			y2[j] = c*j*m + 73*j*j + n;
		}
	}
/* add a*b+c+d to all y values. Do this 100 times. */
	for (i = 0; i <= 99; i++) {
		for (j = 0; j <= 99; j++) {
			y0[j] += a*b+c+d;
			y1[j] += a*b+c+d;
			y2[j] += a*b+c+d;
		}
	}

/* bubblesort each array */
	for (i = 0; i <= 99; i++) {
		for (k = 99; k >= 1; k--) {
			if (y0[k-1] > y0[k]) {
				temp = y0[k];
				y0[k] = y0[k-1];
				y0[k-1] = temp;
			}
			if (y1[k-1] > y1[k]) {
				temp = y1[k];
				y1[k] = y1[k-1];
Š				y1[k-1] = temp;
			}
			if (y2[k-1] > y2[k]) {
				temp = y2[k];
				y2[k] = y2[k-1];
				y2[k-1] = temp;
			}
		}
	}

	/*  now compute areas */
	for (j = 0; j <= 99; j++) {
		area[0] += y0[j];
		area[1] += y1[j];
		area[2] += y2[j];
	}

	return;
   }


[LISTING TWO]

#include <stdio.h>
long area[3];
void compute_areas(void);

main()
{
	int i;
	extern long area[3];
	compute_areas();
	for(i = 0; i <= 2; i++) printf("The approximate area of function %d is %ld\n", i, area[i]);

}
void compute_areas(void)
{	long temp, y0[100], y1[100], y2[100];
	extern long area[3];
	int i, k, a, b, c, d, n, m, j;

	a = 2; b = 5; c = 1; d = 3;
	area[0] = area[1] = area[2] = temp = 0;

 /*  compute 100 initial y values for all functions and approximate area under curves. Do this 100 times. */
	for (i = 0; i <= 99; i++) {
		for (j = 0; j <= 99; j++) {
			n = j-1;
			m = j+1;
			y0[j] = a*j*n + 48*j - 4;
			y1[j] = d*j +40;
			y2[j] = c*j*j*m - 73*j*j;
		}
	}

/* add 14 to all y values. Do this 100 times. */
Š	for (i = 0; i <= 99; i++) {
		for (j = 0; j <= 99; j++) {
			y0[j] += 14;
			y1[j] += 14;
			y2[j] += 14;
		}
	}

/* bubblesort each array */
	for (i = 0; i <= 99; i++) {
		for (k = 99; k >= 1; k--) {
			if (y0[k-1] > y0[k]) {
				temp = y0[k];
				y0[k] = y0[k-1];
				y0[k-1] = temp;
			}
			if (y1[k-1] > y1[k]) {
				temp = y1[k];
				y1[k] = y1[k-1];
				y1[k-1] = temp;
			}
			if (y2[k-1] > y2[k]) {
				temp = y2[k];
				y2[k] = y2[k-1];
				y2[k-1] = temp;
			}
		}
	}

	/*  now compute areas */
	for (j = 0; j <= 99; j++) {
		area[0] += y0[j];
		area[1] += y1[j];
		area[2] += y2[j];
	}

	return;
}               


[LISTING THREE]

#include <stdio.h>
long area[3];
void compute_areas(void);

main()
{
	int i;
	extern long area[3];
	compute_areas();
	for(i = 0; i <= 2; i++) printf("The approximate area of function %d is %ld\n", i, area[i]);
}

void compute_areas(void)
Š{	long temp, y0[100], y1[100], y2[100];
	extern long area[3];
	int i, k, j;

	area[0] = area[1] = area[2] = temp = 0;

 /*  compute 100 initial y values for all functions and approximate area under curves. Do this 100 times. */
	for (i = 0; i <= 99; i++) {
		for (j = 0; j <= 99; j++) {
			y0[j] = 2*j*j - 50*j +10;
			y1[j] = 3*j + 54;
			y2[j] = j*j*j - 72*j + 14;
		}
	}

/* bubblesort each array */
	for (i = 0; i <= 99; i++) {
		for (k = 99; k >= 1; k--) {
			if (y0[k-1] > y0[k]) {
				temp = y0[k];
				y0[k] = y0[k-1];
				y0[k-1] = temp;
			}
			if (y1[k-1] > y1[k]) {
				temp = y1[k];
				y1[k] = y1[k-1];
				y1[k-1] = temp;
			}
			if (y2[k-1] > y2[k]) {
				temp = y2[k];
				y2[k] = y2[k-1];
				y2[k-1] = temp;
			}
		}
	}

	/*  now compute areas */
	for (j = 0; j <= 99; j++) {
		area[0] += y0[j];
		area[1] += y1[j];
		area[2] += y2[j];
	}

	return;
}


[Example 1.  ]

void main(void)
{
	int  x, y, *p;
	p = &x;
	x = 1; y = 2; z = 6
	for(k = 1; k <= 100; k++) {
Š			k += x + y + z;
			*p = k;
	}
)