/* float.c
*
*   Examine floating point numbers
*
*/
#include <stdio.h>
#include <math.h>

typedef	union {
		float v;
		long iv;
} NUMBER;

void from_number(NUMBER f, int *sign, int *exponent, long *matissa);
float to_number(int sign, int exponent, long mantissa);
void print_number(NUMBER f);

int main()
{
	int i;
	int sign, exponent;
	long mantissa;
	double error;
	NUMBER f, g;
	for (i=0; i<=32; i++) {
		printf("number %2d:   ",i);
		f.v = i;
		print_number(f);
		from_number(f,&sign,&exponent,&mantissa);
		g.v = to_number(sign,exponent,mantissa);
		if (f.v!=g.v) printf("*** conversion failed ***\n");
	}
	printf("\n\n");
	printf("number 1/2: "); f.v = 0.5; print_number(f);
	printf("number 1/4: "); f.v = 0.25; print_number(f);
	printf("number 1/10:  "); f.v = 0.10; print_number(f);
	printf("FLT_EPSILON  ");
	f.v = to_number(0,127,1L)-to_number(0,127,0L);
	print_number(f);

	printf("\n\n");
	f.v = 0.0;
	g.v = 0.1;
	for (i=0; i<10; i++) f.v += g.v;
	error = fabs(f.v-1.0);
	printf("0.1 added 10 times:        error (%8.2e) ",error);
	print_number(f);
	f.v = 0.0;
	g.v = 0.01;
	for (i=0; i<100; i++) f.v += g.v;
	error = fabs(f.v-1.0);
	printf("0.01 added 100 times:      error (%8.2e) ",error);
	print_number(f);
	f.v = 0.0;
	g.v = 0.001;
	for (i=0; i<1000; i++) f.v += g.v;
	error = fabs(f.v-1.0);
	printf("0.001 added 1,000 times:   error (%8.2e) ",error);
	print_number(f);
	f.v = 0.0;
	g.v = 0.0001;
	for (i=0; i<10000; i++) f.v += g.v;
	error = fabs(f.v-1.0);
	printf("0.0001 added 10,000 times: error (%8.2e) ",error);
	print_number(f);
	
	printf("\n\n");
	for (i=0; i<4; i++) {
		f.v = to_number(0,i,0L);
		print_number(f);
	}

	printf("\n\n");
	f.v = to_number(0,0xff,0L); print_number(f);

	for (i=0; i<4; i++) {
		f.v = to_number(0,0xff-i,0x7fffff);
		print_number(f);
	}
	return 0;
}

void print_number(NUMBER f)
{
	int sign, exponent;
	long mantissa;
	sign = (f.iv>>31);
	exponent = (f.iv>>23)&0xff;
	mantissa = (f.iv)&0x7fffff;
	printf("%d %2x %6lx  %20.14g\n",sign,exponent,mantissa,f.v);
}

void from_number(NUMBER f, int *sign, int *exponent, long *mantissa)
{
	*sign = (f.iv>>31);
	*exponent = (f.iv>>23)&0xff;
	*mantissa = (f.iv)&0x7fffff;
}

float to_number(int sign, int exponent, long mantissa)
{
	NUMBER f;
	f.iv = ((sign&1)<<8) | (exponent&0xff);
	f.iv = (f.iv<<23) | (mantissa&0x7fffff);
	return f.v;
}