exploring_properties_of_floating_point_numbers.c

/*

    This program explores the properties of floating-point numbers

*/
#include<stdio.h>
#include<math.h>


//this function expects to accept the void pointer to float
//it prints the bits' values of the single-precision floating-point number
//the sign bit goes on the left, then goes the exponent, the mantissa (fraction) appears on the right
void showBitsInFloat (const void * pointer);

//this function expects to accept the void pointer to double
//it prints the bits' values of the double-precision floating-point number
//the sign bit goes on the left, then goes the exponent, the mantissa (fraction) appears on the right
void showBitsInDouble (const void * pointer);

int main()
{
    printf("\nadding a small value to a large value can be dangerous\n");
    
    float var1 = 1000000;
    float var2 = 1000000;
    printf("\nvar1 befor looping   %f\n", var1); 
    printf("var2 befor looping   %f\n\n", var2);        

    for (int i = 0; i < 1000000; i++)
    {
        var1 += 1;
        var2 += 0.01;
    }

    printf("var1 after looping 1000000 times and adding 1    =  %f\n", var1); 
    printf("var2 after looping 1000000 times and adding 0.01 =  %f\n\n", var2); 

    printf("--------------------------------------------------\n\n");
    printf("comparing floating-point numbers can be dangerous\n\n");

    //comparing floating-point numbers can be dangerous
    float var3 = 0.1;
    double var4 = 0.1;
    
    printf("double var4 = %f | float var3 = %f \n\n", var4, var3);

    if (var3 == var4)
    {
        printf("var3 and var4 are equal \n");
    }
    else if (var4 > var3)
    {
        printf("var4 is greater than var3 \n");
    }
    else if (var3 > var4)
    {
        printf("var3 is greater than var4 \n");
    }
    
    printf("\n");

    printf("var3 in binary: ");
    showBitsInFloat(&var3);
    printf("var4 in binary: ");
    showBitsInDouble(&var4);

    /////////////////////////////////////////////
    printf("---------\n\n");
    float var5 = 0.2;
    double var6 = 0.2;
    
    printf("double var6 = %f | float var5 = %f \n\n", var6, var5);

    if (var6 == var5)
    {
        printf("var6 and var5 are equal \n");
    }
    else if (var6 > var5)
    {
        printf("var6 is greater than var5 \n");
    }
    else if (var5 > var6)
    {
        printf("var5 is greater than var6 \n");
    }

    printf("\n");

    printf("va5 in binary: ");
    showBitsInFloat(&var5);
    printf("var6 in binary: ");
    showBitsInDouble(&var6);

    //////////////////////////////////////
    printf("---------\n\n");

    float var7  = 0.5;
    double var8 = 0.5;
    
    printf("double var8 = %f | float var7 = %f \n\n", var8, var7);

    if (var7 == var8)
    {
        printf("var7 and var8 are equal \n");
    }
    else if (var8 > var7)
    {
        printf("var8 is greater than var7 \n");
    }
    else if (var7 > var8)
    {
        printf("var7 is greater than var8 \n");
    }

    printf("\n");

    printf("var7 in binary: ");
    showBitsInFloat(&var7);
    printf("var8 in binary: ");
    showBitsInDouble(&var8);

    printf("--------------------------------------------------\n\n");

    printf("the distributive rule does not necessarily apply to floating-point numbers\n\n");

    double y = 0.11;
    double x = 0.22;
    double z = 0.33;
    double r1 = y * x + y * z;
    double r2 = y * (x + z);

     
    printf("r1 = y * x + y * z =  %f\n", r1);
    printf("r2 = y * (x + z)   =  %f\n\n", r2);

    if (r1 != r2)
        printf("r1 and r2 are NOT equal\n\n");
    
    printf("r1 in binary:  ");
    showBitsInDouble(&r1);
    printf("r2 in binary:  ");
    showBitsInDouble(&r2);

    printf("--------------------------------------------------\n\n");
    
    printf("the associative rule does not necessarily apply to floating-point numbers\n\n");
    
    double a = 0.1111;
    double b = 0.2222;
    double c = 0.3333;
    double res1 = (a + b) + c;
    double res2 = a + (b + c);

     
    printf("res1 = (a + b) + c  =  %f\n", res1);
    printf("res2 = a + (b + c)  =  %f\n\n", res2);

    if (res1 != res2)
        printf("res1 and res2 are NOT equal\n\n");
    
    printf("res1 in binary:  ");
    showBitsInDouble(&res1);
    printf("res2 in binary:  ");
    showBitsInDouble(&res2);

    printf("--------------------------------------------------\n\n");

    printf("*****infinity in calculations******\n");

    double infin = INFINITY;
    printf("Positive infinity:                      ");
    showBitsInDouble(&infin);

    double dv1 = pow (10, 308);
    double dv2 = dv1;
    printf ("dv1 = dv2 = 10^308 in binary(double):   ");
    showBitsInDouble(&dv1);

    double dv3 = dv1 * dv2;                   //infinity due to overflow
    printf("dv1 * dv2:                              ");
    showBitsInDouble(&dv3);

    double dv4 = 1.0 / 0.0;                   //infinity due to division by zero
    printf("division of a positive number by zero:  ");
    showBitsInDouble(&dv4);

    double dv55 = 1.0 / INFINITY;
    printf("division of 1.0 by infinity:            ");
    showBitsInDouble(&dv55);

    double dv66 = INFINITY / INFINITY;
    printf("Infinity over infinity:                 ");
    showBitsInDouble(&dv66);

    double dv77 = INFINITY / pow(10, 300);
    printf("Infinity divided by 10^300:             ");
    showBitsInDouble(&dv77);

    double dv88 = INFINITY - INFINITY;
    printf("Infinity - Infinity:                    ");
    showBitsInDouble(&dv88);

    double dv99 = INFINITY * INFINITY;
    printf("Infinity * Infinity:                    ");
    showBitsInDouble(&dv99);

    printf("--------------------------------------------------\n\n");

    printf("******* NaN in calculations *********\n");
   
    double nan = NAN;
    printf("NaN:                                   ");
    showBitsInDouble(&nan);
    
    
    double dv5 = 0.0 / 0.0;                    //nan due to zero over zero
    printf("zero over zero:                        "); 
    showBitsInDouble(&dv5);
    

    double dv6 = 1.0 / NAN;
    printf("1 divided by NaN:                      ");
    showBitsInDouble(&dv6);


    double dv7 = 0.0 / NAN;
    printf("0.0 divided by NaN:                    ");
    showBitsInDouble(&dv7);

    double dv8 = 1.0 + NAN;
    printf("1 + NaN:                               ");
    showBitsInDouble(&dv8); 

    double dv9 = NAN + INFINITY;
    printf("NaN + Infinity:                        ");   
    showBitsInDouble(&dv9);

    double dv10 = NAN * INFINITY;
    printf("NaN * Infinity:                        ");   
    showBitsInDouble(&dv10);    

    return 0;
}

void showBitsInFloat (const void * pointer)
{
    unsigned int * intPoint  = (unsigned int *) pointer;
    unsigned int bitPosition = 0x80000000;
    unsigned char iteration  = 0;
    

    while(iteration<32)
    {
        if(bitPosition & *intPoint)
            printf("1");
        else
            printf("0"); 
        
        if(iteration == 0 || iteration == 8)
            printf(" ");

        bitPosition >>= 1;
        iteration++;             
    }

    printf("\n\n");    
} 

void showBitsInDouble (const void * pointer)
{
    unsigned long int * longIntPoint = (unsigned long int *) pointer;
    unsigned long int bitPosition    = 0x8000000000000000;
    unsigned char iteration          = 0;

    while(iteration<64)
    {
        if(bitPosition & *longIntPoint)
            printf("1");
        else
            printf("0"); 
        
        if(iteration == 0 || iteration == 11)
            printf(" ");

        bitPosition >>= 1;
        iteration++;             
    }

    printf("\n\n"); 
}