Difference between float and double in C/C++

Last Updated : 23 Jun, 2023

To represent floating point numbers, we use float, double, and long double. What's the difference? double has 2x more precision than float. float is a 32-bit IEEE 754 single precision Floating Point Number - 1 bit for the sign, 8 bits for the exponent, and 23* for the value. float has 7 decimal digits of precision. double is a 64-bit IEEE 754 double precision Floating Point Number - 1 bit for the sign, 11 bits for the exponent, and 52* bits for the value. double has 15 decimal digits of precision.

Let's take an example: For a quadratic equation x^2 - 4.0000000 x + 3.9999999 = 0, the exact roots to 10 significant digits are, r1 = 2.000316228 and r2 = 1.999683772. Notice the difference in using float and double.

C++

// C program to demonstrate
// double and float precision values

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

// utility function which calculate roots of
// quadratic equation using double values
void double_solve(double a, double b, double c)
{
    double d = b * b - 4.0 * a * c;
    double sd = sqrt(d);
    double r1 = (-b + sd) / (2.0 * a);
    double r2 = (-b - sd) / (2.0 * a);
    printf(" % .5f\t % .5f\n ", r1, r2);
}

// utility function which calculate roots of
// quadratic equation using float values
void float_solve(float a, float b, float c)
{
    float d = b * b - 4.0f * a * c;
    float sd = sqrtf(d);
    float r1 = (-b + sd) / (2.0f * a);
    float r2 = (-b - sd) / (2.0f * a);
    printf(" % .5f\t % .5f\n ", r1, r2);
}

// driver program
int main()
{
    float fa = 1.0f;
    float fb = -4.0000000f;
    float fc = 3.9999999f;
    double da = 1.0;
    double db = -4.0000000;
    double dc = 3.9999999;

    printf("roots of equation x^2- 4.0000000 x + 3.9999999= "
           "0 are: \n ");
    printf("for float values: \n");
    float_solve(fa, fb, fc);

    printf("for double values: \n");
    double_solve(da, db, dc);
    return 0;
}

Output

roots of equation x2- 4.0000000 x + 3.9999999= 0 are: 
 for float values: 
  2.00000      2.00000
 for double values: 
  2.00032      1.99968

Complexity Analysis

The time complexity of the given code is O(1)
The auxiliary space complexity of the code is also O(1)