Why is scanf taking the wrong input for large floa

问题:

This question already has an answer here:

• Is floating point math broken? 30 answers

#include <stdio.h>

int main() { 
float k;
    scanf("%f", &k);
    printf("%f", k);
} 

In this simple program when I enter a number containing at most 8 digits then it is displayed correctly.

But if I exceed 8 digits i.e. for the input 123456789 the output is 123456792.

Why this is happening? Well the fun fact is that if I enter any number between 123456789 and 123456796 then it always shows 123456792.

Is it something related to the 8 decimal precision of floating numbers?

回答1:

Floating point types have a limited precision. For a float on your machine, which appears to be 32 bit, it has 24 bits of precision (23 explictly stored, 1 implied). That means integers greater than ~16000000, which require more than 24 bits to store, can't be represented exactly with this datatype.

For example, the value 123456789 you used has a binary representation of:

111 0101 1011 1100 1101 0001 0101

This value takes up 27 bits which is more than is available. So it is rounded to the closest value that can be stored with 23 bits, which is 123456792. In binary:

111 0101 1011 1100 1101 0001 1000

For this value, the lower 3 bits with value 0 are not explicitly stored.