C: convert double to float, preserving decimal point precision

Question

i wanted to convert double to float in C, but wanted to preserve the decimal point exactly as possible without any changes...

for example, let's say i have

   double d = 0.1108;
   double dd = 639728.170000;
   double ddd = 345.2345678

now correct me if i am wrong, i know that floating point precision is about 5 numbers after the dot. can i get those five numbers after the dot exactly as the double had it? so that above results as follows:

   float f = x(d);
   float ff = x(dd);
   float fff = x(ddd);

   printf("%f\n%f\n%f\n", f, ff, fff);

it should print

   0.1108
   639728.17000
   345.23456

all digits after the precision limit (which i assume as 5) would be truncated.

Solution 1

float and double don't store decimal places. They store binary places: float is (assuming IEEE 754) 24 significant bits (7.22 decimal digits) and double is 53 significant bits (15.95 significant digits).

Converting from double to float will give you the closest possible float, so rounding won't help you. Goining the other way may give you "noise" digits in the decimal representation.

#include <stdio.h>

int main(void) {
    double orig = 12345.67;
    float f = (float) orig;
    printf("%.17g\n", f); // prints 12345.669921875
    return 0;
}

To get a double approximation to the nice decimal value you intended, you can write something like:

double round_to_decimal(float f) {
    char buf[42];
    sprintf(buf, "%.7g", f); // round to 7 decimal digits
    return atof(buf);
}

Solution 2

A float generally has about 7 digits of precision, regardless of the position of the decimal point. So if you want 5 digits of precision after the decimal, you'll need to limit the range of the numbers to less than somewhere around +/-100.

Comments

[dan04]

@davidvandebunte: That's only in C++. The question is tagged as C.

[csl]

Going through a string in round_to_decimal seems like a horrible idea. Surely there must be a much better way to do it with some math.