Normally I don't provide answers to homework problems, but since this is such a bad problem, I'm making an exception.
Before I proceed, let me say that the original problem is meaningless and impossible. Since it's impossible, there's no good way to solve it. So the program I'm going to present has a number of problems, some quite serious.
The core of the program does what the problem asks: As long as the fractional part of one of the numbers is not 0, it multiplies the number by 10. Computing "the fractional part of the number" is performed by an auxiliary function I've written, fractionalpart()
. First we'll look at the program, then I'll explain its remaining problems.
#include <stdio.h>
float in[] = {9.8, 5.0, 4.45};
int out[3];
float fractionalpart(float f)
{
return f - (int)f;
}
int main()
{
int i;
for(i = 0; i < 3; i++) {
float tmp = in[i];
while(fractionalpart(tmp) > 0.001) {
tmp = tmp * 10;
}
out[i] = tmp;
}
printf("out:\n");
for(i = 0; i < 3; i++) printf("%d\n", out[i]);
}
The problems this has relate to the fact that, on an ordinary computer using ordinary floating-point representations, there is no such number as 9.8. There's no such number as 4.45, either. What you thought was the float
number 4.45, for example, is represented internally as something like 4.44999980926513671875. So a "proper" version of this program would multiply it by 10 a total of twenty times, converting it to 444999980926513671875. But that number won't even fit in a 64-bit integer!
So this program cheats: it doesn't loop until the fractional part is exactly 0; it instead loops until the fractional part is less than 0.001. Where did that number come from? The answer is: nowhere, I pulled it out of the air, it seemed like a good guess. You can experiment with bigger or smaller fudge factors if you like.
The bigger problem -- and you've probably thought of this already -- is that the program assumes that the "fractional part" actually does go down to something like 0.001 or 0.0001. But that's not necessarily true! As we just saw, the number 4.45 is "really" 4.44999980926513671875 inside, so after multiplying by 10 twice, it looks like the program is going to have an integer value of 444 (not 445), and the fractional part is going to be 0.999980926513671875, which is not less than 0.001, so the program is going to keep going!
Actually, it doesn't keep going, it does get the "right answer", at least on my machine (and I think I know why), but there are probably plenty of numbers (roughly half of them, actually) where there will be an intermediate result more like 0.999 than 0.001, and this program will do the wrong thing.
I hate posting code with serious problems like this, it's very tempting to try to write an "improved" version, but it would be much messier, and really, the original question is such a horrible one that it just isn't worth it. (It would be instructive to figure out and explain why this program does seems to work, at least most of the time -- why it doesn't get confused by the occasional 0.999 value -- but I don't have time for that just now, either.)