c++ floating point precision loss: 3015/0.00025298

问题:

The problem.

Microsoft Visual C++ 2005 compiler, 32bit windows xp sp3, amd 64 x2 cpu.

Code:

double a = 3015.0; 
double b = 0.00025298219406977296;
//*((unsigned __int64*)(&a)) == 0x40a78e0000000000  
//*((unsigned __int64*)(&b)) == 0x3f30945640000000  
double f = a/b;//3015/0.00025298219406977296;

the result of calculation (i.e. "f") is 11917835.000000000 (((unsigned __int64)(&f)) == 0x4166bb4160000000) although it should be 11917834.814763514 (i.e. ((unsigned __int64)(&f)) == 0x4166bb415a128aef).
I.e. fractional part is lost.
Unfortunately, I need fractional part to be correct.

Questions:
1) Why does this happen?
2) How can I fix the problem?

Additional info:
0) The result is taken directly from "watch" window (it wasn't printed, and I didn't forget to set printing precision). I also provided hex dump of floating point variable, so I'm absolutely sure about calculation result.
1) The disassembly of f = a/b is:

fld         qword ptr [a]  
fdiv        qword ptr [b]  
fstp        qword ptr [f]  

2) f = 3015/0.00025298219406977296; yields correct result (f == 11917834.814763514 , ((unsigned __int64)(&f)) == 0x4166bb415a128aef ), but it looks like in this case result is simply calculated during compile-time:

fld         qword ptr [__real@4166bb415a128aef (828EA0h)]  
fstp        qword ptr [f]  

So, how can I fix this problem?

P.S. I've found a temporary workaround (i need only fractional part of division, so I simply use f = fmod(a/b)/b at the moment), but I still would like to know how to fix this problem properly - double precision is supposed to be 16 decimal digits, so such calculation isn't supposed to cause problems.

回答1:

Are you using directx in your program anywhere as that causes the floating point unit to get switched to single precision mode unless you specifically tell it not to when you create the device and would cause exactly this

回答2:

Interestingly, if you declare both a and b as floats, you will get exactly 11917835.000000000. So my guess is that there is a conversion to single precision happening somewhere, either in how the constants are interpreted or later on in the calculations.

Either case is a bit surprising, though, considering how simple your code is. You are not using any exotic compiler directives, forcing single precision for all floating point numbers?

Edit: Have you actually confirmed that the compiled program generates an incorrect result? Otherwise, the most likely candidate for the (erroneous) single precision conversion would be the debugger.

回答3:

If you need precise math, don't use floating point.

Do yourself a favor and get a BigNum library with rational number support.

回答4:

I'd guess you're printing out the number without specifying a precision. Try this:

#include <iostream>
#include <iomanip>

int main() { 
    double a = 3015.0; 
    double b = 0.00025298219406977296;
    double f = a/b;

    std::cout << std::fixed << std::setprecision(15) << f << std::endl;
    return 0;
}

This produces:

11917834.814763514000000

Which looks correct to me. I'm using VC++ 2008 instead of 2005, but I'd guess the difference is in your code, not the compiler.

回答5:

Are you sure you're examining the value of f right after the fstp instruction? If you've got optimizations turned on perhaps the watch window could be showing a value taken at some later point (this seems a bit plausible as you say you're looking at the fractional part of f later - does some instruction wind up masking it out somehow?)