Currency handling is almost never done with rationals (numerator and denominator) and is frequently (and correctly so!) done with fixed or floating point decimal types.
Currency, taxes, rebates, etc. handling is NEVER done with floating point.
Whatever you do with money you need predictable, reproducible results. It is norm that calculations are checked by software at two companies on both sides of transaction. Any discrepancies are alarms, bug reports, unhappy customers.
Every significant operation is exactly specified with rounding rules, etc.
For card payments and especially on terminals usually BCD is used.
For everything else usually some kind of arbitrary length decimal library (BigInteger, BigDecimal).
Nonsense. I’ve seen real banking code at reputable banks that uses floats.
> Whatever you do with money you need predictable, reproducible results.
Floats aren’t random. They’re perfectly deterministic, predictable and reproducible. If you do the same operation in two places you get the same result.
When people talk about non-determinism of floating point, what they usually mean is non-associativity, that is (x+y)+z may not be exactly equal to x+(y+z).
Good example of this, in Python 3:
>>> (0.1 + 0.2) + 0.3
0.6000000000000001
>>> 0.1 + (0.2 + 0.3)
0.6It's not an optimisation if it changes the result! And if you use non-standard flags that's your problem.
MP3 is an optimization of WAV, yet it changes the result.
Some applications are ok with reducing precision of calculations because they are not sensitive enough to small inaccuracies or they take effort to control inaccuarcies.
For example, graphics applications are typically heavy in FP calculations and yet they tend to not care much about precision and much more about performance. For those applications reducing accuracy for slight performance increase is likely win.
That's not exactly true in real hardware, or at least it wasn't until ~10 years ago. With the x87 FPU, internal precision was 80 bits, while the x86 registers were at most 64 bits. So, depending on the way the program would transfer data between the CPU and FPU your could get different results. It is very likely that different compilers and different optimization decisions could change the way these operations were implemented, so you would get slight differences between different versions of the software.
There are/were also several global FP flags that could get changed by other programs running on the same CPU/FPU that could impact the result of calculations. So, if you want 100% reproducible FP, you would have to either audit all software running on the same machine to ensure it doesn't touch those flags, or set the flags yourself for every FP calculation in your your program.
Secondly, on mainstream implementations, strictfp is already documented the same as default! They're planning to remove it anyway as it's a no-op in almost all cases.
See JEP 306.
If you use it. Which is not the default. Your original claim remains false.
That's something FP does not provide and it makes it completely unusable for accounting.
That seems like a completely arbitrary requirement. Do accounting laws prohibit sort? Does 1 + 1 have to equal green on Tuesdays?
Each operation is accounted on two opposite sides of various account in a way that always keeps sides balanced (ie. they must sum up to the same value).
When you go to your bank account, for example, you have various sums on both sides of your account. Yet when you sum them up they MUST agree or you will be crying blood and suing your bank.
Wonder if JS does something similar or not.
Also, changes applied to the FP co-processor by other processes on the machine could impact your process, regardless of your own compilation settings.
That's ancient history. Compilers don't use that instruction set any more in normal operation.
GCC, Java, LLVM, etc, will normally emit SSE2 in order to be standards compliant. They will only relax this if you tell them to, then it's your problem.
I believe there is still quite a bit of cautionary discussion of floating point numbers that was written in the age of the x87, so it's important to understand that people were not just misunderstanding IEEE754, even though their concerns are no longer applicable to modern hardware.
Poor souls that use FP for accounting are scourge of the industry and source of jokes.
For anything imprecise and scientific, doubles will normally work well.
Accounting rules regarding truncation and rounding as specified, seems unaccounted for by most until they meet such stringent reqs.
0.3 is exactly representable in radix-10 floating point but not radix-2 FP (would be rounded to a maximum of 0.5 ulp error as seen in the title), for instance, just as 1/3 = 0.3333... is exactly representable in radix-3 floating point but neither radix-2 or radix-10 FP, etc.
> It's easy to write a program that sums up 0.01 until the result is not equal to n * 0.01.
It's not easy to do that if you use a floating point decimal type, like I recommended. For instance, using C#'s decimal, that will take you somewhere in the neighborhood of 10 to the 26 iterations. With a binary floating point number, it's less than 10.
Many languages have no decimal support built in or at least it is not the default type. With a binary type the rounding becomes already visible after 10959 additions of 1 cent.
#include <stdbool.h>
#include <stdio.h>
#include <string.h>
bool compare(int cents, float sum) {
char buf[20], floatbuf[24];
int len;
bool result;
len = sprintf(buf, "%d", cents / 100 ) ;
sprintf(buf + len , ".%02d" , cents % 100 ) ;
sprintf(floatbuf, "%0.2f", sum) ;
result = ! strcmp(buf, floatbuf) ;
if (! result)
printf( "Cents: %d, exact: %s, calculated %s\n", cents, buf, floatbuf) ;
return result;
}
int main() {
float cent = 0.01f, sum = 0.0f;
for (int i=0 ; compare(i, sum) ; i++) {
sum += cent;
}
return 0;
}
Cents: 10959, exact: 109.59, calculated 109.60
Precisely. That's why I specified ~ 10^26 addition operations.
But they still can't precisely represent quantities like 1/3 or pi.
No, it's not. The widely recommended way of solving this problem is to use fixed-point numbers. Or, if one's language/platform does not support fixed-point numbers, then the widely recommended way of solving this problem is to emulate fixed-point numbers with integers.
There is zero legitimate reason to use floating-point numbers in this context, regardless of whether those numbers are in base-2 or base-10 or base-pi or whatever. The absolute smallest unit of currency any (US) financial institution is ever likely to use is the mill (one tenth of a cent), and you can represent 9,223,372,036,854,775,807 of them in a 64-bit signed integer. That's more than $9 quadrillion, which is 121-ish times the current gross world product; if you're really at the point where you need to represent such massive amounts of money (and/or do arithmetic on them), then you can probably afford to design and fabricate your own 128-bit computer to do those calculations instead of even shoehorning it onto a 64-bit CPU, let alone resorting to floating-point.
Regardless of all that, my actual point (pun intended) is that there are plenty of big ERP systems (e.g. NetSuite) that use binary floating point numbers for monetary values, and that's phenomenally bad.
Like commonly happens doing financial calculations, especially doing interest calculations.