Re: Data Cash Lang German Pna Zip Ra
Genciana Haggins
Your Microsoft Windows regional settings will influence how your date/time, numeric, and currency data types appear when you apply formatting options. Windows supports a variety of languages, plus currency and date/time formats for the countries/regions that use those languages.
For example, you might use forward slashes to enter a date value for a Date/Time field (for example, 11/19/2023), but when you apply the General Date display format, it may or may not display the forward slashes, depending on the regional settings for Windows.
This principle also applies to numeric and financial data. You can enter currency amounts that use the English pound symbol (), but Access may display those values in euros, because that is the currency symbol selected for Windows.
Click the tab that contains the settings that you want to modify, and make your changes. For example, to change part or all of a number format, click the Numbers tab and change the setting that you want.
Because floats and doubles cannot accurately represent the base 10 multiples that we use for money. This issue isn't just for Java, it's for any programming language that uses base 2 floating-point types.
However, for the purpose of counting money, at least for countries whose money is valued within an order of magnitude of the US dollar, usually all you need is to be able to store multiples of 10-2, so it doesn't really matter that 1/3 can't be represented.
The problem with floats and doubles is that the vast majority of money-like numbers don't have an exact representation as an integer times a power of 2. In fact, the only multiples of 0.01 between 0 and 1 (which are significant when dealing with money because they're integer cents) that can be represented exactly as an IEEE-754 binary floating-point number are 0, 0.25, 0.5, 0.75 and 1. All the others are off by a small amount. As an analogy to the 0.333333 example, if you take the floating-point value for 0.01 and you multiply it by 10, you won't get 0.1. Instead you will get something like 0.099999999786...
Representing money as a double or float will probably look good at first as the software rounds off the tiny errors, but as you perform more additions, subtractions, multiplications and divisions on inexact numbers, errors will compound and you'll end up with values that are visibly not accurate. This makes floats and doubles inadequate for dealing with money, where perfect accuracy for multiples of base 10 powers is required.
A solution that works in just about any language is to use integers instead, and count cents. For instance, 1025 would be $10.25. Several languages also have built-in types to deal with money. Among others, Java has the BigDecimal class, and Rust has the rust_decimal crate, and C# has the decimal type.
This is not a matter of accuracy, nor is it a matter of precision. It is a matter of meeting the expectations of humans who use base 10 for calculations instead of base 2. For example, using doubles for financial calculations does not produce answers that are "wrong" in a mathematical sense, but it can produce answers that are not what is expected in a financial sense.
Using a calculator, or calculating results by hand, 1.40 * 165 = 231 exactly. However, internally using doubles, on my compiler / operating system environment, it is stored as a binary number close to 230.99999... so if you truncate the number, you get 230 instead of 231. You may reason that rounding instead of truncating would have given the desired result of 231. That is true, but rounding always involves truncation. Whatever rounding technique you use, there are still boundary conditions like this one that will round down when you expect it to round up. They are rare enough that they often will not be found through casual testing or observation. You may have to write some code to search for examples that illustrate outcomes that do not behave as expected.
Assume you want to round something to the nearest penny. So you take your final result, multiply by 100, add 0.5, truncate, then divide the result by 100 to get back to pennies. If the internal number you stored was 3.46499999.... instead of 3.465, you are going to get 3.46 instead 3.47 when you round the number to the nearest penny. But your base 10 calculations may have indicated that the answer should be 3.465 exactly, which clearly should round up to 3.47, not down to 3.46. These kinds of things happen occasionally in real life when you use doubles for financial calculations. It is rare, so it often goes unnoticed as an issue, but it happens.
I'm troubled by some of these responses. I think doubles and floats have a place in financial calculations. Certainly, when adding and subtracting non-fractional monetary amounts there will be no loss of precision when using integer classes or BigDecimal classes. But when performing more complex operations, you often end up with results that go out several or many decimal places, no matter how you store the numbers. The issue is how you present the result.
If your result is on the borderline between being rounded up and rounded down, and that last penny really matters, you should be probably be telling the viewer that the answer is nearly in the middle - by displaying more decimal places.
I'll risk being downvoted, but I think the unsuitability of floating point numbers for currency calculations is overrated. As long as you make sure you do the cent-rounding correctly and have enough significant digits to work with in order to counter the binary-decimal representation mismatch explained by zneak, there will be no problem.
Of course, you have to stay within reason; e.g. a simple webshop would probably never experience any problem with double precision floats, but if you do e.g. accounting or anything else that requires adding a large (unrestricted) amount of numbers, you wouldn't want to touch floating point numbers with a ten foot pole.
The problem is that the IEEE spec doesn't have a way to exactly represent all fractions, some of them end up as repeating fractions so you end up with approximation errors. Since accountants like things to come out exactly to the penny, and customers will be annoyed if they pay their bill and after the payment is processed they owe .01 and they get charged a fee or can't close their account, it's better to use exact types like decimal (in C#) or java.math.BigDecimal in Java.
It's not that the error isn't controllable if you round: see this article by Peter Lawrey. It's just easier not to have to round in the first place. Most applications that handle money don't call for a lot of math, the operations consist of adding things or allocating amounts to different buckets. Introducing floating point and rounding just complicates things.
While it's true that floating point type can represent only approximatively decimal data, it's also true that if one rounds numbers to the necessary precision before presenting them, one obtains the correct result. Usually.
It must be said that even if you use fixed point arithmetic you still have to round numbers, were it not for the fact that BigInteger and BigDecimal give errors if you obtain periodic decimal numbers. So there is an approximation also here.
You can refer to guava's FuzzyCompare method to get more idea. The parameter tolerance is the key. We dealt with this problem for a securities trading application and we did an exhaustive research on what tolerances to use for different numerical values in different ranges.
Also, there might be situations when you're tempted to use Double wrappers as a map key with hash map being the implementation. It is very risky because Double.equals and hash code for example values "0.5" & "0.6 - 0.1" will cause a big mess.
The only reliable way to use a perfect representation of results(Use a custom Fraction data type that will batch division operations to the last step) and only convert to decimal notation in the last step.
Arbitrary precision won't help because there always can be numbers that has so many decimal places, or some results such as 0.6666666... No arbitrary representation will cover the last example. So you will have small errors in each step.
Coming from a non-computer science background (physics and engineering), I tend to look at problems from a different perspective. For me, the reason why I wouldn't use a double or float in a mathematical calculation is that I would lose too much information.
I'm not a computer scientist by training. However, I tend to lean towards either BigDecimal in Java or decimal in C#. I haven't tried the other solutions I've listed, but they are probably very good as well.
For me, I like BigDecimal because of the methods it supports. C#'s decimal is very nice, but I haven't had the chance to work with it as much as I'd like. I do scientific calculations of interest to me in my spare time, and BigDecimal seems to work very well because I can set the precision of my floating point numbers. The disadvantage to BigDecimal? It can be slow at times, especially if you're using the divide method.
To add on previous answers, there is also the option of implementing Joda-Money in Java, besides BigDecimal, when dealing with the problem addressed in the question. Java module name is org.joda.money.
Float is binary form of Decimal with different design; they are two different things. There are little errors between two types when converted to each other. Also, float is designed to represent infinite large number of values for scientific. That means it is designed to lost precision to extreme small and extreme large number with that fixed number of bytes. Decimal can't represent infinite number of values, it bounds to just that number of decimal digits. So Float and Decimal are for different purpose.
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