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I know that a float isn't appropriate to store currency values because of rounding errors. Is there a standard way to represent money in C++?

I've looked in the boost library and found nothing about it. In java, it seems that BigInteger is the way but I couldn't find an equivalent in C++. I could write my own money class, but prefer not to do so if there is something tested.

Bo Persson
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    For informations, there are no more or less rounding errors using binary representation or decimal representation (see 1/3=0.333...). Using decimal representation just let you have the same rounding errors as if you were doing it by hand. (easier to check/match results) – Offirmo Aug 29 '12 at 08:04
  • @Offirmo: True. However, if you do financial computations, a lot of errors might root in the fact that decimal currencies will have to be converted to binary currencies. – Sebastian Mach Jan 25 '17 at 05:26

21 Answers21

34

Don't store it just as cents, since you'll accumulate errors when multiplying for taxes and interest pretty quickly. At the very least, keep an extra two significant digits: $12.45 would be stored as 124,500. If you keep it in a signed 32 bit integer, you'll have $200,000 to work with (positive or negative). If you need bigger numbers or more precision, a signed 64 bit integer will likely give you all the space you'll need for a long time.

It might be of some help to wrap this value in a class, to give you one place for creating these values, doing arithmetic on them, and formatting them for display. This would also give you a central place to carry around which currency it being stored (USD, CAD, EURO, etc).

Eclipse
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    how did you get at 2,000,000? you can store up to about 2 billion cents in a signed 32-bit integer, which are about 20 million dollars. take 2 digits off that for a little more precision and you're left with about 200 thousand dollars. – wilhelmtell Sep 24 '11 at 19:26
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    exactly how big can a 64-bit integer hold using two extra precision digits? – Assimilater Apr 04 '15 at 05:59
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    Also, I see this post is quite old, does it still reflect the best way to store currency? Or has something been added to c++14 and/or boost that would be better now? – Assimilater Apr 04 '15 at 06:00
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    On the contrary. The storage should be of cents, because there is no such thing as sub-cent amounts of money. When calculating, one should be careful to use appropriate types and round correctly and in a timely fashion. – einpoklum Apr 09 '18 at 19:33
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    @einpoklum cents only require up to 2 decimal places, but investment transactions frequently operate with values between 4-6 decimal places instead. So storage may need higher precision than cents provides. – Remy Lebeau Apr 04 '19 at 05:14
  • @RemyLebeau: I didn't know that. So, I guess it depends on what OP is trying to do. – einpoklum Apr 04 '19 at 08:08
30

Having dealt with this in actual financial systems, I can tell you you probably want to use a number with at least 6 decimal places of precision (assuming USD). Hopefully since you're talking about currency values you won't go way out of whack here. There are proposals for adding decimal types to C++, but I don't know of any that are actually out there yet.

The best native C++ type to use here would be long double.

The problem with other approaches that simply use an int is that you have to store more than just your cents. Often financial transactions are multiplied by non-integer values and that's going to get you in trouble since $100.25 translated to 10025 * 0.000123523 (e.g. APR) is going cause problems. You're going to eventually end up in floating point land and the conversions are going to cost you a lot.

Now the problem doesn't happen in most simple situations. I'll give you a precise example:

Given several thousand currency values, if you multiply each by a percentage and then add them up, you will end up with a different number than if you had multiplied the total by that percentage if you do not keep enough decimal places. Now this might work in some situations, but you'll often be several pennies off pretty quickly. In my general experience making sure you keep a precision of up to 6 decimal places (making sure that the remaining precision is available for the whole number part).

Also understand that it doesn't matter what type you store it with if you do math in a less precise fashion. If your math is being done in single precision land, then it doesn't matter if you're storing it in double precision. Your precision will be correct to the least precise calculation.

Now that said, if you do no math other than simple addition or subtraction and then store the number then you'll be fine, but as soon as anything more complex than that shows up, you're going to be in trouble.

Orion Adrian
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    Could you expand your objection to ints, or provide a reference? The sample calculation you provided leads to a result of $0.01 or 1 using ints. It is not obvious to me why this is not the correct answer. – Jeffrey L Whitledge Sep 29 '08 at 17:54
  • See above example. I can provide more, but in this situation, it's usually pretty straight forward. I wrote financial forecasting software and you can't get away with integers and rounding. You need to store more than just cents, but also fractional cents. Eventually rounding issues will get you. – Orion Adrian Sep 29 '08 at 18:21
  • I've written some point-of-sale software and my solution to this problem (manifested as sum(discounts-per-line-item) != discount-on-order-total) is to make sure you always do the calculation that you mean. The problem space should dictate a summation of small percentages or a percentage of a sum. – Jeffrey L Whitledge Sep 29 '08 at 19:15
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    @Jeffrey (and others) - In addtion to what Orion already said, Financial systems need to be able to cope with a very wide range of numbers. Shares on stock markets (and in particular foreign exchange rates) are calculated to fractions of a penny ($0.000001) while other currencies such as the Zimbabwean dollar experience hyper inflation (http://en.wikipedia.org/wiki/Zimbabwean_dollar#Exchange_rate_history) to the point where even systems working with doubles cannot cope with the large values being used. So using int, long int etc really is not an option. – jmc Jun 25 '12 at 20:59
24

Look in to the relatively recent Intelr Decimal Floating-Point Math Library. It's specifically for finance applications and implements some of the new standards for binary floating point arithmetic (IEEE 754r).

jblocksom
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14

The biggest issue is rounding itself!

19% of 42,50 € = 8,075 €. Due to the German rules for rounding this is 8,08 €. The problem is, that (at least on my machine) 8,075 can't be represented as double. Even if I change the variable in the debugger to this value, I end up with 8,0749999....

And this is where my rounding function (and any other on floating point logic that I can think of) fails, since it produces 8,07 €. The significant digit is 4 and so the value is rounded down. And that is plain wrong and you can't do anything about it unless you avoid using floating point values wherever possible.

It works great if you represent 42,50 € as Integer 42500000.

42500000 * 19 / 100 = 8075000. Now you can apply the rounding rule above 8080000. This can easily be transformed to a currency value for display reasons. 8,08 €.

But I would always wrap that up in a class.

user331471
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9

I would suggest that you keep a variable for the number of cents instead of dollars. That should remove the rounding errors. Displaying it in the standards dollars/cents format should be a view concern.

Rontologist
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    This doesn't actually solve the problem since you often have to do more than just add to these numbers and then you're going to have problems as you're going to be loosing precision. $100.25 translated to 10025 * 0.0745234 APR is going to cause problems. – Orion Adrian Sep 29 '08 at 15:50
  • If I recall it correctly, there's a standard somewhere that says you should keep a minimum of 4 digits for common operations - that's why COM's "Currency" gave you 4. If foreign currencies are involved, you would probably need more. – Joe Pineda Sep 29 '08 at 20:22
  • I've explained the problem of least precision in precision-based calculations in my answer to this question. Ultimately even if you store the number in integer form you're going to have to do calculations in something else. Whatever that something else is should be the storage mechanism. – Orion Adrian Sep 29 '08 at 20:23
  • @Joe: 4 decimal places is the minimum really. I ended using 6 for my calculations to get penny resolution on check operations. But unless you do all your math in integer form, you're going to have issues because if you cast (implicitly or explicitly) you're going to end up in floating point land. – Orion Adrian Sep 29 '08 at 20:27
9

You can try decimal data type:

https://github.com/vpiotr/decimal_for_cpp

Designed to store money-oriented values (money balance, currency rate, interest rate), user-defined precision. Up to 19 digits.

It's header-only solution for C++.

Piotr
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9

You say you've looked in the boost library and found nothing about there. But there you have multiprecision/cpp_dec_float which says:

The radix of this type is 10. As a result it can behave subtly differently from base-2 types.

So if you're already using Boost, this should be good to currency values and operations, as its base 10 number and 50 or 100 digits precision (a lot).

See:

#include <iostream>
#include <iomanip>
#include <boost/multiprecision/cpp_dec_float.hpp>

int main()
{
    float bogus = 1.0 / 3.0;
    boost::multiprecision::cpp_dec_float_50 correct = 1.0 / 3.0;

    std::cout << std::setprecision(16) << std::fixed 
              << "float: " << bogus << std::endl
              << "cpp_dec_float: " << correct << std::endl;
          
    return 0;
}

Output:

float: 0.3333333432674408

cpp_dec_float: 0.3333333333333333

*I'm not saying float (base 2) is bad and decimal (base 10) is good. They just behave differently...

** I know this is an old post and boost::multiprecision was introduced in 2013, so wanted to remark it here.

Community
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Fernando
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  • -1 This answer demonstrates an incorrect usage of the decimal data type in the Boost multiprecision library. The `cpp_dec_float_50 correct` type in this answer will have the same precision and underlying representation as a double. See my answer here: https://stackoverflow.com/a/73551215/6358210 for a more detailed explanation of why this answer is misleading plus an example of how to correctly use the Boost multiprecision decimal type. – nessus_pp Aug 31 '22 at 05:29
7

Know YOUR range of data.

A float is only good for 6 to 7 digits of precision, so that means a max of about +-9999.99 without rounding. It is useless for most financial applications.

A double is good for 13 digits, thus: +-99,999,999,999.99, Still be careful when using large numbers. Recognize the subtracting two similar results strips away much of the precision (See a book on Numerical Analysis for potential problems).

32 bit integer is good to +-2Billion (scaling to pennies will drop 2 decimal places)

64 bit integer will handle any money, but again, be careful when converting, and multiplying by various rates in your app that might be floats/doubles.

The key is to understand your problem domain. What legal requirements do you have for accuracy? How will you display the values? How often will conversion take place? Do you need internationalization? Make sure you can answer these questions before you make your decision.

Dan Hewett
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5

Whatever type you do decide on, I would recommend wrapping it up in a "typedef" so you can change it at a different time.

Jordan Parmer
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    Given that typedef introduces only an alias and exposes you to implicit number conversions, I would instead pack it into a class. – Sebastian Mach Jan 25 '17 at 05:31
4

It depends on your business requirements with regards to rounding. The safest way is to store an integer with the required precision and know when/how to apply rounding.

Douglas Mayle
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  • This will get expensive though in terms of conversion issues. You'll be doing a conversion each time you do anything with the value since it's unlikely every floating point value in the system will be this kind of integer. – Orion Adrian Sep 29 '08 at 18:23
  • As in my answer, the precision of value is equal to the precision of the least precise calculation. Integer * Float is going to use float precision. For C++, the entire chain should be long double precision. – Orion Adrian Sep 29 '08 at 18:29
  • What you don't seem to realize, Orion is that not all values can be stored in a float. As such, odd little math errors can creep into your calculation if you don't know where and when you are rounding to clean up errors. – Douglas Mayle Sep 30 '08 at 18:15
4

Store the dollar and cent amount as two separate integers.

kmiklas
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2

Integers, always--store it as cents (or whatever your lowest currency is where you are programming for.) The problem is that no matter what you do with floating point someday you'll find a situation where the calculation will differ if you do it in floating point. Rounding at the last minute is not the answer as real currency calculations are rounded as they go.

You can't avoid the problem by changing the order of operations, either--this fails when you have a percentage that leaves you without a proper binary representation. Accountants will freak if you are off by a single penny.

Loren Pechtel
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1

I would recommend using a long int to store the currency in the smallest denomination (for example, American money would be cents), if a decimal based currency is being used.

Very important: be sure to name all of your currency values according to what they actually contain. (Example: account_balance_cents) This will avoid a lot of problems down the line.

(Another example where this comes up is percentages. Never name a value "XXX_percent" when it actually contains a ratio not multiplied by a hundred.)

Jeffrey L Whitledge
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1

The solution is simple, store to whatever accuracy is required, as a shifted integer. But when reading in convert to a double float, so that calculations suffer fewer rounding errors. Then when storing in the database multiply to whatever integer accuracy is needed, but before truncating as an integer add +/- 1/10 to compensate for truncation errors, or +/- 51/100 to round. Easy peasy.

Laurie
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1

As other answers have pointed out, you should either:

  1. Use an integer type to store whole units of your currency (ex: $1) and fractional units (ex: 10 cents) separately.

  2. Use a base 10 decimal data type that can exactly represent real decimal numbers such as 0.1. This is important since financial calculations are based on a base 10 number system.

The choice will depend on the problem you are trying to solve. For example, if you only need to add or subtract currency values then the integer approach might be sensible. If you are building a more complex system dealing with financial securities then the decimal data type approach may be more appropriate.

As another answer points out, Boost provides a base 10 floating point number type that serves as a drop-in replacement for the native C++ floating-point types, but with much greater precision. This might be convenient to use if your project already uses other Boost libraries.

The following example shows how to properly use this decimal type:

#include <iostream>
#include <boost/multiprecision/cpp_dec_float.hpp>

using namespace std;
using namespace boost::multiprecision;

int main() {
    std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_50>::max_digits10) << std::endl;
    double d1 = 1.0 / 10.0;
    cpp_dec_float_50 dec_incorrect = 1.0 / 10.0;  // Incorrect! We are constructing our decimal data type from the binary representation of the double value of 1.0 / 10.0
    cpp_dec_float_50 dec_correct(cpp_dec_float_50(1.0) / 10.0);
    cpp_dec_float_50 dec_correct2("0.1");  // Constructing from a decimal digit string.
    std::cout << d1 << std::endl;  // 0.1000000000000000055511151231257827021181583404541015625
    std::cout << dec_incorrect << std::endl;  // 0.1000000000000000055511151231257827021181583404541015625
    std::cout << dec_correct << std::endl;  // 0.1
    std::cout << dec_correct2 << std::endl;  // 0.1
    return 0;
}

Notice how even if we define a decimal data type but construct it from a binary representation of a double, then we will not obtain the precision that we expect. In the example above, both the double d1 and the cpp_dec_float_50 dec_incorrect are the same because of this. Notice how they are both "correct" to about 17 decimal places which is what we would expect of a double in a 64-bit system.

Finally, note that the boost multiprecision library can be significantly slower than the fastest high precision implementations available. This becomes evident at high digit counts (about 50+); at low digit counts the Boost implementation can be comparable other, faster implementations.

Sources:

  1. https://www.boost.org/doc/libs/1_80_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/floatbuiltinctor.html
  2. https://www.boost.org/doc/libs/1_80_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/caveats.html
nessus_pp
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0

The GMP library has "bignum" implementations that you can use for arbitrary sized integer calculations needed for dealing with money. See the documentation for mpz_class (warning: this is horribly incomplete though, full range of arithmetic operators are provided).

Greg Rogers
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One option is to store $10.01 as 1001, and do all calculations in pennies, dividing by 100D when you display the values.

Or, use floats, and only round at the last possible moment.

Often the problems can be mitigated by changing order of operations.

Instead of value * .10 for a 10% discount, use (value * 10)/100, which will help significantly. (remember .1 is a repeating binary)

Chris Cudmore
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    Never use floats. Try representing $0.60 as float. Financial code (AKA code for a bank) is not allowed to have rounding errors => no floats. – Martin York Sep 29 '08 at 16:02
  • 0.6 can't be stored as a float or a double. Most real numbers can't be, floating point are just approximations. Here's the output I get for a couple of numbers (0.6 and 8.075): float: 0.60000002384185791000 float: 8.07499980926513670000 double: 0.59999999999999998000 double: 8.07499999999999930000 – Superfly Jon Mar 27 '15 at 09:21
0

I'd use signed long for 32-bit and signed long long for 64-bit. This will give you maximum storage capacity for the underlying quantity itself. I would then develop two custom manipulators. One that converts that quantity based on exchange rates, and one that formats that quantity into your currency of choice. You can develop more manipulators for various financial operations / and rules.

0

This is a very old post, but I figured I update it a little since it's been a while and things have changed. I have posted some code below which represents the best way I have been able to represent money using the long long integer data type in the C programming language.

#include <stdio.h>

int main()
{
    // make BIG money from cents and dollars
    signed long long int cents = 0;
    signed long long int dollars = 0;

    // get the amount of cents
    printf("Enter the amount of cents: ");
    scanf("%lld", &cents);

    // get the amount of dollars
    printf("Enter the amount of dollars: ");
    scanf("%lld", &dollars);

    // calculate the amount of dollars
    long long int totalDollars = dollars + (cents / 100);

    // calculate the amount of cents
    long long int totalCents = cents % 100;

    // print the amount of dollars and cents
    printf("The total amount is: %lld dollars and %lld cents\n", totalDollars, totalCents);
}
brff19
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-1

Our financial institution uses "double". Since we're a "fixed income" shop, we have lots of nasty complicated algorithms that use double anyway. The trick is to be sure that your end-user presentation does not overstep the precision of double. For example, when we have a list of trades with a total in trillions of dollars, we got to be sure that we don't print garbage due to rounding issues.

-2

go ahead and write you own money (http://junit.sourceforge.net/doc/testinfected/testing.htm) or currency () class (depending on what you need). and test it.