Exact decimal datatype for C++?

问题:

PHP has a decimal type, which doesn't have the "inaccuracy" of floats and doubles, so that 2.5 + 2.5 = 5 and not 4.999999999978325 or something like that.

So I wonder if there is such a data type implementation for C or C++?

回答1:

Yes:

There are arbitrary precision libraries for C++.
A good example is The GNU Multiple Precision arithmetic library.

回答2:

The Boost.Multiprecision library has a decimal based floating point template class called cpp_dec_float, for which you can specify any precision you want.

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

int main()
{
    namespace mp = boost::multiprecision;
    // here I'm using a predefined type that stores 100 digits,
    // but you can create custom types very easily with any level
    // of precision you want.
    typedef mp::cpp_dec_float_100 decimal;

    decimal tiny("0.0000000000000000000000000000000000000000000001");
    decimal huge("100000000000000000000000000000000000000000000000");
    decimal a = tiny;         

    while (a != huge)
    {
        std::cout.precision(100);
        std::cout << std::fixed << a << '\n';
        a *= 10;
    }    
}

回答3:

If you are looking for data type supporting money / currency then try this: https://github.com/vpiotr/decimal_for_cpp

(it's header-only solution)

回答4:

There will be always some precision. On any computer in any number representation there will be always numbers which can be represented accurately, and other numbers which can't.

• Computers use a base 2 system. Numbers such as 0.5 (2^-1), 0.125 (2^-3), 0.325 (2^-2 + 2^-3) will be represented accurately (0.1, 0.001, 0.011 for the above cases).

• In a base 3 system those numbers cannot be represented accurately (half would be 0.111111...), but other numbers can be accurate (e.g. 2/3 would be 0.2)

• Even in human base 10 system there are numbers which can't be represented accurately, for example 1/3.

• You can use rational number representation and all the above will be accurate (1/2, 1/3, 3/8 etc.) but there will be always some irrational numbers too. You are also practically limited by the sizes of the integers of this representation.

• For every non-representable number you can extend the representation to include it explicitly. (e.g. compare rational numbers and a representation a/b + c/d*sqrt(2)), but there will be always more numbers which still cannot be represented accurately. There is a mathematical proof that says so.

So - let me ask you this: what exactly do you need? Maybe precise computation on decimal-based numbers, e.g. in some monetary calculation?

回答5:

What you're asking is anti-physics.

What phyton (and C++ as well) do is cut off the inaccuracy by rounding the result at the time to print it out, by reducing the number of significant digits:

double x = 2.5;
x += 2.5;
std::cout << x << std::endl;

just makes x to be printed with 6 decimal digit precision (while x itself has more than 12), and will be rounded as 5, cutting away the imprecision.

Alternatives are not using floating point at all, and implement data types that do just integer "scaled" arithmetic: 25/10 + 25/10 = 50/10;

Note, however, that this will reduce the upper limit represented by each integer type. The gain in precision (and exactness) will result in a faster reach to overflow.

Rational arithmetic is also possible (each number is represented by a "numarator" and a "denominator"), with no precision loss against divisions, (that -in fact- are not done unless exact) but again, with increasing values as the number of operation grows (the less "rational" is the number, the bigger are the numerator and denominator) with greater risk of overflow.

In other word the fact a finite number of bits is used (no matter how organized) will always result in a loss you have to pay on the side of small on on the side of big numbers.

回答6:

I presume you are talking about the Binary Calculator in PHP. No, there isn't one in the C runtime or STL. But you can write your own if you are so inclined.

Here is a C++ version of BCMath compiled using Facebook's HipHop for PHP: http://fossies.org/dox/facebook-hiphop-php-cf9b612/dir_2abbe3fda61b755422f6c6bae0a5444a.html

回答7:

Being a higher level language PHP just cuts off what you call "inaccuracy" but it's certainly there. In C/C++ you can achieve similar effect by casting the result to integer type.