dtoa vs sprintf vs Grisu3 algorithm

Question

What is the best way to render double precision numbers as strings in C++?

I ran across the article Here be dragons: advances in problems you didn’t even know you had which discusses printing floating point numbers.

I have been using sprintf. I don't understand why I would need to modify the code?

Answer 1

If you are happy with sprintf_s you shouldn't change. However if you need to format your output in a way that is not supported by your library, you might need to reimplement a specialized version of sprintf (with any of the known algorithms).

For example JavaScript has very precise requirements on how its numbers must be printed (see section 9.8.1 of the specification). The correct output can't be accomplished by simply calling sprintf. Indeed, Grisu has been developed to implement correct number-printing for a JavaScript compiler.

Grisu is also faster than sprintf, but unless floating-point printing is a bottleneck in your application this should not be a reason to switch to a different library.

Answer 2

You might want to use something like Grisu (or a faster method) because it gives you the shortest decimal representation with round trip guarantee unlike sprintf which only takes a fixed precision. The good news is that C++20 includes std::format that gives you this by default. For example:

printf("%.*g", std::numeric_limits<double>::max_digits10, 0.3);

prints 0.29999999999999999 while

puts(fmt::format("{}", 0.3).c_str());

prints 0.3 (godbolt).

In the meantime you can use the {fmt} library, std::format is based on. {fmt} also provides the print function that makes this even easier and more efficient (godbolt):

fmt::print("{}", 0.3);

Disclaimer: I'm the author of {fmt} and C++20 std::format.

Answer 3

Ahah !

The problem outlined in the article you give is that for some numbers, the computer displays something that is theoritically correct but not what we, humans, would have used.

For example, like the article says, 1.2999999... = 1.3, so if your result is 1.3, it's (quite) correct for the computer to display it as 1.299999999... But that's not what you would have seen...

Now the question is why does the computer do that ? The reason is the computer compute in base 2 (binary) and that we usually compute in base 10 (decimal). The results are the same (thanks god !) but the internal storage and the representation are not.

Some numbers looks nice when displayed in base 10, like 1.3 for example, but others don't, for example 1/3 = 0.333333333.... It's the same in base 2, some numbers "looks" nice in base 2 (usually when composed of fractions of 2) and other not. When the computer stores number internally, it may not be able to store it "exactly" and store the closest possible representation, even if the number looked "finite" in decimal. So yes, in this case, it "drifts" a little bit. If you do that again and again, you may lose precision. But there is no other way (unless using special math libs able to store fractions)

The problem arise when the computer tries to give you back in base 10 the number you gave it. Then the computer may gives you 1.299999 instead of the 1.3 you were expected.

That's also the reason why you should never compare floats with ==, <, >, but instead use the special functions islessgreater(a, b) isgreater(a, b) etc.

So the actual function you use (sprintf) is fine and as exact as it can, it gives you correct values, you just have to know that when dealing with floats, 1.2999999 at maximum precision is OK if you were expecting 1.3

Now if you want to "pretty print" those numbers to have the best "human" representation (base 10), you may want to use a special library, like your grisu3 which will try to undo the drift that may have happen and align the number to the closest base 10 representation.

Now the library cannot use a crystal ball and find what numbers were drifted or not, so it may happen that you really meant 1.2999999 at maximum precision as stored in the computer and the lib will "convert" it to 1.3... But it's not worse nor less precise than displaying 1.29999 instead of 1.3.

If you need a good readability, such lib will be useful. If not, it's just a waste of time.

Hope this help !

Answer 4

The best way to do this in any reasonable language is:

1. Use your language's runtime library. Don't ever roll your own. Even if you have the knowledge and curiosity to write it, you don't want to test it and you don't want to maintain it.
2. If you notice any misbehavior from the runtime library conversion, file a bug.
3. If these conversions are a measurable bottleneck for your program, don't try to make them faster. Instead, find a way to avoid doing them at all. Instead of storing numbers as strings, just store the floating-point data (after possibly controlling for endianness). If you need a string representation, use a hexadecimal floating-point format instead.

I don't mean to discourage you, or anyone. These are actually fascinating functions to work on, but they are also shocking complex, and trying to design good test coverage for any non-naive implementation is even more involved. Don't get started unless you're prepared to spend months thinking about the problem.

Answer 5

In C++ why aren't you using iostreams? You should probably be using cout for the console and ostringstream for string-oriented output (unless you have a very specific need to use a printf family method).

You shouldn't worry about formatting performance unless actual profiling shows that CPU is the bottleneck (compared to say I/O).

Answer 6

void outputdouble( ostringstream & oss, double d )
{
    oss.precision( 5 );
    oss << d;
}

http://www.cplusplus.com/reference/iostream/ostringstream/