Re: why tostring for number use LUA_NUMBER_FMT "%.14g", not "%.16g" ?

[Coda Highland <chighland@...>]

On Sat, Sep 7, 2013 at 1:51 PM, Leo Razoumov <slonik.az@gmail.com> wrote:
> On 9/7/13, pulleyzzz_gmail <pulleyzzz@gmail.com> wrote:
>> for this code:
>>
>> a=tostring(1/3)
>> print(1/3==tonumber(a))  -- false
>>
>> --if use .16g
>>
>> a=string.format('%.16g',1/3)
>> print(1/3==tonumber(a))  -- true
>>
>
> Changing format to "%.16g" would not solve your problem of comparing
> floats with == operator.
>
> 1/3 is computed in Lua natively in binary representation.
>
> a=string.format('%.16g',1/3) is a binary representation converted to a
> finite length
> base-10 number. Very often it cannot be done without loss of accuracy.
> Next, you are converting it to binary again with tonumber(a) which
> causes another loss of accuracy.
>
> As a rule of thumb do not compare floats with == operator. It will
> lead to subtle and
> difficult to catch errors.
>
> --Leo--
>

This answer, while technically correct, is actually misguided.

1/3 == 1/3 is guaranteed to be true. It's the same expression. (1/6 +
1/6 == 1/3 is a different question.)

But when you're discussing SERIALIZING floats, %.14g is not
sufficient. %.16g is sufficient to uniquely identify every possible
double-precision IEEE floating point number with a clean round trip.

So there IS a valid question to be asked here: Why SHOULDN'T
tostring() use %.16g?

/s/ Adam