This further optimizes floating point parsing (specifically with a large
amount of digits). The commit shaves additional 20% of the run time for
750-digit numbers. No performance degradation is noticeable for small
numbers.
Although it might seem like we've switched to more generic functions,
which must run slower, it is not the case. The time required to parse
"1", for example, decreased by 1%. For numbers with more digits, the
effect is more noticeable: 8-digit numbers are parsed ~5% faster; for
gigantic 750-digit numbers, parsing is 2 times faster.
The later result is achieved by using UFixedBigInt<64>::wide_multiply
instead of u128::operator*(u128).
Similar to decimal floating point parsing the current strtod hex float
parsing gives a lot of incorrect results. We can use a similar technique
as with decimal parsing however hex floats are much simpler as we don't
need to scale with a power of 5.
For hex floats we just provide the parse_first_hexfloat API as there is
currently no need for a parse_hexfloat_completely API.
Again the accepted input for parse_first_hexfloat is very lenient and
any validation should be done before calling this method.
This is based on the paper by Daniel Lemire called
"Number parsing at a Gigabyte per second", currently available at
https://arxiv.org/abs/2101.11408
An implementation can be found at
https://github.com/fastfloat/fast_float
To support both strtod like methods and String::to_double we have two
different APIs. The parse_first_floating_point gives back both the
result, next character to read and the error/out of range status.
Out of range here means we rounded to infinity 0.
The other API, parse_floating_point_completely, will return a floating
point only if the given character range contains just the floating point
and nothing else. This can be much faster as we can skip actually
computing the value if we notice we did not parse the whole range.
Both of these APIs support a very lenient format to be usable in as many
places as possible. Also it does not check for "named" values like
"nan", "inf", "NAN" etc. Because this can be different for every usage.
For integers and small values this new method is not faster and often
even a tiny bit slower than the current strtod implementation. However
the strtod implementation is wrong for a lot of values and has a much
less predictable running time.
For correctness this method was tested against known string -> double
datasets from https://github.com/nigeltao/parse-number-fxx-test-data
This method gives 100% accuracy.
The old strtod gave an incorrect value in over 50% of the numbers
tested.
