Following discussions in PR #16666, this commit updates the float
formatting code to improve the `repr` reversibility, i.e. the percentage of
valid floating point numbers that do parse back to the same number when
formatted by `repr` (in CPython it's 100%).
This new code offers a choice of 3 float conversion methods, depending on
the desired tradeoff between code size and conversion precision:
- BASIC method is the smallest code footprint
- APPROX method uses an iterative method to approximate the exact
representation, which is a bit slower but but does not have a big impact
on code size. It provides `repr` reversibility on >99.8% of the cases in
double precision, and on >98.5% in single precision (except with REPR_C,
where reversibility is 100% as the last two bits are not taken into
account).
- EXACT method uses higher-precision floats during conversion, which
provides perfect results but has a higher impact on code size. It is
faster than APPROX method, and faster than the CPython equivalent
implementation. It is however not available on all compilers when using
FLOAT_IMPL_DOUBLE.
Here is the table comparing the impact of the three conversion methods on
code footprint on PYBV10 (using single-precision floats) and reversibility
rate for both single-precision and double-precision floats. The table
includes current situation as a baseline for the comparison:
PYBV10 REPR_C FLOAT DOUBLE
current = 364688 12.9% 27.6% 37.9%
basic = 364812 85.6% 60.5% 85.7%
approx = 365080 100.0% 98.5% 99.8%
exact = 366408 100.0% 100.0% 100.0%
Signed-off-by: Yoctopuce dev <dev@yoctopuce.com>
Rework the conversion of floats to decimal strings so it aligns precisely
with the conversion of strings to floats in parsenum.c. This is to avoid
rendering 1eX as 9.99999eX-1 etc. This is achieved by removing the power-
of-10 tables and using pow() to compute the exponent directly, and that's
done efficiently by first estimating the power-of-10 exponent from the
power-of-2 exponent in the floating-point representation.
Code size is reduced by roughly 100 to 200 bytes by this commit.
Signed-off-by: Dan Ellis <dan.ellis@gmail.com>
This adds the Python files in the tests/ directory to be formatted with
./tools/codeformat.py. The basics/ subdirectory is excluded for now so we
aren't changing too much at once.
In a few places `# fmt: off`/`# fmt: on` was used where the code had
special formatting for readability or where the test was actually testing
the specific formatting.
Prior to this patch, some architectures (eg unix x86) could render floats
with "negative" digits, like ")". For example, '%.23e' % 1e-80 would come
out as "1.0000000000000000/)/(,*0e-80". This patch fixes the known cases.
Prior to this patch, some architectures (eg unix x86) could render floats
with a ":" character in them, eg 1e+39 would come out as ":e+38" (":" is
just after "9" in ASCII so this is like 10e+38). This patch fixes some of
these cases.
Prior to this patch the %f formatting of some FP values could be off by up
to 1, eg '%.0f' % 123 would return "122" (unix x64). Depending on the FP
precision (single vs double) certain numbers would format correctly, but
others wolud not. This patch should fix all cases of rounding for %f.
