py/formatfloat: Improve accuracy of float formatting code.

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>

1 files changed, 14 insertions, 3 deletions

diff --git a/tests/float/float_format.py b/tests/float/float_format.py
index 98ed0eb09..0eb8b232b 100644
--- a/tests/float/float_format.py
+++ b/tests/float/float_format.py
@@ -2,14 +2,25 @@
 
 # general rounding
 for val in (116, 1111, 1234, 5010, 11111):
-    print("%.0f" % val)
-    print("%.1f" % val)
-    print("%.3f" % val)
+    print("Test on %d / 1000:" % val)
+    for fmt in ("%.5e", "%.3e", "%.1e", "%.0e", "%.3f", "%.1f", "%.0f", "%.3g", "%.1g", "%.0g"):
+        print(fmt, fmt % (val / 1000))
+
+# make sure round-up to the next unit is handled properly
+for val in range(4, 9):
+    divi = 10**val
+    print("Test on 99994 / (10 ** %d):" % val)
+    for fmt in ("%.5e", "%.3e", "%.1e", "%.0e", "%.3f", "%.1f", "%.0f", "%.3g", "%.1g", "%.0g"):
+        print(fmt, fmt % (99994 / divi))
 
 # make sure rounding is done at the correct precision
 for prec in range(8):
     print(("%%.%df" % prec) % 6e-5)
 
+# make sure trailing zeroes are added properly
+for prec in range(8):
+    print(("%%.%df" % prec) % 1e19)
+
 # check certain cases that had a digit value of 10 render as a ":" character
 print("%.2e" % float("9" * 51 + "e-39"))
 print("%.2e" % float("9" * 40 + "e-21"))