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, 43 insertions, 0 deletions

diff --git a/tests/float/float_struct_e_doubleprec.py b/tests/float/float_struct_e_doubleprec.py
new file mode 100644
index 000000000..403fbc5db
--- /dev/null
+++ b/tests/float/float_struct_e_doubleprec.py
@@ -0,0 +1,43 @@
+# Test struct pack/unpack with 'e' typecode.
+
+try:
+    import struct
+except ImportError:
+    print("SKIP")
+    raise SystemExit
+
+test_values = (
+    1e-7,
+    2e-7,
+    1e-6,
+    1e-5,
+    1e-4,
+    1e-3,
+    1e-2,
+    0.1,
+    0,
+    1,
+    2,
+    4,
+    8,
+    10,
+    100,
+    1e3,
+    1e4,
+    6e4,
+    float("inf"),
+)
+
+for j in test_values:
+    for i in (j, -j):
+        x = struct.pack("<e", i)
+        v = struct.unpack("<e", x)[0]
+        print("%.7f %s %.15f %s" % (i, x, v, i == v))
+
+# In CPython, packing a float that doesn't fit into a half-float raises OverflowError.
+# But in MicroPython it does not, but rather stores the value as inf.
+# This test is here for coverage.
+try:
+    struct.pack("e", 1e15)
+except OverflowError:
+    pass