As per PEP 485, this function appeared in for Python 3.5. Configured via
MICROPY_PY_MATH_ISCLOSE which is disabled by default, but enabled for the
ports which already have MICROPY_PY_MATH_SPECIAL_FUNCTIONS enabled.
Nan and inf (signed and unsigned) are also handled correctly by using
signbit (they were also handled correctly with "val<0", but that didn't
handle -0.0 correctly). A test case is added for this behaviour.
This commit adds the math.factorial function in two variants:
- squared difference, which is faster than the naive version, relatively
compact, and non-recursive;
- a mildly optimised recursive version, faster than the above one.
There are some more optimisations that could be done, but they tend to take
more code, and more storage space. The recursive version seems like a
sensible compromise.
The new function is disabled by default, and uses the non-optimised version
by default if it is enabled. The options are MICROPY_PY_MATH_FACTORIAL
and MICROPY_OPT_MATH_FACTORIAL.
Printing of uPy floats can differ by the floating-point precision on
different architectures (eg 64-bit vs 32-bit x86), so it's not possible to
using printing of floats in some parts of this test. Instead we can just
check for equivalence with what is known to be the correct answer.
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.
Float parsing (both single and double precision) may have a relative error
of order the floating point precision, so adjust tests to take this into
account by not printing all of the digits of the answer.
Prior to this patch, a float literal that was close to subnormal would
have a loss of precision when parsed. The worst case was something like
float('10000000000000000000e-326') which returned 0.0.
This patch improves parsing of floating point numbers by converting all the
digits (integer and fractional) together into a number 1 or greater, and
then applying the correct power of 10 at the very end. In particular the
multiple "multiply by 0.1" operations to build a fraction are now combined
together and applied at the same time as the exponent, at the very end.
This helps to retain precision during parsing of floats, and also includes
a check that the number doesn't overflow during the parsing. One benefit
is that a float will have the same value no matter where the decimal point
is located, eg 1.23 == 123e-2.
This patch changes how most of the plain math functions are implemented:
there are now two generic math wrapper functions that take a pointer to a
math function (like sin, cos) and perform the necessary conversion to and
from MicroPython types. This helps to reduce code size. The generic
functions can also check for math domain errors in a generic way, by
testing if the result is NaN or infinity combined with finite inputs.
The result is that, with this patch, all math functions now have full
domain error checking (even gamma and lgamma) and code size has decreased
for most ports. Code size changes in bytes for those with the math module
are:
unix x64: -432
unix nanbox: -792
stm32: -88
esp8266: +12
Tests are also added to check domain errors are handled correctly.
This returns a complex number, following CPython behaviour. For ports that
don't have complex numbers enabled this will raise a ValueError which gives
a fail-safe for scripts that were written assuming complex numbers exist.
IEEE floating point is specified such that a comparison of NaN with itself
returns false, and Python respects these semantics. This patch makes uPy
also have these semantics. The fix has a minor impact on the speed of the
object-equality fast-path, but that seems to be unavoidable and it's much
more important to have correct behaviour (especially in this case where
the wrong answer for nan==nan is silently returned).
These are now returned as "operation not supported" instead of raising
TypeError. In particular, this fixes equality for float vs incompatible
types, which now properly results in False instead of exception. This
also paves the road to support reverse operation (e.g. __radd__) with
float objects.
This is achieved by introducing mp_obj_get_float_maybe(), similar to
existing mp_obj_get_int_maybe().
This patch fixes 2 things when printing a floating-point number that
requires rounding up of the mantissa:
- retain the correct precision; eg 0.99 becomes 1.0, not 1.00
- if the exponent goes from -1 to 0 then render it as +0, not -0
I.e. they don't run successfully with MICROPY_LONGINT_IMPL_NONE
and MICROPY_LONGINT_IMPL_LONGLONG (the problem is that they generate
different output than CPython, TODO to fix that).
The use of large literal numbers is a big no-no when it comes to writing
programs which work with different int representations. Also, some checks
are pretty adhoc (e.g using struct module to check for 64-bitness). This
change bases entire detection on sys.maxsize and integer operarions, and
thus more correct, even if longer.
Note that this change doesn't mean that any of these tests can pass with
anything but MPZ - even despite checking for various int representations,
the tests aren't written to be portable among them.
Damien George