(the latter renamed to _PyLong_Frexp) now use the same core code. The
exponent produced by _PyLong_Frexp now has type Py_ssize_t instead of the
previously used int, and no longer needs scaling by PyLong_SHIFT. This
frees the math module from having to know anything about the PyLong
implementation. This closes issue #5576.
(high_bits << PyLong_SHIFT) + low_bits with
(high_bits << PyLong_SHIFT) | low_bits
in Objects/longobject.c. Motivation:
- shouldn't unnecessarily mix bit ops with arithmetic ops (style)
- this pattern should be spelt the same way thoughout (consistency)
- it's very very very slightly faster: no need to worry about
carries to the high digit (nano-optimization).
correctly rounded, using round-half-to-even. This ensures that the
value of float(n) doesn't depend on whether we're using 15-bit digits
or 30-bit digits for Python longs.
The basic algorithm remains the same; the most significant speedups
come from the following three changes:
(1) normalize by shifting instead of multiplying and dividing
(2) the old algorithm usually did an unnecessary extra iteration of
the outer loop; remove this. As a special case, this means that
long divisions with a single-digit result run twice as fast as
before.
(3) make inner loop much tighter.
Various benchmarks show speedups of between 50% and 150% for long
integer divisions and modulo operations.
and cleanups in Objects/longobject.c. The most significant change is that
longs now use less memory: average savings are 2 bytes per long on 32-bit
systems and 6 bytes per long on 64-bit systems. (This memory saving already
exists in py3k.)
