1) _mpd_qdivmod() uses the context precision only in two places, and
the new code should be exactly equivalent to the previous code.
2) Remove misleading comment.
3) The quotient *is* an integer with exponent 0, so calling mpd_qtrunc()
is pointless.
4) Replace two instances of identical code by a single one.
5) Use _mpd_cmp_abs() instead of mpd_cmp_total_mag(): the operands
are not special.
6) Don't clear MPD_Rounded in the status (with the current code it should
not be set within the function).
2) _mpd_qpow_mpd(): Abort the loop for all specials, not only infinity.
3) _mpd_qpow_mpd(): Make the function more general and distinguish between
zero clamping and folding down the exponent. The latter case is currently
handled by setting context->clamp to 0 before calling the function.
4) _mpd_qpow_int(): Add one to the work precision in case of a negative
exponent. This is to get the same relative error (0.1 * 10**-prec)
for both positive and negative exponents. The previous relative
error for negative exponents was (0.2 * 10**-prec).
Both errors are _before_ the final rounding to the context precision.
in struct tm, time.struct_time objects returned by time.gmtime(),
time.localtime() and time.strptime() functions now have tm_zone and
tm_gmtoff attributes. Original patch by Paul Boddie.
Fix also its value on Windows and Linux according to its documentation:
"adjustable" indicates if the clock *can be* adjusted, not if it is or was
adjusted.
In most cases, it is not possible to indicate if a clock is or was adjusted.
2) Abort the loop for all specials, not only infinity.
3) Make the function more general and distinguish between zero clamping
and folding down the exponent. The latter case is currently handled
by setting context->clamp to 0 before calling the function.
2) Add rigorous error analysis to _mpd_qlog10 (ACL2 proofs exist).
3) Use the relative error as a basis for the interval generation in the
correction loop (same as in _mpd_qln()).
List all of them in the comment.
2) Use the recently stated relative error of _mpd_qln() to generate the
interval for the exact value of ln(x). See also the comment in mpd_qexp().
open() and io.TextIOWrapper are now calling locale.getpreferredencoding(False)
instead of locale.getpreferredencoding() in text mode if the encoding is not
specified. Don't change temporary the locale encoding using locale.setlocale(),
use the current locale encoding instead of the user preferred encoding.
Explain also in open() documentation that locale.getpreferredencoding(False) is
called if the encoding is not specified.
Underflow to zero hasn't changed: _mpd_qexp() internally uses MIN_EMIN,
so the result would also underflow to zero for all emin > MIN_EMIN.
In case digits are left, the informal argument is as follows: Underflow can
occur only once in the last multiplication of the power stage (in the Horner
stage Underflow provably cannot occur, and if Underflow occurred twice in
the power stage, the result would underflow to zero on the second occasion).
Since there is no double rounding during Underflow, the effective work
precision is now 1 <= result->digits < prec. It can be shown by a somewhat
tedious argument that abs(result - e**x) < ulp(result, result->digits).
Therefore the correct rounding loop now uses ulp(result, result->digits)
to generate the bounds for e**x in case of Underflow.
An issue in ctypes.c_longdouble, ctypes.c_double, and ctypes.c_float that
caused an incorrect exception to be returned in the case of overflow has been
fixed.
An issue in ctypes.c_longdouble, ctypes.c_double, and ctypes.c_float that
caused an incorrect exception to be returned in the case of overflow has been
fixed.
-----------------------
1) Reduce the number of iterations in the Horner scheme for operands with
a negative adjusted exponent. Previously the number was overestimated
quite generously.
2) The function _mpd_get_exp_iterations() now has an ACL2 proof and
is rewritten accordingly.
3) The proof relies on abs(op) > 9 * 10**(-prec-1), so operands without
that property are now handled by the new function _mpd_qexp_check_one().
4) The error analysis for the evaluation of the truncated Taylor series
in Hull&Abrham's paper relies on the fact that the reduced operand
'r' has fewer than context.prec digits.
Since the operands may have more than context.prec digits, a new ACL2
proof covers the case that r.digits > context.prec. To facilitate the
proof, the Horner step now uses fma instead of rounding twice in
multiply/add.
Changes in mpd_qexp():
----------------------
1) Fix a bound in the correct rounding loop that was too optimistic. In
practice results were always correctly rounded, because it is unlikely
that the error in _mpd_qexp() ever reaches the theoretical maximum.
Removed futimens as it is now redundant.
Changed shutil.copystat to use st_atime_ns and st_mtime_ns from os.stat
and ns= parameter to utime--it once again preserves exact metadata on Linux!
doko@ubuntu.com
Nadeem Vawda
Stefan Krah
Antoine Pitrou
Martin v. Löwis
Alexander Belopolsky
Eli Bendersky
Victor Stinner
Richard Oudkerk
Gregory P. Smith
Kristjan Valur Jonsson
Meador Inge
Vinay Sajip
Benjamin Peterson
Hynek Schlawack
Eric V. Smith
Brian Curtin
Ross Lagerwall
Mark Dickinson
Larry Hastings