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Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation.
Contributed by the Spaces project, INRIA Lorraine.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License (either version 2.1
of the License, or, at your option, any later version) and the GNU General
Public License as published by the Free Software Foundation (most of MPFR is
under the former, some under the latter).
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
02111-1307, USA.
##############################################################################
Documentation:
- add a description of the algorithms used + proof of correctness
- mpfr_set_prec: add an explanation of how to speed up calculations
which increase their precision at each step.
- solve the problem with @pxref{Custom Allocation,,, gmp,GNU MP}
[gives broken link on the html version]
Installation:
- from Kevin Ryde <user42@zip.com.au>:
Determine the exp2/exp3 thresholds using tune/tuneup.c.
A start has been made on this, but there's a noticable step-effect
in the times making them cross back and forward between which is
faster. Hopefully this will go away with improvements to the exp
code.
- Build a dynamic library (.so / .dll).
Changes in existing functions:
- merge mpfr_inp_str and mpfr_set_str (cf glibc sscanf/fscanf)
[mpfr_set_str -> with final '\0',
mpfr_strtofr -> without final '\0', returns the number of characters
read (or name mpfr_strtod suggested by Kevin, see below)]
- [suggestion from Kevin:]
[This has stalled on the gmp side, there'll be no hurry to do it in
mpfr until it's finalized in mpf.]
char * mpf_strto (mpz_t ROP, const char *STR)
Read a floating point number from a string. If successful the
result is stored in ROP and the return value points to the
character after those parsed. If STR doesn't start with a valid
number then the return value is `NULL' and the value in ROP is
undefined.
Parsing follows the standard C `strtod' function (*note Parsing of
Integers: (libc)Parsing of Integers.). This means optional
leading whitespace, an optional `+' or `-', mantissa digits, and an
optional exponent consisting of an `e' or `E', an optional sign,
and digits. A hex mantissa can be given with a leading `0x' or
`0X', in which case `p' or `P' introduces the exponent (still in
decimal). In addition `inf' or `infinity' with an optional sign,
or `nan' or `nan(..chars..)', all non case significant, can be
given.
There must be at least one digit in the mantissa for the number to
be valid. If an exponent has no digits it's ignored and parsing
stops after the mantissa. If an `0x' or `0X' is not followed by
hexadecimal digits, parsing stops after the `0'.
Note that in the hex format the exponent represents a power of 2,
ie. the result is MANTISSA*2^EXPONENT. This is as per the `%a'
format in `printf' (*note Formatted Output Strings::).
`mpf_t' does not currently support NaNs or infinities. The value
stored to ROP for these is undefined.
The decimal point character, or string, expected is taken from the
current locale on systems providing `localeconv'. [end of suggestion]
- in mpfr_set_str, possibly accept other strings, like those accepted
by strtod.
- mpfr_can_round:
1) remove the first rounding mode (rnd1) that was giving the direction of
the error. We'll consider now that the sign of the error is unknown.
This will simplify the code, should not loose too much since in most
cases we call mpfr_can_round with rnd1 = nearest, and should detect cases
with exact results that may loop.
2) change the meaning of the 2nd argument (err). Currently the error is
at most 2^(MPFR_EXP(b)-err), i.e. err is the relative shift wrt the
most significant bit of the approximation. I propose that the error
is now at most 2^err ulps of the approximation, i.e.
2^(MPFR_EXP(b)-MPFR_PREC(b)+err).
3) the current code performs two computations to check if we can round:
it checks if both round(approx-error) and round(approx+error) give
the same result. One computation is enough: for example in directed
rounding, if the round bit is 0 (resp. 1), we just have to check
round(approx-error) (resp. round(approx+error)).
New functions to implement:
- modf (to extract integer and fractional parts), suggested by
Dmitry Antipov <dmitry.antipov@mail.ru> Thu, 13 Jun 2002
- those from LIA: missing secant, cosecant, cotangent (trigo/hyperbolic)
- atan2
- mpfr_root to compute x^(1/n) for n integer, similar to mpz_root
[suggested by Damien Fisher, damien@maths.usyd.edu.au, 20 Jul 2003,
and Mark Watkins <watkins@maths.usyd.edu.au>, 23 Jul 2003]
- mpfr_fmod (mpfr_t, mpfr_srcptr, mpfr_srcptr, mp_rnd_t)
[suggested by Tomas Zahradnicky <tomas@24uSoftware.com>, 29 Nov 2003]
Kevin: Might want to be called mpfr_mod, to match mpz_mod.
-> we probably want to allow both mpfr_fmod and mpfr_mod.
- mpfr_fms for a-b*c
[suggested by Tomas Zahradnicky <tomas@24uSoftware.com>, 29 Nov 2003]
- 1/sqrt(x) [Regis Dupont <dupont@lix.polytechnique.fr>, 15 Sep 2004]
Efficiency:
- implement range reduction in sin/cos/tan for large arguments
(currently too slow for 2^1024)
- mpfr_asin/acos are too slow for small values (2^(-1021) for example)
- idem for mpfr_atanh (2^(-1021) for example)
- improve generic.c to work for number of terms <> 2^k
- rewrite mpfr_greater_p... as native code.
- mpfr_mul(a,b,c): truncate b,c when their precision is larger than that of a
- mpfr_tanh is inefficient is x is large (Pb of overflow too).
Should compute tanh(x)-1=-2/(exp(2x)+1) instead?
- mpf_t uses a scheme where the number of limbs actually present can
be less than the selected precision, thereby allowing low precision
values (for instance small integers) to be stored and manipulated in
an mpf_t efficiently.
Perhaps mpfr should get something similar, especially if looking to
replace mpf with mpfr, though it'd be a major change. Alternately
perhaps those mpfr routines like mpfr_mul where optimizations are
possible through stripping low zero bits or limbs could check for
that (this would be less efficient but easier).
Miscellaneous:
- rename mpf2mpfr.h to gmp-mpf2mpfr.h?
(will wait until mpfr is fully integrated into gmp :-)
- from Kevin Ryde <user42@zip.com.au>:
Also for pi.c, a pre-calculated compiled-in pi to a few thousand
digits would be good value I think. After all, say 10000 bits using
1250 bytes would still be small compared to the code size!
Store pi in round to zero mode (to recover other modes).
- problem when reading a float followed by a character, for example 1.5*x
[from Fabrice.Rouillier@loria.fr, Mon, 04 Dec 2000]
- add a new rounding mode: rounding away from 0. This can be easily
implemented as follows: round to zero, and if the result is inexact,
add one ulp to the mantissa.
- add a new rounding mode: round to nearest, with ties away from zero
(will be in 754r, could be used by mpfr_round)
- check/define the sign of infinity for gamma(-integer)
- add tests of the ternary value for constants
Reentrancy / Thread-Safety:
- Temporary changes to emin/emax are not safe (all uses of
mpfr_save_emin_emax, eg. mpfr_set_q).
- Global variables for caching in mpfr_const_log2 and mpfr_const_pi
are not safe.
Portability:
- [Kevin about texp.c long strings]
For strings longer than c99 guarantees, it might be cleaner to
introduce a "tests_strdupcat" or something to concatenate literal
strings into newly allocated memory. I thought I'd done that in a
couple of places already. Arrays of chars are not much fun.
Possible future MPF / MPFR integration:
- mpf routines can become "extern inline"s calling mpfr equivalents,
probably just with GMP_RNDZ hard coded, since that's what mpf has
always done.
- Want to preserve the mpf_t structure size, for binary compatibility.
Breaking compatibility would cause lots of pain and potential subtle
breakage for users. If the fields in mpf_t are not enough then
extra space under _mp_d can be used.
- mpf_sgn has been a macro directly accessing the _mp_size field, so a
compatible representation would be required. At worst that field
could be maintained for mpf_sgn, but not otherwise used internally.
mpf_sgn should probably throw an exception if called with NaN, since
there's no useful value it can return, so it might want to become a
function. Inlined copies in existing binaries would hopefully never
see a NaN, if they only do old-style mpf things.
- mpfr routines replacing mpf routines must be reentrant and thread
safe, since of course that's what has been documented for mpf.
- mpfr_random will not be wanted since there's no corresponding
mpf_random and new routines should not use the old style global
random state.
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