\input texinfo
+@ignore
+Copyright (C) 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Andreas Enge, Philippe Th\'eveny, Paul Zimmermann
+
+This file is part of the MPC Library.
+
+The MPC Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The MPC 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 MPC 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.
+@end ignore
+
+@ignore
+A recent version of makeinfo is required: at least version 4.2, where copying
+was introduced.
+@end ignore
+
@setfilename mpc.info
-@include version.texi
-@settitle GNU MPC @value{VERSION}
+@settitle MPC @value{VERSION}
@synindex tp fn
+@iftex
+@afourpaper
+@end iftex
-@set MINGMP 4.3.2
-@set MINMPFR 2.4.2
+@include version.texi
@set AUTHORS Andreas Enge, Philippe Th@'eveny, Paul Zimmermann
-
-@copying
-This manual is for GNU MPC, a library for multiple precision complex arithmetic,
-version @value{VERSION} of @value{UPDATED-MONTH}.
-
-Copyright @copyright{} 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 INRIA
-
-@quotation
-Permission is granted to copy, distribute and/or modify this document
-under the terms of the GNU Free Documentation License, Version 1.3 or
-any later version published by the Free Software Foundation; with no
-Invariant Sections. A copy of the license is included in the section
-entitled ``GNU Free Documentation License.''
-@end quotation
-@end copying
+@set COPYRIGHTDATES 2002, 2003, 2004, 2005, 2007, 2008, 2009
+@ifinfo
+@format
+START-INFO-DIR-ENTRY
+* mpc: (mpc.info). Multiple Precision Complex Library.
+END-INFO-DIR-ENTRY
+@end format
+@end ifinfo
@iftex
-@afourpaper
+@finalout
@end iftex
-@tex
-\global\parindent=0pt
-\global\parskip=8pt
-\global\baselineskip=13pt
-@end tex
-@dircategory GNU Packages
-@direntry
-* mpc: (mpc)Multiple Precision Complex Library.
-@end direntry
+@copying
+@ifinfo
+This is the manual for MPC, a library for multiple precision complex arithmetic,
+version @value{VERSION}, of @value{UPDATED-MONTH}.
+@end ifinfo
+
+@sp 1
+Copyright (C) @value{COPYRIGHTDATES} @value{AUTHORS}
+
+@sp 2
+
+Permission is granted to make and distribute verbatim copies of
+this manual provided the copyright notice and this permission notice
+are preserved on all copies.
+
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the entire
+resulting derived work is distributed under the terms of a permission
+notice identical to this one.
+
+Permission is granted to copy and distribute translations of this manual
+into another language, under the above conditions for modified versions.
+@end copying
+
+@setchapternewpage on
@titlepage
-@title GNU MPC
-@subtitle The GNU Multiple Precision Complex Library
+
+@title MPC
+@subtitle The Multiple Precision Complex Library
@subtitle Edition @value{VERSION}
@subtitle @value{UPDATED-MONTH}
+
@author @value{AUTHORS}
+
+@tex
+\global\parindent=0pt
+\global\parskip=8pt
+\global\baselineskip=13pt
+@end tex
+
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage
-
+@headings double
@ifnottex
-@node Top
-@top GNU MPC
+@node Top, Copying, (dir), (dir)
+
+@top MPC
-This manual documents how to install and use the GNU Multiple Precision
+This manual documents how to install and use the Multiple Precision
Complex Library, version @value{VERSION}
@end ifnottex
@menu
-* Copying:: GNU MPC Copying Conditions (LGPL).
-* Introduction to GNU MPC:: Brief introduction to GNU MPC.
-* Installing GNU MPC:: How to configure and compile the GNU MPC library.
+* Copying:: MPC Copying Conditions (LGPL).
+* Introduction to MPC:: Brief introduction to MPC.
+* Installing MPC:: How to configure and compile the MPC library.
* Reporting Bugs:: How to usefully report bugs.
-* GNU MPC Basics:: What every GNU MPC user should know.
+* MPC Basics:: What every MPC user should know.
* Complex Functions:: Functions for arithmetic on complex numbers.
+* Contributors::
* References::
* Concept Index::
* Function Index::
-* GNU Free Documentation License::
@end menu
-@c @times{} made available as a "x" in info and html (already works in tex).
+@c @times{} made available as a "*" in info and html (already works in tex).
@ifnottex
@macro times
-x
+*
@end macro
@end ifnottex
-
-@node Copying
-@unnumbered GNU MPC Copying Conditions
+@node Copying, Introduction to MPC, Top, Top
+@comment node-name, next, previous, up
+@unnumbered MPC Copying Conditions
@cindex Copying conditions
-@cindex Conditions for copying GNU MPC
+@cindex Conditions for copying MPC
-GNU MPC is free software; you can redistribute it and/or modify it under
-the terms of the GNU Lesser General Public License as published by the
-Free Software Foundation; either version 3 of the License, or (at your
-option) any later version.
-
-GNU MPC 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.
+The MPC Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version, see the file COPYING.LIB.
-You should have received a copy of the GNU Lesser General Public License
-along with this program. If not, see @uref{http://www.gnu.org/licenses/}.
+The MPC 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.
+@node Introduction to MPC, Installing MPC, Copying, Top
+@comment node-name, next, previous, up
+@chapter Introduction to MPC
-@node Introduction to GNU MPC
-@chapter Introduction to GNU MPC
-
-GNU MPC is a portable library written in C for arbitrary precision arithmetic
-on complex numbers providing correct rounding. It implements a multiprecision
-equivalent of the C99 standard.
+MPC is a portable library written in C for arbitrary precision arithmetic
+on complex numbers providing correct rounding. Ultimately, it
+should implement a multiprecision equivalent of the C99 standard.
It builds upon the GNU MP and the GNU MPFR libraries.
@section How to use this Manual
-Everyone should read @ref{GNU MPC Basics}. If you need to install the library
-yourself, you need to read @ref{Installing GNU MPC}, too.
+Everyone should read @ref{MPC Basics}. If you need to install the library
+yourself, you need to read @ref{Installing MPC}, too.
The remainder of the manual can be used for later reference, although it is
probably a good idea to skim through it.
-@node Installing GNU MPC
-@chapter Installing GNU MPC
+@node Installing MPC, Reporting Bugs, Introduction to MPC, Top
+@comment node-name, next, previous, up
+@chapter Installing MPC
@cindex Installation
-To build GNU MPC, you first have to install GNU MP (version @value{MINGMP} or higher) and
-GNU MPFR (version @value{MINMPFR} or higher) on your computer. You need a C compiler;
-GCC version 4.4 or higher is recommended, since GNU MPC may trigger a bug in previous
-versions, see the thread at
-@uref{http://lists.gforge.inria.fr/pipermail/mpc-discuss/2011-February/000823.html}.
-And you need a
+To build MPC, you first have to install GNU MP (version 4.2 or higher) and
+GNU MPFR (version 2.3.1 or higher) on your computer. You need a C compiler,
+preferably GCC, but any reasonable compiler should work. And you need a
standard Unix @samp{make} program, plus some other standard Unix utility
programs.
@item
@samp{./configure}
-if GMP and GNU MPFR are installed into standard directories, that is, directories
+if GMP and MPFR are installed into standard directories, that is, directories
that are searched by default by the compiler and the linking tools.
@samp{./configure --with-gmp=<gmp_install_dir>}
@samp{./configure --with-mpfr=<mpfr_install_dir>}
-is used to indicate a different location where GNU MPFR is
-installed. Alternatively, you can specify directly GNU MPFR include and GNU MPFR lib
+is used to indicate a different location where MPFR is
+installed. Alternatively, you can specify directly MPFR include and MPFR lib
directories with @samp{./configure --with-mpf-lib=<mpfr_lib_dir>
--with-mpfr-include=<mpfr_include_dir>}.
specify an alternative installation location instead of
@file{/usr/local}; see @samp{make install} below.
-To enable checking for memory leaks using @command{valgrind} during
-@code{make check}, add the parameter @code{--enable-valgrind-tests}.
-
-If for debugging purposes you wish to log calls to GNU MPC functions from
-within your code, add the parameter @samp{--enable-logging}.
-In your code, replace the inclusion of @file{mpc.h} by @file{mpc-log.h}
-and link the executable dynamically.
-Then all calls to functions with only complex arguments are printed to
-@file{stderr} in the following form: First, the function name is given,
-followed by its type such as @samp{c_cc}, meaning that the function has
-one complex result (one @samp{c} in front of the @samp{_}), computed from
-two complex arguments (two @samp{c} after the @samp{_}). Then, the
-precisions of the real and the imaginary part of the first result is given,
-followed by the second one and so on. Finally, for each argument, the
-precisions of its real and imaginary part are specified and the argument
-itself is printed in hexadecimal via the function
-@code{mpc_out_str}
-(@pxref{String and Stream Input and Output}).
-The option requires a dynamic library, so it may not be combined with
-@code{--disable-shared}.
-
Use @samp{./configure --help} for an exhaustive list of parameters.
@item
@samp{make}
-This compiles GNU MPC in the working directory.
+This compiles MPC in the working directory.
@item
@samp{make check}
-This will make sure GNU MPC was built correctly.
+This will make sure MPC was built correctly.
If you get error messages, please report them to
@samp{mpc-discuss@@lists.gforge.inria.fr} (@xref{Reporting Bugs}, for
@section Known Build Problems
-On AIX, if GMP was built with the 64-bit ABI, before building and testing GNU MPC,
+On AIX, if GMP was built with the 64-bit ABI, before building and testing MPC,
it might be necessary to set the @samp{OBJECT_MODE} environment variable to 64
by, e.g.,
@samp{export OBJECT_MODE=64}
This has been tested with the C compiler IBM XL C/C++ Enterprise Edition
-V8.0 for AIX, version: 08.00.0000.0021, GMP 4.2.4 and GNU MPFR 2.4.1.
+V8.0 for AIX, version: 08.00.0000.0021, GMP 4.2.4 and MPFR 2.4.1.
Please report any other problems you encounter to
@samp{mpc-discuss@@lists.gforge.inria.fr}.
@xref{Reporting Bugs}.
-@node Reporting Bugs
+@node Reporting Bugs, MPC Basics, Installing MPC, Top
+@comment node-name, next, previous, up
@chapter Reporting Bugs
@cindex Reporting bugs
-If you think you have found a bug in the GNU MPC library,
+If you think you have found a bug in the MPC library,
please investigate
and report it. We have made this library available to you, and it is not to ask
too much from you, to ask you to report the bugs that you find.
If you think something in this manual is unclear, or downright incorrect, or if
the language needs to be improved, please send a note to the same address.
-@node GNU MPC Basics
-@chapter GNU MPC Basics
+@node MPC Basics, Complex Functions, Reporting Bugs, Top
+@comment node-name, next, previous, up
+@chapter MPC Basics
@cindex @file{mpc.h}
-All declarations needed to use GNU MPC are collected in the include file
+All declarations needed to use MPC are collected in the include file
@file{mpc.h}. It is designed to work with both C and C++ compilers.
-You should include that file in any program using the GNU MPC library
+You should include that file in any program using the MPC library
by adding the line
@example
#include "mpc.h"
The C data type for such objects is @code{mpc_t}.
@cindex Precision
-@tindex @code{mpfr_prec_t}
+@tindex @code{mp_prec_t}
@noindent
The @dfn{Precision} is the number of bits used to represent the mantissa
of the real and imaginary parts;
-the corresponding C data type is @code{mpfr_prec_t}.
+the corresponding C data type is @code{mp_prec_t}.
For more details on the allowed precision range,
@ifinfo
-@pxref{Nomenclature and Types,,, mpfr.info,GNU MPFR}.
+@pxref{Nomenclature and Types,,, mpfr.info,MPFR}.
@end ifinfo
@ifnotinfo
-see Section ``Nomenclature and Types'' in @cite{GNU MPFR}.
+see Section ``Nomenclature and Types'' in @cite{MPFR}.
@end ifnotinfo
@cindex Rounding Mode
@section Function Classes
-There is only one class of functions in the GNU MPC library, namely functions for
+There is only one class of functions in the MPC library, namely functions for
complex arithmetic. The function names begin with @code{mpc_}. The
associated type is @code{mpc_t}.
-@section GNU MPC Variable Conventions
+@section MPC Variable Conventions
-As a general rule, all GNU MPC functions expect output arguments before input
+As a general rule, all MPC functions expect output arguments before input
arguments. This notation is based on an analogy with the assignment operator.
-GNU MPC allows you to use the same variable for both input and output in the same
+MPC allows you to use the same variable for both input and output in the same
expression. For example, the main function for floating-point multiplication,
@code{mpc_mul}, can be used like this: @code{mpc_mul (x, x, x, rnd_mode)}.
This
computes the square of @var{x} with rounding mode @code{rnd_mode}
and puts the result back in @var{x}.
-Before you can assign to an GNU MPC variable, you need to initialize it by calling
+Before you can assign to an MPC variable, you need to initialize it by calling
one of the special initialization functions. When you are done with a
variable, you need to clear it out, using one of the functions for that
purpose.
Instead, initialize it before entering the loop, and clear it out after the
loop has exited.
-You do not need to be concerned about allocating additional space for GNU MPC
+You do not need to be concerned about allocating additional space for MPC
variables, since each of its real and imaginary part
has a mantissa of fixed size.
Hence unless you change its precision, or clear and reinitialize it,
@anchor{return-value}
@section Return Value
-Most GNU MPC functions have a return value of type @code{int}, which is used
+Most MPC functions have a return value of type @code{int}, which is used
to indicate the position of the rounded real and imaginary parts with respect
to the exact (infinite precision) values.
If this integer is @code{i}, the macros @code{MPC_INEX_RE(i)} and
whether the rounded value is the same, larger or smaller then
the exact result.
-Some functions, such as @code{mpc_sin_cos}, compute two complex results;
-the macros @code{MPC_INEX1(i)} and @code{MPC_INEX2(i)}, applied to
-the return value @code{i} of such a function, yield the exactness value
-corresponding to the first or the second computed value, respectively.
-
@section Branch Cuts And Special Values
Some complex functions have branch cuts, across which the function is
-discontinous. In GNU MPC, the branch cuts chosen are the same as those
+discontinous. In MPC, the branch cuts chosen are the same as those
specified for the corresponding functions in the ISO C99 standard.
Likewise, when evaluated at a point whose real or imaginary part is
standard.
-@node Complex Functions
+@node Complex Functions, Contributors, MPC Basics, Top
+@comment node-name, next, previous, up
@chapter Complex Functions
@cindex Complex functions
The complex functions expect arguments of type @code{mpc_t}.
-The GNU MPC floating-point functions have an interface that is similar to the
+The MPC floating-point functions have an interface that is similar to the
GNU MP
integer functions. The function prefix for operations on complex numbers is
@code{mpc_}.
operation exactly (with ``infinite precision''), and round the result to
the destination variable precision with the given rounding mode.
-The GNU MPC complex functions are intended to be a smooth extension
+The MPC complex functions are intended to be a smooth extension
of the IEEE P754 arithmetic. The results obtained on one
computer should not differ from the results obtained on a computer with a
different word size.
@menu
* Initializing Complex Numbers::
* Assigning Complex Numbers::
-* Converting Complex Numbers::
* String and Stream Input and Output::
* Complex Comparison::
* Projection & Decomposing::
* Internals::
@end menu
-@node Initializing Complex Numbers
+@node Initializing Complex Numbers, Assigning Complex Numbers, Complex Functions, Complex Functions
+@comment node-name, next, previous, up
@section Initialization Functions
An @code{mpc_t} object must be initialized before storing the first value in
it. The functions @code{mpc_init2} and @code{mpc_init3}
are used for that purpose.
-@deftypefun void mpc_init2 (mpc_t @var{z}, mpfr_prec_t @var{prec})
+@deftypefun void mpc_init2 (mpc_t @var{z}, mp_prec_t @var{prec})
Initialize @var{z} to precision @var{prec} bits
and set its real and imaginary parts to NaN.
Normally, a variable should be initialized once only
or at least be cleared, using @code{mpc_clear}, between initializations.
@end deftypefun
-@deftypefun void mpc_init3 (mpc_t @var{z}, mpfr_prec_t @var{prec_r}, mpfr_prec_t @var{prec_i})
+@deftypefun void mpc_init3 (mpc_t @var{z}, mp_prec_t @var{prec_r}, mp_prec_t @var{prec_i})
Initialize @var{z} with the precision of its real part being
@var{prec_r} bits and the precision of its imaginary part being
@var{prec_i} bits, and set the real and imaginary parts to NaN.
iterative algorithms like Newton-Raphson, making the computation precision
closely match the actual accurate part of the numbers.
-@deftypefun void mpc_set_prec (mpc_t @var{x}, mpfr_prec_t @var{prec})
+@deftypefun void mpc_set_prec (mpc_t @var{x}, mp_prec_t @var{prec})
Reset the precision of @var{x} to be @strong{exactly} @var{prec} bits,
and set its real/imaginary parts to NaN.
The previous value stored in @var{x} is lost. It is equivalent to
case the current allocated space for the mantissa of @var{x} is sufficient.
@end deftypefun
-@deftypefun mpfr_prec_t mpc_get_prec (mpc_t @var{x})
+@deftypefun mp_prec_t mpc_get_prec (mpc_t @var{x})
If the real and imaginary part of @var{x} have the same precision, it is returned,
otherwise, 0 is returned.
@end deftypefun
-@deftypefun void mpc_get_prec2 (mpfr_prec_t* @var{pr}, mpfr_prec_t* @var{pi}, mpc_t @var{x})
+@deftypefun void mpc_get_prec2 (mp_prec_t* @var{pr}, mp_prec_t* @var{pi}, mpc_t @var{x})
Returns the precision of the real part of @var{x} via @var{pr} and of its imaginary part
via @var{pi}.
@end deftypefun
-@node Assigning Complex Numbers
+@node Assigning Complex Numbers, String and Stream Input and Output, Initializing Complex Numbers, Complex Functions
+@comment node-name, next, previous, up
@section Assignment Functions
@cindex Complex assignment functions
These functions assign new values to already initialized complex numbers
(@pxref{Initializing Complex Numbers}).
-When using any functions with @code{intmax_t} or @code{uintmax_t}
-parameters, you must include
-@code{<stdint.h>} or @code{<inttypes.h>} @emph{before} @file{mpc.h}, to allow
+When using any functions with @code{intmax_t} parameter, you must include
+@code{<stdint.h>} or @code{<inttypes.h>} before @file{mpc.h}, to allow
@file{mpc.h} to define prototypes for these functions.
-Similarly, functions with parameters of type @code{complex} or
-@code{long complex} are defined only if @code{<complex.h>} is included
-@emph{before} @file{mpc.h}.
If you need assignment functions that are not in the current API, you can
define them using the @code{MPC_SET_X_Y} macro (@pxref{Advanced Functions}).
@deftypefunx int mpc_set_sj (mpc_t @var{rop}, intmax_t @var{op}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_d (mpc_t @var{rop}, double @var{op}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_ld (mpc_t @var{rop}, long double @var{op}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_set_dc (mpc_t @var{rop}, double _Complex @var{op}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_set_ldc (mpc_t @var{rop}, long double _Complex @var{op}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_z (mpc_t @var{rop}, mpz_t @var{op} mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_q (mpc_t @var{rop}, mpq_t @var{op} mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_f (mpc_t @var{rop}, mpf_t @var{op} mpc_rnd_t @var{rnd})
@deftypefunx int mpc_set_fr_fr (mpc_t @var{rop}, mpfr_t @var{op1}, mpfr_t @var{op2}, mpc_rnd_t @var{rnd})
Set the real part of @var{rop} from @var{op1}, and its imaginary part from
@var{op2}, according to the rounding mode @var{rnd}.
-
-Beware that the behaviour of @code{mpc_set_fr_fr} is undefined if @var{op1}
-or @var{op2} is a pointer to the real or imaginary part of @var{rop}.
-To exchange the real and the imaginary part of a complex number, either use
-@code{mpfr_swap (mpc_realref (rop), mpc_imagref (rop))}, which also exchanges
-the precisions of the two parts; or use a temporary variable.
@end deftypefun
For functions assigning complex variables from strings or input streams,
-@pxref{String and Stream Input and Output}.
+@pxref{string-io,,String and Stream Input and Output}.
@deftypefun void mpc_set_nan (mpc_t @var{rop})
Set @var{rop} to Nan+i*NaN.
@end deftypefun
-@node Converting Complex Numbers
-@section Conversion Functions
-@cindex Conversion functions
-
-The following functions are available only if @code{<complex.h>}
-is included @emph{before} @file{mpc.h}.
-
-@deftypefun double _Complex mpc_get_dc (mpc_t @var{op}, mpc_rnd_t @var{rnd})
-@deftypefunx {long double _Complex} mpc_get_ldc (mpc_t @var{op}, mpc_rnd_t @var{rnd})
-Convert @var{op} to a C complex number, using the rounding mode @var{rnd}.
-@end deftypefun
-
-
-For functions converting complex variables to strings or stream output,
-@pxref{String and Stream Input and Output}.
-
-
-@node String and Stream Input and Output
-@section String and Stream Input and Output
+@node String and Stream Input and Output, Complex Comparison, Assigning Complex Numbers, Complex Functions
+@comment node-name, next, previous, up
@cindex String and stream input and output
+@anchor{string-io}
+@section String and Stream Input and Output
@deftypefun int mpc_strtoc (mpc_t @var{rop}, const char *@var{nptr}, char **@var{endptr}, int @var{base}, mpc_rnd_t @var{rnd})
Read a complex number from a string @var{nptr} in base @var{base}, rounded to
The form of a floating-point number depends on the base and is described
in the documentation of @code{mpfr_strtofr}
@ifinfo
-(@pxref{Assignment Functions,,, mpfr.info,GNU MPFR}).
+(@pxref{Assignment Functions,,, mpfr.info,MPFR}).
@end ifinfo
@ifnotinfo
-in the GNU MPFR manual.
+in the MPFR manual.
@end ifnotinfo
For instance, @code{"3.1415926"}, @code{"(1.25e+7 +.17)"}, @code{"(@@nan@@
2)"} and @code{"(-0 -7)"} are valid strings for @var{base} = 10.
@end deftypefun
-@node Complex Comparison
-@section Comparison Functions
+@node Complex Comparison, Projection & Decomposing, String and Stream Input and Output, Complex Functions
+@comment node-name, next, previous, up
@cindex Complex comparisons functions
@cindex Comparison functions
+@section Comparison Functions
@deftypefn Function int mpc_cmp (mpc_t @var{op1}, mpc_t @var{op2})
@deftypefnx Function int mpc_cmp_si_si (mpc_t @var{op1}, long int @var{op2r}, long int @var{op2i})
@end deftypefn
-@node Projection & Decomposing
+@node Projection & Decomposing, Basic Arithmetic, Complex Comparison, Complex Functions
+@comment node-name, next, previous, up
@section Projection and Decomposing Functions
@cindex Projection and Decomposing Functions
@end deftypefn
-@node Basic Arithmetic
+@node Basic Arithmetic, Power Functions and Logarithm, Projection & Decomposing, Complex Functions
+@comment node-name, next, previous, up
@section Basic Arithmetic Functions
@cindex Complex arithmetic functions
@cindex Arithmetic functions
All the following functions are designed in such a way that, when working
with real numbers instead of complex numbers, their complexity should
-essentially be the same as with the GNU MPFR library, with only a marginal
-overhead due to the GNU MPC layer.
+essentially be the same as with the MPFR library, with only a marginal
+overhead due to the MPC layer.
@deftypefun int mpc_add (mpc_t @var{rop}, mpc_t @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_add_ui (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
For @code{mpc_ui_ui_sub}, @var{op1} is @var{re1} + @var{im1}.
@end deftypefn
-@deftypefun int mpc_neg (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
-Set @var{rop} to @minus{}@var{op} rounded according to @var{rnd}.
-Just changes the sign if @var{rop} and @var{op} are the same variable.
-@end deftypefun
-
@deftypefun int mpc_mul (mpc_t @var{rop}, mpc_t @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_mul_ui (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_mul_si (mpc_t @var{rop}, mpc_t @var{op1}, long int @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_mul_fr (mpc_t @var{rop}, mpc_t @var{op1}, mpfr_t @var{op2}, mpc_rnd_t @var{rnd})
Set @var{rop} to @var{op1} times @var{op2} rounded according to @var{rnd}.
-Note: for @code{mpc_mul}, in case @var{op1} and @var{op2} have the same value,
-use @code{mpc_sqr} for better efficiency.
@end deftypefun
@deftypefun int mpc_mul_i (mpc_t @var{rop}, mpc_t @var{op}, int @var{sgn}, mpc_rnd_t @var{rnd})
Set @var{rop} to the square of @var{op} rounded according to @var{rnd}.
@end deftypefun
-@deftypefun int mpc_fma (mpc_t @var{rop}, mpc_t @var{op1}, mpc_t @var{op2}, mpc_t @var{op3}, mpc_rnd_t @var{rnd})
-Set @var{rop} to @var{op1}*@var{op2}+@var{op3},
-rounded according to @var{rnd}, with only one final rounding.
-@end deftypefun
-
@deftypefun int mpc_div (mpc_t @var{rop}, mpc_t @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_div_ui (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_div_fr (mpc_t @var{rop}, mpc_t @var{op1}, mpfr_t @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_ui_div (mpc_t @var{rop}, unsigned long int @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
+@deftypefunx int mpc_div_fr (mpc_t @var{rop}, mpc_t @var{op1}, mpfr_t @var{op2}, mpc_rnd_t @var{rnd})
@deftypefunx int mpc_fr_div (mpc_t @var{rop}, mpfr_t @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
Set @var{rop} to @var{op1}/@var{op2} rounded according to @var{rnd}.
+For @code{mpc_div} and @code{mpc_ui_div}, the return value may fail to
+recognize some exact results. The sign of returned value is
+significant only for @code{mpc_div_ui}.
+@end deftypefun
+
+@deftypefun int mpc_neg (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
+Set @var{rop} to @minus{}@var{op} rounded according to @var{rnd}.
+Just changes the sign if @var{rop} and @var{op} are the same variable.
@end deftypefun
@deftypefun int mpc_conj (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
@deftypefun int mpc_abs (mpfr_t @var{rop}, mpc_t @var{op}, mpfr_rnd_t @var{rnd})
Set the floating-point number @var{rop} to the absolute value of @var{op},
rounded in the direction @var{rnd}.
+The returned value is zero iff the result is exact.
@end deftypefun
@deftypefun int mpc_norm (mpfr_t @var{rop}, mpc_t @var{op}, mpfr_rnd_t @var{rnd})
Set the floating-point number @var{rop} to the norm of @var{op}
(i.e., the square of its absolute value),
rounded in the direction @var{rnd}.
+The returned value is zero iff the result is exact.
+Note that the destination is of type @code{mpfr_t}, not @code{mpc_t}.
@end deftypefun
-@deftypefun int mpc_mul_2ui (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_mul_2si (mpc_t @var{rop}, mpc_t @var{op1}, long int @var{op2}, mpc_rnd_t @var{rnd})
+@deftypefun int mpc_mul_2exp (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
Set @var{rop} to @var{op1} times 2 raised to @var{op2}
-rounded according to @var{rnd}. Just modifies the exponents
+rounded according to @var{rnd}. Just increases the exponents
of the real and imaginary parts by @var{op2}
when @var{rop} and @var{op1} are identical.
@end deftypefun
-@deftypefun int mpc_div_2ui (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_div_2ui (mpc_t @var{rop}, mpc_t @var{op1}, long int @var{op2}, mpc_rnd_t @var{rnd})
+@deftypefun int mpc_div_2exp (mpc_t @var{rop}, mpc_t @var{op1}, unsigned long int @var{op2}, mpc_rnd_t @var{rnd})
Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}
-rounded according to @var{rnd}. Just modifies the exponents
+rounded according to @var{rnd}. Just decreases the exponents
of the real and imaginary parts by @var{op2}
when @var{rop} and @var{op1} are identical.
@end deftypefun
-@node Power Functions and Logarithm
+@node Power Functions and Logarithm, Trigonometric Functions, Basic Arithmetic, Complex Functions
+@comment node-name, next, previous, up
@section Power Functions and Logarithm
@cindex Power functions
@cindex Logarithm
@deftypefun int mpc_sqrt (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
Set @var{rop} to the square root of @var{op} rounded according to @var{rnd}.
-The returned value @var{rop} has a non-negative real part, and if its real
-part is zero, a non-negative imaginary part.
@end deftypefun
@deftypefun int mpc_pow (mpc_t @var{rop}, mpc_t @var{op1}, mpc_t @var{op2}, mpc_rnd_t @var{rnd})
For @code{mpc_pow_d}, @code{mpc_pow_ld}, @code{mpc_pow_si}, @code{mpc_pow_ui},
@code{mpc_pow_z} and @code{mpc_pow_fr},
the imaginary part of @var{op2} is considered as +0.
-When both @var{op1} and @var{op2} are zero, the result has real part 1,
-and imaginary part 0, with sign being the opposite of that of @var{op2}.
@end deftypefun
@deftypefun int mpc_exp (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
@end deftypefun
@deftypefun int mpc_log (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
-@deftypefunx int mpc_log10 (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
-Set @var{rop} to the natural and base-10 logarithm of @var{op} respectively,
+Set @var{rop} to the logarithm of @var{op},
rounded according to @var{rnd} with the precision of @var{rop}.
The principal branch is chosen, with the branch cut on the negative real axis,
so that the imaginary part of the result lies in
-@math{]-\pi , \pi]} and @math{]-\pi/log(10) , \pi/log(10)]} respectively.
+@math{]-\pi , \pi]}.
@end deftypefun
-@node Trigonometric Functions
+@node Trigonometric Functions, Miscellaneous Complex Functions, Power Functions and Logarithm, Complex Functions
+@comment node-name, next, previous, up
@section Trigonometric Functions
@cindex Trigonometric functions
rounded according to @var{rnd} with the precision of @var{rop}.
@end deftypefun
-@deftypefun int mpc_sin_cos (mpc_t @var{rop_sin}, mpc_t @var{rop_cos}, mpc_t @var{op}, mpc_rnd_t @var{rnd_sin}, mpc_rnd_t @var{rnd_cos})
-Set @var{rop_sin} to the sine of @var{op},
-rounded according to @var{rnd_sin} with the precision of @var{rop_sin},
-and @var{rop_cos} to the cosine of @var{op},
-rounded according to @var{rnd_cos} with the precision of @var{rop_cos}.
-@end deftypefun
-
@deftypefun int mpc_tan (mpc_t @var{rop}, mpc_t @var{op}, mpc_rnd_t @var{rnd})
Set @var{rop} to the tangent of @var{op},
rounded according to @var{rnd} with the precision of @var{rop}.
The branch cut of @var{mpc_acosh} is @math{(-\infty, 1)}.
@end deftypefun
-@node Miscellaneous Complex Functions
+@node Miscellaneous Complex Functions, Advanced Functions, Trigonometric Functions, Complex Functions
+@comment node-name, next, previous, up
@section Miscellaneous Functions
@cindex Miscellaneous complex functions
@end deftypefun
@deftypefun {const char *} mpc_get_version (void)
-Return the GNU MPC version, as a null-terminated string.
+Return the MPC version, as a null-terminated string.
@end deftypefun
@defmac MPC_VERSION
@defmacx MPC_VERSION_MINOR
@defmacx MPC_VERSION_PATCHLEVEL
@defmacx MPC_VERSION_STRING
-@code{MPC_VERSION} is the version of GNU MPC as a preprocessing constant.
+@code{MPC_VERSION} is the version of MPC as a preprocessing constant.
@code{MPC_VERSION_MAJOR}, @code{MPC_VERSION_MINOR} and
@code{MPC_VERSION_PATCHLEVEL} are respectively the major, minor and
-patch level of GNU MPC version, as preprocessing constants.
+patch level of MPC version, as preprocessing constants.
@code{MPC_VERSION_STRING} is the version as a string constant, which
can be compared to the result of @code{mpc_get_version} to check at
run time the header file and library used match:
fprintf (stderr, "Warning: header and library do not match\n");
@end example
Note: Obtaining different strings is not necessarily an error, as in
-general, a program compiled with some old GNU MPC version can be
-dynamically linked with a newer GNU MPC library version (if allowed by the
+general, a program compiled with some old MPC version can be
+dynamically linked with a newer MPC library version (if allowed by the
library versioning system).
@end defmac
@deftypefn Macro long MPC_VERSION_NUM (@var{major}, @var{minor}, @var{patchlevel})
Create an integer in the same format as used by @code{MPC_VERSION} from the
given @var{major}, @var{minor} and @var{patchlevel}.
-Here is an example of how to check the GNU MPC version at compile time:
+Here is an example of how to check the MPC version at compile time:
@example
#if (!defined(MPC_VERSION) || (MPC_VERSION<MPC_VERSION_NUM(2,1,0)))
-# error "Wrong GNU MPC version."
+# error "Wrong MPC version."
#endif
@end example
@end deftypefn
-@node Advanced Functions
+@node Advanced Functions, Internals, Miscellaneous Complex Functions, Complex Functions
+@comment node-name, next, previous, up
@section Advanced Functions
@defmac MPC_SET_X_Y (@var{real_suffix}, @var{imag_suffix}, @var{rop}, @var{real}, @var{imag}, @var{rnd})
@end defmac
-@node Internals
+@node Internals, , Advanced Functions, Complex Functions
+@comment node-name, next, previous, up
@section Internals
These macros and
-functions are mainly designed for the implementation of GNU MPC,
+functions are mainly designed for the implementation of MPC,
but may be useful for users too.
However, no upward compatibility is guaranteed.
You need to include @code{mpc-impl.h} to use them.
of the real and imaginary parts of a complex number.
-@node References
+@node Contributors, References, Complex Functions, Top
+@comment node-name, next, previous, up
+@unnumbered Contributors
+
+The main developers of the MPC library are Andreas Enge,
+Philippe Th@'eveny and Paul Zimmermann.
+Patrick P@'elissier has helped cleaning up the code.
+Marc Helbling contributed the @code{mpc_ui_sub} and
+@code{mpc_ui_ui_sub} functions.
+
+@node References, Concept Index, Contributors, Top
+@comment node-name, next, previous, up
@unnumbered References
@itemize @bullet
@item
Guillaume Hanrot, Vincent Lef@`evre, Patrick P@'elissier, Paul Zimmermann et al.
-@code{mpfr} -- A library for multiple-precision floating-point computations with exact rounding.
+@code{mpfr} -- A library for multiple-precision floating-point computations with exact rounding.
Version 2.4.1, @url{http://www.mpfr.org}.
@item
@end itemize
-@node Concept Index
+@node Concept Index, Function Index, References, Top
+@comment node-name, next, previous, up
@unnumbered Concept Index
@printindex cp
-@node Function Index
-@unnumbered Function Index
+@node Function Index, , Concept Index, Top
+@comment node-name, next, previous, up
+@unnumbered Function and Type Index
@printindex fn
-@node GNU Free Documentation License
-@appendix GNU Free Documentation License
-@include fdl-1.3.texi
-
@ifnothtml
@contents
@end ifnothtml
-
@bye
projects / platform / upstream / mpc.git / blobdiff