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This is ../mpfr.info, produced by makeinfo version 4.12 from
../mpfr.texi.
This manual documents how to install and use the Multiple Precision
Floating-Point Reliable Library, version 2.4.1.
Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,
2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software
Foundation, Inc.
Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License, Version
1.2 or any later version published by the Free Software Foundation;
with no Invariant Sections, with no Front-Cover Texts, and with no
Back-Cover Texts. A copy of the license is included in *note GNU Free
Documentation License::.
INFO-DIR-SECTION Software libraries
START-INFO-DIR-ENTRY
* mpfr: (mpfr). Multiple Precision Floating-Point Reliable Library.
END-INFO-DIR-ENTRY

File: mpfr.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir)
GNU MPFR
********
This manual documents how to install and use the Multiple Precision
Floating-Point Reliable Library, version 2.4.1.
Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,
2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software
Foundation, Inc.
Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License, Version
1.2 or any later version published by the Free Software Foundation;
with no Invariant Sections, with no Front-Cover Texts, and with no
Back-Cover Texts. A copy of the license is included in *note GNU Free
Documentation License::.
* Menu:
* Copying:: MPFR Copying Conditions (LGPL).
* Introduction to MPFR:: Brief introduction to GNU MPFR.
* Installing MPFR:: How to configure and compile the MPFR library.
* Reporting Bugs:: How to usefully report bugs.
* MPFR Basics:: What every MPFR user should now.
* MPFR Interface:: MPFR functions and macros.
* Contributors::
* References::
* GNU Free Documentation License::
* Concept Index::
* Function Index::

File: mpfr.info, Node: Copying, Next: Introduction to MPFR, Prev: Top, Up: Top
MPFR Copying Conditions
***********************
This library is "free"; this means that everyone is free to use it and
free to redistribute it on a free basis. The library is not in the
public domain; it is copyrighted and there are restrictions on its
distribution, but these restrictions are designed to permit everything
that a good cooperating citizen would want to do. What is not allowed
is to try to prevent others from further sharing any version of this
library that they might get from you.
Specifically, we want to make sure that you have the right to give
away copies of the library, that you receive source code or else can
get it if you want it, that you can change this library or use pieces
of it in new free programs, and that you know you can do these things.
To make sure that everyone has such rights, we have to forbid you to
deprive anyone else of these rights. For example, if you distribute
copies of the GNU MPFR library, you must give the recipients all the
rights that you have. You must make sure that they, too, receive or
can get the source code. And you must tell them their rights.
Also, for our own protection, we must make certain that everyone
finds out that there is no warranty for the GNU MPFR library. If it is
modified by someone else and passed on, we want their recipients to
know that what they have is not what we distributed, so that any
problems introduced by others will not reflect on our reputation.
The precise conditions of the license for the GNU MPFR library are
found in the Lesser General Public License that accompanies the source
code. See the file COPYING.LIB.

File: mpfr.info, Node: Introduction to MPFR, Next: Installing MPFR, Prev: Copying, Up: Top
1 Introduction to MPFR
**********************
MPFR is a portable library written in C for arbitrary precision
arithmetic on floating-point numbers. It is based on the GNU MP library.
It aims to extend the class of floating-point numbers provided by the
GNU MP library by a precise semantics. The main differences with the
`mpf' class from GNU MP are:
* the MPFR code is portable, i.e. the result of any operation does
not depend (or should not) on the machine word size
`mp_bits_per_limb' (32 or 64 on most machines);
* the precision in bits can be set exactly to any valid value for
each variable (including very small precision);
* MPFR provides the four rounding modes from the IEEE 754-1985
standard.
In particular, with a precision of 53 bits, MPFR should be able to
exactly reproduce all computations with double-precision machine
floating-point numbers (e.g., `double' type in C, with a C
implementation that rigorously follows Annex F of the ISO C99 standard
and `FP_CONTRACT' pragma set to `OFF') on the four arithmetic
operations and the square root, except the default exponent range is
much wider and subnormal numbers are not implemented (but can be
emulated).
This version of MPFR is released under the GNU Lesser General Public
License, Version 2.1 or any later version. It is permitted to link
MPFR to most non-free programs, as long as when distributing them the
MPFR source code and a means to re-link with a modified MPFR library is
provided.
1.1 How to Use This Manual
==========================
Everyone should read *note MPFR Basics::. If you need to install the
library yourself, you need to read *note Installing MPFR::, too.
The rest of the manual can be used for later reference, although it
is probably a good idea to glance through it.

File: mpfr.info, Node: Installing MPFR, Next: Reporting Bugs, Prev: Introduction to MPFR, Up: Top
2 Installing MPFR
*****************
2.1 How to Install
==================
Here are the steps needed to install the library on Unix systems (more
details are provided in the `INSTALL' file):
1. To build MPFR, you first have to install GNU MP (version 4.1 or
higher) on your computer. You need a C compiler, preferably GCC,
but any reasonable compiler should work. And you need a standard
Unix `make' program, plus some other standard Unix utility
programs.
2. In the MPFR build directory, type `./configure'
This will prepare the build and setup the options according to
your system. If you get error messages, you might check that you
use the same compiler and compile options as for GNU MP (see the
`INSTALL' file).
3. `make'
This will compile MPFR, and create a library archive file
`libmpfr.a'. A dynamic library may be produced too (see
configure).
4. `make check'
This will make sure MPFR was built correctly. If you get error
messages, please report this to `mpfr@loria.fr'. (*Note Reporting
Bugs::, for information on what to include in useful bug reports.)
5. `make install'
This will copy the files `mpfr.h' and `mpf2mpfr.h' to the directory
`/usr/local/include', the file `libmpfr.a' to the directory
`/usr/local/lib', and the file `mpfr.info' to the directory
`/usr/local/share/info' (or if you passed the `--prefix' option to
`configure', using the prefix directory given as argument to
`--prefix' instead of `/usr/local').
2.2 Other `make' Targets
========================
There are some other useful make targets:
* `mpfr.info' or `info'
Create an info version of the manual, in `mpfr.info'.
* `mpfr.pdf' or `pdf'
Create a PDF version of the manual, in `mpfr.pdf'.
* `mpfr.dvi' or `dvi'
Create a DVI version of the manual, in `mpfr.dvi'.
* `mpfr.ps' or `ps'
Create a Postscript version of the manual, in `mpfr.ps'.
* `mpfr.html' or `html'
Create a HTML version of the manual, in several pages in the
directory `mpfr.html'; if you want only one output HTML file, then
type `makeinfo --html --no-split mpfr.texi' instead.
* `clean'
Delete all object files and archive files, but not the
configuration files.
* `distclean'
Delete all files not included in the distribution.
* `uninstall'
Delete all files copied by `make install'.
2.3 Build Problems
==================
In case of problem, please read the `INSTALL' file carefully before
reporting a bug, in particular section "In case of problem". Some
problems are due to bad configuration on the user side (not specific to
MPFR). Problems are also mentioned in the FAQ
`http://www.mpfr.org/faq.html'.
Please report problems to `mpfr@loria.fr'. *Note Reporting Bugs::.
Some bug fixes are available on the MPFR 2.4.1 web page
`http://www.mpfr.org/mpfr-2.4.1/'.
2.4 Getting the Latest Version of MPFR
======================================
The latest version of MPFR is available from
`ftp://ftp.gnu.org/gnu/mpfr/' or `http://www.mpfr.org/'.

File: mpfr.info, Node: Reporting Bugs, Next: MPFR Basics, Prev: Installing MPFR, Up: Top
3 Reporting Bugs
****************
If you think you have found a bug in the MPFR library, first have a look
on the MPFR 2.4.1 web page `http://www.mpfr.org/mpfr-2.4.1/' and the
FAQ `http://www.mpfr.org/faq.html': perhaps this bug is already known,
in which case you may find there a workaround for it. Otherwise, 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.
There are a few things you should think about when you put your bug
report together.
You have to send us a test case that makes it possible for us to
reproduce the bug. Include instructions on how to run the test case.
You also have to explain what is wrong; if you get a crash, or if
the results printed are incorrect and in that case, in what way.
Please include compiler version information in your bug report. This
can be extracted using `cc -V' on some machines, or, if you're using
gcc, `gcc -v'. Also, include the output from `uname -a' and the MPFR
version (the GMP version may be useful too).
If your bug report is good, we will do our best to help you to get a
corrected version of the library; if the bug report is poor, we will
not do anything about it (aside of chiding you to send better bug
reports).
Send your bug report to: `mpfr@loria.fr'.
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.

File: mpfr.info, Node: MPFR Basics, Next: MPFR Interface, Prev: Reporting Bugs, Up: Top
4 MPFR Basics
*************
4.1 Headers and Libraries
=========================
All declarations needed to use MPFR are collected in the include file
`mpfr.h'. It is designed to work with both C and C++ compilers. You
should include that file in any program using the MPFR library:
#include <mpfr.h>
Note however that prototypes for MPFR functions with `FILE *'
parameters are provided only if `<stdio.h>' is included too (before
`mpfr.h').
#include <stdio.h>
#include <mpfr.h>
Likewise `<stdarg.h>' (or `<varargs.h>') is required for prototypes
with `va_list' parameters, such as `mpfr_vprintf'.
You can avoid the use of MPFR macros encapsulating functions by
defining the `MPFR_USE_NO_MACRO' macro before `mpfr.h' is included. In
general this should not be necessary, but this can be useful when
debugging user code: with some macros, the compiler may emit spurious
warnings with some warning options, and macros can prevent some
prototype checking.
All programs using MPFR must link against both `libmpfr' and
`libgmp' libraries. On a typical Unix-like system this can be done
with `-lmpfr -lgmp' (in that order), for example
gcc myprogram.c -lmpfr -lgmp
MPFR is built using Libtool and an application can use that to link
if desired, *note GNU Libtool: (libtool.info)Top.
If MPFR has been installed to a non-standard location, then it may be
necessary to set up environment variables such as `C_INCLUDE_PATH' and
`LIBRARY_PATH', or use `-I' and `-L' compiler options, in order to
point to the right directories. For a shared library, it may also be
necessary to set up some sort of run-time library path (e.g.,
`LD_LIBRARY_PATH') on some systems. Please read the `INSTALL' file for
additional information.
4.2 Nomenclature and Types
==========================
A "floating-point number" or "float" for short, is an arbitrary
precision significand (also called mantissa) with a limited precision
exponent. The C data type for such objects is `mpfr_t' (internally
defined as a one-element array of a structure, and `mpfr_ptr' is the C
data type representing a pointer to this structure). A floating-point
number can have three special values: Not-a-Number (NaN) or plus or
minus Infinity. NaN represents an uninitialized object, the result of
an invalid operation (like 0 divided by 0), or a value that cannot be
determined (like +Infinity minus +Infinity). Moreover, like in the IEEE
754-1985 standard, zero is signed, i.e. there are both +0 and -0; the
behavior is the same as in the IEEE 754-1985 standard and it is
generalized to the other functions supported by MPFR.
The "precision" is the number of bits used to represent the significand
of a floating-point number; the corresponding C data type is
`mp_prec_t'. The precision can be any integer between `MPFR_PREC_MIN'
and `MPFR_PREC_MAX'. In the current implementation, `MPFR_PREC_MIN' is
equal to 2.
Warning! MPFR needs to increase the precision internally, in order to
provide accurate results (and in particular, correct rounding). Do not
attempt to set the precision to any value near `MPFR_PREC_MAX',
otherwise MPFR will abort due to an assertion failure. Moreover, you
may reach some memory limit on your platform, in which case the program
may abort, crash or have undefined behavior (depending on your C
implementation).
The "rounding mode" specifies the way to round the result of a
floating-point operation, in case the exact result can not be
represented exactly in the destination significand; the corresponding C
data type is `mp_rnd_t'.
A "limb" means the part of a multi-precision number that fits in a
single word. (We chose this word because a limb of the human body is
analogous to a digit, only larger, and containing several digits.)
Normally a limb contains 32 or 64 bits. The C data type for a limb is
`mp_limb_t'.
4.3 Function Classes
====================
There is only one class of functions in the MPFR library:
1. Functions for floating-point arithmetic, with names beginning with
`mpfr_'. The associated type is `mpfr_t'.
4.4 MPFR Variable Conventions
=============================
As a general rule, all MPFR functions expect output arguments before
input arguments. This notation is based on an analogy with the
assignment operator.
MPFR 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, `mpfr_mul', can be used like this:
`mpfr_mul (x, x, x, rnd_mode)'. This computes the square of X with
rounding mode `rnd_mode' and puts the result back in X.
Before you can assign to an MPFR variable, you need to initialize it
by calling one of the special initialization functions. When you're
done with a variable, you need to clear it out, using one of the
functions for that purpose.
A variable should only be initialized once, or at least cleared out
between each initialization. After a variable has been initialized, it
may be assigned to any number of times.
For efficiency reasons, avoid to initialize and clear out a variable
in loops. 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 MPFR variables, since any variable has a significand of fixed size.
Hence unless you change its precision, or clear and reinitialize it, a
floating-point variable will have the same allocated space during all
its life.
4.5 Rounding Modes
==================
The following four rounding modes are supported:
* `GMP_RNDN': round to nearest
* `GMP_RNDZ': round toward zero
* `GMP_RNDU': round toward plus infinity
* `GMP_RNDD': round toward minus infinity
The `round to nearest' mode works as in the IEEE 754-1985 standard:
in case the number to be rounded lies exactly in the middle of two
representable numbers, it is rounded to the one with the least
significant bit set to zero. For example, the number 5/2, which is
represented by (10.1) in binary, is rounded to (10.0)=2 with a
precision of two bits, and not to (11.0)=3. This rule avoids the
"drift" phenomenon mentioned by Knuth in volume 2 of The Art of
Computer Programming (Section 4.2.2).
Most MPFR functions take as first argument the destination variable,
as second and following arguments the input variables, as last argument
a rounding mode, and have a return value of type `int', called the
"ternary value". The value stored in the destination variable is
correctly rounded, i.e. MPFR behaves as if it computed the result with
an infinite precision, then rounded it to the precision of this
variable. The input variables are regarded as exact (in particular,
their precision does not affect the result).
As a consequence, in case of a non-zero real rounded result, the
error on the result is less or equal to 1/2 ulp (unit in the last
place) of the target in the rounding to nearest mode, and less than 1
ulp of the target in the directed rounding modes (a ulp is the weight
of the least significant represented bit of the target after rounding).
Unless documented otherwise, functions returning an `int' return a
ternary value. If the ternary value is zero, it means that the value
stored in the destination variable is the exact result of the
corresponding mathematical function. If the ternary value is positive
(resp. negative), it means the value stored in the destination variable
is greater (resp. lower) than the exact result. For example with the
`GMP_RNDU' rounding mode, the ternary value is usually positive, except
when the result is exact, in which case it is zero. In the case of an
infinite result, it is considered as inexact when it was obtained by
overflow, and exact otherwise. A NaN result (Not-a-Number) always
corresponds to an exact return value. The opposite of a returned
ternary value is guaranteed to be representable in an `int'.
Unless documented otherwise, functions returning a `1' (or any other
value specified in this manual) for special cases (like `acos(0)')
should return an overflow or an underflow if `1' is not representable
in the current exponent range.
4.6 Floating-Point Values on Special Numbers
============================================
This section specifies the floating-point values (of type `mpfr_t')
returned by MPFR functions. For functions returning several values (like
`mpfr_sin_cos'), the rules apply to each result separately.
Functions can have one or several input arguments. An input point is
a mapping from these input arguments to the set of the MPFR numbers.
When none of its components are NaN, an input point can also be seen as
a tuple in the extended real numbers (the set of the real numbers with
both infinities).
When the input point is in the domain of the mathematical function,
the result is rounded as described in Section "Rounding Modes" (but see
below for the specification of the sign of an exact zero). Otherwise
the general rules from this section apply unless stated otherwise in
the description of the MPFR function (*note MPFR Interface::).
When the input point is not in the domain of the mathematical
function but is in its closure in the extended real numbers and the
function can be extended by continuity, the result is the obtained
limit. Examples: `mpfr_hypot' on (+Inf,0) gives +Inf. But `mpfr_pow'
cannot be defined on (1,+Inf) using this rule, as one can find
sequences (X_N,Y_N) such that X_N goes to 1, Y_N goes to +Inf and X_N
to the Y_N goes to any positive value when N goes to the infinity.
When the input point is in the closure of the domain of the
mathematical function and an input argument is +0 (resp. -0), one
considers the limit when the corresponding argument approaches 0 from
above (resp. below). If the limit is not defined (e.g., `mpfr_log' on
-0), the behavior must be specified in the description of the MPFR
function.
When the result is equal to 0, its sign is determined by considering
the limit as if the input point were not in the domain: If one
approaches 0 from above (resp. below), the result is +0 (resp. -0). In
the other cases, the sign must be specified in the description of the
MPFR function. Example: `mpfr_sin' on +0 gives +0.
When the input point is not in the closure of the domain of the
function, the result is NaN. Example: `mpfr_sqrt' on -17 gives NaN.
When an input argument is NaN, the result is NaN, possibly except
when a partial function is constant on the finite floating-point
numbers; such a case is always explicitly specified in *note MPFR
Interface::. Example: `mpfr_hypot' on (NaN,0) gives NaN, but
`mpfr_hypot' on (NaN,+Inf) gives +Inf (as specified in *note Special
Functions::), since for any finite input X, `mpfr_hypot' on (X,+Inf)
gives +Inf.
4.7 Exceptions
==============
MPFR supports 5 exception types:
* Underflow: An underflow occurs when the exact result of a function
is a non-zero real number and the result obtained after the
rounding, assuming an unbounded exponent range (for the rounding),
has an exponent smaller than the minimum exponent of the current
range. In the round-to-nearest mode, the halfway case is rounded
toward zero.
Note: This is not the single definition of the underflow. MPFR
chooses to consider the underflow after rounding. The underflow
before rounding can also be defined. For instance, consider a
function that has the exact result 7 multiplied by two to the power
E-4, where E is the smallest exponent (for a significand between
1/2 and 1) in the current range, with a 2-bit target precision and
rounding toward plus infinity. The exact result has the exponent
E-1. With the underflow before rounding, such a function call
would yield an underflow, as E-1 is outside the current exponent
range. However, MPFR first considers the rounded result assuming
an unbounded exponent range. The exact result cannot be
represented exactly in precision 2, and here, it is rounded to 0.5
times 2 to E, which is representable in the current exponent
range. As a consequence, this will not yield an underflow in MPFR.
* Overflow: An overflow occurs when the exact result of a function
is a non-zero real number and the result obtained after the
rounding, assuming an unbounded exponent range (for the rounding),
has an exponent larger than the maximum exponent of the current
range. In the round-to-nearest mode, the result is infinite.
* NaN: A NaN exception occurs when the result of a function is a NaN.
* Inexact: An inexact exception occurs when the result of a function
cannot be represented exactly and must be rounded.
* Range error: A range exception occurs when a function that does
not return a MPFR number (such as comparisons and conversions to
an integer) has an invalid result (e.g. an argument is NaN in
`mpfr_cmp' or in a conversion to an integer).
MPFR has a global flag for each exception, which can be cleared, set
or tested by functions described in *note Exception Related Functions::.
Differences with the ISO C99 standard:
* In C, only quiet NaNs are specified, and a NaN propagation does not
raise an invalid exception. Unless explicitly stated otherwise,
MPFR sets the NaN flag whenever a NaN is generated, even when a
NaN is propagated (e.g. in NaN + NaN), as if all NaNs were
signaling.
* An invalid exception in C corresponds to either a NaN exception or
a range error in MPFR.
4.8 Memory Handling
===================
MPFR functions may create caches, e.g. when computing constants such as
Pi, either because the user has called a function like `mpfr_const_pi'
directly or because such a function was called internally by the MPFR
library itself to compute some other function.
At any time, the user can free the various caches with
`mpfr_free_cache'. It is strongly advised to do that before terminating
a thread, or before exiting when using tools like `valgrind' (to avoid
memory leaks being reported).
MPFR internal data such as flags, the exponent range, the default
precision and rounding mode, and caches (i.e., data that are not
accessed via parameters) are either global (if MPFR has not been
compiled as thread safe) or per-thread (thread local storage).

File: mpfr.info, Node: MPFR Interface, Next: Contributors, Prev: MPFR Basics, Up: Top
5 MPFR Interface
****************
The floating-point functions expect arguments of type `mpfr_t'.
The MPFR floating-point functions have an interface that is similar
to the GNU MP integer functions. The function prefix for
floating-point operations is `mpfr_'.
There is one significant characteristic of floating-point numbers
that has motivated a difference between this function class and other
GNU MP function classes: the inherent inexactness of floating-point
arithmetic. The user has to specify the precision for each variable.
A computation that assigns a variable will take place with the
precision of the assigned variable; the cost of that computation should
not depend from the precision of variables used as input (on average).
The semantics of a calculation in MPFR is specified as follows:
Compute the requested operation exactly (with "infinite accuracy"), and
round the result to the precision of the destination variable, with the
given rounding mode. The MPFR floating-point functions are intended to
be a smooth extension of the IEEE 754-1985 arithmetic. The results
obtained on one computer should not differ from the results obtained on
a computer with a different word size.
MPFR does not keep track of the accuracy of a computation. This is
left to the user or to a higher layer. As a consequence, if two
variables are used to store only a few significant bits, and their
product is stored in a variable with large precision, then MPFR will
still compute the result with full precision.
The value of the standard C macro `errno' may be set to non-zero by
any MPFR function or macro, whether or not there is an error.
* Menu:
* Initialization Functions::
* Assignment Functions::
* Combined Initialization and Assignment Functions::
* Conversion Functions::
* Basic Arithmetic Functions::
* Comparison Functions::
* Special Functions::
* Input and Output Functions::
* Formatted Output Functions::
* Integer Related Functions::
* Rounding Related Functions::
* Miscellaneous Functions::
* Exception Related Functions::
* Compatibility with MPF::
* Custom Interface::
* Internals::

File: mpfr.info, Node: Initialization Functions, Next: Assignment Functions, Prev: MPFR Interface, Up: MPFR Interface
5.1 Initialization Functions
============================
An `mpfr_t' object must be initialized before storing the first value in
it. The functions `mpfr_init' and `mpfr_init2' are used for that
purpose.
-- Function: void mpfr_init2 (mpfr_t X, mp_prec_t PREC)
Initialize X, set its precision to be *exactly* PREC bits and its
value to NaN. (Warning: the corresponding `mpf' functions
initialize to zero instead.)
Normally, a variable should be initialized once only or at least
be cleared, using `mpfr_clear', between initializations. To
change the precision of a variable which has already been
initialized, use `mpfr_set_prec'. The precision PREC must be an
integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX' (otherwise the
behavior is undefined).
-- Function: void mpfr_inits2 (mp_prec_t PREC, mpfr_t X, ...)
Initialize all the `mpfr_t' variables of the given `va_list', set
their precision to be *exactly* PREC bits and their value to NaN.
See `mpfr_init2' for more details. The `va_list' is assumed to be
composed only of type `mpfr_t' (or equivalently `mpfr_ptr'). It
begins from X. It ends when it encounters a null pointer (whose
type must also be `mpfr_ptr').
-- Function: void mpfr_clear (mpfr_t X)
Free the space occupied by X. Make sure to call this function for
all `mpfr_t' variables when you are done with them.
-- Function: void mpfr_clears (mpfr_t X, ...)
Free the space occupied by all the `mpfr_t' variables of the given
`va_list'. See `mpfr_clear' for more details. The `va_list' is
assumed to be composed only of type `mpfr_t' (or equivalently
`mpfr_ptr'). It begins from X. It ends when it encounters a null
pointer (whose type must also be `mpfr_ptr').
Here is an example of how to use multiple initialization functions:
{
mpfr_t x, y, z, t;
mpfr_inits2 (256, x, y, z, t, (mpfr_ptr) 0);
...
mpfr_clears (x, y, z, t, (mpfr_ptr) 0);
}
-- Function: void mpfr_init (mpfr_t X)
Initialize X and set its value to NaN.
Normally, a variable should be initialized once only or at least
be cleared, using `mpfr_clear', between initializations. The
precision of X is the default precision, which can be changed by a
call to `mpfr_set_default_prec'.
Warning! In a given program, some other libraries might change the
default precision and not restore it. Thus it is safer to use
`mpfr_init2'.
-- Function: void mpfr_inits (mpfr_t X, ...)
Initialize all the `mpfr_t' variables of the given `va_list', set
their precision to be the default precision and their value to NaN.
See `mpfr_init' for more details. The `va_list' is assumed to be
composed only of type `mpfr_t' (or equivalently `mpfr_ptr'). It
begins from X. It ends when it encounters a null pointer (whose
type must also be `mpfr_ptr').
Warning! In a given program, some other libraries might change the
default precision and not restore it. Thus it is safer to use
`mpfr_inits2'.
-- Macro: MPFR_DECL_INIT (NAME, PREC)
This macro declares NAME as an automatic variable of type `mpfr_t',
initializes it and sets its precision to be *exactly* PREC bits
and its value to NaN. NAME must be a valid identifier. You must
use this macro in the declaration section. This macro is much
faster than using `mpfr_init2' but has some drawbacks:
* You *must not* call `mpfr_clear' with variables created with
this macro (the storage is allocated at the point of
declaration and deallocated when the brace-level is exited).
* You *cannot* change their precision.
* You *should not* create variables with huge precision with
this macro.
* Your compiler must support `Non-Constant Initializers'
(standard in C++ and ISO C99) and `Token Pasting' (standard
in ISO C89). If PREC is not a constant expression, your
compiler must support `variable-length automatic arrays'
(standard in ISO C99). `GCC 2.95.3' and above supports all
these features. If you compile your program with gcc in c89
mode and with `-pedantic', you may want to define the
`MPFR_USE_EXTENSION' macro to avoid warnings due to the
`MPFR_DECL_INIT' implementation.
-- Function: void mpfr_set_default_prec (mp_prec_t PREC)
Set the default precision to be *exactly* PREC bits. The
precision of a variable means the number of bits used to store its
significand. All subsequent calls to `mpfr_init' will use this
precision, but previously initialized variables are unaffected.
This default precision is set to 53 bits initially. The precision
can be any integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX'.
-- Function: mp_prec_t mpfr_get_default_prec (void)
Return the default MPFR precision in bits.
Here is an example on how to initialize floating-point variables:
{
mpfr_t x, y;
mpfr_init (x); /* use default precision */
mpfr_init2 (y, 256); /* precision _exactly_ 256 bits */
...
/* When the program is about to exit, do ... */
mpfr_clear (x);
mpfr_clear (y);
mpfr_free_cache ();
}
The following functions are useful for changing the precision during
a calculation. A typical use would be for adjusting the precision
gradually in iterative algorithms like Newton-Raphson, making the
computation precision closely match the actual accurate part of the
numbers.
-- Function: void mpfr_set_prec (mpfr_t X, mp_prec_t PREC)
Reset the precision of X to be *exactly* PREC bits, and set its
value to NaN. The previous value stored in X is lost. It is
equivalent to a call to `mpfr_clear(x)' followed by a call to
`mpfr_init2(x, prec)', but more efficient as no allocation is done
in case the current allocated space for the significand of X is
enough. The precision PREC can be any integer between
`MPFR_PREC_MIN' and `MPFR_PREC_MAX'.
In case you want to keep the previous value stored in X, use
`mpfr_prec_round' instead.
-- Function: mp_prec_t mpfr_get_prec (mpfr_t X)
Return the precision actually used for assignments of X, i.e. the
number of bits used to store its significand.

File: mpfr.info, Node: Assignment Functions, Next: Combined Initialization and Assignment Functions, Prev: Initialization Functions, Up: MPFR Interface
5.2 Assignment Functions
========================
These functions assign new values to already initialized floats (*note
Initialization Functions::). When using any functions using `intmax_t',
you must include `<stdint.h>' or `<inttypes.h>' before `mpfr.h', to
allow `mpfr.h' to define prototypes for these functions.
-- Function: int mpfr_set (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_set_ui (mpfr_t ROP, unsigned long int OP,
mp_rnd_t RND)
-- Function: int mpfr_set_si (mpfr_t ROP, long int OP, mp_rnd_t RND)
-- Function: int mpfr_set_uj (mpfr_t ROP, uintmax_t OP, mp_rnd_t RND)
-- Function: int mpfr_set_sj (mpfr_t ROP, intmax_t OP, mp_rnd_t RND)
-- Function: int mpfr_set_d (mpfr_t ROP, double OP, mp_rnd_t RND)
-- Function: int mpfr_set_ld (mpfr_t ROP, long double OP, mp_rnd_t RND)
-- Function: int mpfr_set_decimal64 (mpfr_t ROP, _Decimal64 OP,
mp_rnd_t RND)
-- Function: int mpfr_set_z (mpfr_t ROP, mpz_t OP, mp_rnd_t RND)
-- Function: int mpfr_set_q (mpfr_t ROP, mpq_t OP, mp_rnd_t RND)
-- Function: int mpfr_set_f (mpfr_t ROP, mpf_t OP, mp_rnd_t RND)
Set the value of ROP from OP, rounded toward the given direction
RND. Note that the input 0 is converted to +0 by `mpfr_set_ui',
`mpfr_set_si', `mpfr_set_sj', `mpfr_set_uj', `mpfr_set_z',
`mpfr_set_q' and `mpfr_set_f', regardless of the rounding mode.
If the system does not support the IEEE-754 standard, `mpfr_set_d',
`mpfr_set_ld' and `mpfr_set_decimal64' might not preserve the
signed zeros. The `mpfr_set_decimal64' function is built only
with the configure option `--enable-decimal-float', which also
requires `--with-gmp-build', and when the compiler or system
provides the `_Decimal64' data type (GCC version 4.2.0 is known to
support this data type, but only when configured with
`--enable-decimal-float' too). `mpfr_set_q' might not be able to
work if the numerator (or the denominator) can not be
representable as a `mpfr_t'.
Note: If you want to store a floating-point constant to a `mpfr_t',
you should use `mpfr_set_str' (or one of the MPFR constant
functions, such as `mpfr_const_pi' for Pi) instead of `mpfr_set_d',
`mpfr_set_ld' or `mpfr_set_decimal64'. Otherwise the
floating-point constant will be first converted into a
reduced-precision (e.g., 53-bit) binary number before MPFR can
work with it.
-- Function: int mpfr_set_ui_2exp (mpfr_t ROP, unsigned long int OP,
mp_exp_t E, mp_rnd_t RND)
-- Function: int mpfr_set_si_2exp (mpfr_t ROP, long int OP, mp_exp_t
E, mp_rnd_t RND)
-- Function: int mpfr_set_uj_2exp (mpfr_t ROP, uintmax_t OP, intmax_t
E, mp_rnd_t RND)
-- Function: int mpfr_set_sj_2exp (mpfr_t ROP, intmax_t OP, intmax_t
E, mp_rnd_t RND)
Set the value of ROP from OP multiplied by two to the power E,
rounded toward the given direction RND. Note that the input 0 is
converted to +0.
-- Function: int mpfr_set_str (mpfr_t ROP, const char *S, int BASE,
mp_rnd_t RND)
Set ROP to the value of the string S in base BASE, rounded in the
direction RND. See the documentation of `mpfr_strtofr' for a
detailed description of the valid string formats. Contrary to
`mpfr_strtofr', `mpfr_set_str' requires the _whole_ string to
represent a valid floating-point number. This function returns 0
if the entire string up to the final null character is a valid
number in base BASE; otherwise it returns -1, and ROP may have
changed.
-- Function: int mpfr_strtofr (mpfr_t ROP, const char *NPTR, char
**ENDPTR, int BASE, mp_rnd_t RND)
Read a floating-point number from a string NPTR in base BASE,
rounded in the direction RND; BASE must be either 0 (to detect the
base, as described below) or a number from 2 to 36 (otherwise the
behavior is undefined). If NPTR starts with valid data, the result
is stored in ROP and `*ENDPTR' points to the character just after
the valid data (if ENDPTR is not a null pointer); otherwise ROP is
set to zero and the value of NPTR is stored in the location
referenced by ENDPTR (if ENDPTR is not a null pointer). The usual
ternary value is returned.
Parsing follows the standard C `strtod' function with some
extensions. Case is ignored. After optional leading whitespace,
one has a subject sequence consisting of an optional sign (`+' or
`-'), and either numeric data or special data. The subject
sequence is defined as the longest initial subsequence of the
input string, starting with the first non-whitespace character,
that is of the expected form.
The form of numeric data is a non-empty sequence of significand
digits with an optional decimal point, and an optional exponent
consisting of an exponent prefix followed by an optional sign and
a non-empty sequence of decimal digits. A significand digit is
either a decimal digit or a Latin letter (62 possible characters),
with `a' = 10, `b' = 11, ..., `z' = 35; its value must be strictly
less than the base. The decimal point can be either the one
defined by the current locale or the period (the first one is
accepted for consistency with the C standard and the practice, the
second one is accepted to allow the programmer to provide MPFR
numbers from strings in a way that does not depend on the current
locale). The exponent prefix can be `e' or `E' for bases up to
10, or `@' in any base; it indicates a multiplication by a power
of the base. In bases 2 and 16, the exponent prefix can also be
`p' or `P', in which case it introduces a binary exponent: it
indicates a multiplication by a power of 2 (there is a difference
only for base 16). The value of an exponent is always written in
base 10. In base 2, the significand can start with `0b' or `0B',
and in base 16, it can start with `0x' or `0X'.
If the argument BASE is 0, then the base is automatically detected
as follows. If the significand starts with `0b' or `0B', base 2 is
assumed. If the significand starts with `0x' or `0X', base 16 is
assumed. Otherwise base 10 is assumed.
Note: The exponent must contain at least a digit. Otherwise the
possible exponent prefix and sign are not part of the number
(which ends with the significand). Similarly, if `0b', `0B', `0x'
or `0X' is not followed by a binary/hexadecimal digit, then the
subject sequence stops at the character `0'.
Special data (for infinities and NaN) can be `@inf@' or
`@nan@(n-char-sequence)', and if BASE <= 16, it can also be
`infinity', `inf', `nan' or `nan(n-char-sequence)', all case
insensitive. A `n-char-sequence' is a non-empty string containing
only digits, Latin letters and the underscore (0, 1, 2, ..., 9, a,
b, ..., z, A, B, ..., Z, _). Note: one has an optional sign for
all data, even NaN.
-- Function: void mpfr_set_inf (mpfr_t X, int SIGN)
-- Function: void mpfr_set_nan (mpfr_t X)
Set the variable X to infinity or NaN (Not-a-Number) respectively.
In `mpfr_set_inf', X is set to plus infinity iff SIGN is
nonnegative.
-- Function: void mpfr_swap (mpfr_t X, mpfr_t Y)
Swap the values X and Y efficiently. Warning: the precisions are
exchanged too; in case the precisions are different, `mpfr_swap'
is thus not equivalent to three `mpfr_set' calls using a third
auxiliary variable.

File: mpfr.info, Node: Combined Initialization and Assignment Functions, Next: Conversion Functions, Prev: Assignment Functions, Up: MPFR Interface
5.3 Combined Initialization and Assignment Functions
====================================================
-- Macro: int mpfr_init_set (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Macro: int mpfr_init_set_ui (mpfr_t ROP, unsigned long int OP,
mp_rnd_t RND)
-- Macro: int mpfr_init_set_si (mpfr_t ROP, signed long int OP,
mp_rnd_t RND)
-- Macro: int mpfr_init_set_d (mpfr_t ROP, double OP, mp_rnd_t RND)
-- Macro: int mpfr_init_set_ld (mpfr_t ROP, long double OP, mp_rnd_t
RND)
-- Macro: int mpfr_init_set_z (mpfr_t ROP, mpz_t OP, mp_rnd_t RND)
-- Macro: int mpfr_init_set_q (mpfr_t ROP, mpq_t OP, mp_rnd_t RND)
-- Macro: int mpfr_init_set_f (mpfr_t ROP, mpf_t OP, mp_rnd_t RND)
Initialize ROP and set its value from OP, rounded in the direction
RND. The precision of ROP will be taken from the active default
precision, as set by `mpfr_set_default_prec'.
-- Function: int mpfr_init_set_str (mpfr_t X, const char *S, int BASE,
mp_rnd_t RND)
Initialize X and set its value from the string S in base BASE,
rounded in the direction RND. See `mpfr_set_str'.

File: mpfr.info, Node: Conversion Functions, Next: Basic Arithmetic Functions, Prev: Combined Initialization and Assignment Functions, Up: MPFR Interface
5.4 Conversion Functions
========================
-- Function: double mpfr_get_d (mpfr_t OP, mp_rnd_t RND)
-- Function: long double mpfr_get_ld (mpfr_t OP, mp_rnd_t RND)
-- Function: _Decimal64 mpfr_get_decimal64 (mpfr_t OP, mp_rnd_t RND)
Convert OP to a `double' (respectively `_Decimal64' or `long
double'), using the rounding mode RND. If OP is NaN, some fixed
NaN (either quiet or signaling) or the result of 0.0/0.0 is
returned. If OP is ±Inf, an infinity of the same sign or the
result of ±1.0/0.0 is returned. If OP is zero, these functions
return a zero, trying to preserve its sign, if possible. The
`mpfr_get_decimal64' function is built only under some conditions:
see the documentation of `mpfr_set_decimal64'.
-- Function: double mpfr_get_d_2exp (long *EXP, mpfr_t OP, mp_rnd_t
RND)
-- Function: long double mpfr_get_ld_2exp (long *EXP, mpfr_t OP,
mp_rnd_t RND)
Return D and set EXP such that 0.5<=abs(D)<1 and D times 2 raised
to EXP equals OP rounded to double (resp. long double) precision,
using the given rounding mode. If OP is zero, then a zero of the
same sign (or an unsigned zero, if the implementation does not
have signed zeros) is returned, and EXP is set to 0. If OP is NaN
or an infinity, then the corresponding double precision (resp.
long-double precision) value is returned, and EXP is undefined.
-- Function: long mpfr_get_si (mpfr_t OP, mp_rnd_t RND)
-- Function: unsigned long mpfr_get_ui (mpfr_t OP, mp_rnd_t RND)
-- Function: intmax_t mpfr_get_sj (mpfr_t OP, mp_rnd_t RND)
-- Function: uintmax_t mpfr_get_uj (mpfr_t OP, mp_rnd_t RND)
Convert OP to a `long', an `unsigned long', an `intmax_t' or an
`uintmax_t' (respectively) after rounding it with respect to RND.
If OP is NaN, the result is undefined. If OP is too big for the
return type, it returns the maximum or the minimum of the
corresponding C type, depending on the direction of the overflow.
The _erange_ flag is set too. See also `mpfr_fits_slong_p',
`mpfr_fits_ulong_p', `mpfr_fits_intmax_p' and
`mpfr_fits_uintmax_p'.
-- Function: mp_exp_t mpfr_get_z_exp (mpz_t ROP, mpfr_t OP)
Put the scaled significand of OP (regarded as an integer, with the
precision of OP) into ROP, and return the exponent EXP (which may
be outside the current exponent range) such that OP exactly equals
ROP multiplied by two exponent EXP. If the exponent is not
representable in the `mp_exp_t' type, the behavior is undefined.
-- Function: void mpfr_get_z (mpz_t ROP, mpfr_t OP, mp_rnd_t RND)
Convert OP to a `mpz_t', after rounding it with respect to RND. If
OP is NaN or Inf, the result is undefined.
-- Function: int mpfr_get_f (mpf_t ROP, mpfr_t OP, mp_rnd_t RND)
Convert OP to a `mpf_t', after rounding it with respect to RND.
Return zero iff no error occurred, in particular a non-zero value
is returned if OP is NaN or Inf, which do not exist in `mpf'.
-- Function: char * mpfr_get_str (char *STR, mp_exp_t *EXPPTR, int B,
size_t N, mpfr_t OP, mp_rnd_t RND)
Convert OP to a string of digits in base B, with rounding in the
direction RND, where N is either zero (see below) or the number of
significant digits; in the latter case, N must be greater or equal
to 2. The base may vary from 2 to 36.
The generated string is a fraction, with an implicit radix point
immediately to the left of the first digit. For example, the
number -3.1416 would be returned as "-31416" in the string and 1
written at EXPPTR. If RND is to nearest, and OP is exactly in the
middle of two possible outputs, the one with an even last digit is
chosen (for an odd base, this may not correspond to an even
significand).
If N is zero, the number of digits of the significand is chosen
large enough so that re-reading the printed value with the same
precision, assuming both output and input use rounding to nearest,
will recover the original value of OP. More precisely, in most
cases, the chosen precision of STR is the minimal precision
depending on N and B only that satisfies the above property, i.e.,
m = 1 + ceil(N*log(2)/log(B)), but in some very rare cases, it
might be m+1.
If STR is a null pointer, space for the significand is allocated
using the current allocation function, and a pointer to the string
is returned. To free the returned string, you must use
`mpfr_free_str'.
If STR is not a null pointer, it should point to a block of storage
large enough for the significand, i.e., at least `max(N + 2, 7)'.
The extra two bytes are for a possible minus sign, and for the
terminating null character.
If the input number is an ordinary number, the exponent is written
through the pointer EXPPTR (the current minimal exponent for 0).
A pointer to the string is returned, unless there is an error, in
which case a null pointer is returned.
-- Function: void mpfr_free_str (char *STR)
Free a string allocated by `mpfr_get_str' using the current
unallocation function (preliminary interface). The block is
assumed to be `strlen(STR)+1' bytes. For more information about
how it is done: *note Custom Allocation: (gmp.info)Custom
Allocation.
-- Function: int mpfr_fits_ulong_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_slong_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_uint_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_sint_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_ushort_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_sshort_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_intmax_p (mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_fits_uintmax_p (mpfr_t OP, mp_rnd_t RND)
Return non-zero if OP would fit in the respective C data type, when
rounded to an integer in the direction RND.

File: mpfr.info, Node: Basic Arithmetic Functions, Next: Comparison Functions, Prev: Conversion Functions, Up: MPFR Interface
5.5 Basic Arithmetic Functions
==============================
-- Function: int mpfr_add (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_add_ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_add_si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
-- Function: int mpfr_add_d (mpfr_t ROP, mpfr_t OP1, double OP2,
mp_rnd_t RND)
-- Function: int mpfr_add_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_add_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2,
mp_rnd_t RND)
Set ROP to OP1 + OP2 rounded in the direction RND. For types
having no signed zero, it is considered unsigned (i.e. (+0) + 0 =
(+0) and (-0) + 0 = (-0)). The `mpfr_add_d' function assumes that
the radix of the `double' type is a power of 2, with a precision
at most that declared by the C implementation (macro
`IEEE_DBL_MANT_DIG', and if not defined 53 bits).
-- Function: int mpfr_sub (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_ui_sub (mpfr_t ROP, unsigned long int OP1,
mpfr_t OP2, mp_rnd_t RND)
-- Function: int mpfr_sub_ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_si_sub (mpfr_t ROP, long int OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_sub_si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
-- Function: int mpfr_d_sub (mpfr_t ROP, double OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_sub_d (mpfr_t ROP, mpfr_t OP1, double OP2,
mp_rnd_t RND)
-- Function: int mpfr_sub_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_sub_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2,
mp_rnd_t RND)
Set ROP to OP1 - OP2 rounded in the direction RND. For types
having no signed zero, it is considered unsigned (i.e. (+0) - 0 =
(+0), (-0) - 0 = (-0), 0 - (+0) = (-0) and 0 - (-0) = (+0)). The
same restrictions than for `mpfr_add_d' apply to `mpfr_d_sub' and
`mpfr_sub_d'.
-- Function: int mpfr_mul (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_mul_ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_mul_si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
-- Function: int mpfr_mul_d (mpfr_t ROP, mpfr_t OP1, double OP2,
mp_rnd_t RND)
-- Function: int mpfr_mul_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_mul_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2,
mp_rnd_t RND)
Set ROP to OP1 times OP2 rounded in the direction RND. When a
result is zero, its sign is the product of the signs of the
operands (for types having no signed zero, it is considered
positive). The same restrictions than for `mpfr_add_d' apply to
`mpfr_mul_d'.
-- Function: int mpfr_sqr (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the square of OP rounded in the direction RND.
-- Function: int mpfr_div (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_ui_div (mpfr_t ROP, unsigned long int OP1,
mpfr_t OP2, mp_rnd_t RND)
-- Function: int mpfr_div_ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_si_div (mpfr_t ROP, long int OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_div_si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
-- Function: int mpfr_d_div (mpfr_t ROP, double OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_div_d (mpfr_t ROP, mpfr_t OP1, double OP2,
mp_rnd_t RND)
-- Function: int mpfr_div_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_div_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2,
mp_rnd_t RND)
Set ROP to OP1/OP2 rounded in the direction RND. When a result is
zero, its sign is the product of the signs of the operands (for
types having no signed zero, it is considered positive). The same
restrictions than for `mpfr_add_d' apply to `mpfr_d_div' and
`mpfr_div_d'.
-- Function: int mpfr_sqrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_sqrt_ui (mpfr_t ROP, unsigned long int OP,
mp_rnd_t RND)
Set ROP to the square root of OP rounded in the direction RND.
Return -0 if OP is -0 (to be consistent with the IEEE 754-1985
standard). Set ROP to NaN if OP is negative.
-- Function: int mpfr_rec_sqrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the reciprocal square root of OP rounded in the
direction RND. Return +Inf if OP is ±0, and +0 if OP is +Inf. Set
ROP to NaN if OP is negative.
-- Function: int mpfr_cbrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_root (mpfr_t ROP, mpfr_t OP, unsigned long int
K, mp_rnd_t RND)
Set ROP to the cubic root (resp. the Kth root) of OP rounded in
the direction RND. An odd (resp. even) root of a negative number
(including -Inf) returns a negative number (resp. NaN). The Kth
root of -0 is defined to be -0, whatever the parity of K.
-- Function: int mpfr_pow (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_pow_ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_pow_si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
-- Function: int mpfr_pow_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2,
mp_rnd_t RND)
-- Function: int mpfr_ui_pow_ui (mpfr_t ROP, unsigned long int OP1,
unsigned long int OP2, mp_rnd_t RND)
-- Function: int mpfr_ui_pow (mpfr_t ROP, unsigned long int OP1,
mpfr_t OP2, mp_rnd_t RND)
Set ROP to OP1 raised to OP2, rounded in the direction RND.
Special values are currently handled as described in the ISO C99
standard for the `pow' function (note this may change in future
versions):
* `pow(±0, Y)' returns plus or minus infinity for Y a negative
odd integer.
* `pow(±0, Y)' returns plus infinity for Y negative and not an
odd integer.
* `pow(±0, Y)' returns plus or minus zero for Y a positive odd
integer.
* `pow(±0, Y)' returns plus zero for Y positive and not an odd
integer.
* `pow(-1, ±Inf)' returns 1.
* `pow(+1, Y)' returns 1 for any Y, even a NaN.
* `pow(X, ±0)' returns 1 for any X, even a NaN.
* `pow(X, Y)' returns NaN for finite negative X and finite
non-integer Y.
* `pow(X, -Inf)' returns plus infinity for 0 < abs(x) < 1, and
plus zero for abs(x) > 1.
* `pow(X, +Inf)' returns plus zero for 0 < abs(x) < 1, and plus
infinity for abs(x) > 1.
* `pow(-Inf, Y)' returns minus zero for Y a negative odd
integer.
* `pow(-Inf, Y)' returns plus zero for Y negative and not an
odd integer.
* `pow(-Inf, Y)' returns minus infinity for Y a positive odd
integer.
* `pow(-Inf, Y)' returns plus infinity for Y positive and not
an odd integer.
* `pow(+Inf, Y)' returns plus zero for Y negative, and plus
infinity for Y positive.
-- Function: int mpfr_neg (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to -OP rounded in the direction RND. Just changes the
sign if ROP and OP are the same variable.
-- Function: int mpfr_abs (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the absolute value of OP, rounded in the direction RND.
Just changes the sign if ROP and OP are the same variable.
-- Function: int mpfr_dim (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Set ROP to the positive difference of OP1 and OP2, i.e., OP1 - OP2
rounded in the direction RND if OP1 > OP2, and +0 otherwise.
Returns NaN when OP1 or OP2 is NaN.
-- Function: int mpfr_mul_2ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_mul_2si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
Set ROP to OP1 times 2 raised to OP2 rounded in the direction RND.
Just increases the exponent by OP2 when ROP and OP1 are identical.
-- Function: int mpfr_div_2ui (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_div_2si (mpfr_t ROP, mpfr_t OP1, long int OP2,
mp_rnd_t RND)
Set ROP to OP1 divided by 2 raised to OP2 rounded in the direction
RND. Just decreases the exponent by OP2 when ROP and OP1 are
identical.

File: mpfr.info, Node: Comparison Functions, Next: Special Functions, Prev: Basic Arithmetic Functions, Up: MPFR Interface
5.6 Comparison Functions
========================
-- Function: int mpfr_cmp (mpfr_t OP1, mpfr_t OP2)
-- Function: int mpfr_cmp_ui (mpfr_t OP1, unsigned long int OP2)
-- Function: int mpfr_cmp_si (mpfr_t OP1, signed long int OP2)
-- Function: int mpfr_cmp_d (mpfr_t OP1, double OP2)
-- Function: int mpfr_cmp_ld (mpfr_t OP1, long double OP2)
-- Function: int mpfr_cmp_z (mpfr_t OP1, mpz_t OP2)
-- Function: int mpfr_cmp_q (mpfr_t OP1, mpq_t OP2)
-- Function: int mpfr_cmp_f (mpfr_t OP1, mpf_t OP2)
Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero
if OP1 = OP2, and a negative value if OP1 < OP2. Both OP1 and OP2
are considered to their full own precision, which may differ. If
one of the operands is NaN, set the _erange_ flag and return zero.
Note: These functions may be useful to distinguish the three
possible cases. If you need to distinguish two cases only, it is
recommended to use the predicate functions (e.g., `mpfr_equal_p'
for the equality) described below; they behave like the IEEE-754
comparisons, in particular when one or both arguments are NaN. But
only floating-point numbers can be compared (you may need to do a
conversion first).
-- Function: int mpfr_cmp_ui_2exp (mpfr_t OP1, unsigned long int OP2,
mp_exp_t E)
-- Function: int mpfr_cmp_si_2exp (mpfr_t OP1, long int OP2, mp_exp_t
E)
Compare OP1 and OP2 multiplied by two to the power E. Similar as
above.
-- Function: int mpfr_cmpabs (mpfr_t OP1, mpfr_t OP2)
Compare |OP1| and |OP2|. Return a positive value if |OP1| >
|OP2|, zero if |OP1| = |OP2|, and a negative value if |OP1| <
|OP2|. If one of the operands is NaN, set the _erange_ flag and
return zero.
-- Function: int mpfr_nan_p (mpfr_t OP)
-- Function: int mpfr_inf_p (mpfr_t OP)
-- Function: int mpfr_number_p (mpfr_t OP)
-- Function: int mpfr_zero_p (mpfr_t OP)
Return non-zero if OP is respectively NaN, an infinity, an ordinary
number (i.e. neither NaN nor an infinity) or zero. Return zero
otherwise.
-- Macro: int mpfr_sgn (mpfr_t OP)
Return a positive value if OP > 0, zero if OP = 0, and a negative
value if OP < 0. If the operand is NaN, set the _erange_ flag and
return zero.
-- Function: int mpfr_greater_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 > OP2, zero otherwise.
-- Function: int mpfr_greaterequal_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 >= OP2, zero otherwise.
-- Function: int mpfr_less_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 < OP2, zero otherwise.
-- Function: int mpfr_lessequal_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 <= OP2, zero otherwise.
-- Function: int mpfr_lessgreater_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 < OP2 or OP1 > OP2 (i.e. neither OP1, nor
OP2 is NaN, and OP1 <> OP2), zero otherwise (i.e. OP1 and/or OP2
are NaN, or OP1 = OP2).
-- Function: int mpfr_equal_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 = OP2, zero otherwise (i.e. OP1 and/or OP2
are NaN, or OP1 <> OP2).
-- Function: int mpfr_unordered_p (mpfr_t OP1, mpfr_t OP2)
Return non-zero if OP1 or OP2 is a NaN (i.e. they cannot be
compared), zero otherwise.

File: mpfr.info, Node: Special Functions, Next: Input and Output Functions, Prev: Comparison Functions, Up: MPFR Interface
5.7 Special Functions
=====================
All those functions, except explicitly stated, return zero for an exact
return value, a positive value for a return value larger than the exact
result, and a negative value otherwise.
Important note: in some domains, computing special functions (either
with correct or incorrect rounding) is expensive, even for small
precision, for example the trigonometric and Bessel functions for large
argument.
-- Function: int mpfr_log (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_log2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_log10 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the natural logarithm of OP, log2(OP) or log10(OP),
respectively, rounded in the direction RND. Return -Inf if OP is
-0 (i.e. the sign of the zero has no influence on the result).
-- Function: int mpfr_exp (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_exp2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_exp10 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the exponential of OP, to 2 power of OP or to 10 power
of OP, respectively, rounded in the direction RND.
-- Function: int mpfr_cos (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_sin (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_tan (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the cosine of OP, sine of OP, tangent of OP, rounded in
the direction RND.
-- Function: int mpfr_sec (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_csc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_cot (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the secant of OP, cosecant of OP, cotangent of OP,
rounded in the direction RND.
-- Function: int mpfr_sin_cos (mpfr_t SOP, mpfr_t COP, mpfr_t OP,
mp_rnd_t RND)
Set simultaneously SOP to the sine of OP and
COP to the cosine of OP, rounded in the direction RND with the
corresponding precisions of SOP and COP, which must be different
variables. Return 0 iff both results are exact.
-- Function: int mpfr_acos (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_asin (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_atan (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the arc-cosine, arc-sine or arc-tangent of OP, rounded
in the direction RND. Note that since `acos(-1)' returns the
floating-point number closest to Pi according to the given
rounding mode, this number might not be in the output range 0 <=
ROP < \pi of the arc-cosine function; still, the result lies in
the image of the output range by the rounding function. The same
holds for `asin(-1)', `asin(1)', `atan(-Inf)', `atan(+Inf)'.
-- Function: int mpfr_atan2 (mpfr_t ROP, mpfr_t Y, mpfr_t X, mp_rnd_t
RND)
Set ROP to the arc-tangent2 of Y and X, rounded in the direction
RND: if `x > 0', `atan2(y, x) = atan (y/x)'; if `x < 0', `atan2(y,
x) = sign(y)*(Pi - atan (abs(y/x)))'. As for `atan', in case the
exact mathematical result is +Pi or -Pi, its rounded result might
be outside the function output range.
`atan2(y, 0)' does not raise any floating-point exception.
Special values are currently handled as described in the ISO C99
standard for the `atan2' function (note this may change in future
versions):
* `atan2(+0, -0)' returns +Pi.
* `atan2(-0, -0)' returns -Pi.
* `atan2(+0, +0)' returns +0.
* `atan2(-0, +0)' returns -0.
* `atan2(+0, x)' returns +Pi for x < 0.
* `atan2(-0, x)' returns -Pi for x < 0.
* `atan2(+0, x)' returns +0 for x > 0.
* `atan2(-0, x)' returns -0 for x > 0.
* `atan2(y, 0)' returns -Pi/2 for y < 0.
* `atan2(y, 0)' returns +Pi/2 for y > 0.
* `atan2(+Inf, -Inf)' returns +3*Pi/4.
* `atan2(-Inf, -Inf)' returns -3*Pi/4.
* `atan2(+Inf, +Inf)' returns +Pi/4.
* `atan2(-Inf, +Inf)' returns -Pi/4.
* `atan2(+Inf, x)' returns +Pi/2 for finite x.
* `atan2(-Inf, x)' returns -Pi/2 for finite x.
* `atan2(y, -Inf)' returns +Pi for finite y > 0.
* `atan2(y, -Inf)' returns -Pi for finite y < 0.
* `atan2(y, +Inf)' returns +0 for finite y > 0.
* `atan2(y, +Inf)' returns -0 for finite y < 0.
-- Function: int mpfr_cosh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_sinh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_tanh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the hyperbolic cosine, sine or tangent of OP, rounded
in the direction RND.
-- Function: int mpfr_sinh_cosh (mpfr_t SOP, mpfr_t COP, mpfr_t OP,
mp_rnd_t RND)
Set simultaneously SOP to the hyperbolic sine of OP and
COP to the hyperbolic cosine of OP, rounded in the
direction RND with the corresponding precision of SOP and COP
which must be different variables. Return 0 iff both results are
exact.
-- Function: int mpfr_sech (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_csch (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_coth (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the hyperbolic secant of OP, cosecant of OP, cotangent
of OP, rounded in the direction RND.
-- Function: int mpfr_acosh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_asinh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_atanh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the inverse hyperbolic cosine, sine or tangent of OP,
rounded in the direction RND.
-- Function: int mpfr_fac_ui (mpfr_t ROP, unsigned long int OP,
mp_rnd_t RND)
Set ROP to the factorial of the `unsigned long int' OP, rounded in
the direction RND.
-- Function: int mpfr_log1p (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the logarithm of one plus OP, rounded in the direction
RND.
-- Function: int mpfr_expm1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the exponential of OP minus one, rounded in the
direction RND.
-- Function: int mpfr_eint (mpfr_t Y, mpfr_t X, mp_rnd_t RND)
Set Y to the exponential integral of X, rounded in the direction
RND. For positive X, the exponential integral is the sum of
Euler's constant, of the logarithm of X, and of the sum for k from
1 to infinity of X to the power k, divided by k and factorial(k).
For negative X, the returned value is NaN.
-- Function: int mpfr_li2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND_MODE)
Set ROP to real part of the dilogarithm of OP, rounded in the
direction RND_MODE. The dilogarithm function is defined here as
the integral of -log(1-t)/t from 0 to x.
-- Function: int mpfr_gamma (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the Gamma function on OP, rounded in the
direction RND. When OP is a negative integer, NaN is returned.
-- Function: int mpfr_lngamma (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the logarithm of the Gamma function on OP,
rounded in the direction RND. When -2K-1 <= X <= -2K, K being a
non-negative integer, NaN is returned. See also `mpfr_lgamma'.
-- Function: int mpfr_lgamma (mpfr_t ROP, int *SIGNP, mpfr_t OP,
mp_rnd_t RND)
Set ROP to the value of the logarithm of the absolute value of the
Gamma function on OP, rounded in the direction RND. The sign (1 or
-1) of Gamma(OP) is returned in the object pointed to by SIGNP.
When OP is an infinity or a non-positive integer, +Inf is
returned. When OP is NaN, -Inf or a negative integer, *SIGNP is
undefined, and when OP is ±0, *SIGNP is the sign of the zero.
-- Function: int mpfr_zeta (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_zeta_ui (mpfr_t ROP, unsigned long OP, mp_rnd_t
RND)
Set ROP to the value of the Riemann Zeta function on OP, rounded
in the direction RND.
-- Function: int mpfr_erf (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the error function on OP, rounded in the
direction RND.
-- Function: int mpfr_erfc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the complementary error function on OP,
rounded in the direction RND.
-- Function: int mpfr_j0 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_j1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_jn (mpfr_t ROP, long N, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the first kind Bessel function of order 0,
1 and N on OP, rounded in the direction RND. When OP is NaN, ROP
is always set to NaN. When OP is plus or minus Infinity, ROP is
set to +0. When OP is zero, and N is not zero, ROP is +0 or -0
depending on the parity and sign of N, and the sign of OP.
-- Function: int mpfr_y0 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_y1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_yn (mpfr_t ROP, long N, mpfr_t OP, mp_rnd_t RND)
Set ROP to the value of the second kind Bessel function of order
0, 1 and N on OP, rounded in the direction RND. When OP is NaN or
negative, ROP is always set to NaN. When OP is +Inf, ROP is +0.
When OP is zero, ROP is +Inf or -Inf depending on the parity and
sign of N.
-- Function: int mpfr_fma (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, mpfr_t
OP3, mp_rnd_t RND)
Set ROP to (OP1 times OP2) + OP3, rounded in the direction RND.
-- Function: int mpfr_fms (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, mpfr_t
OP3, mp_rnd_t RND)
Set ROP to (OP1 times OP2) - OP3, rounded in the direction RND.
-- Function: int mpfr_agm (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Set ROP to the arithmetic-geometric mean of OP1 and OP2, rounded
in the direction RND. The arithmetic-geometric mean is the common
limit of the sequences u[n] and v[n], where u[0]=OP1, v[0]=OP2,
u[n+1] is the arithmetic mean of u[n] and v[n], and v[n+1] is the
geometric mean of u[n] and v[n]. If any operand is negative, the
return value is NaN.
-- Function: int mpfr_hypot (mpfr_t ROP, mpfr_t X, mpfr_t Y, mp_rnd_t
RND)
Set ROP to the Euclidean norm of X and Y, i.e. the square root of
the sum of the squares of X and Y, rounded in the direction RND.
Special values are currently handled as described in Section
F.9.4.3 of the ISO C99 standard, for the `hypot' function (note
this may change in future versions): If X or Y is an infinity,
then plus infinity is returned in ROP, even if the other number is
NaN.
-- Function: int mpfr_const_log2 (mpfr_t ROP, mp_rnd_t RND)
-- Function: int mpfr_const_pi (mpfr_t ROP, mp_rnd_t RND)
-- Function: int mpfr_const_euler (mpfr_t ROP, mp_rnd_t RND)
-- Function: int mpfr_const_catalan (mpfr_t ROP, mp_rnd_t RND)
Set ROP to the logarithm of 2, the value of Pi, of Euler's
constant 0.577..., of Catalan's constant 0.915..., respectively,
rounded in the direction RND. These functions cache the computed
values to avoid other calculations if a lower or equal precision
is requested. To free these caches, use `mpfr_free_cache'.
-- Function: void mpfr_free_cache (void)
Free various caches used by MPFR internally, in particular the
caches used by the functions computing constants (currently
`mpfr_const_log2', `mpfr_const_pi', `mpfr_const_euler' and
`mpfr_const_catalan'). You should call this function before
terminating a thread, even if you did not call these functions
directly (they could have been called internally).
-- Function: int mpfr_sum (mpfr_t ROP, mpfr_ptr const TAB[], unsigned
long N, mp_rnd_t RND)
Set RET to the sum of all elements of TAB whose size is N, rounded
in the direction RND. Warning, TAB is a table of pointers to
mpfr_t, not a table of mpfr_t (preliminary interface). The returned
`int' value is zero when the computed value is the exact value,
and non-zero when this cannot be guaranteed, without giving the
direction of the error as the other functions do.

File: mpfr.info, Node: Input and Output Functions, Next: Formatted Output Functions, Prev: Special Functions, Up: MPFR Interface
5.8 Input and Output Functions
==============================
This section describes functions that perform input from an input/output
stream, and functions that output to an input/output stream. Passing a
null pointer for a `stream' to any of these functions will make them
read from `stdin' and write to `stdout', respectively.
When using any of these functions, you must include the `<stdio.h>'
standard header before `mpfr.h', to allow `mpfr.h' to define prototypes
for these functions.
-- Function: size_t mpfr_out_str (FILE *STREAM, int BASE, size_t N,
mpfr_t OP, mp_rnd_t RND)
Output OP on stream STREAM, as a string of digits in base BASE,
rounded in the direction RND. The base may vary from 2 to 36.
Print N significant digits exactly, or if N is 0, enough digits so
that OP can be read back exactly (see `mpfr_get_str').
In addition to the significant digits, a decimal point (defined by
the current locale) at the right of the first digit and a trailing
exponent in base 10, in the form `eNNN', are printed. If BASE is
greater than 10, `@' will be used instead of `e' as exponent
delimiter.
Return the number of bytes written, or if an error occurred,
return 0.
-- Function: size_t mpfr_inp_str (mpfr_t ROP, FILE *STREAM, int BASE,
mp_rnd_t RND)
Input a string in base BASE from stream STREAM, rounded in the
direction RND, and put the read float in ROP.
This function reads a word (defined as a sequence of characters
between whitespace) and parses it using `mpfr_set_str' (it may
change). See the documentation of `mpfr_strtofr' for a detailed
description of the valid string formats.
Return the number of bytes read, or if an error occurred, return 0.

File: mpfr.info, Node: Formatted Output Functions, Next: Integer Related Functions, Prev: Input and Output Functions, Up: MPFR Interface
5.9 Formatted Output Functions
==============================
5.9.1 Requirements
------------------
The class of `mpfr_printf' functions provides formatted output in a
similar manner as the standard C `printf'. These functions are defined
only if your system supports ISO C variadic functions and the
corresponding argument access macros.
When using any of these functions, you must include the `<stdio.h>'
standard header before `mpfr.h', to allow `mpfr.h' to define prototypes
for these functions.
5.9.2 Format String
-------------------
The format specification accepted by `mpfr_printf' is an extension of
the `printf' one. The conversion specification is of the form:
% [flags] [width] [.[precision]] [type] [rounding] conv
`flags', `width', and `precision' have the same meaning as for the
standard C function `printf' (in particular, notice that the precision
is related to the number of digits displayed in the base chosen by
`conv' and not related to the internal precision of the `mpfr_t'
variable). `mpfr_printf' accepts the same `type' specifiers as `gmp'
(except the non-standard and deprecated `q', use `ll' instead), plus
`R' and `P':
`h' `short'
`hh' `char'
`j' `intmax_t' or `uintmax_t'
`l' `long' or `wchar_t'
`ll' `long long'
`L' `long double'
`t' `ptrdiff_t'
`z' `size_t'
`F' `mpf_t', float conversions
`Q' `mpq_t', integer conversions
`M' `mp_limb_t', integer conversions
`N' `mp_limb_t' array, integer conversions
`Z' `mpz_t', integer conversions
`R' `mpfr_t' input, float conversions
`P' `mpfr_prec_t' input, integer conversions
The `type' specifiers have the same restrictions as those mentioned
in the GMP documentation: *note Formatted Output Strings:
(gmp.info)Formatted Output Strings. More precisely, except for `R' and
`P' (which are defined by MPFR), the `type' specifiers are supported
only if they are supported by `gmp_printf' in your GMP build; this
implies that the standard specifiers, such as `t', must _also_ be
supported by your C library if you want to use them.
The `rounding' specifier is specific to `mpfr_t' parameter and shall
not be used with other types. `mpfr_printf' accepts the same conversion
specifier character `conv' as `gmp_printf' plus `b'.
The `P' type outputs the precision of an `mpfr_t' variable. It is
needed because the `mpfr_prec_t' type does not necessarily correspond
to an `unsigned int' or any fixed standard type. For example:
mpfr_t x;
mpfr_prec_t p;
mpfr_init (x);
...
p = mpfr_get_prec (x);
mpfr_printf ("variable x with %Pu bits", p);
The `R' type is used for a `mpfr_t' output and can be followed by a
rounding specifier denoted by one of the following characters:
`U' round toward plus infinity
`D' round toward minus infinity
`Z' round toward zero
`N' round to nearest
`*' rounding mode (as a `mpfr_rnd_t')
indicated by the argument just before
the corresponding `mpfr_t' variable.
If the precision field is not empty, the `mpfr_t' number is rounded
to the given precision in the direction specified by the rounding mode.
If the precision field is empty (as in `%.Rf'), the number is displayed
with enough digits so that it can be read back exactly (assuming
rounding to nearest, see `mpfr_get_str'). If no rounding is specified,
the `mpfr_t' argument is rounded to nearest. The following three
examples are equivalent:
mpfr_t x;
mpfr_init (x);
...
mpfr_printf ("%.128Rf", x);
mpfr_printf ("%.128RNf", x);
mpfr_printf ("%.128R*f", GMP_RNDN, x);
`mpfr_printf' also adds a new conversion specifier `b' which
displays the `mpfr_t' parameter in binary, the behavior is undefined
with other parameter type. The `conv' specifiers allowed with `mpfr_t'
parameter are:
`a' `A' hex float, C99 style
`b' binary output
`e' `E' scientific format float
`f' fixed point float
`g' `G' fixed or scientific float
In case of non-decimal output, only the significand is written in the
specified base, the exponent is always displayed in decimal. Special
values are always displayed as `nan', `-inf', and `inf' for `a', `b',
`e', `f', and `g' specifiers and `NAN', `-INF', and `INF' for `A', `E',
`F', and `G' specifiers. In binary output, the precision is silently
increased up to 2 if it equals 1.
5.9.3 Functions
---------------
-- Function: int mpfr_fprintf (FILE *STREAM, const char *TEMPLATE, ...)
-- Function: int mpfr_vfprintf (FILE *STREAM, const char *TEMPLATE,
va_list AP)
Print to the stream STREAM the optional arguments under the
control of the template string TEMPLATE.
Return the number of characters written or a negative value if an
error occurred. If the number of characters which ought to be
written appears to exceed the maximum limit for an `int', nothing
is written in the stream, the function returns -1, sets the
_erange_ flag, and (in POSIX system only) `errno' is set to
`EOVERFLOW'.
-- Function: int mpfr_printf (const char *TEMPLATE, ...)
-- Function: int mpfr_vprintf (const char *TEMPLATE, va_list AP)
Print to STDOUT the optional arguments under the control of the
template string TEMPLATE.
Return the number of characters written or a negative value if an
error occurred. If the number of characters which ought to be
written appears to exceed the maximum limit for an `int', nothing
is written in `stdout', the function returns -1, sets the _erange_
flag, and (in POSIX system only) `errno' is set to `EOVERFLOW'.
-- Function: int mpfr_sprintf (char *BUF, const char *TEMPLATE, ...)
-- Function: int mpfr_vsprintf (char *BUF, const char *TEMPLATE,
va_list AP)
Form a null-terminated string in BUF. No overlap is permitted
between BUF and the other arguments.
Return the number of characters written in the array BUF not
counting the terminating null character or a negative value if an
error occurred. If the number of characters which ought to be
written appears to exceed the maximum limit for an `int', nothing
is written in BUF, the function returns -1, sets the _erange_
flag, and (in POSIX system only) `errno' is set to `EOVERFLOW'.
-- Function: int mpfr_snprintf (char *BUF, size_t N, const char
*TEMPLATE, ...)
-- Function: int mpfr_vsnprintf (char *BUF, size_t N, const char
*TEMPLATE, va_list AP)
Form a null-terminated string in BUF. If N is zero, nothing is
written and BUF may be a null pointer, otherwise, the `n-1' first
characters are written in BUF and the N-th is a null character.
Return the number of characters that would have been written had N
be sufficiently large, not counting the terminating null character
or a negative value if an error occurred. If the number of
characters produced by the optional arguments under the control of
the template string TEMPLATE appears to exceed the maximum limit
for an `int', nothing is written in BUF, the function returns -1,
sets the _erange_ flag, and (in POSIX system only) `errno' is set
to `EOVERFLOW'.
-- Function: int mpfr_asprintf (char **STR, const char *TEMPLATE, ...)
-- Function: int mpfr_vasprintf (char **STR, const char *TEMPLATE,
va_list AP)
Write their output as a null terminated string in a block of
memory allocated using the current allocation function. A pointer
to the block is stored in STR. The block of memory must be freed
using `mpfr_free_str'.
The return value is the number of characters written in the
string, excluding the null-terminator or a negative value if an
error occurred. If the number of characters produced by the
optional arguments under the control of the template string
TEMPLATE appears to exceed the maximum limit for an `int', STR is
a null pointer, the function returns -1, sets the _erange_ flag,
and (in POSIX system only) `errno' is set to `EOVERFLOW'.

File: mpfr.info, Node: Integer Related Functions, Next: Rounding Related Functions, Prev: Formatted Output Functions, Up: MPFR Interface
5.10 Integer and Remainder Related Functions
============================================
-- Function: int mpfr_rint (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_ceil (mpfr_t ROP, mpfr_t OP)
-- Function: int mpfr_floor (mpfr_t ROP, mpfr_t OP)
-- Function: int mpfr_round (mpfr_t ROP, mpfr_t OP)
-- Function: int mpfr_trunc (mpfr_t ROP, mpfr_t OP)
Set ROP to OP rounded to an integer. `mpfr_rint' rounds to the
nearest representable integer in the given rounding mode,
`mpfr_ceil' rounds to the next higher or equal representable
integer, `mpfr_floor' to the next lower or equal representable
integer, `mpfr_round' to the nearest representable integer,
rounding halfway cases away from zero, and `mpfr_trunc' to the
next representable integer toward zero.
The returned value is zero when the result is exact, positive when
it is greater than the original value of OP, and negative when it
is smaller. More precisely, the returned value is 0 when OP is an
integer representable in ROP, 1 or -1 when OP is an integer that
is not representable in ROP, 2 or -2 when OP is not an integer.
Note that `mpfr_round' is different from `mpfr_rint' called with
the rounding to nearest mode (where halfway cases are rounded to
an even integer or significand). Note also that no double rounding
is performed; for instance, 4.5 (100.1 in binary) is rounded by
`mpfr_round' to 4 (100 in binary) in 2-bit precision, though
`round(4.5)' is equal to 5 and 5 (101 in binary) is rounded to 6
(110 in binary) in 2-bit precision.
-- Function: int mpfr_rint_ceil (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_rint_floor (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_rint_round (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
-- Function: int mpfr_rint_trunc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to OP rounded to an integer. `mpfr_rint_ceil' rounds to
the next higher or equal integer, `mpfr_rint_floor' to the next
lower or equal integer, `mpfr_rint_round' to the nearest integer,
rounding halfway cases away from zero, and `mpfr_rint_trunc' to
the next integer toward zero. If the result is not representable,
it is rounded in the direction RND. The returned value is the
ternary value associated with the considered round-to-integer
function (regarded in the same way as any other mathematical
function).
-- Function: int mpfr_frac (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND)
Set ROP to the fractional part of OP, having the same sign as OP,
rounded in the direction RND (unlike in `mpfr_rint', RND affects
only how the exact fractional part is rounded, not how the
fractional part is generated).
-- Function: int mpfr_modf (mpfr_t IOP, mpfr_t FOP, mpfr_t OP,
mp_rnd_t RND)
Set simultaneously IOP to the integral part of OP and FOP to the
fractional part of OP, rounded in the direction RND with the
corresponding precision of IOP and FOP (equivalent to
`mpfr_trunc(IOP, OP, RND)' and `mpfr_frac(FOP, OP, RND)'). The
variables IOP and FOP must be different. Return 0 iff both results
are exact.
-- Function: int mpfr_fmod (mpfr_t R, mpfr_t X, mpfr_t Y, mp_rnd_t RND)
-- Function: int mpfr_remainder (mpfr_t R, mpfr_t X, mpfr_t Y,
mp_rnd_t RND)
-- Function: int mpfr_remquo (mpfr_t R, long* Q, mpfr_t X, mpfr_t Y,
mp_rnd_t RND)
Set R to the value of x - n y, rounded according to the direction
RND, where n is the integer quotient of X divided by Y, defined as
follows: n is rounded toward zero for `mpfr_fmod', and to the
nearest integer (ties rounded to even) for `mpfr_remainder' and
`mpfr_remquo'.
Special values are handled as described in Section F.9.7.1 of the
ISO C99 standard: If X is infinite or Y is zero, R is NaN. If Y
is infinite and X is finite, R is X rounded to the precision of R.
If R is zero, it has the sign of X. The return value is the
ternary value corresponding to R.
Additionally, `mpfr_remquo' stores the low significant bits from
the quotient in *Q (more precisely the number of bits in a `long'
minus one), with the sign of X divided by Y (except if those low
bits are all zero, in which case zero is returned). Note that X
may be so large in magnitude relative to Y that an exact
representation of the quotient is not practical. `mpfr_remainder'
and `mpfr_remquo' functions are useful for additive argument
reduction.
-- Function: int mpfr_integer_p (mpfr_t OP)
Return non-zero iff OP is an integer.

File: mpfr.info, Node: Rounding Related Functions, Next: Miscellaneous Functions, Prev: Integer Related Functions, Up: MPFR Interface
5.11 Rounding Related Functions
===============================
-- Function: void mpfr_set_default_rounding_mode (mp_rnd_t RND)
Set the default rounding mode to RND. The default rounding mode
is to nearest initially.
-- Function: mp_rnd_t mpfr_get_default_rounding_mode (void)
Get the default rounding mode.
-- Function: int mpfr_prec_round (mpfr_t X, mp_prec_t PREC, mp_rnd_t
RND)
Round X according to RND with precision PREC, which must be an
integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX' (otherwise the
behavior is undefined). If PREC is greater or equal to the
precision of X, then new space is allocated for the significand,
and it is filled with zeros. Otherwise, the significand is
rounded to precision PREC with the given direction. In both cases,
the precision of X is changed to PREC.
-- Function: int mpfr_round_prec (mpfr_t X, mp_rnd_t RND, mp_prec_t
PREC)
[This function is obsolete. Please use `mpfr_prec_round' instead.]
-- Function: int mpfr_can_round (mpfr_t B, mp_exp_t ERR, mp_rnd_t
RND1, mp_rnd_t RND2, mp_prec_t PREC)
Assuming B is an approximation of an unknown number X in the
direction RND1 with error at most two to the power E(b)-ERR where
E(b) is the exponent of B, return a non-zero value if one is able
to round correctly X to precision PREC with the direction RND2,
and 0 otherwise (including for NaN and Inf). This function *does
not modify* its arguments.
Note: if one wants to also determine the correct ternary value
when rounding B to precision PREC, a useful trick is the following: if (mpfr_can_round (b, err, rnd1, GMP_RNDZ, prec + (rnd2 == GMP_RNDN)))
...
Indeed, if RND2 is `GMP_RNDN', this will check if one can round
to PREC+1 bits with a directed rounding: if so, one can surely
round to nearest to PREC bits, and in addition one can determine
the correct ternary value, which would not be the case when B is
near from a value exactly representable on PREC bits.
-- Function: const char * mpfr_print_rnd_mode (mp_rnd_t RND)
Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ)
corresponding to the rounding mode RND or a null pointer if RND is
an invalid rounding mode.

File: mpfr.info, Node: Miscellaneous Functions, Next: Exception Related Functions, Prev: Rounding Related Functions, Up: MPFR Interface
5.12 Miscellaneous Functions
============================
-- Function: void mpfr_nexttoward (mpfr_t X, mpfr_t Y)
If X or Y is NaN, set X to NaN. Otherwise, if X is different from
Y, replace X by the next floating-point number (with the precision
of X and the current exponent range) in the direction of Y, if
there is one (the infinite values are seen as the smallest and
largest floating-point numbers). If the result is zero, it keeps
the same sign. No underflow or overflow is generated.
-- Function: void mpfr_nextabove (mpfr_t X)
Equivalent to `mpfr_nexttoward' where Y is plus infinity.
-- Function: void mpfr_nextbelow (mpfr_t X)
Equivalent to `mpfr_nexttoward' where Y is minus infinity.
-- Function: int mpfr_min (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Set ROP to the minimum of OP1 and OP2. If OP1 and OP2 are both
NaN, then ROP is set to NaN. If OP1 or OP2 is NaN, then ROP is set
to the numeric value. If OP1 and OP2 are zeros of different signs,
then ROP is set to -0.
-- Function: int mpfr_max (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Set ROP to the maximum of OP1 and OP2. If OP1 and OP2 are both
NaN, then ROP is set to NaN. If OP1 or OP2 is NaN, then ROP is set
to the numeric value. If OP1 and OP2 are zeros of different signs,
then ROP is set to +0.
-- Function: int mpfr_urandomb (mpfr_t ROP, gmp_randstate_t STATE)
Generate a uniformly distributed random float in the interval 0 <=
ROP < 1. More precisely, the number can be seen as a float with a
random non-normalized significand and exponent 0, which is then
normalized (thus if E denotes the exponent after normalization,
then the least -E significant bits of the significand are always
0). Return 0, unless the exponent is not in the current exponent
range, in which case ROP is set to NaN and a non-zero value is
returned (this should never happen in practice, except in very
specific cases). The second argument is a `gmp_randstate_t'
structure which should be created using the GMP `gmp_randinit'
function, see the GMP manual.
-- Function: void mpfr_random (mpfr_t ROP)
Generate a uniformly distributed random float in the interval 0 <=
ROP < 1.
This function is deprecated and will be suppressed in the next
release; `mpfr_urandomb' should be used instead.
-- Function: void mpfr_random2 (mpfr_t ROP, mp_size_t SIZE, mp_exp_t
EXP)
Generate a random float of at most SIZE limbs, with long strings of
zeros and ones in the binary representation. The exponent of the
number is in the interval -EXP to EXP. This function is useful for
testing functions and algorithms, since this kind of random
numbers have proven to be more likely to trigger corner-case bugs.
Negative random numbers are generated when SIZE is negative. Put
+0 in ROP when size if zero. The internal state of the default
pseudorandom number generator is modified by a call to this
function (the same one as GMP if MPFR was built using
`--with-gmp-build').
This function is deprecated and will be suppressed in the next
release.
-- Function: mp_exp_t mpfr_get_exp (mpfr_t X)
Get the exponent of X, assuming that X is a non-zero ordinary
number and the significand is chosen in [1/2,1). The behavior for
NaN, infinity or zero is undefined.
-- Function: int mpfr_set_exp (mpfr_t X, mp_exp_t E)
Set the exponent of X if E is in the current exponent range, and
return 0 (even if X is not a non-zero ordinary number); otherwise,
return a non-zero value. The significand is assumed to be in
[1/2,1).
-- Function: int mpfr_signbit (mpfr_t OP)
Return a non-zero value iff OP has its sign bit set (i.e. if it is
negative, -0, or a NaN whose representation has its sign bit set).
-- Function: int mpfr_setsign (mpfr_t ROP, mpfr_t OP, int S, mp_rnd_t
RND)
Set the value of ROP from OP, rounded toward the given direction
RND, then set (resp. clear) its sign bit if S is non-zero (resp.
zero), even when OP is a NaN.
-- Function: int mpfr_copysign (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Set the value of ROP from OP1, rounded toward the given direction
RND, then set its sign bit to that of OP2 (even when OP1 or OP2 is
a NaN). This function is equivalent to `mpfr_setsign (ROP, OP1,
mpfr_signbit (OP2), RND)'.
-- Function: const char * mpfr_get_version (void)
Return the MPFR version, as a null-terminated string.
-- Macro: MPFR_VERSION
-- Macro: MPFR_VERSION_MAJOR
-- Macro: MPFR_VERSION_MINOR
-- Macro: MPFR_VERSION_PATCHLEVEL
-- Macro: MPFR_VERSION_STRING
`MPFR_VERSION' is the version of MPFR as a preprocessing constant.
`MPFR_VERSION_MAJOR', `MPFR_VERSION_MINOR' and
`MPFR_VERSION_PATCHLEVEL' are respectively the major, minor and
patch level of MPFR version, as preprocessing constants.
`MPFR_VERSION_STRING' is the version (with an optional suffix, used
in development and pre-release versions) as a string constant,
which can be compared to the result of `mpfr_get_version' to check
at run time the header file and library used match:
if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING))
fprintf (stderr, "Warning: header and library do not match\n");
Note: Obtaining different strings is not necessarily an error, as
in general, a program compiled with some old MPFR version can be
dynamically linked with a newer MPFR library version (if allowed
by the library versioning system).
-- Macro: long MPFR_VERSION_NUM (MAJOR, MINOR, PATCHLEVEL)
Create an integer in the same format as used by `MPFR_VERSION'
from the given MAJOR, MINOR and PATCHLEVEL. Here is an example of
how to check the MPFR version at compile time:
#if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0)))
# error "Wrong MPFR version."
#endif
-- Function: const char * mpfr_get_patches (void)
Return a null-terminated string containing the ids of the patches
applied to the MPFR library (contents of the `PATCHES' file),
separated by spaces. Note: If the program has been compiled with
an older MPFR version and is dynamically linked with a new MPFR
library version, the ids of the patches applied to the old
(compile-time) MPFR version are not available (however this
information should not have much interest in general).

File: mpfr.info, Node: Exception Related Functions, Next: Compatibility with MPF, Prev: Miscellaneous Functions, Up: MPFR Interface
5.13 Exception Related Functions
================================
-- Function: mp_exp_t mpfr_get_emin (void)
-- Function: mp_exp_t mpfr_get_emax (void)
Return the (current) smallest and largest exponents allowed for a
floating-point variable. The smallest positive value of a
floating-point variable is one half times 2 raised to the smallest
exponent and the largest value has the form (1 - epsilon) times 2
raised to the largest exponent.
-- Function: int mpfr_set_emin (mp_exp_t EXP)
-- Function: int mpfr_set_emax (mp_exp_t EXP)
Set the smallest and largest exponents allowed for a
floating-point variable. Return a non-zero value when EXP is not
in the range accepted by the implementation (in that case the
smallest or largest exponent is not changed), and zero otherwise.
If the user changes the exponent range, it is her/his
responsibility to check that all current floating-point variables
are in the new allowed range (for example using
`mpfr_check_range'), otherwise the subsequent behavior will be
undefined, in the sense of the ISO C standard.
-- Function: mp_exp_t mpfr_get_emin_min (void)
-- Function: mp_exp_t mpfr_get_emin_max (void)
-- Function: mp_exp_t mpfr_get_emax_min (void)
-- Function: mp_exp_t mpfr_get_emax_max (void)
Return the minimum and maximum of the smallest and largest
exponents allowed for `mpfr_set_emin' and `mpfr_set_emax'. These
values are implementation dependent; it is possible to create a non
portable program by writing `mpfr_set_emax(mpfr_get_emax_max())'
and `mpfr_set_emin(mpfr_get_emin_min())' since the values of the
smallest and largest exponents become implementation dependent.
-- Function: int mpfr_check_range (mpfr_t X, int T, mp_rnd_t RND)
This function forces X to be in the current range of acceptable
values, T being the current ternary value: negative if X is
smaller than the exact value, positive if X is larger than the
exact value and zero if X is exact (before the call). It generates
an underflow or an overflow if the exponent of X is outside the
current allowed range; the value of T may be used to avoid a
double rounding. This function returns zero if the rounded result
is equal to the exact one, a positive value if the rounded result
is larger than the exact one, a negative value if the rounded
result is smaller than the exact one. Note that unlike most
functions, the result is compared to the exact one, not the input
value X, i.e. the ternary value is propagated.
Note: If X is an infinity and T is different from zero (i.e., if
the rounded result is an inexact infinity), then the overflow flag
is set. This is useful because `mpfr_check_range' is typically
called (at least in MPFR functions) after restoring the flags that
could have been set due to internal computations.
-- Function: int mpfr_subnormalize (mpfr_t X, int T, mp_rnd_t RND)
This function rounds X emulating subnormal number arithmetic: if X
is outside the subnormal exponent range, it just propagates the
ternary value T; otherwise, it rounds X to precision
`EXP(x)-emin+1' according to rounding mode RND and previous
ternary value T, avoiding double rounding problems. More
precisely in the subnormal domain, denoting by E the value of
`emin', X is rounded in fixed-point arithmetic to an integer
multiple of two to the power E-1; as a consequence, 1.5 multiplied
by two to the power E-1 when T is zero is rounded to two to the
power E with rounding to nearest.
`PREC(x)' is not modified by this function. RND and T must be the
used rounding mode for computing X and the returned ternary value
when computing X. The subnormal exponent range is from `emin' to
`emin+PREC(x)-1'. If the result cannot be represented in the
current exponent range (due to a too small `emax'), the behavior
is undefined. Note that unlike most functions, the result is
compared to the exact one, not the input value X, i.e. the ternary
value is propagated. This is a preliminary interface.
This is an example of how to emulate double IEEE-754 arithmetic
using MPFR:
{
mpfr_t xa, xb;
int i;
volatile double a, b;
mpfr_set_default_prec (53);
mpfr_set_emin (-1073);
mpfr_set_emax (1024);
mpfr_init (xa); mpfr_init (xb);
b = 34.3; mpfr_set_d (xb, b, GMP_RNDN);
a = 0x1.1235P-1021; mpfr_set_d (xa, a, GMP_RNDN);
a /= b;
i = mpfr_div (xa, xa, xb, GMP_RNDN);
i = mpfr_subnormalize (xa, i, GMP_RNDN);
mpfr_clear (xa); mpfr_clear (xb);
}
Warning: this emulates a double IEEE-754 arithmetic with correct
rounding in the subnormal range, which may not be the case for your
hardware.
-- Function: void mpfr_clear_underflow (void)
-- Function: void mpfr_clear_overflow (void)
-- Function: void mpfr_clear_nanflag (void)
-- Function: void mpfr_clear_inexflag (void)
-- Function: void mpfr_clear_erangeflag (void)
Clear the underflow, overflow, invalid, inexact and _erange_ flags.
-- Function: void mpfr_set_underflow (void)
-- Function: void mpfr_set_overflow (void)
-- Function: void mpfr_set_nanflag (void)
-- Function: void mpfr_set_inexflag (void)
-- Function: void mpfr_set_erangeflag (void)
Set the underflow, overflow, invalid, inexact and _erange_ flags.
-- Function: void mpfr_clear_flags (void)
Clear all global flags (underflow, overflow, inexact, invalid,
_erange_).
-- Function: int mpfr_underflow_p (void)
-- Function: int mpfr_overflow_p (void)
-- Function: int mpfr_nanflag_p (void)
-- Function: int mpfr_inexflag_p (void)
-- Function: int mpfr_erangeflag_p (void)
Return the corresponding (underflow, overflow, invalid, inexact,
_erange_) flag, which is non-zero iff the flag is set.

File: mpfr.info, Node: Compatibility with MPF, Next: Custom Interface, Prev: Exception Related Functions, Up: MPFR Interface
5.14 Compatibility With MPF
===========================
A header file `mpf2mpfr.h' is included in the distribution of MPFR for
compatibility with the GNU MP class MPF. After inserting the following
two lines after the `#include <gmp.h>' line,
#include <mpfr.h>
#include <mpf2mpfr.h>
any program written for MPF can be compiled directly with MPFR without
any changes. All operations are then performed with the default MPFR
rounding mode, which can be reset with `mpfr_set_default_rounding_mode'.
Warning: the `mpf_init' and `mpf_init2' functions initialize to
zero, whereas the corresponding MPFR functions initialize to NaN: this
is useful to detect uninitialized values, but is slightly incompatible
with `mpf'.
-- Function: void mpfr_set_prec_raw (mpfr_t X, mp_prec_t PREC)
Reset the precision of X to be *exactly* PREC bits. The only
difference with `mpfr_set_prec' is that PREC is assumed to be
small enough so that the significand fits into the current
allocated memory space for X. Otherwise the behavior is undefined.
-- Function: int mpfr_eq (mpfr_t OP1, mpfr_t OP2, unsigned long int
OP3)
Return non-zero if OP1 and OP2 are both non-zero ordinary numbers
with the same exponent and the same first OP3 bits, both zero, or
both infinities of the same sign. Return zero otherwise. This
function is defined for compatibility with `mpf'. Do not use it if
you want to know whether two numbers are close to each other; for
instance, 1.011111 and 1.100000 are currently regarded as
different for any value of OP3 larger than 1 (but this may change
in the next release).
-- Function: void mpfr_reldiff (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2,
mp_rnd_t RND)
Compute the relative difference between OP1 and OP2 and store the
result in ROP. This function does not guarantee the correct
rounding on the relative difference; it just computes
|OP1-OP2|/OP1, using the rounding mode RND for all operations and
the precision of ROP.
-- Function: int mpfr_mul_2exp (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
-- Function: int mpfr_div_2exp (mpfr_t ROP, mpfr_t OP1, unsigned long
int OP2, mp_rnd_t RND)
See `mpfr_mul_2ui' and `mpfr_div_2ui'. These functions are only
kept for compatibility with MPF.

File: mpfr.info, Node: Custom Interface, Next: Internals, Prev: Compatibility with MPF, Up: MPFR Interface
5.15 Custom Interface
=====================
Some applications use a stack to handle the memory and their objects.
However, the MPFR memory design is not well suited for such a thing. So
that such applications are able to use MPFR, an auxiliary memory
interface has been created: the Custom Interface.
The following interface allows them to use MPFR in two ways:
* Either they directly store the MPFR FP number as a `mpfr_t' on the
stack.
* Either they store their own representation of a FP number on the
stack and construct a new temporary `mpfr_t' each time it is
needed.
Nothing has to be done to destroy the FP numbers except garbaging
the used memory: all the memory stuff (allocating, destroying,
garbaging) is kept to the application.
Each function in this interface is also implemented as a macro for
efficiency reasons: for example `mpfr_custom_init (s, p)' uses the
macro, while `(mpfr_custom_init) (s, p)' uses the function.
Note 1: MPFR functions may still initialize temporary FP numbers
using standard mpfr_init. See Custom Allocation (GNU MP).
Note 2: MPFR functions may use the cached functions (mpfr_const_pi
for example), even if they are not explicitly called. You have to call
`mpfr_free_cache' each time you garbage the memory iff mpfr_init,
through GMP Custom Allocation, allocates its memory on the application
stack.
Note 3: This interface is preliminary.
-- Function: size_t mpfr_custom_get_size (mp_prec_t PREC)
Return the needed size in bytes to store the significand of a FP
number of precision PREC.
-- Function: void mpfr_custom_init (void *SIGNIFICAND, mp_prec_t PREC)
Initialize a significand of precision PREC. SIGNIFICAND must be
an area of `mpfr_custom_get_size (prec)' bytes at least and be
suitably aligned for an array of `mp_limb_t'.
-- Function: void mpfr_custom_init_set (mpfr_t X, int KIND, mp_exp_t
EXP, mp_prec_t PREC, void *SIGNIFICAND)
Perform a dummy initialization of a `mpfr_t' and set it to:
* if `ABS(kind) == MPFR_NAN_KIND', X is set to NaN;
* if `ABS(kind) == MPFR_INF_KIND', X is set to the infinity of
sign `sign(kind)';
* if `ABS(kind) == MPFR_ZERO_KIND', X is set to the zero of
sign `sign(kind)';
* if `ABS(kind) == MPFR_REGULAR_KIND', X is set to a regular
number: `x = sign(kind)*significand*2^exp'
In all cases, it uses SIGNIFICAND directly for further computing
involving X. It will not allocate anything. A FP number
initialized with this function cannot be resized using
`mpfr_set_prec', or cleared using `mpfr_clear'! SIGNIFICAND must
have been initialized with `mpfr_custom_init' using the same
precision PREC.
-- Function: int mpfr_custom_get_kind (mpfr_t X)
Return the current kind of a `mpfr_t' as used by
`mpfr_custom_init_set'. The behavior of this function for any
`mpfr_t' not initialized with `mpfr_custom_init_set' is undefined.
-- Function: void * mpfr_custom_get_mantissa (mpfr_t X)
Return a pointer to the significand used by a `mpfr_t' initialized
with `mpfr_custom_init_set'. The behavior of this function for
any `mpfr_t' not initialized with `mpfr_custom_init_set' is
undefined.
-- Function: mp_exp_t mpfr_custom_get_exp (mpfr_t X)
Return the exponent of X, assuming that X is a non-zero ordinary
number. The return value for NaN, Infinity or Zero is unspecified
but does not produce any trap. The behavior of this function for
any `mpfr_t' not initialized with `mpfr_custom_init_set' is
undefined.
-- Function: void mpfr_custom_move (mpfr_t X, void *NEW_POSITION)
Inform MPFR that the significand has moved due to a garbage collect
and update its new position to `new_position'. However the
application has to move the significand and the `mpfr_t' itself.
The behavior of this function for any `mpfr_t' not initialized
with `mpfr_custom_init_set' is undefined.
See the test suite for examples.

File: mpfr.info, Node: Internals, Prev: Custom Interface, Up: MPFR Interface
5.16 Internals
==============
The following types and functions were mainly designed for the
implementation of MPFR, but may be useful for users too. However no
upward compatibility is guaranteed. You may need to include
`mpfr-impl.h' to use them.
The `mpfr_t' type consists of four fields.
* The `_mpfr_prec' field is used to store the precision of the
variable (in bits); this is not less than `MPFR_PREC_MIN'.
* The `_mpfr_sign' field is used to store the sign of the variable.
* The `_mpfr_exp' field stores the exponent. An exponent of 0 means
a radix point just above the most significant limb. Non-zero
values n are a multiplier 2^n relative to that point. A NaN, an
infinity and a zero are indicated by a special value of the
exponent.
* Finally, the `_mpfr_d' is a pointer to the limbs, least
significant limbs stored first. The number of limbs in use is
controlled by `_mpfr_prec', namely
ceil(`_mpfr_prec'/`mp_bits_per_limb'). Non-singular values always
have the most significant bit of the most significant limb set to
1. When the precision does not correspond to a whole number of
limbs, the excess bits at the low end of the data are zero.

File: mpfr.info, Node: Contributors, Next: References, Prev: MPFR Interface, Up: Top
Contributors
************
The main developers of MPFR are Guillaume Hanrot, Vincent Lefèvre,
Patrick Pélissier, Philippe Théveny and Paul Zimmermann.
Sylvie Boldo from ENS-Lyon, France, contributed the functions
`mpfr_agm' and `mpfr_log'. Emmanuel Jeandel, from ENS-Lyon too,
contributed the generic hypergeometric code, as well as the `mpfr_exp3',
a first implementation of the sine and cosine, and improved versions of
`mpfr_const_log2' and `mpfr_const_pi'. Mathieu Dutour contributed the
functions `mpfr_atan' and `mpfr_asin', and a previous version of
`mpfr_gamma'; David Daney contributed the hyperbolic and inverse
hyperbolic functions, the base-2 exponential, and the factorial
function. Fabrice Rouillier contributed the original version of
`mul_ui.c', the `gmp_op.c' file, and helped to the Microsoft Windows
porting. Jean-Luc Rémy contributed the `mpfr_zeta' code. Ludovic
Meunier helped in the design of the `mpfr_erf' code. Damien Stehlé
contributed the `mpfr_get_ld_2exp' function.
We would like to thank Jean-Michel Muller and Joris van der Hoeven
for very fruitful discussions at the beginning of that project,
Torbjörn Granlund and Kevin Ryde for their help about design issues,
and Nathalie Revol for her careful reading of a previous version of
this documentation. Kevin Ryde did a tremendous job for the
portability of MPFR in 2002-2004.
The development of the MPFR library would not have been possible
without the continuous support of INRIA, and of the LORIA (Nancy,
France) and LIP (Lyon, France) laboratories. In particular the main
authors were or are members of the PolKA, Spaces, Cacao project-teams
at LORIA and of the Arenaire project-team at LIP. This project was
started during the Fiable (reliable in French) action supported by
INRIA, and continued during the AOC action. The development of MPFR
was also supported by a grant (202F0659 00 MPN 121) from the Conseil
Régional de Lorraine in 2002, and from INRIA by an "associate engineer"
grant (2003-2005) and an "opération de développement logiciel" grant
(2007-2009).

File: mpfr.info, Node: References, Next: GNU Free Documentation License, Prev: Contributors, Up: Top
References
**********
* Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick
Pélissier and Paul Zimmermann, "MPFR: A Multiple-Precision Binary
Floating-Point Library With Correct Rounding", ACM Transactions on
Mathematical Software, volume 33, issue 2, article 13, 15 pages,
2007, `http://doi.acm.org/10.1145/1236463.1236468'.
* Torbjörn Granlund, "GNU MP: The GNU Multiple Precision Arithmetic
Library", version 4.2.2, 2007, `http://gmplib.org'.
* IEEE standard for binary floating-point arithmetic, Technical
Report ANSI-IEEE Standard 754-1985, New York, 1985. Approved
March 21, 1985: IEEE Standards Board; approved July 26, 1985:
American National Standards Institute, 18 pages.
* Donald E. Knuth, "The Art of Computer Programming", vol 2,
"Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
* Jean-Michel Muller, "Elementary Functions, Algorithms and
Implementation", Birkhauser, Boston, 2nd edition, 2006.

File: mpfr.info, Node: GNU Free Documentation License, Next: Concept Index, Prev: References, Up: Top
Appendix A GNU Free Documentation License
*****************************************
Version 1.2, November 2002
Copyright (C) 2000,2001,2002 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
Everyone is permitted to copy and distribute verbatim copies
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A.1 ADDENDUM: How to use this License for your documents
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File: mpfr.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top
Concept Index
*************
�[index�]
* Menu:
* Accuracy: MPFR Interface. (line 28)
* Arithmetic functions: Basic Arithmetic Functions.
(line 3)
* Assignment functions: Assignment Functions. (line 3)
* Basic arithmetic functions: Basic Arithmetic Functions.
(line 3)
* Combined initialization and assignment functions: Combined Initialization and Assignment Functions.
(line 3)
* Comparison functions: Comparison Functions. (line 3)
* Compatibility with MPF: Compatibility with MPF.
(line 3)
* Conditions for copying MPFR: Copying. (line 6)
* Conversion functions: Conversion Functions. (line 3)
* Copying conditions: Copying. (line 6)
* Custom interface: Custom Interface. (line 3)
* Exception related functions: Exception Related Functions.
(line 3)
* FDL, GNU Free Documentation License: GNU Free Documentation License.
(line 6)
* Float arithmetic functions: Basic Arithmetic Functions.
(line 3)
* Float comparisons functions: Comparison Functions. (line 3)
* Float functions: MPFR Interface. (line 6)
* Float input and output functions: Input and Output Functions.
(line 3)
* Float output functions: Formatted Output Functions.
(line 3)
* Floating-point functions: MPFR Interface. (line 6)
* Floating-point number: MPFR Basics. (line 52)
* GNU Free Documentation License: GNU Free Documentation License.
(line 6)
* I/O functions <1>: Formatted Output Functions.
(line 3)
* I/O functions: Input and Output Functions.
(line 3)
* Initialization functions: Initialization Functions.
(line 3)
* Input functions: Input and Output Functions.
(line 3)
* Installation: Installing MPFR. (line 6)
* Integer related functions: Integer Related Functions.
(line 3)
* Internals: Internals. (line 3)
* libmpfr: MPFR Basics. (line 32)
* Libraries: MPFR Basics. (line 32)
* Libtool: MPFR Basics. (line 38)
* Limb: MPFR Basics. (line 84)
* Linking: MPFR Basics. (line 32)
* Miscellaneous float functions: Miscellaneous Functions.
(line 3)
* mpfr.h: MPFR Basics. (line 9)
* Output functions <1>: Formatted Output Functions.
(line 3)
* Output functions: Input and Output Functions.
(line 3)
* Precision <1>: MPFR Interface. (line 20)
* Precision: MPFR Basics. (line 65)
* Reporting bugs: Reporting Bugs. (line 6)
* Rounding mode related functions: Rounding Related Functions.
(line 3)
* Rounding Modes: MPFR Basics. (line 79)
* Special functions: Special Functions. (line 3)
* stdarg.h: MPFR Basics. (line 22)
* stdio.h: MPFR Basics. (line 15)

File: mpfr.info, Node: Function Index, Prev: Concept Index, Up: Top
Function and Type Index
***********************
�[index�]
* Menu:
* mp_prec_t: MPFR Basics. (line 65)
* mp_rnd_t: MPFR Basics. (line 79)
* mpfr_abs: Basic Arithmetic Functions.
(line 177)
* mpfr_acos: Special Functions. (line 48)
* mpfr_acosh: Special Functions. (line 131)
* mpfr_add: Basic Arithmetic Functions.
(line 8)
* mpfr_add_d: Basic Arithmetic Functions.
(line 14)
* mpfr_add_q: Basic Arithmetic Functions.
(line 18)
* mpfr_add_si: Basic Arithmetic Functions.
(line 12)
* mpfr_add_ui: Basic Arithmetic Functions.
(line 10)
* mpfr_add_z: Basic Arithmetic Functions.
(line 16)
* mpfr_agm: Special Functions. (line 221)
* mpfr_asin: Special Functions. (line 49)
* mpfr_asinh: Special Functions. (line 132)
* mpfr_asprintf: Formatted Output Functions.
(line 171)
* mpfr_atan: Special Functions. (line 50)
* mpfr_atan2: Special Functions. (line 60)
* mpfr_atanh: Special Functions. (line 133)
* mpfr_can_round: Rounding Related Functions.
(line 29)
* mpfr_cbrt: Basic Arithmetic Functions.
(line 107)
* mpfr_ceil: Integer Related Functions.
(line 8)
* mpfr_check_range: Exception Related Functions.
(line 38)
* mpfr_clear: Initialization Functions.
(line 31)
* mpfr_clear_erangeflag: Exception Related Functions.
(line 111)
* mpfr_clear_flags: Exception Related Functions.
(line 121)
* mpfr_clear_inexflag: Exception Related Functions.
(line 110)
* mpfr_clear_nanflag: Exception Related Functions.
(line 109)
* mpfr_clear_overflow: Exception Related Functions.
(line 108)
* mpfr_clear_underflow: Exception Related Functions.
(line 107)
* mpfr_clears: Initialization Functions.
(line 35)
* mpfr_cmp: Comparison Functions.
(line 7)
* mpfr_cmp_d: Comparison Functions.
(line 10)
* mpfr_cmp_f: Comparison Functions.
(line 14)
* mpfr_cmp_ld: Comparison Functions.
(line 11)
* mpfr_cmp_q: Comparison Functions.
(line 13)
* mpfr_cmp_si: Comparison Functions.
(line 9)
* mpfr_cmp_si_2exp: Comparison Functions.
(line 31)
* mpfr_cmp_ui: Comparison Functions.
(line 8)
* mpfr_cmp_ui_2exp: Comparison Functions.
(line 29)
* mpfr_cmp_z: Comparison Functions.
(line 12)
* mpfr_cmpabs: Comparison Functions.
(line 35)
* mpfr_const_catalan: Special Functions. (line 242)
* mpfr_const_euler: Special Functions. (line 241)
* mpfr_const_log2: Special Functions. (line 239)
* mpfr_const_pi: Special Functions. (line 240)
* mpfr_copysign: Miscellaneous Functions.
(line 93)
* mpfr_cos: Special Functions. (line 29)
* mpfr_cosh: Special Functions. (line 111)
* mpfr_cot: Special Functions. (line 37)
* mpfr_coth: Special Functions. (line 127)
* mpfr_csc: Special Functions. (line 36)
* mpfr_csch: Special Functions. (line 126)
* mpfr_custom_get_exp: Custom Interface. (line 78)
* mpfr_custom_get_kind: Custom Interface. (line 67)
* mpfr_custom_get_mantissa: Custom Interface. (line 72)
* mpfr_custom_get_size: Custom Interface. (line 38)
* mpfr_custom_init: Custom Interface. (line 42)
* mpfr_custom_init_set: Custom Interface. (line 48)
* mpfr_custom_move: Custom Interface. (line 85)
* mpfr_d_div: Basic Arithmetic Functions.
(line 82)
* mpfr_d_sub: Basic Arithmetic Functions.
(line 37)
* MPFR_DECL_INIT: Initialization Functions.
(line 75)
* mpfr_dim: Basic Arithmetic Functions.
(line 182)
* mpfr_div: Basic Arithmetic Functions.
(line 72)
* mpfr_div_2exp: Compatibility with MPF.
(line 49)
* mpfr_div_2si: Basic Arithmetic Functions.
(line 197)
* mpfr_div_2ui: Basic Arithmetic Functions.
(line 195)
* mpfr_div_d: Basic Arithmetic Functions.
(line 84)
* mpfr_div_q: Basic Arithmetic Functions.
(line 88)
* mpfr_div_si: Basic Arithmetic Functions.
(line 80)
* mpfr_div_ui: Basic Arithmetic Functions.
(line 76)
* mpfr_div_z: Basic Arithmetic Functions.
(line 86)
* mpfr_eint: Special Functions. (line 150)
* mpfr_eq: Compatibility with MPF.
(line 28)
* mpfr_equal_p: Comparison Functions.
(line 71)
* mpfr_erangeflag_p: Exception Related Functions.
(line 129)
* mpfr_erf: Special Functions. (line 186)
* mpfr_erfc: Special Functions. (line 190)
* mpfr_exp: Special Functions. (line 23)
* mpfr_exp10: Special Functions. (line 25)
* mpfr_exp2: Special Functions. (line 24)
* mpfr_expm1: Special Functions. (line 146)
* mpfr_fac_ui: Special Functions. (line 138)
* mpfr_fits_intmax_p: Conversion Functions.
(line 113)
* mpfr_fits_sint_p: Conversion Functions.
(line 110)
* mpfr_fits_slong_p: Conversion Functions.
(line 108)
* mpfr_fits_sshort_p: Conversion Functions.
(line 112)
* mpfr_fits_uint_p: Conversion Functions.
(line 109)
* mpfr_fits_uintmax_p: Conversion Functions.
(line 114)
* mpfr_fits_ulong_p: Conversion Functions.
(line 107)
* mpfr_fits_ushort_p: Conversion Functions.
(line 111)
* mpfr_floor: Integer Related Functions.
(line 9)
* mpfr_fma: Special Functions. (line 213)
* mpfr_fmod: Integer Related Functions.
(line 63)
* mpfr_fms: Special Functions. (line 217)
* mpfr_fprintf: Formatted Output Functions.
(line 117)
* mpfr_frac: Integer Related Functions.
(line 48)
* mpfr_free_cache: Special Functions. (line 249)
* mpfr_free_str: Conversion Functions.
(line 100)
* mpfr_gamma: Special Functions. (line 162)
* mpfr_get_d: Conversion Functions.
(line 7)
* mpfr_get_d_2exp: Conversion Functions.
(line 20)
* mpfr_get_decimal64: Conversion Functions.
(line 9)
* mpfr_get_default_prec: Initialization Functions.
(line 109)
* mpfr_get_default_rounding_mode: Rounding Related Functions.
(line 11)
* mpfr_get_emax: Exception Related Functions.
(line 8)
* mpfr_get_emax_max: Exception Related Functions.
(line 30)
* mpfr_get_emax_min: Exception Related Functions.
(line 29)
* mpfr_get_emin: Exception Related Functions.
(line 7)
* mpfr_get_emin_max: Exception Related Functions.
(line 28)
* mpfr_get_emin_min: Exception Related Functions.
(line 27)
* mpfr_get_exp: Miscellaneous Functions.
(line 71)
* mpfr_get_f: Conversion Functions.
(line 55)
* mpfr_get_ld: Conversion Functions.
(line 8)
* mpfr_get_ld_2exp: Conversion Functions.
(line 22)
* mpfr_get_patches: Miscellaneous Functions.
(line 130)
* mpfr_get_prec: Initialization Functions.
(line 143)
* mpfr_get_si: Conversion Functions.
(line 31)
* mpfr_get_sj: Conversion Functions.
(line 33)
* mpfr_get_str: Conversion Functions.
(line 61)
* mpfr_get_ui: Conversion Functions.
(line 32)
* mpfr_get_uj: Conversion Functions.
(line 34)
* mpfr_get_version: Miscellaneous Functions.
(line 99)
* mpfr_get_z: Conversion Functions.
(line 51)
* mpfr_get_z_exp: Conversion Functions.
(line 44)
* mpfr_greater_p: Comparison Functions.
(line 54)
* mpfr_greaterequal_p: Comparison Functions.
(line 57)
* mpfr_hypot: Special Functions. (line 230)
* mpfr_inexflag_p: Exception Related Functions.
(line 128)
* mpfr_inf_p: Comparison Functions.
(line 42)
* mpfr_init: Initialization Functions.
(line 51)
* mpfr_init2: Initialization Functions.
(line 11)
* mpfr_init_set: Combined Initialization and Assignment Functions.
(line 7)
* mpfr_init_set_d: Combined Initialization and Assignment Functions.
(line 12)
* mpfr_init_set_f: Combined Initialization and Assignment Functions.
(line 17)
* mpfr_init_set_ld: Combined Initialization and Assignment Functions.
(line 14)
* mpfr_init_set_q: Combined Initialization and Assignment Functions.
(line 16)
* mpfr_init_set_si: Combined Initialization and Assignment Functions.
(line 11)
* mpfr_init_set_str: Combined Initialization and Assignment Functions.
(line 23)
* mpfr_init_set_ui: Combined Initialization and Assignment Functions.
(line 9)
* mpfr_init_set_z: Combined Initialization and Assignment Functions.
(line 15)
* mpfr_inits: Initialization Functions.
(line 63)
* mpfr_inits2: Initialization Functions.
(line 23)
* mpfr_inp_str: Input and Output Functions.
(line 33)
* mpfr_integer_p: Integer Related Functions.
(line 89)
* mpfr_j0: Special Functions. (line 194)
* mpfr_j1: Special Functions. (line 195)
* mpfr_jn: Special Functions. (line 196)
* mpfr_less_p: Comparison Functions.
(line 60)
* mpfr_lessequal_p: Comparison Functions.
(line 63)
* mpfr_lessgreater_p: Comparison Functions.
(line 66)
* mpfr_lgamma: Special Functions. (line 172)
* mpfr_li2: Special Functions. (line 157)
* mpfr_lngamma: Special Functions. (line 166)
* mpfr_log: Special Functions. (line 16)
* mpfr_log10: Special Functions. (line 18)
* mpfr_log1p: Special Functions. (line 142)
* mpfr_log2: Special Functions. (line 17)
* mpfr_max: Miscellaneous Functions.
(line 29)
* mpfr_min: Miscellaneous Functions.
(line 22)
* mpfr_modf: Integer Related Functions.
(line 55)
* mpfr_mul: Basic Arithmetic Functions.
(line 51)
* mpfr_mul_2exp: Compatibility with MPF.
(line 47)
* mpfr_mul_2si: Basic Arithmetic Functions.
(line 190)
* mpfr_mul_2ui: Basic Arithmetic Functions.
(line 188)
* mpfr_mul_d: Basic Arithmetic Functions.
(line 57)
* mpfr_mul_q: Basic Arithmetic Functions.
(line 61)
* mpfr_mul_si: Basic Arithmetic Functions.
(line 55)
* mpfr_mul_ui: Basic Arithmetic Functions.
(line 53)
* mpfr_mul_z: Basic Arithmetic Functions.
(line 59)
* mpfr_nan_p: Comparison Functions.
(line 41)
* mpfr_nanflag_p: Exception Related Functions.
(line 127)
* mpfr_neg: Basic Arithmetic Functions.
(line 173)
* mpfr_nextabove: Miscellaneous Functions.
(line 15)
* mpfr_nextbelow: Miscellaneous Functions.
(line 18)
* mpfr_nexttoward: Miscellaneous Functions.
(line 7)
* mpfr_number_p: Comparison Functions.
(line 43)
* mpfr_out_str: Input and Output Functions.
(line 17)
* mpfr_overflow_p: Exception Related Functions.
(line 126)
* mpfr_pow: Basic Arithmetic Functions.
(line 116)
* mpfr_pow_si: Basic Arithmetic Functions.
(line 120)
* mpfr_pow_ui: Basic Arithmetic Functions.
(line 118)
* mpfr_pow_z: Basic Arithmetic Functions.
(line 122)
* mpfr_prec_round: Rounding Related Functions.
(line 15)
* mpfr_print_rnd_mode: Rounding Related Functions.
(line 46)
* mpfr_printf: Formatted Output Functions.
(line 130)
* mpfr_random: Miscellaneous Functions.
(line 48)
* mpfr_random2: Miscellaneous Functions.
(line 56)
* mpfr_rec_sqrt: Basic Arithmetic Functions.
(line 102)
* mpfr_reldiff: Compatibility with MPF.
(line 39)
* mpfr_remainder: Integer Related Functions.
(line 65)
* mpfr_remquo: Integer Related Functions.
(line 67)
* mpfr_rint: Integer Related Functions.
(line 7)
* mpfr_rint_ceil: Integer Related Functions.
(line 34)
* mpfr_rint_floor: Integer Related Functions.
(line 35)
* mpfr_rint_round: Integer Related Functions.
(line 36)
* mpfr_rint_trunc: Integer Related Functions.
(line 37)
* mpfr_root: Basic Arithmetic Functions.
(line 109)
* mpfr_round: Integer Related Functions.
(line 10)
* mpfr_round_prec: Rounding Related Functions.
(line 25)
* mpfr_sec: Special Functions. (line 35)
* mpfr_sech: Special Functions. (line 125)
* mpfr_set: Assignment Functions.
(line 12)
* mpfr_set_d: Assignment Functions.
(line 18)
* mpfr_set_decimal64: Assignment Functions.
(line 21)
* mpfr_set_default_prec: Initialization Functions.
(line 101)
* mpfr_set_default_rounding_mode: Rounding Related Functions.
(line 7)
* mpfr_set_emax: Exception Related Functions.
(line 16)
* mpfr_set_emin: Exception Related Functions.
(line 15)
* mpfr_set_erangeflag: Exception Related Functions.
(line 118)
* mpfr_set_exp: Miscellaneous Functions.
(line 76)
* mpfr_set_f: Assignment Functions.
(line 24)
* mpfr_set_inexflag: Exception Related Functions.
(line 117)
* mpfr_set_inf: Assignment Functions.
(line 131)
* mpfr_set_ld: Assignment Functions.
(line 19)
* mpfr_set_nan: Assignment Functions.
(line 132)
* mpfr_set_nanflag: Exception Related Functions.
(line 116)
* mpfr_set_overflow: Exception Related Functions.
(line 115)
* mpfr_set_prec: Initialization Functions.
(line 131)
* mpfr_set_prec_raw: Compatibility with MPF.
(line 21)
* mpfr_set_q: Assignment Functions.
(line 23)
* mpfr_set_si: Assignment Functions.
(line 15)
* mpfr_set_si_2exp: Assignment Functions.
(line 51)
* mpfr_set_sj: Assignment Functions.
(line 17)
* mpfr_set_sj_2exp: Assignment Functions.
(line 55)
* mpfr_set_str: Assignment Functions.
(line 61)
* mpfr_set_ui: Assignment Functions.
(line 14)
* mpfr_set_ui_2exp: Assignment Functions.
(line 49)
* mpfr_set_uj: Assignment Functions.
(line 16)
* mpfr_set_uj_2exp: Assignment Functions.
(line 53)
* mpfr_set_underflow: Exception Related Functions.
(line 114)
* mpfr_set_z: Assignment Functions.
(line 22)
* mpfr_setsign: Miscellaneous Functions.
(line 87)
* mpfr_sgn: Comparison Functions.
(line 49)
* mpfr_si_div: Basic Arithmetic Functions.
(line 78)
* mpfr_si_sub: Basic Arithmetic Functions.
(line 33)
* mpfr_signbit: Miscellaneous Functions.
(line 82)
* mpfr_sin: Special Functions. (line 30)
* mpfr_sin_cos: Special Functions. (line 42)
* mpfr_sinh: Special Functions. (line 112)
* mpfr_sinh_cosh: Special Functions. (line 118)
* mpfr_snprintf: Formatted Output Functions.
(line 155)
* mpfr_sprintf: Formatted Output Functions.
(line 141)
* mpfr_sqr: Basic Arithmetic Functions.
(line 68)
* mpfr_sqrt: Basic Arithmetic Functions.
(line 95)
* mpfr_sqrt_ui: Basic Arithmetic Functions.
(line 97)
* mpfr_strtofr: Assignment Functions.
(line 72)
* mpfr_sub: Basic Arithmetic Functions.
(line 27)
* mpfr_sub_d: Basic Arithmetic Functions.
(line 39)
* mpfr_sub_q: Basic Arithmetic Functions.
(line 43)
* mpfr_sub_si: Basic Arithmetic Functions.
(line 35)
* mpfr_sub_ui: Basic Arithmetic Functions.
(line 31)
* mpfr_sub_z: Basic Arithmetic Functions.
(line 41)
* mpfr_subnormalize: Exception Related Functions.
(line 58)
* mpfr_sum: Special Functions. (line 258)
* mpfr_swap: Assignment Functions.
(line 137)
* mpfr_t: MPFR Basics. (line 52)
* mpfr_tan: Special Functions. (line 31)
* mpfr_tanh: Special Functions. (line 113)
* mpfr_trunc: Integer Related Functions.
(line 11)
* mpfr_ui_div: Basic Arithmetic Functions.
(line 74)
* mpfr_ui_pow: Basic Arithmetic Functions.
(line 126)
* mpfr_ui_pow_ui: Basic Arithmetic Functions.
(line 124)
* mpfr_ui_sub: Basic Arithmetic Functions.
(line 29)
* mpfr_underflow_p: Exception Related Functions.
(line 125)
* mpfr_unordered_p: Comparison Functions.
(line 75)
* mpfr_urandomb: Miscellaneous Functions.
(line 35)
* mpfr_vasprintf: Formatted Output Functions.
(line 173)
* MPFR_VERSION: Miscellaneous Functions.