X-Git-Url: https://oss.titaniummirror.com/gitweb/?a=blobdiff_plain;f=mpfr%2Fmpfr.info;fp=mpfr%2Fmpfr.info;h=0000000000000000000000000000000000000000;hb=37aa8acf60b5c7701cab3d702d2900ca69af7853;hp=e1673794eba5dc2a2f8b5224bb855079c73f1c06;hpb=f12c34b7eaf869b6568b3123727d014202d066e2;p=msp430-gcc.git diff --git a/mpfr/mpfr.info b/mpfr/mpfr.info deleted file mode 100644 index e1673794..00000000 --- a/mpfr/mpfr.info +++ /dev/null @@ -1,3570 +0,0 @@ -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 - - Note however that prototypes for MPFR functions with `FILE *' -parameters are provided only if `' is included too (before -`mpfr.h'). - - #include - #include - - Likewise `' (or `') 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 `' or `' 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 `' -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 `' -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' line, -#include -#include - 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 - of this license document, but changing it is not allowed. - - 0. 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FUTURE REVISIONS OF THIS LICENSE - - The Free Software Foundation may publish new, revised versions of - the GNU Free Documentation License from time to time. Such new - versions will be similar in spirit to the present version, but may - differ in detail to address new problems or concerns. See - `http://www.gnu.org/copyleft/'. - - Each version of the License is given a distinguishing version - number. If the Document specifies that a particular numbered - version of this License "or any later version" applies to it, you - have the option of following the terms and conditions either of - that specified version or of any later version that has been - published (not as a draft) by the Free Software Foundation. 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A copy of the license is included in the section entitled ``GNU - Free Documentation License''. - - If you have Invariant Sections, Front-Cover Texts and Back-Cover -Texts, replace the "with...Texts." line with this: - - with the Invariant Sections being LIST THEIR TITLES, with - the Front-Cover Texts being LIST, and with the Back-Cover Texts - being LIST. - - If you have Invariant Sections without Cover Texts, or some other -combination of the three, merge those two alternatives to suit the -situation. - - If your document contains nontrivial examples of program code, we -recommend releasing these examples in parallel under your choice of -free software license, such as the GNU General Public License, to -permit their use in free software. - - -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. - (line 102) -* MPFR_VERSION_MAJOR: Miscellaneous Functions. - (line 103) -* MPFR_VERSION_MINOR: Miscellaneous Functions. - (line 104) -* MPFR_VERSION_NUM: Miscellaneous Functions. - (line 122) -* MPFR_VERSION_PATCHLEVEL: Miscellaneous Functions. - (line 105) -* MPFR_VERSION_STRING: Miscellaneous Functions. - (line 106) -* mpfr_vfprintf: Formatted Output Functions. - (line 119) -* mpfr_vprintf: Formatted Output Functions. - (line 131) -* mpfr_vsnprintf: Formatted Output Functions. - (line 157) -* mpfr_vsprintf: Formatted Output Functions. - (line 143) -* mpfr_y0: Special Functions. (line 203) -* mpfr_y1: Special Functions. (line 204) -* mpfr_yn: Special Functions. (line 205) -* mpfr_zero_p: Comparison Functions. - (line 44) -* mpfr_zeta: Special Functions. (line 180) -* mpfr_zeta_ui: Special Functions. (line 182) - - - -Tag Table: -Node: Top874 -Node: Copying2113 -Node: Introduction to MPFR3843 -Node: Installing MPFR5755 -Node: Reporting Bugs8997 -Node: MPFR Basics10613 -Node: MPFR Interface25127 -Node: Initialization Functions27351 -Node: Assignment Functions33919 -Node: Combined Initialization and Assignment Functions41669 -Node: Conversion Functions42951 -Node: Basic Arithmetic Functions49151 -Node: Comparison Functions58008 -Node: Special Functions61430 -Node: Input and Output Functions73827 -Node: Formatted Output Functions75757 -Node: Integer Related Functions84168 -Node: Rounding Related Functions89004 -Node: Miscellaneous Functions91474 -Node: Exception Related Functions98260 -Node: Compatibility with MPF104378 -Node: Custom Interface106870 -Node: Internals111053 -Node: Contributors112376 -Node: References114541 -Node: GNU Free Documentation License115655 -Node: Concept Index138098 -Node: Function Index142890 - -End Tag Table - - -Local Variables: -coding: iso-8859-1 -End: