| This is ../mpfr.info, produced by makeinfo version 4.12 from |
| ../mpfr.texi. |
| |
| This manual documents how to install and use the Multiple Precision |
| Floating-Point Reliable Library, version 2.4.1. |
| |
| Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, |
| 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software |
| Foundation, Inc. |
| |
| Permission is granted to copy, distribute and/or modify this |
| document under the terms of the GNU Free Documentation License, Version |
| 1.2 or any later version published by the Free Software Foundation; |
| with no Invariant Sections, with no Front-Cover Texts, and with no |
| Back-Cover Texts. A copy of the license is included in *note GNU Free |
| Documentation License::. |
| |
| INFO-DIR-SECTION Software libraries |
| START-INFO-DIR-ENTRY |
| * mpfr: (mpfr). Multiple Precision Floating-Point Reliable Library. |
| END-INFO-DIR-ENTRY |
| |
| |
| File: mpfr.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir) |
| |
| GNU MPFR |
| ******** |
| |
| This manual documents how to install and use the Multiple Precision |
| Floating-Point Reliable Library, version 2.4.1. |
| |
| Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, |
| 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software |
| Foundation, Inc. |
| |
| Permission is granted to copy, distribute and/or modify this |
| document under the terms of the GNU Free Documentation License, Version |
| 1.2 or any later version published by the Free Software Foundation; |
| with no Invariant Sections, with no Front-Cover Texts, and with no |
| Back-Cover Texts. A copy of the license is included in *note GNU Free |
| Documentation License::. |
| |
| |
| * Menu: |
| |
| * Copying:: MPFR Copying Conditions (LGPL). |
| * Introduction to MPFR:: Brief introduction to GNU MPFR. |
| * Installing MPFR:: How to configure and compile the MPFR library. |
| * Reporting Bugs:: How to usefully report bugs. |
| * MPFR Basics:: What every MPFR user should now. |
| * MPFR Interface:: MPFR functions and macros. |
| * Contributors:: |
| * References:: |
| * GNU Free Documentation License:: |
| * Concept Index:: |
| * Function Index:: |
| |
| |
| File: mpfr.info, Node: Copying, Next: Introduction to MPFR, Prev: Top, Up: Top |
| |
| MPFR Copying Conditions |
| *********************** |
| |
| This library is "free"; this means that everyone is free to use it and |
| free to redistribute it on a free basis. The library is not in the |
| public domain; it is copyrighted and there are restrictions on its |
| distribution, but these restrictions are designed to permit everything |
| that a good cooperating citizen would want to do. What is not allowed |
| is to try to prevent others from further sharing any version of this |
| library that they might get from you. |
| |
| Specifically, we want to make sure that you have the right to give |
| away copies of the library, that you receive source code or else can |
| get it if you want it, that you can change this library or use pieces |
| of it in new free programs, and that you know you can do these things. |
| |
| To make sure that everyone has such rights, we have to forbid you to |
| deprive anyone else of these rights. For example, if you distribute |
| copies of the GNU MPFR library, you must give the recipients all the |
| rights that you have. You must make sure that they, too, receive or |
| can get the source code. And you must tell them their rights. |
| |
| Also, for our own protection, we must make certain that everyone |
| finds out that there is no warranty for the GNU MPFR library. If it is |
| modified by someone else and passed on, we want their recipients to |
| know that what they have is not what we distributed, so that any |
| problems introduced by others will not reflect on our reputation. |
| |
| The precise conditions of the license for the GNU MPFR library are |
| found in the Lesser General Public License that accompanies the source |
| code. See the file COPYING.LIB. |
| |
| |
| File: mpfr.info, Node: Introduction to MPFR, Next: Installing MPFR, Prev: Copying, Up: Top |
| |
| 1 Introduction to MPFR |
| ********************** |
| |
| MPFR is a portable library written in C for arbitrary precision |
| arithmetic on floating-point numbers. It is based on the GNU MP library. |
| It aims to extend the class of floating-point numbers provided by the |
| GNU MP library by a precise semantics. The main differences with the |
| `mpf' class from GNU MP are: |
| |
| * the MPFR code is portable, i.e. the result of any operation does |
| not depend (or should not) on the machine word size |
| `mp_bits_per_limb' (32 or 64 on most machines); |
| |
| * the precision in bits can be set exactly to any valid value for |
| each variable (including very small precision); |
| |
| * MPFR provides the four rounding modes from the IEEE 754-1985 |
| standard. |
| |
| In particular, with a precision of 53 bits, MPFR should be able to |
| exactly reproduce all computations with double-precision machine |
| floating-point numbers (e.g., `double' type in C, with a C |
| implementation that rigorously follows Annex F of the ISO C99 standard |
| and `FP_CONTRACT' pragma set to `OFF') on the four arithmetic |
| operations and the square root, except the default exponent range is |
| much wider and subnormal numbers are not implemented (but can be |
| emulated). |
| |
| This version of MPFR is released under the GNU Lesser General Public |
| License, Version 2.1 or any later version. It is permitted to link |
| MPFR to most non-free programs, as long as when distributing them the |
| MPFR source code and a means to re-link with a modified MPFR library is |
| provided. |
| |
| 1.1 How to Use This Manual |
| ========================== |
| |
| Everyone should read *note MPFR Basics::. If you need to install the |
| library yourself, you need to read *note Installing MPFR::, too. |
| |
| The rest of the manual can be used for later reference, although it |
| is probably a good idea to glance through it. |
| |
| |
| File: mpfr.info, Node: Installing MPFR, Next: Reporting Bugs, Prev: Introduction to MPFR, Up: Top |
| |
| 2 Installing MPFR |
| ***************** |
| |
| 2.1 How to Install |
| ================== |
| |
| Here are the steps needed to install the library on Unix systems (more |
| details are provided in the `INSTALL' file): |
| |
| 1. To build MPFR, you first have to install GNU MP (version 4.1 or |
| higher) on your computer. You need a C compiler, preferably GCC, |
| but any reasonable compiler should work. And you need a standard |
| Unix `make' program, plus some other standard Unix utility |
| programs. |
| |
| 2. In the MPFR build directory, type `./configure' |
| |
| This will prepare the build and setup the options according to |
| your system. If you get error messages, you might check that you |
| use the same compiler and compile options as for GNU MP (see the |
| `INSTALL' file). |
| |
| 3. `make' |
| |
| This will compile MPFR, and create a library archive file |
| `libmpfr.a'. A dynamic library may be produced too (see |
| configure). |
| |
| 4. `make check' |
| |
| This will make sure MPFR was built correctly. If you get error |
| messages, please report this to `mpfr@loria.fr'. (*Note Reporting |
| Bugs::, for information on what to include in useful bug reports.) |
| |
| 5. `make install' |
| |
| This will copy the files `mpfr.h' and `mpf2mpfr.h' to the directory |
| `/usr/local/include', the file `libmpfr.a' to the directory |
| `/usr/local/lib', and the file `mpfr.info' to the directory |
| `/usr/local/share/info' (or if you passed the `--prefix' option to |
| `configure', using the prefix directory given as argument to |
| `--prefix' instead of `/usr/local'). |
| |
| 2.2 Other `make' Targets |
| ======================== |
| |
| There are some other useful make targets: |
| |
| * `mpfr.info' or `info' |
| |
| Create an info version of the manual, in `mpfr.info'. |
| |
| * `mpfr.pdf' or `pdf' |
| |
| Create a PDF version of the manual, in `mpfr.pdf'. |
| |
| * `mpfr.dvi' or `dvi' |
| |
| Create a DVI version of the manual, in `mpfr.dvi'. |
| |
| * `mpfr.ps' or `ps' |
| |
| Create a Postscript version of the manual, in `mpfr.ps'. |
| |
| * `mpfr.html' or `html' |
| |
| Create a HTML version of the manual, in several pages in the |
| directory `mpfr.html'; if you want only one output HTML file, then |
| type `makeinfo --html --no-split mpfr.texi' instead. |
| |
| * `clean' |
| |
| Delete all object files and archive files, but not the |
| configuration files. |
| |
| * `distclean' |
| |
| Delete all files not included in the distribution. |
| |
| * `uninstall' |
| |
| Delete all files copied by `make install'. |
| |
| 2.3 Build Problems |
| ================== |
| |
| In case of problem, please read the `INSTALL' file carefully before |
| reporting a bug, in particular section "In case of problem". Some |
| problems are due to bad configuration on the user side (not specific to |
| MPFR). Problems are also mentioned in the FAQ |
| `http://www.mpfr.org/faq.html'. |
| |
| Please report problems to `mpfr@loria.fr'. *Note Reporting Bugs::. |
| Some bug fixes are available on the MPFR 2.4.1 web page |
| `http://www.mpfr.org/mpfr-2.4.1/'. |
| |
| 2.4 Getting the Latest Version of MPFR |
| ====================================== |
| |
| The latest version of MPFR is available from |
| `ftp://ftp.gnu.org/gnu/mpfr/' or `http://www.mpfr.org/'. |
| |
| |
| File: mpfr.info, Node: Reporting Bugs, Next: MPFR Basics, Prev: Installing MPFR, Up: Top |
| |
| 3 Reporting Bugs |
| **************** |
| |
| If you think you have found a bug in the MPFR library, first have a look |
| on the MPFR 2.4.1 web page `http://www.mpfr.org/mpfr-2.4.1/' and the |
| FAQ `http://www.mpfr.org/faq.html': perhaps this bug is already known, |
| in which case you may find there a workaround for it. Otherwise, please |
| investigate and report it. We have made this library available to you, |
| and it is not to ask too much from you, to ask you to report the bugs |
| that you find. |
| |
| There are a few things you should think about when you put your bug |
| report together. |
| |
| You have to send us a test case that makes it possible for us to |
| reproduce the bug. Include instructions on how to run the test case. |
| |
| You also have to explain what is wrong; if you get a crash, or if |
| the results printed are incorrect and in that case, in what way. |
| |
| Please include compiler version information in your bug report. This |
| can be extracted using `cc -V' on some machines, or, if you're using |
| gcc, `gcc -v'. Also, include the output from `uname -a' and the MPFR |
| version (the GMP version may be useful too). |
| |
| If your bug report is good, we will do our best to help you to get a |
| corrected version of the library; if the bug report is poor, we will |
| not do anything about it (aside of chiding you to send better bug |
| reports). |
| |
| Send your bug report to: `mpfr@loria.fr'. |
| |
| If you think something in this manual is unclear, or downright |
| incorrect, or if the language needs to be improved, please send a note |
| to the same address. |
| |
| |
| File: mpfr.info, Node: MPFR Basics, Next: MPFR Interface, Prev: Reporting Bugs, Up: Top |
| |
| 4 MPFR Basics |
| ************* |
| |
| 4.1 Headers and Libraries |
| ========================= |
| |
| All declarations needed to use MPFR are collected in the include file |
| `mpfr.h'. It is designed to work with both C and C++ compilers. You |
| should include that file in any program using the MPFR library: |
| |
| #include <mpfr.h> |
| |
| Note however that prototypes for MPFR functions with `FILE *' |
| parameters are provided only if `<stdio.h>' is included too (before |
| `mpfr.h'). |
| |
| #include <stdio.h> |
| #include <mpfr.h> |
| |
| Likewise `<stdarg.h>' (or `<varargs.h>') is required for prototypes |
| with `va_list' parameters, such as `mpfr_vprintf'. |
| |
| You can avoid the use of MPFR macros encapsulating functions by |
| defining the `MPFR_USE_NO_MACRO' macro before `mpfr.h' is included. In |
| general this should not be necessary, but this can be useful when |
| debugging user code: with some macros, the compiler may emit spurious |
| warnings with some warning options, and macros can prevent some |
| prototype checking. |
| |
| All programs using MPFR must link against both `libmpfr' and |
| `libgmp' libraries. On a typical Unix-like system this can be done |
| with `-lmpfr -lgmp' (in that order), for example |
| |
| gcc myprogram.c -lmpfr -lgmp |
| |
| MPFR is built using Libtool and an application can use that to link |
| if desired, *note GNU Libtool: (libtool.info)Top. |
| |
| If MPFR has been installed to a non-standard location, then it may be |
| necessary to set up environment variables such as `C_INCLUDE_PATH' and |
| `LIBRARY_PATH', or use `-I' and `-L' compiler options, in order to |
| point to the right directories. For a shared library, it may also be |
| necessary to set up some sort of run-time library path (e.g., |
| `LD_LIBRARY_PATH') on some systems. Please read the `INSTALL' file for |
| additional information. |
| |
| 4.2 Nomenclature and Types |
| ========================== |
| |
| A "floating-point number" or "float" for short, is an arbitrary |
| precision significand (also called mantissa) with a limited precision |
| exponent. The C data type for such objects is `mpfr_t' (internally |
| defined as a one-element array of a structure, and `mpfr_ptr' is the C |
| data type representing a pointer to this structure). A floating-point |
| number can have three special values: Not-a-Number (NaN) or plus or |
| minus Infinity. NaN represents an uninitialized object, the result of |
| an invalid operation (like 0 divided by 0), or a value that cannot be |
| determined (like +Infinity minus +Infinity). Moreover, like in the IEEE |
| 754-1985 standard, zero is signed, i.e. there are both +0 and -0; the |
| behavior is the same as in the IEEE 754-1985 standard and it is |
| generalized to the other functions supported by MPFR. |
| |
| The "precision" is the number of bits used to represent the significand |
| of a floating-point number; the corresponding C data type is |
| `mp_prec_t'. The precision can be any integer between `MPFR_PREC_MIN' |
| and `MPFR_PREC_MAX'. In the current implementation, `MPFR_PREC_MIN' is |
| equal to 2. |
| |
| Warning! MPFR needs to increase the precision internally, in order to |
| provide accurate results (and in particular, correct rounding). Do not |
| attempt to set the precision to any value near `MPFR_PREC_MAX', |
| otherwise MPFR will abort due to an assertion failure. Moreover, you |
| may reach some memory limit on your platform, in which case the program |
| may abort, crash or have undefined behavior (depending on your C |
| implementation). |
| |
| The "rounding mode" specifies the way to round the result of a |
| floating-point operation, in case the exact result can not be |
| represented exactly in the destination significand; the corresponding C |
| data type is `mp_rnd_t'. |
| |
| A "limb" means the part of a multi-precision number that fits in a |
| single word. (We chose this word because a limb of the human body is |
| analogous to a digit, only larger, and containing several digits.) |
| Normally a limb contains 32 or 64 bits. The C data type for a limb is |
| `mp_limb_t'. |
| |
| 4.3 Function Classes |
| ==================== |
| |
| There is only one class of functions in the MPFR library: |
| |
| 1. Functions for floating-point arithmetic, with names beginning with |
| `mpfr_'. The associated type is `mpfr_t'. |
| |
| 4.4 MPFR Variable Conventions |
| ============================= |
| |
| As a general rule, all MPFR functions expect output arguments before |
| input arguments. This notation is based on an analogy with the |
| assignment operator. |
| |
| MPFR allows you to use the same variable for both input and output |
| in the same expression. For example, the main function for |
| floating-point multiplication, `mpfr_mul', can be used like this: |
| `mpfr_mul (x, x, x, rnd_mode)'. This computes the square of X with |
| rounding mode `rnd_mode' and puts the result back in X. |
| |
| Before you can assign to an MPFR variable, you need to initialize it |
| by calling one of the special initialization functions. When you're |
| done with a variable, you need to clear it out, using one of the |
| functions for that purpose. |
| |
| A variable should only be initialized once, or at least cleared out |
| between each initialization. After a variable has been initialized, it |
| may be assigned to any number of times. |
| |
| For efficiency reasons, avoid to initialize and clear out a variable |
| in loops. Instead, initialize it before entering the loop, and clear |
| it out after the loop has exited. |
| |
| You do not need to be concerned about allocating additional space |
| for MPFR variables, since any variable has a significand of fixed size. |
| Hence unless you change its precision, or clear and reinitialize it, a |
| floating-point variable will have the same allocated space during all |
| its life. |
| |
| 4.5 Rounding Modes |
| ================== |
| |
| The following four rounding modes are supported: |
| |
| * `GMP_RNDN': round to nearest |
| |
| * `GMP_RNDZ': round toward zero |
| |
| * `GMP_RNDU': round toward plus infinity |
| |
| * `GMP_RNDD': round toward minus infinity |
| |
| The `round to nearest' mode works as in the IEEE 754-1985 standard: |
| in case the number to be rounded lies exactly in the middle of two |
| representable numbers, it is rounded to the one with the least |
| significant bit set to zero. For example, the number 5/2, which is |
| represented by (10.1) in binary, is rounded to (10.0)=2 with a |
| precision of two bits, and not to (11.0)=3. This rule avoids the |
| "drift" phenomenon mentioned by Knuth in volume 2 of The Art of |
| Computer Programming (Section 4.2.2). |
| |
| Most MPFR functions take as first argument the destination variable, |
| as second and following arguments the input variables, as last argument |
| a rounding mode, and have a return value of type `int', called the |
| "ternary value". The value stored in the destination variable is |
| correctly rounded, i.e. MPFR behaves as if it computed the result with |
| an infinite precision, then rounded it to the precision of this |
| variable. The input variables are regarded as exact (in particular, |
| their precision does not affect the result). |
| |
| As a consequence, in case of a non-zero real rounded result, the |
| error on the result is less or equal to 1/2 ulp (unit in the last |
| place) of the target in the rounding to nearest mode, and less than 1 |
| ulp of the target in the directed rounding modes (a ulp is the weight |
| of the least significant represented bit of the target after rounding). |
| |
| Unless documented otherwise, functions returning an `int' return a |
| ternary value. If the ternary value is zero, it means that the value |
| stored in the destination variable is the exact result of the |
| corresponding mathematical function. If the ternary value is positive |
| (resp. negative), it means the value stored in the destination variable |
| is greater (resp. lower) than the exact result. For example with the |
| `GMP_RNDU' rounding mode, the ternary value is usually positive, except |
| when the result is exact, in which case it is zero. In the case of an |
| infinite result, it is considered as inexact when it was obtained by |
| overflow, and exact otherwise. A NaN result (Not-a-Number) always |
| corresponds to an exact return value. The opposite of a returned |
| ternary value is guaranteed to be representable in an `int'. |
| |
| Unless documented otherwise, functions returning a `1' (or any other |
| value specified in this manual) for special cases (like `acos(0)') |
| should return an overflow or an underflow if `1' is not representable |
| in the current exponent range. |
| |
| 4.6 Floating-Point Values on Special Numbers |
| ============================================ |
| |
| This section specifies the floating-point values (of type `mpfr_t') |
| returned by MPFR functions. For functions returning several values (like |
| `mpfr_sin_cos'), the rules apply to each result separately. |
| |
| Functions can have one or several input arguments. An input point is |
| a mapping from these input arguments to the set of the MPFR numbers. |
| When none of its components are NaN, an input point can also be seen as |
| a tuple in the extended real numbers (the set of the real numbers with |
| both infinities). |
| |
| When the input point is in the domain of the mathematical function, |
| the result is rounded as described in Section "Rounding Modes" (but see |
| below for the specification of the sign of an exact zero). Otherwise |
| the general rules from this section apply unless stated otherwise in |
| the description of the MPFR function (*note MPFR Interface::). |
| |
| When the input point is not in the domain of the mathematical |
| function but is in its closure in the extended real numbers and the |
| function can be extended by continuity, the result is the obtained |
| limit. Examples: `mpfr_hypot' on (+Inf,0) gives +Inf. But `mpfr_pow' |
| cannot be defined on (1,+Inf) using this rule, as one can find |
| sequences (X_N,Y_N) such that X_N goes to 1, Y_N goes to +Inf and X_N |
| to the Y_N goes to any positive value when N goes to the infinity. |
| |
| When the input point is in the closure of the domain of the |
| mathematical function and an input argument is +0 (resp. -0), one |
| considers the limit when the corresponding argument approaches 0 from |
| above (resp. below). If the limit is not defined (e.g., `mpfr_log' on |
| -0), the behavior must be specified in the description of the MPFR |
| function. |
| |
| When the result is equal to 0, its sign is determined by considering |
| the limit as if the input point were not in the domain: If one |
| approaches 0 from above (resp. below), the result is +0 (resp. -0). In |
| the other cases, the sign must be specified in the description of the |
| MPFR function. Example: `mpfr_sin' on +0 gives +0. |
| |
| When the input point is not in the closure of the domain of the |
| function, the result is NaN. Example: `mpfr_sqrt' on -17 gives NaN. |
| |
| When an input argument is NaN, the result is NaN, possibly except |
| when a partial function is constant on the finite floating-point |
| numbers; such a case is always explicitly specified in *note MPFR |
| Interface::. Example: `mpfr_hypot' on (NaN,0) gives NaN, but |
| `mpfr_hypot' on (NaN,+Inf) gives +Inf (as specified in *note Special |
| Functions::), since for any finite input X, `mpfr_hypot' on (X,+Inf) |
| gives +Inf. |
| |
| 4.7 Exceptions |
| ============== |
| |
| MPFR supports 5 exception types: |
| |
| * Underflow: An underflow occurs when the exact result of a function |
| is a non-zero real number and the result obtained after the |
| rounding, assuming an unbounded exponent range (for the rounding), |
| has an exponent smaller than the minimum exponent of the current |
| range. In the round-to-nearest mode, the halfway case is rounded |
| toward zero. |
| |
| Note: This is not the single definition of the underflow. MPFR |
| chooses to consider the underflow after rounding. The underflow |
| before rounding can also be defined. For instance, consider a |
| function that has the exact result 7 multiplied by two to the power |
| E-4, where E is the smallest exponent (for a significand between |
| 1/2 and 1) in the current range, with a 2-bit target precision and |
| rounding toward plus infinity. The exact result has the exponent |
| E-1. With the underflow before rounding, such a function call |
| would yield an underflow, as E-1 is outside the current exponent |
| range. However, MPFR first considers the rounded result assuming |
| an unbounded exponent range. The exact result cannot be |
| represented exactly in precision 2, and here, it is rounded to 0.5 |
| times 2 to E, which is representable in the current exponent |
| range. As a consequence, this will not yield an underflow in MPFR. |
| |
| * Overflow: An overflow occurs when the exact result of a function |
| is a non-zero real number and the result obtained after the |
| rounding, assuming an unbounded exponent range (for the rounding), |
| has an exponent larger than the maximum exponent of the current |
| range. In the round-to-nearest mode, the result is infinite. |
| |
| * NaN: A NaN exception occurs when the result of a function is a NaN. |
| |
| * Inexact: An inexact exception occurs when the result of a function |
| cannot be represented exactly and must be rounded. |
| |
| * Range error: A range exception occurs when a function that does |
| not return a MPFR number (such as comparisons and conversions to |
| an integer) has an invalid result (e.g. an argument is NaN in |
| `mpfr_cmp' or in a conversion to an integer). |
| |
| |
| MPFR has a global flag for each exception, which can be cleared, set |
| or tested by functions described in *note Exception Related Functions::. |
| |
| Differences with the ISO C99 standard: |
| |
| * In C, only quiet NaNs are specified, and a NaN propagation does not |
| raise an invalid exception. Unless explicitly stated otherwise, |
| MPFR sets the NaN flag whenever a NaN is generated, even when a |
| NaN is propagated (e.g. in NaN + NaN), as if all NaNs were |
| signaling. |
| |
| * An invalid exception in C corresponds to either a NaN exception or |
| a range error in MPFR. |
| |
| |
| 4.8 Memory Handling |
| =================== |
| |
| MPFR functions may create caches, e.g. when computing constants such as |
| Pi, either because the user has called a function like `mpfr_const_pi' |
| directly or because such a function was called internally by the MPFR |
| library itself to compute some other function. |
| |
| At any time, the user can free the various caches with |
| `mpfr_free_cache'. It is strongly advised to do that before terminating |
| a thread, or before exiting when using tools like `valgrind' (to avoid |
| memory leaks being reported). |
| |
| MPFR internal data such as flags, the exponent range, the default |
| precision and rounding mode, and caches (i.e., data that are not |
| accessed via parameters) are either global (if MPFR has not been |
| compiled as thread safe) or per-thread (thread local storage). |
| |
| |
| File: mpfr.info, Node: MPFR Interface, Next: Contributors, Prev: MPFR Basics, Up: Top |
| |
| 5 MPFR Interface |
| **************** |
| |
| The floating-point functions expect arguments of type `mpfr_t'. |
| |
| The MPFR floating-point functions have an interface that is similar |
| to the GNU MP integer functions. The function prefix for |
| floating-point operations is `mpfr_'. |
| |
| There is one significant characteristic of floating-point numbers |
| that has motivated a difference between this function class and other |
| GNU MP function classes: the inherent inexactness of floating-point |
| arithmetic. The user has to specify the precision for each variable. |
| A computation that assigns a variable will take place with the |
| precision of the assigned variable; the cost of that computation should |
| not depend from the precision of variables used as input (on average). |
| |
| The semantics of a calculation in MPFR is specified as follows: |
| Compute the requested operation exactly (with "infinite accuracy"), and |
| round the result to the precision of the destination variable, with the |
| given rounding mode. The MPFR floating-point functions are intended to |
| be a smooth extension of the IEEE 754-1985 arithmetic. The results |
| obtained on one computer should not differ from the results obtained on |
| a computer with a different word size. |
| |
| MPFR does not keep track of the accuracy of a computation. This is |
| left to the user or to a higher layer. As a consequence, if two |
| variables are used to store only a few significant bits, and their |
| product is stored in a variable with large precision, then MPFR will |
| still compute the result with full precision. |
| |
| The value of the standard C macro `errno' may be set to non-zero by |
| any MPFR function or macro, whether or not there is an error. |
| |
| * Menu: |
| |
| * Initialization Functions:: |
| * Assignment Functions:: |
| * Combined Initialization and Assignment Functions:: |
| * Conversion Functions:: |
| * Basic Arithmetic Functions:: |
| * Comparison Functions:: |
| * Special Functions:: |
| * Input and Output Functions:: |
| * Formatted Output Functions:: |
| * Integer Related Functions:: |
| * Rounding Related Functions:: |
| * Miscellaneous Functions:: |
| * Exception Related Functions:: |
| * Compatibility with MPF:: |
| * Custom Interface:: |
| * Internals:: |
| |
| |
| File: mpfr.info, Node: Initialization Functions, Next: Assignment Functions, Prev: MPFR Interface, Up: MPFR Interface |
| |
| 5.1 Initialization Functions |
| ============================ |
| |
| An `mpfr_t' object must be initialized before storing the first value in |
| it. The functions `mpfr_init' and `mpfr_init2' are used for that |
| purpose. |
| |
| -- Function: void mpfr_init2 (mpfr_t X, mp_prec_t PREC) |
| Initialize X, set its precision to be *exactly* PREC bits and its |
| value to NaN. (Warning: the corresponding `mpf' functions |
| initialize to zero instead.) |
| |
| Normally, a variable should be initialized once only or at least |
| be cleared, using `mpfr_clear', between initializations. To |
| change the precision of a variable which has already been |
| initialized, use `mpfr_set_prec'. The precision PREC must be an |
| integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX' (otherwise the |
| behavior is undefined). |
| |
| -- Function: void mpfr_inits2 (mp_prec_t PREC, mpfr_t X, ...) |
| Initialize all the `mpfr_t' variables of the given `va_list', set |
| their precision to be *exactly* PREC bits and their value to NaN. |
| See `mpfr_init2' for more details. The `va_list' is assumed to be |
| composed only of type `mpfr_t' (or equivalently `mpfr_ptr'). It |
| begins from X. It ends when it encounters a null pointer (whose |
| type must also be `mpfr_ptr'). |
| |
| -- Function: void mpfr_clear (mpfr_t X) |
| Free the space occupied by X. Make sure to call this function for |
| all `mpfr_t' variables when you are done with them. |
| |
| -- Function: void mpfr_clears (mpfr_t X, ...) |
| Free the space occupied by all the `mpfr_t' variables of the given |
| `va_list'. See `mpfr_clear' for more details. The `va_list' is |
| assumed to be composed only of type `mpfr_t' (or equivalently |
| `mpfr_ptr'). It begins from X. It ends when it encounters a null |
| pointer (whose type must also be `mpfr_ptr'). |
| |
| Here is an example of how to use multiple initialization functions: |
| |
| { |
| mpfr_t x, y, z, t; |
| mpfr_inits2 (256, x, y, z, t, (mpfr_ptr) 0); |
| ... |
| mpfr_clears (x, y, z, t, (mpfr_ptr) 0); |
| } |
| |
| -- Function: void mpfr_init (mpfr_t X) |
| Initialize X and set its value to NaN. |
| |
| Normally, a variable should be initialized once only or at least |
| be cleared, using `mpfr_clear', between initializations. The |
| precision of X is the default precision, which can be changed by a |
| call to `mpfr_set_default_prec'. |
| |
| Warning! In a given program, some other libraries might change the |
| default precision and not restore it. Thus it is safer to use |
| `mpfr_init2'. |
| |
| -- Function: void mpfr_inits (mpfr_t X, ...) |
| Initialize all the `mpfr_t' variables of the given `va_list', set |
| their precision to be the default precision and their value to NaN. |
| See `mpfr_init' for more details. The `va_list' is assumed to be |
| composed only of type `mpfr_t' (or equivalently `mpfr_ptr'). It |
| begins from X. It ends when it encounters a null pointer (whose |
| type must also be `mpfr_ptr'). |
| |
| Warning! In a given program, some other libraries might change the |
| default precision and not restore it. Thus it is safer to use |
| `mpfr_inits2'. |
| |
| -- Macro: MPFR_DECL_INIT (NAME, PREC) |
| This macro declares NAME as an automatic variable of type `mpfr_t', |
| initializes it and sets its precision to be *exactly* PREC bits |
| and its value to NaN. NAME must be a valid identifier. You must |
| use this macro in the declaration section. This macro is much |
| faster than using `mpfr_init2' but has some drawbacks: |
| |
| * You *must not* call `mpfr_clear' with variables created with |
| this macro (the storage is allocated at the point of |
| declaration and deallocated when the brace-level is exited). |
| |
| * You *cannot* change their precision. |
| |
| * You *should not* create variables with huge precision with |
| this macro. |
| |
| * Your compiler must support `Non-Constant Initializers' |
| (standard in C++ and ISO C99) and `Token Pasting' (standard |
| in ISO C89). If PREC is not a constant expression, your |
| compiler must support `variable-length automatic arrays' |
| (standard in ISO C99). `GCC 2.95.3' and above supports all |
| these features. If you compile your program with gcc in c89 |
| mode and with `-pedantic', you may want to define the |
| `MPFR_USE_EXTENSION' macro to avoid warnings due to the |
| `MPFR_DECL_INIT' implementation. |
| |
| -- Function: void mpfr_set_default_prec (mp_prec_t PREC) |
| Set the default precision to be *exactly* PREC bits. The |
| precision of a variable means the number of bits used to store its |
| significand. All subsequent calls to `mpfr_init' will use this |
| precision, but previously initialized variables are unaffected. |
| This default precision is set to 53 bits initially. The precision |
| can be any integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX'. |
| |
| -- Function: mp_prec_t mpfr_get_default_prec (void) |
| Return the default MPFR precision in bits. |
| |
| Here is an example on how to initialize floating-point variables: |
| |
| { |
| mpfr_t x, y; |
| mpfr_init (x); /* use default precision */ |
| mpfr_init2 (y, 256); /* precision _exactly_ 256 bits */ |
| ... |
| /* When the program is about to exit, do ... */ |
| mpfr_clear (x); |
| mpfr_clear (y); |
| mpfr_free_cache (); |
| } |
| |
| The following functions are useful for changing the precision during |
| a calculation. A typical use would be for adjusting the precision |
| gradually in iterative algorithms like Newton-Raphson, making the |
| computation precision closely match the actual accurate part of the |
| numbers. |
| |
| -- Function: void mpfr_set_prec (mpfr_t X, mp_prec_t PREC) |
| Reset the precision of X to be *exactly* PREC bits, and set its |
| value to NaN. The previous value stored in X is lost. It is |
| equivalent to a call to `mpfr_clear(x)' followed by a call to |
| `mpfr_init2(x, prec)', but more efficient as no allocation is done |
| in case the current allocated space for the significand of X is |
| enough. The precision PREC can be any integer between |
| `MPFR_PREC_MIN' and `MPFR_PREC_MAX'. |
| |
| In case you want to keep the previous value stored in X, use |
| `mpfr_prec_round' instead. |
| |
| -- Function: mp_prec_t mpfr_get_prec (mpfr_t X) |
| Return the precision actually used for assignments of X, i.e. the |
| number of bits used to store its significand. |
| |
| |
| File: mpfr.info, Node: Assignment Functions, Next: Combined Initialization and Assignment Functions, Prev: Initialization Functions, Up: MPFR Interface |
| |
| 5.2 Assignment Functions |
| ======================== |
| |
| These functions assign new values to already initialized floats (*note |
| Initialization Functions::). When using any functions using `intmax_t', |
| you must include `<stdint.h>' or `<inttypes.h>' before `mpfr.h', to |
| allow `mpfr.h' to define prototypes for these functions. |
| |
| -- Function: int mpfr_set (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_ui (mpfr_t ROP, unsigned long int OP, |
| mp_rnd_t RND) |
| -- Function: int mpfr_set_si (mpfr_t ROP, long int OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_uj (mpfr_t ROP, uintmax_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_sj (mpfr_t ROP, intmax_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_d (mpfr_t ROP, double OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_ld (mpfr_t ROP, long double OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_decimal64 (mpfr_t ROP, _Decimal64 OP, |
| mp_rnd_t RND) |
| -- Function: int mpfr_set_z (mpfr_t ROP, mpz_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_q (mpfr_t ROP, mpq_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_set_f (mpfr_t ROP, mpf_t OP, mp_rnd_t RND) |
| Set the value of ROP from OP, rounded toward the given direction |
| RND. Note that the input 0 is converted to +0 by `mpfr_set_ui', |
| `mpfr_set_si', `mpfr_set_sj', `mpfr_set_uj', `mpfr_set_z', |
| `mpfr_set_q' and `mpfr_set_f', regardless of the rounding mode. |
| If the system does not support the IEEE-754 standard, `mpfr_set_d', |
| `mpfr_set_ld' and `mpfr_set_decimal64' might not preserve the |
| signed zeros. The `mpfr_set_decimal64' function is built only |
| with the configure option `--enable-decimal-float', which also |
| requires `--with-gmp-build', and when the compiler or system |
| provides the `_Decimal64' data type (GCC version 4.2.0 is known to |
| support this data type, but only when configured with |
| `--enable-decimal-float' too). `mpfr_set_q' might not be able to |
| work if the numerator (or the denominator) can not be |
| representable as a `mpfr_t'. |
| |
| Note: If you want to store a floating-point constant to a `mpfr_t', |
| you should use `mpfr_set_str' (or one of the MPFR constant |
| functions, such as `mpfr_const_pi' for Pi) instead of `mpfr_set_d', |
| `mpfr_set_ld' or `mpfr_set_decimal64'. Otherwise the |
| floating-point constant will be first converted into a |
| reduced-precision (e.g., 53-bit) binary number before MPFR can |
| work with it. |
| |
| -- Function: int mpfr_set_ui_2exp (mpfr_t ROP, unsigned long int OP, |
| mp_exp_t E, mp_rnd_t RND) |
| -- Function: int mpfr_set_si_2exp (mpfr_t ROP, long int OP, mp_exp_t |
| E, mp_rnd_t RND) |
| -- Function: int mpfr_set_uj_2exp (mpfr_t ROP, uintmax_t OP, intmax_t |
| E, mp_rnd_t RND) |
| -- Function: int mpfr_set_sj_2exp (mpfr_t ROP, intmax_t OP, intmax_t |
| E, mp_rnd_t RND) |
| Set the value of ROP from OP multiplied by two to the power E, |
| rounded toward the given direction RND. Note that the input 0 is |
| converted to +0. |
| |
| -- Function: int mpfr_set_str (mpfr_t ROP, const char *S, int BASE, |
| mp_rnd_t RND) |
| Set ROP to the value of the string S in base BASE, rounded in the |
| direction RND. See the documentation of `mpfr_strtofr' for a |
| detailed description of the valid string formats. Contrary to |
| `mpfr_strtofr', `mpfr_set_str' requires the _whole_ string to |
| represent a valid floating-point number. This function returns 0 |
| if the entire string up to the final null character is a valid |
| number in base BASE; otherwise it returns -1, and ROP may have |
| changed. |
| |
| -- Function: int mpfr_strtofr (mpfr_t ROP, const char *NPTR, char |
| **ENDPTR, int BASE, mp_rnd_t RND) |
| Read a floating-point number from a string NPTR in base BASE, |
| rounded in the direction RND; BASE must be either 0 (to detect the |
| base, as described below) or a number from 2 to 36 (otherwise the |
| behavior is undefined). If NPTR starts with valid data, the result |
| is stored in ROP and `*ENDPTR' points to the character just after |
| the valid data (if ENDPTR is not a null pointer); otherwise ROP is |
| set to zero and the value of NPTR is stored in the location |
| referenced by ENDPTR (if ENDPTR is not a null pointer). The usual |
| ternary value is returned. |
| |
| Parsing follows the standard C `strtod' function with some |
| extensions. Case is ignored. After optional leading whitespace, |
| one has a subject sequence consisting of an optional sign (`+' or |
| `-'), and either numeric data or special data. The subject |
| sequence is defined as the longest initial subsequence of the |
| input string, starting with the first non-whitespace character, |
| that is of the expected form. |
| |
| The form of numeric data is a non-empty sequence of significand |
| digits with an optional decimal point, and an optional exponent |
| consisting of an exponent prefix followed by an optional sign and |
| a non-empty sequence of decimal digits. A significand digit is |
| either a decimal digit or a Latin letter (62 possible characters), |
| with `a' = 10, `b' = 11, ..., `z' = 35; its value must be strictly |
| less than the base. The decimal point can be either the one |
| defined by the current locale or the period (the first one is |
| accepted for consistency with the C standard and the practice, the |
| second one is accepted to allow the programmer to provide MPFR |
| numbers from strings in a way that does not depend on the current |
| locale). The exponent prefix can be `e' or `E' for bases up to |
| 10, or `@' in any base; it indicates a multiplication by a power |
| of the base. In bases 2 and 16, the exponent prefix can also be |
| `p' or `P', in which case it introduces a binary exponent: it |
| indicates a multiplication by a power of 2 (there is a difference |
| only for base 16). The value of an exponent is always written in |
| base 10. In base 2, the significand can start with `0b' or `0B', |
| and in base 16, it can start with `0x' or `0X'. |
| |
| If the argument BASE is 0, then the base is automatically detected |
| as follows. If the significand starts with `0b' or `0B', base 2 is |
| assumed. If the significand starts with `0x' or `0X', base 16 is |
| assumed. Otherwise base 10 is assumed. |
| |
| Note: The exponent must contain at least a digit. Otherwise the |
| possible exponent prefix and sign are not part of the number |
| (which ends with the significand). Similarly, if `0b', `0B', `0x' |
| or `0X' is not followed by a binary/hexadecimal digit, then the |
| subject sequence stops at the character `0'. |
| |
| Special data (for infinities and NaN) can be `@inf@' or |
| `@nan@(n-char-sequence)', and if BASE <= 16, it can also be |
| `infinity', `inf', `nan' or `nan(n-char-sequence)', all case |
| insensitive. A `n-char-sequence' is a non-empty string containing |
| only digits, Latin letters and the underscore (0, 1, 2, ..., 9, a, |
| b, ..., z, A, B, ..., Z, _). Note: one has an optional sign for |
| all data, even NaN. |
| |
| |
| -- Function: void mpfr_set_inf (mpfr_t X, int SIGN) |
| -- Function: void mpfr_set_nan (mpfr_t X) |
| Set the variable X to infinity or NaN (Not-a-Number) respectively. |
| In `mpfr_set_inf', X is set to plus infinity iff SIGN is |
| nonnegative. |
| |
| -- Function: void mpfr_swap (mpfr_t X, mpfr_t Y) |
| Swap the values X and Y efficiently. Warning: the precisions are |
| exchanged too; in case the precisions are different, `mpfr_swap' |
| is thus not equivalent to three `mpfr_set' calls using a third |
| auxiliary variable. |
| |
| |
| File: mpfr.info, Node: Combined Initialization and Assignment Functions, Next: Conversion Functions, Prev: Assignment Functions, Up: MPFR Interface |
| |
| 5.3 Combined Initialization and Assignment Functions |
| ==================================================== |
| |
| -- Macro: int mpfr_init_set (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_ui (mpfr_t ROP, unsigned long int OP, |
| mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_si (mpfr_t ROP, signed long int OP, |
| mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_d (mpfr_t ROP, double OP, mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_ld (mpfr_t ROP, long double OP, mp_rnd_t |
| RND) |
| -- Macro: int mpfr_init_set_z (mpfr_t ROP, mpz_t OP, mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_q (mpfr_t ROP, mpq_t OP, mp_rnd_t RND) |
| -- Macro: int mpfr_init_set_f (mpfr_t ROP, mpf_t OP, mp_rnd_t RND) |
| Initialize ROP and set its value from OP, rounded in the direction |
| RND. The precision of ROP will be taken from the active default |
| precision, as set by `mpfr_set_default_prec'. |
| |
| -- Function: int mpfr_init_set_str (mpfr_t X, const char *S, int BASE, |
| mp_rnd_t RND) |
| Initialize X and set its value from the string S in base BASE, |
| rounded in the direction RND. See `mpfr_set_str'. |
| |
| |
| File: mpfr.info, Node: Conversion Functions, Next: Basic Arithmetic Functions, Prev: Combined Initialization and Assignment Functions, Up: MPFR Interface |
| |
| 5.4 Conversion Functions |
| ======================== |
| |
| -- Function: double mpfr_get_d (mpfr_t OP, mp_rnd_t RND) |
| -- Function: long double mpfr_get_ld (mpfr_t OP, mp_rnd_t RND) |
| -- Function: _Decimal64 mpfr_get_decimal64 (mpfr_t OP, mp_rnd_t RND) |
| Convert OP to a `double' (respectively `_Decimal64' or `long |
| double'), using the rounding mode RND. If OP is NaN, some fixed |
| NaN (either quiet or signaling) or the result of 0.0/0.0 is |
| returned. If OP is ±Inf, an infinity of the same sign or the |
| result of ±1.0/0.0 is returned. If OP is zero, these functions |
| return a zero, trying to preserve its sign, if possible. The |
| `mpfr_get_decimal64' function is built only under some conditions: |
| see the documentation of `mpfr_set_decimal64'. |
| |
| -- Function: double mpfr_get_d_2exp (long *EXP, mpfr_t OP, mp_rnd_t |
| RND) |
| -- Function: long double mpfr_get_ld_2exp (long *EXP, mpfr_t OP, |
| mp_rnd_t RND) |
| Return D and set EXP such that 0.5<=abs(D)<1 and D times 2 raised |
| to EXP equals OP rounded to double (resp. long double) precision, |
| using the given rounding mode. If OP is zero, then a zero of the |
| same sign (or an unsigned zero, if the implementation does not |
| have signed zeros) is returned, and EXP is set to 0. If OP is NaN |
| or an infinity, then the corresponding double precision (resp. |
| long-double precision) value is returned, and EXP is undefined. |
| |
| -- Function: long mpfr_get_si (mpfr_t OP, mp_rnd_t RND) |
| -- Function: unsigned long mpfr_get_ui (mpfr_t OP, mp_rnd_t RND) |
| -- Function: intmax_t mpfr_get_sj (mpfr_t OP, mp_rnd_t RND) |
| -- Function: uintmax_t mpfr_get_uj (mpfr_t OP, mp_rnd_t RND) |
| Convert OP to a `long', an `unsigned long', an `intmax_t' or an |
| `uintmax_t' (respectively) after rounding it with respect to RND. |
| If OP is NaN, the result is undefined. If OP is too big for the |
| return type, it returns the maximum or the minimum of the |
| corresponding C type, depending on the direction of the overflow. |
| The _erange_ flag is set too. See also `mpfr_fits_slong_p', |
| `mpfr_fits_ulong_p', `mpfr_fits_intmax_p' and |
| `mpfr_fits_uintmax_p'. |
| |
| -- Function: mp_exp_t mpfr_get_z_exp (mpz_t ROP, mpfr_t OP) |
| Put the scaled significand of OP (regarded as an integer, with the |
| precision of OP) into ROP, and return the exponent EXP (which may |
| be outside the current exponent range) such that OP exactly equals |
| ROP multiplied by two exponent EXP. If the exponent is not |
| representable in the `mp_exp_t' type, the behavior is undefined. |
| |
| -- Function: void mpfr_get_z (mpz_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Convert OP to a `mpz_t', after rounding it with respect to RND. If |
| OP is NaN or Inf, the result is undefined. |
| |
| -- Function: int mpfr_get_f (mpf_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Convert OP to a `mpf_t', after rounding it with respect to RND. |
| Return zero iff no error occurred, in particular a non-zero value |
| is returned if OP is NaN or Inf, which do not exist in `mpf'. |
| |
| -- Function: char * mpfr_get_str (char *STR, mp_exp_t *EXPPTR, int B, |
| size_t N, mpfr_t OP, mp_rnd_t RND) |
| Convert OP to a string of digits in base B, with rounding in the |
| direction RND, where N is either zero (see below) or the number of |
| significant digits; in the latter case, N must be greater or equal |
| to 2. The base may vary from 2 to 36. |
| |
| The generated string is a fraction, with an implicit radix point |
| immediately to the left of the first digit. For example, the |
| number -3.1416 would be returned as "-31416" in the string and 1 |
| written at EXPPTR. If RND is to nearest, and OP is exactly in the |
| middle of two possible outputs, the one with an even last digit is |
| chosen (for an odd base, this may not correspond to an even |
| significand). |
| |
| If N is zero, the number of digits of the significand is chosen |
| large enough so that re-reading the printed value with the same |
| precision, assuming both output and input use rounding to nearest, |
| will recover the original value of OP. More precisely, in most |
| cases, the chosen precision of STR is the minimal precision |
| depending on N and B only that satisfies the above property, i.e., |
| m = 1 + ceil(N*log(2)/log(B)), but in some very rare cases, it |
| might be m+1. |
| |
| If STR is a null pointer, space for the significand is allocated |
| using the current allocation function, and a pointer to the string |
| is returned. To free the returned string, you must use |
| `mpfr_free_str'. |
| |
| If STR is not a null pointer, it should point to a block of storage |
| large enough for the significand, i.e., at least `max(N + 2, 7)'. |
| The extra two bytes are for a possible minus sign, and for the |
| terminating null character. |
| |
| If the input number is an ordinary number, the exponent is written |
| through the pointer EXPPTR (the current minimal exponent for 0). |
| |
| A pointer to the string is returned, unless there is an error, in |
| which case a null pointer is returned. |
| |
| -- Function: void mpfr_free_str (char *STR) |
| Free a string allocated by `mpfr_get_str' using the current |
| unallocation function (preliminary interface). The block is |
| assumed to be `strlen(STR)+1' bytes. For more information about |
| how it is done: *note Custom Allocation: (gmp.info)Custom |
| Allocation. |
| |
| -- Function: int mpfr_fits_ulong_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_slong_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_uint_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_sint_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_ushort_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_sshort_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_intmax_p (mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_fits_uintmax_p (mpfr_t OP, mp_rnd_t RND) |
| Return non-zero if OP would fit in the respective C data type, when |
| rounded to an integer in the direction RND. |
| |
| |
| File: mpfr.info, Node: Basic Arithmetic Functions, Next: Comparison Functions, Prev: Conversion Functions, Up: MPFR Interface |
| |
| 5.5 Basic Arithmetic Functions |
| ============================== |
| |
| -- Function: int mpfr_add (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_add_ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_add_si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_add_d (mpfr_t ROP, mpfr_t OP1, double OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_add_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_add_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1 + OP2 rounded in the direction RND. For types |
| having no signed zero, it is considered unsigned (i.e. (+0) + 0 = |
| (+0) and (-0) + 0 = (-0)). The `mpfr_add_d' function assumes that |
| the radix of the `double' type is a power of 2, with a precision |
| at most that declared by the C implementation (macro |
| `IEEE_DBL_MANT_DIG', and if not defined 53 bits). |
| |
| -- Function: int mpfr_sub (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_ui_sub (mpfr_t ROP, unsigned long int OP1, |
| mpfr_t OP2, mp_rnd_t RND) |
| -- Function: int mpfr_sub_ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_si_sub (mpfr_t ROP, long int OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_sub_si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_d_sub (mpfr_t ROP, double OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_sub_d (mpfr_t ROP, mpfr_t OP1, double OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_sub_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_sub_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1 - OP2 rounded in the direction RND. For types |
| having no signed zero, it is considered unsigned (i.e. (+0) - 0 = |
| (+0), (-0) - 0 = (-0), 0 - (+0) = (-0) and 0 - (-0) = (+0)). The |
| same restrictions than for `mpfr_add_d' apply to `mpfr_d_sub' and |
| `mpfr_sub_d'. |
| |
| -- Function: int mpfr_mul (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_mul_ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_mul_si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_mul_d (mpfr_t ROP, mpfr_t OP1, double OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_mul_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_mul_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1 times OP2 rounded in the direction RND. When a |
| result is zero, its sign is the product of the signs of the |
| operands (for types having no signed zero, it is considered |
| positive). The same restrictions than for `mpfr_add_d' apply to |
| `mpfr_mul_d'. |
| |
| -- Function: int mpfr_sqr (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the square of OP rounded in the direction RND. |
| |
| -- Function: int mpfr_div (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_ui_div (mpfr_t ROP, unsigned long int OP1, |
| mpfr_t OP2, mp_rnd_t RND) |
| -- Function: int mpfr_div_ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_si_div (mpfr_t ROP, long int OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_div_si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_d_div (mpfr_t ROP, double OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_div_d (mpfr_t ROP, mpfr_t OP1, double OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_div_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_div_q (mpfr_t ROP, mpfr_t OP1, mpq_t OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1/OP2 rounded in the direction RND. When a result is |
| zero, its sign is the product of the signs of the operands (for |
| types having no signed zero, it is considered positive). The same |
| restrictions than for `mpfr_add_d' apply to `mpfr_d_div' and |
| `mpfr_div_d'. |
| |
| -- Function: int mpfr_sqrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_sqrt_ui (mpfr_t ROP, unsigned long int OP, |
| mp_rnd_t RND) |
| Set ROP to the square root of OP rounded in the direction RND. |
| Return -0 if OP is -0 (to be consistent with the IEEE 754-1985 |
| standard). Set ROP to NaN if OP is negative. |
| |
| -- Function: int mpfr_rec_sqrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the reciprocal square root of OP rounded in the |
| direction RND. Return +Inf if OP is ±0, and +0 if OP is +Inf. Set |
| ROP to NaN if OP is negative. |
| |
| -- Function: int mpfr_cbrt (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_root (mpfr_t ROP, mpfr_t OP, unsigned long int |
| K, mp_rnd_t RND) |
| Set ROP to the cubic root (resp. the Kth root) of OP rounded in |
| the direction RND. An odd (resp. even) root of a negative number |
| (including -Inf) returns a negative number (resp. NaN). The Kth |
| root of -0 is defined to be -0, whatever the parity of K. |
| |
| -- Function: int mpfr_pow (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_pow_ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_pow_si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_pow_z (mpfr_t ROP, mpfr_t OP1, mpz_t OP2, |
| mp_rnd_t RND) |
| -- Function: int mpfr_ui_pow_ui (mpfr_t ROP, unsigned long int OP1, |
| unsigned long int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_ui_pow (mpfr_t ROP, unsigned long int OP1, |
| mpfr_t OP2, mp_rnd_t RND) |
| Set ROP to OP1 raised to OP2, rounded in the direction RND. |
| Special values are currently handled as described in the ISO C99 |
| standard for the `pow' function (note this may change in future |
| versions): |
| * `pow(±0, Y)' returns plus or minus infinity for Y a negative |
| odd integer. |
| |
| * `pow(±0, Y)' returns plus infinity for Y negative and not an |
| odd integer. |
| |
| * `pow(±0, Y)' returns plus or minus zero for Y a positive odd |
| integer. |
| |
| * `pow(±0, Y)' returns plus zero for Y positive and not an odd |
| integer. |
| |
| * `pow(-1, ±Inf)' returns 1. |
| |
| * `pow(+1, Y)' returns 1 for any Y, even a NaN. |
| |
| * `pow(X, ±0)' returns 1 for any X, even a NaN. |
| |
| * `pow(X, Y)' returns NaN for finite negative X and finite |
| non-integer Y. |
| |
| * `pow(X, -Inf)' returns plus infinity for 0 < abs(x) < 1, and |
| plus zero for abs(x) > 1. |
| |
| * `pow(X, +Inf)' returns plus zero for 0 < abs(x) < 1, and plus |
| infinity for abs(x) > 1. |
| |
| * `pow(-Inf, Y)' returns minus zero for Y a negative odd |
| integer. |
| |
| * `pow(-Inf, Y)' returns plus zero for Y negative and not an |
| odd integer. |
| |
| * `pow(-Inf, Y)' returns minus infinity for Y a positive odd |
| integer. |
| |
| * `pow(-Inf, Y)' returns plus infinity for Y positive and not |
| an odd integer. |
| |
| * `pow(+Inf, Y)' returns plus zero for Y negative, and plus |
| infinity for Y positive. |
| |
| -- Function: int mpfr_neg (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to -OP rounded in the direction RND. Just changes the |
| sign if ROP and OP are the same variable. |
| |
| -- Function: int mpfr_abs (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the absolute value of OP, rounded in the direction RND. |
| Just changes the sign if ROP and OP are the same variable. |
| |
| -- Function: int mpfr_dim (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Set ROP to the positive difference of OP1 and OP2, i.e., OP1 - OP2 |
| rounded in the direction RND if OP1 > OP2, and +0 otherwise. |
| Returns NaN when OP1 or OP2 is NaN. |
| |
| -- Function: int mpfr_mul_2ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_mul_2si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1 times 2 raised to OP2 rounded in the direction RND. |
| Just increases the exponent by OP2 when ROP and OP1 are identical. |
| |
| -- Function: int mpfr_div_2ui (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_div_2si (mpfr_t ROP, mpfr_t OP1, long int OP2, |
| mp_rnd_t RND) |
| Set ROP to OP1 divided by 2 raised to OP2 rounded in the direction |
| RND. Just decreases the exponent by OP2 when ROP and OP1 are |
| identical. |
| |
| |
| File: mpfr.info, Node: Comparison Functions, Next: Special Functions, Prev: Basic Arithmetic Functions, Up: MPFR Interface |
| |
| 5.6 Comparison Functions |
| ======================== |
| |
| -- Function: int mpfr_cmp (mpfr_t OP1, mpfr_t OP2) |
| -- Function: int mpfr_cmp_ui (mpfr_t OP1, unsigned long int OP2) |
| -- Function: int mpfr_cmp_si (mpfr_t OP1, signed long int OP2) |
| -- Function: int mpfr_cmp_d (mpfr_t OP1, double OP2) |
| -- Function: int mpfr_cmp_ld (mpfr_t OP1, long double OP2) |
| -- Function: int mpfr_cmp_z (mpfr_t OP1, mpz_t OP2) |
| -- Function: int mpfr_cmp_q (mpfr_t OP1, mpq_t OP2) |
| -- Function: int mpfr_cmp_f (mpfr_t OP1, mpf_t OP2) |
| Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero |
| if OP1 = OP2, and a negative value if OP1 < OP2. Both OP1 and OP2 |
| are considered to their full own precision, which may differ. If |
| one of the operands is NaN, set the _erange_ flag and return zero. |
| |
| Note: These functions may be useful to distinguish the three |
| possible cases. If you need to distinguish two cases only, it is |
| recommended to use the predicate functions (e.g., `mpfr_equal_p' |
| for the equality) described below; they behave like the IEEE-754 |
| comparisons, in particular when one or both arguments are NaN. But |
| only floating-point numbers can be compared (you may need to do a |
| conversion first). |
| |
| -- Function: int mpfr_cmp_ui_2exp (mpfr_t OP1, unsigned long int OP2, |
| mp_exp_t E) |
| -- Function: int mpfr_cmp_si_2exp (mpfr_t OP1, long int OP2, mp_exp_t |
| E) |
| Compare OP1 and OP2 multiplied by two to the power E. Similar as |
| above. |
| |
| -- Function: int mpfr_cmpabs (mpfr_t OP1, mpfr_t OP2) |
| Compare |OP1| and |OP2|. Return a positive value if |OP1| > |
| |OP2|, zero if |OP1| = |OP2|, and a negative value if |OP1| < |
| |OP2|. If one of the operands is NaN, set the _erange_ flag and |
| return zero. |
| |
| -- Function: int mpfr_nan_p (mpfr_t OP) |
| -- Function: int mpfr_inf_p (mpfr_t OP) |
| -- Function: int mpfr_number_p (mpfr_t OP) |
| -- Function: int mpfr_zero_p (mpfr_t OP) |
| Return non-zero if OP is respectively NaN, an infinity, an ordinary |
| number (i.e. neither NaN nor an infinity) or zero. Return zero |
| otherwise. |
| |
| -- Macro: int mpfr_sgn (mpfr_t OP) |
| Return a positive value if OP > 0, zero if OP = 0, and a negative |
| value if OP < 0. If the operand is NaN, set the _erange_ flag and |
| return zero. |
| |
| -- Function: int mpfr_greater_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 > OP2, zero otherwise. |
| |
| -- Function: int mpfr_greaterequal_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 >= OP2, zero otherwise. |
| |
| -- Function: int mpfr_less_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 < OP2, zero otherwise. |
| |
| -- Function: int mpfr_lessequal_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 <= OP2, zero otherwise. |
| |
| -- Function: int mpfr_lessgreater_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 < OP2 or OP1 > OP2 (i.e. neither OP1, nor |
| OP2 is NaN, and OP1 <> OP2), zero otherwise (i.e. OP1 and/or OP2 |
| are NaN, or OP1 = OP2). |
| |
| -- Function: int mpfr_equal_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 = OP2, zero otherwise (i.e. OP1 and/or OP2 |
| are NaN, or OP1 <> OP2). |
| |
| -- Function: int mpfr_unordered_p (mpfr_t OP1, mpfr_t OP2) |
| Return non-zero if OP1 or OP2 is a NaN (i.e. they cannot be |
| compared), zero otherwise. |
| |
| |
| File: mpfr.info, Node: Special Functions, Next: Input and Output Functions, Prev: Comparison Functions, Up: MPFR Interface |
| |
| 5.7 Special Functions |
| ===================== |
| |
| All those functions, except explicitly stated, return zero for an exact |
| return value, a positive value for a return value larger than the exact |
| result, and a negative value otherwise. |
| |
| Important note: in some domains, computing special functions (either |
| with correct or incorrect rounding) is expensive, even for small |
| precision, for example the trigonometric and Bessel functions for large |
| argument. |
| |
| -- Function: int mpfr_log (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_log2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_log10 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the natural logarithm of OP, log2(OP) or log10(OP), |
| respectively, rounded in the direction RND. Return -Inf if OP is |
| -0 (i.e. the sign of the zero has no influence on the result). |
| |
| -- Function: int mpfr_exp (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_exp2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_exp10 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the exponential of OP, to 2 power of OP or to 10 power |
| of OP, respectively, rounded in the direction RND. |
| |
| -- Function: int mpfr_cos (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_sin (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_tan (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the cosine of OP, sine of OP, tangent of OP, rounded in |
| the direction RND. |
| |
| -- Function: int mpfr_sec (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_csc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_cot (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the secant of OP, cosecant of OP, cotangent of OP, |
| rounded in the direction RND. |
| |
| -- Function: int mpfr_sin_cos (mpfr_t SOP, mpfr_t COP, mpfr_t OP, |
| mp_rnd_t RND) |
| Set simultaneously SOP to the sine of OP and |
| COP to the cosine of OP, rounded in the direction RND with the |
| corresponding precisions of SOP and COP, which must be different |
| variables. Return 0 iff both results are exact. |
| |
| -- Function: int mpfr_acos (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_asin (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_atan (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the arc-cosine, arc-sine or arc-tangent of OP, rounded |
| in the direction RND. Note that since `acos(-1)' returns the |
| floating-point number closest to Pi according to the given |
| rounding mode, this number might not be in the output range 0 <= |
| ROP < \pi of the arc-cosine function; still, the result lies in |
| the image of the output range by the rounding function. The same |
| holds for `asin(-1)', `asin(1)', `atan(-Inf)', `atan(+Inf)'. |
| |
| -- Function: int mpfr_atan2 (mpfr_t ROP, mpfr_t Y, mpfr_t X, mp_rnd_t |
| RND) |
| Set ROP to the arc-tangent2 of Y and X, rounded in the direction |
| RND: if `x > 0', `atan2(y, x) = atan (y/x)'; if `x < 0', `atan2(y, |
| x) = sign(y)*(Pi - atan (abs(y/x)))'. As for `atan', in case the |
| exact mathematical result is +Pi or -Pi, its rounded result might |
| be outside the function output range. |
| |
| `atan2(y, 0)' does not raise any floating-point exception. |
| Special values are currently handled as described in the ISO C99 |
| standard for the `atan2' function (note this may change in future |
| versions): |
| * `atan2(+0, -0)' returns +Pi. |
| |
| * `atan2(-0, -0)' returns -Pi. |
| |
| * `atan2(+0, +0)' returns +0. |
| |
| * `atan2(-0, +0)' returns -0. |
| |
| * `atan2(+0, x)' returns +Pi for x < 0. |
| |
| * `atan2(-0, x)' returns -Pi for x < 0. |
| |
| * `atan2(+0, x)' returns +0 for x > 0. |
| |
| * `atan2(-0, x)' returns -0 for x > 0. |
| |
| * `atan2(y, 0)' returns -Pi/2 for y < 0. |
| |
| * `atan2(y, 0)' returns +Pi/2 for y > 0. |
| |
| * `atan2(+Inf, -Inf)' returns +3*Pi/4. |
| |
| * `atan2(-Inf, -Inf)' returns -3*Pi/4. |
| |
| * `atan2(+Inf, +Inf)' returns +Pi/4. |
| |
| * `atan2(-Inf, +Inf)' returns -Pi/4. |
| |
| * `atan2(+Inf, x)' returns +Pi/2 for finite x. |
| |
| * `atan2(-Inf, x)' returns -Pi/2 for finite x. |
| |
| * `atan2(y, -Inf)' returns +Pi for finite y > 0. |
| |
| * `atan2(y, -Inf)' returns -Pi for finite y < 0. |
| |
| * `atan2(y, +Inf)' returns +0 for finite y > 0. |
| |
| * `atan2(y, +Inf)' returns -0 for finite y < 0. |
| |
| -- Function: int mpfr_cosh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_sinh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_tanh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the hyperbolic cosine, sine or tangent of OP, rounded |
| in the direction RND. |
| |
| -- Function: int mpfr_sinh_cosh (mpfr_t SOP, mpfr_t COP, mpfr_t OP, |
| mp_rnd_t RND) |
| Set simultaneously SOP to the hyperbolic sine of OP and |
| COP to the hyperbolic cosine of OP, rounded in the |
| direction RND with the corresponding precision of SOP and COP |
| which must be different variables. Return 0 iff both results are |
| exact. |
| |
| -- Function: int mpfr_sech (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_csch (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_coth (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the hyperbolic secant of OP, cosecant of OP, cotangent |
| of OP, rounded in the direction RND. |
| |
| -- Function: int mpfr_acosh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_asinh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_atanh (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the inverse hyperbolic cosine, sine or tangent of OP, |
| rounded in the direction RND. |
| |
| -- Function: int mpfr_fac_ui (mpfr_t ROP, unsigned long int OP, |
| mp_rnd_t RND) |
| Set ROP to the factorial of the `unsigned long int' OP, rounded in |
| the direction RND. |
| |
| -- Function: int mpfr_log1p (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the logarithm of one plus OP, rounded in the direction |
| RND. |
| |
| -- Function: int mpfr_expm1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the exponential of OP minus one, rounded in the |
| direction RND. |
| |
| -- Function: int mpfr_eint (mpfr_t Y, mpfr_t X, mp_rnd_t RND) |
| Set Y to the exponential integral of X, rounded in the direction |
| RND. For positive X, the exponential integral is the sum of |
| Euler's constant, of the logarithm of X, and of the sum for k from |
| 1 to infinity of X to the power k, divided by k and factorial(k). |
| For negative X, the returned value is NaN. |
| |
| -- Function: int mpfr_li2 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND_MODE) |
| Set ROP to real part of the dilogarithm of OP, rounded in the |
| direction RND_MODE. The dilogarithm function is defined here as |
| the integral of -log(1-t)/t from 0 to x. |
| |
| -- Function: int mpfr_gamma (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the Gamma function on OP, rounded in the |
| direction RND. When OP is a negative integer, NaN is returned. |
| |
| -- Function: int mpfr_lngamma (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the logarithm of the Gamma function on OP, |
| rounded in the direction RND. When -2K-1 <= X <= -2K, K being a |
| non-negative integer, NaN is returned. See also `mpfr_lgamma'. |
| |
| -- Function: int mpfr_lgamma (mpfr_t ROP, int *SIGNP, mpfr_t OP, |
| mp_rnd_t RND) |
| Set ROP to the value of the logarithm of the absolute value of the |
| Gamma function on OP, rounded in the direction RND. The sign (1 or |
| -1) of Gamma(OP) is returned in the object pointed to by SIGNP. |
| When OP is an infinity or a non-positive integer, +Inf is |
| returned. When OP is NaN, -Inf or a negative integer, *SIGNP is |
| undefined, and when OP is ±0, *SIGNP is the sign of the zero. |
| |
| -- Function: int mpfr_zeta (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_zeta_ui (mpfr_t ROP, unsigned long OP, mp_rnd_t |
| RND) |
| Set ROP to the value of the Riemann Zeta function on OP, rounded |
| in the direction RND. |
| |
| -- Function: int mpfr_erf (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the error function on OP, rounded in the |
| direction RND. |
| |
| -- Function: int mpfr_erfc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the complementary error function on OP, |
| rounded in the direction RND. |
| |
| -- Function: int mpfr_j0 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_j1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_jn (mpfr_t ROP, long N, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the first kind Bessel function of order 0, |
| 1 and N on OP, rounded in the direction RND. When OP is NaN, ROP |
| is always set to NaN. When OP is plus or minus Infinity, ROP is |
| set to +0. When OP is zero, and N is not zero, ROP is +0 or -0 |
| depending on the parity and sign of N, and the sign of OP. |
| |
| -- Function: int mpfr_y0 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_y1 (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_yn (mpfr_t ROP, long N, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the value of the second kind Bessel function of order |
| 0, 1 and N on OP, rounded in the direction RND. When OP is NaN or |
| negative, ROP is always set to NaN. When OP is +Inf, ROP is +0. |
| When OP is zero, ROP is +Inf or -Inf depending on the parity and |
| sign of N. |
| |
| -- Function: int mpfr_fma (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, mpfr_t |
| OP3, mp_rnd_t RND) |
| Set ROP to (OP1 times OP2) + OP3, rounded in the direction RND. |
| |
| -- Function: int mpfr_fms (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, mpfr_t |
| OP3, mp_rnd_t RND) |
| Set ROP to (OP1 times OP2) - OP3, rounded in the direction RND. |
| |
| -- Function: int mpfr_agm (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Set ROP to the arithmetic-geometric mean of OP1 and OP2, rounded |
| in the direction RND. The arithmetic-geometric mean is the common |
| limit of the sequences u[n] and v[n], where u[0]=OP1, v[0]=OP2, |
| u[n+1] is the arithmetic mean of u[n] and v[n], and v[n+1] is the |
| geometric mean of u[n] and v[n]. If any operand is negative, the |
| return value is NaN. |
| |
| -- Function: int mpfr_hypot (mpfr_t ROP, mpfr_t X, mpfr_t Y, mp_rnd_t |
| RND) |
| Set ROP to the Euclidean norm of X and Y, i.e. the square root of |
| the sum of the squares of X and Y, rounded in the direction RND. |
| Special values are currently handled as described in Section |
| F.9.4.3 of the ISO C99 standard, for the `hypot' function (note |
| this may change in future versions): If X or Y is an infinity, |
| then plus infinity is returned in ROP, even if the other number is |
| NaN. |
| |
| -- Function: int mpfr_const_log2 (mpfr_t ROP, mp_rnd_t RND) |
| -- Function: int mpfr_const_pi (mpfr_t ROP, mp_rnd_t RND) |
| -- Function: int mpfr_const_euler (mpfr_t ROP, mp_rnd_t RND) |
| -- Function: int mpfr_const_catalan (mpfr_t ROP, mp_rnd_t RND) |
| Set ROP to the logarithm of 2, the value of Pi, of Euler's |
| constant 0.577..., of Catalan's constant 0.915..., respectively, |
| rounded in the direction RND. These functions cache the computed |
| values to avoid other calculations if a lower or equal precision |
| is requested. To free these caches, use `mpfr_free_cache'. |
| |
| -- Function: void mpfr_free_cache (void) |
| Free various caches used by MPFR internally, in particular the |
| caches used by the functions computing constants (currently |
| `mpfr_const_log2', `mpfr_const_pi', `mpfr_const_euler' and |
| `mpfr_const_catalan'). You should call this function before |
| terminating a thread, even if you did not call these functions |
| directly (they could have been called internally). |
| |
| -- Function: int mpfr_sum (mpfr_t ROP, mpfr_ptr const TAB[], unsigned |
| long N, mp_rnd_t RND) |
| Set RET to the sum of all elements of TAB whose size is N, rounded |
| in the direction RND. Warning, TAB is a table of pointers to |
| mpfr_t, not a table of mpfr_t (preliminary interface). The returned |
| `int' value is zero when the computed value is the exact value, |
| and non-zero when this cannot be guaranteed, without giving the |
| direction of the error as the other functions do. |
| |
| |
| File: mpfr.info, Node: Input and Output Functions, Next: Formatted Output Functions, Prev: Special Functions, Up: MPFR Interface |
| |
| 5.8 Input and Output Functions |
| ============================== |
| |
| This section describes functions that perform input from an input/output |
| stream, and functions that output to an input/output stream. Passing a |
| null pointer for a `stream' to any of these functions will make them |
| read from `stdin' and write to `stdout', respectively. |
| |
| When using any of these functions, you must include the `<stdio.h>' |
| standard header before `mpfr.h', to allow `mpfr.h' to define prototypes |
| for these functions. |
| |
| -- Function: size_t mpfr_out_str (FILE *STREAM, int BASE, size_t N, |
| mpfr_t OP, mp_rnd_t RND) |
| Output OP on stream STREAM, as a string of digits in base BASE, |
| rounded in the direction RND. The base may vary from 2 to 36. |
| Print N significant digits exactly, or if N is 0, enough digits so |
| that OP can be read back exactly (see `mpfr_get_str'). |
| |
| In addition to the significant digits, a decimal point (defined by |
| the current locale) at the right of the first digit and a trailing |
| exponent in base 10, in the form `eNNN', are printed. If BASE is |
| greater than 10, `@' will be used instead of `e' as exponent |
| delimiter. |
| |
| Return the number of bytes written, or if an error occurred, |
| return 0. |
| |
| -- Function: size_t mpfr_inp_str (mpfr_t ROP, FILE *STREAM, int BASE, |
| mp_rnd_t RND) |
| Input a string in base BASE from stream STREAM, rounded in the |
| direction RND, and put the read float in ROP. |
| |
| This function reads a word (defined as a sequence of characters |
| between whitespace) and parses it using `mpfr_set_str' (it may |
| change). See the documentation of `mpfr_strtofr' for a detailed |
| description of the valid string formats. |
| |
| Return the number of bytes read, or if an error occurred, return 0. |
| |
| |
| File: mpfr.info, Node: Formatted Output Functions, Next: Integer Related Functions, Prev: Input and Output Functions, Up: MPFR Interface |
| |
| 5.9 Formatted Output Functions |
| ============================== |
| |
| 5.9.1 Requirements |
| ------------------ |
| |
| The class of `mpfr_printf' functions provides formatted output in a |
| similar manner as the standard C `printf'. These functions are defined |
| only if your system supports ISO C variadic functions and the |
| corresponding argument access macros. |
| |
| When using any of these functions, you must include the `<stdio.h>' |
| standard header before `mpfr.h', to allow `mpfr.h' to define prototypes |
| for these functions. |
| |
| 5.9.2 Format String |
| ------------------- |
| |
| The format specification accepted by `mpfr_printf' is an extension of |
| the `printf' one. The conversion specification is of the form: |
| % [flags] [width] [.[precision]] [type] [rounding] conv |
| `flags', `width', and `precision' have the same meaning as for the |
| standard C function `printf' (in particular, notice that the precision |
| is related to the number of digits displayed in the base chosen by |
| `conv' and not related to the internal precision of the `mpfr_t' |
| variable). `mpfr_printf' accepts the same `type' specifiers as `gmp' |
| (except the non-standard and deprecated `q', use `ll' instead), plus |
| `R' and `P': |
| |
| `h' `short' |
| `hh' `char' |
| `j' `intmax_t' or `uintmax_t' |
| `l' `long' or `wchar_t' |
| `ll' `long long' |
| `L' `long double' |
| `t' `ptrdiff_t' |
| `z' `size_t' |
| `F' `mpf_t', float conversions |
| `Q' `mpq_t', integer conversions |
| `M' `mp_limb_t', integer conversions |
| `N' `mp_limb_t' array, integer conversions |
| `Z' `mpz_t', integer conversions |
| `R' `mpfr_t' input, float conversions |
| `P' `mpfr_prec_t' input, integer conversions |
| |
| The `type' specifiers have the same restrictions as those mentioned |
| in the GMP documentation: *note Formatted Output Strings: |
| (gmp.info)Formatted Output Strings. More precisely, except for `R' and |
| `P' (which are defined by MPFR), the `type' specifiers are supported |
| only if they are supported by `gmp_printf' in your GMP build; this |
| implies that the standard specifiers, such as `t', must _also_ be |
| supported by your C library if you want to use them. |
| |
| The `rounding' specifier is specific to `mpfr_t' parameter and shall |
| not be used with other types. `mpfr_printf' accepts the same conversion |
| specifier character `conv' as `gmp_printf' plus `b'. |
| |
| The `P' type outputs the precision of an `mpfr_t' variable. It is |
| needed because the `mpfr_prec_t' type does not necessarily correspond |
| to an `unsigned int' or any fixed standard type. For example: |
| mpfr_t x; |
| mpfr_prec_t p; |
| mpfr_init (x); |
| ... |
| p = mpfr_get_prec (x); |
| mpfr_printf ("variable x with %Pu bits", p); |
| |
| The `R' type is used for a `mpfr_t' output and can be followed by a |
| rounding specifier denoted by one of the following characters: |
| |
| `U' round toward plus infinity |
| `D' round toward minus infinity |
| `Z' round toward zero |
| `N' round to nearest |
| `*' rounding mode (as a `mpfr_rnd_t') |
| indicated by the argument just before |
| the corresponding `mpfr_t' variable. |
| |
| If the precision field is not empty, the `mpfr_t' number is rounded |
| to the given precision in the direction specified by the rounding mode. |
| If the precision field is empty (as in `%.Rf'), the number is displayed |
| with enough digits so that it can be read back exactly (assuming |
| rounding to nearest, see `mpfr_get_str'). If no rounding is specified, |
| the `mpfr_t' argument is rounded to nearest. The following three |
| examples are equivalent: |
| mpfr_t x; |
| mpfr_init (x); |
| ... |
| mpfr_printf ("%.128Rf", x); |
| mpfr_printf ("%.128RNf", x); |
| mpfr_printf ("%.128R*f", GMP_RNDN, x); |
| |
| `mpfr_printf' also adds a new conversion specifier `b' which |
| displays the `mpfr_t' parameter in binary, the behavior is undefined |
| with other parameter type. The `conv' specifiers allowed with `mpfr_t' |
| parameter are: |
| |
| `a' `A' hex float, C99 style |
| `b' binary output |
| `e' `E' scientific format float |
| `f' fixed point float |
| `g' `G' fixed or scientific float |
| |
| In case of non-decimal output, only the significand is written in the |
| specified base, the exponent is always displayed in decimal. Special |
| values are always displayed as `nan', `-inf', and `inf' for `a', `b', |
| `e', `f', and `g' specifiers and `NAN', `-INF', and `INF' for `A', `E', |
| `F', and `G' specifiers. In binary output, the precision is silently |
| increased up to 2 if it equals 1. |
| |
| 5.9.3 Functions |
| --------------- |
| |
| -- Function: int mpfr_fprintf (FILE *STREAM, const char *TEMPLATE, ...) |
| -- Function: int mpfr_vfprintf (FILE *STREAM, const char *TEMPLATE, |
| va_list AP) |
| Print to the stream STREAM the optional arguments under the |
| control of the template string TEMPLATE. |
| |
| Return the number of characters written or a negative value if an |
| error occurred. If the number of characters which ought to be |
| written appears to exceed the maximum limit for an `int', nothing |
| is written in the stream, the function returns -1, sets the |
| _erange_ flag, and (in POSIX system only) `errno' is set to |
| `EOVERFLOW'. |
| |
| -- Function: int mpfr_printf (const char *TEMPLATE, ...) |
| -- Function: int mpfr_vprintf (const char *TEMPLATE, va_list AP) |
| Print to STDOUT the optional arguments under the control of the |
| template string TEMPLATE. |
| |
| Return the number of characters written or a negative value if an |
| error occurred. If the number of characters which ought to be |
| written appears to exceed the maximum limit for an `int', nothing |
| is written in `stdout', the function returns -1, sets the _erange_ |
| flag, and (in POSIX system only) `errno' is set to `EOVERFLOW'. |
| |
| -- Function: int mpfr_sprintf (char *BUF, const char *TEMPLATE, ...) |
| -- Function: int mpfr_vsprintf (char *BUF, const char *TEMPLATE, |
| va_list AP) |
| Form a null-terminated string in BUF. No overlap is permitted |
| between BUF and the other arguments. |
| |
| Return the number of characters written in the array BUF not |
| counting the terminating null character or a negative value if an |
| error occurred. If the number of characters which ought to be |
| written appears to exceed the maximum limit for an `int', nothing |
| is written in BUF, the function returns -1, sets the _erange_ |
| flag, and (in POSIX system only) `errno' is set to `EOVERFLOW'. |
| |
| -- Function: int mpfr_snprintf (char *BUF, size_t N, const char |
| *TEMPLATE, ...) |
| -- Function: int mpfr_vsnprintf (char *BUF, size_t N, const char |
| *TEMPLATE, va_list AP) |
| Form a null-terminated string in BUF. If N is zero, nothing is |
| written and BUF may be a null pointer, otherwise, the `n-1' first |
| characters are written in BUF and the N-th is a null character. |
| |
| Return the number of characters that would have been written had N |
| be sufficiently large, not counting the terminating null character |
| or a negative value if an error occurred. If the number of |
| characters produced by the optional arguments under the control of |
| the template string TEMPLATE appears to exceed the maximum limit |
| for an `int', nothing is written in BUF, the function returns -1, |
| sets the _erange_ flag, and (in POSIX system only) `errno' is set |
| to `EOVERFLOW'. |
| |
| -- Function: int mpfr_asprintf (char **STR, const char *TEMPLATE, ...) |
| -- Function: int mpfr_vasprintf (char **STR, const char *TEMPLATE, |
| va_list AP) |
| Write their output as a null terminated string in a block of |
| memory allocated using the current allocation function. A pointer |
| to the block is stored in STR. The block of memory must be freed |
| using `mpfr_free_str'. |
| |
| The return value is the number of characters written in the |
| string, excluding the null-terminator or a negative value if an |
| error occurred. If the number of characters produced by the |
| optional arguments under the control of the template string |
| TEMPLATE appears to exceed the maximum limit for an `int', STR is |
| a null pointer, the function returns -1, sets the _erange_ flag, |
| and (in POSIX system only) `errno' is set to `EOVERFLOW'. |
| |
| |
| File: mpfr.info, Node: Integer Related Functions, Next: Rounding Related Functions, Prev: Formatted Output Functions, Up: MPFR Interface |
| |
| 5.10 Integer and Remainder Related Functions |
| ============================================ |
| |
| -- Function: int mpfr_rint (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_ceil (mpfr_t ROP, mpfr_t OP) |
| -- Function: int mpfr_floor (mpfr_t ROP, mpfr_t OP) |
| -- Function: int mpfr_round (mpfr_t ROP, mpfr_t OP) |
| -- Function: int mpfr_trunc (mpfr_t ROP, mpfr_t OP) |
| Set ROP to OP rounded to an integer. `mpfr_rint' rounds to the |
| nearest representable integer in the given rounding mode, |
| `mpfr_ceil' rounds to the next higher or equal representable |
| integer, `mpfr_floor' to the next lower or equal representable |
| integer, `mpfr_round' to the nearest representable integer, |
| rounding halfway cases away from zero, and `mpfr_trunc' to the |
| next representable integer toward zero. |
| |
| The returned value is zero when the result is exact, positive when |
| it is greater than the original value of OP, and negative when it |
| is smaller. More precisely, the returned value is 0 when OP is an |
| integer representable in ROP, 1 or -1 when OP is an integer that |
| is not representable in ROP, 2 or -2 when OP is not an integer. |
| |
| Note that `mpfr_round' is different from `mpfr_rint' called with |
| the rounding to nearest mode (where halfway cases are rounded to |
| an even integer or significand). Note also that no double rounding |
| is performed; for instance, 4.5 (100.1 in binary) is rounded by |
| `mpfr_round' to 4 (100 in binary) in 2-bit precision, though |
| `round(4.5)' is equal to 5 and 5 (101 in binary) is rounded to 6 |
| (110 in binary) in 2-bit precision. |
| |
| -- Function: int mpfr_rint_ceil (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_rint_floor (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_rint_round (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| -- Function: int mpfr_rint_trunc (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to OP rounded to an integer. `mpfr_rint_ceil' rounds to |
| the next higher or equal integer, `mpfr_rint_floor' to the next |
| lower or equal integer, `mpfr_rint_round' to the nearest integer, |
| rounding halfway cases away from zero, and `mpfr_rint_trunc' to |
| the next integer toward zero. If the result is not representable, |
| it is rounded in the direction RND. The returned value is the |
| ternary value associated with the considered round-to-integer |
| function (regarded in the same way as any other mathematical |
| function). |
| |
| -- Function: int mpfr_frac (mpfr_t ROP, mpfr_t OP, mp_rnd_t RND) |
| Set ROP to the fractional part of OP, having the same sign as OP, |
| rounded in the direction RND (unlike in `mpfr_rint', RND affects |
| only how the exact fractional part is rounded, not how the |
| fractional part is generated). |
| |
| -- Function: int mpfr_modf (mpfr_t IOP, mpfr_t FOP, mpfr_t OP, |
| mp_rnd_t RND) |
| Set simultaneously IOP to the integral part of OP and FOP to the |
| fractional part of OP, rounded in the direction RND with the |
| corresponding precision of IOP and FOP (equivalent to |
| `mpfr_trunc(IOP, OP, RND)' and `mpfr_frac(FOP, OP, RND)'). The |
| variables IOP and FOP must be different. Return 0 iff both results |
| are exact. |
| |
| -- Function: int mpfr_fmod (mpfr_t R, mpfr_t X, mpfr_t Y, mp_rnd_t RND) |
| -- Function: int mpfr_remainder (mpfr_t R, mpfr_t X, mpfr_t Y, |
| mp_rnd_t RND) |
| -- Function: int mpfr_remquo (mpfr_t R, long* Q, mpfr_t X, mpfr_t Y, |
| mp_rnd_t RND) |
| Set R to the value of x - n y, rounded according to the direction |
| RND, where n is the integer quotient of X divided by Y, defined as |
| follows: n is rounded toward zero for `mpfr_fmod', and to the |
| nearest integer (ties rounded to even) for `mpfr_remainder' and |
| `mpfr_remquo'. |
| |
| Special values are handled as described in Section F.9.7.1 of the |
| ISO C99 standard: If X is infinite or Y is zero, R is NaN. If Y |
| is infinite and X is finite, R is X rounded to the precision of R. |
| If R is zero, it has the sign of X. The return value is the |
| ternary value corresponding to R. |
| |
| Additionally, `mpfr_remquo' stores the low significant bits from |
| the quotient in *Q (more precisely the number of bits in a `long' |
| minus one), with the sign of X divided by Y (except if those low |
| bits are all zero, in which case zero is returned). Note that X |
| may be so large in magnitude relative to Y that an exact |
| representation of the quotient is not practical. `mpfr_remainder' |
| and `mpfr_remquo' functions are useful for additive argument |
| reduction. |
| |
| -- Function: int mpfr_integer_p (mpfr_t OP) |
| Return non-zero iff OP is an integer. |
| |
| |
| File: mpfr.info, Node: Rounding Related Functions, Next: Miscellaneous Functions, Prev: Integer Related Functions, Up: MPFR Interface |
| |
| 5.11 Rounding Related Functions |
| =============================== |
| |
| -- Function: void mpfr_set_default_rounding_mode (mp_rnd_t RND) |
| Set the default rounding mode to RND. The default rounding mode |
| is to nearest initially. |
| |
| -- Function: mp_rnd_t mpfr_get_default_rounding_mode (void) |
| Get the default rounding mode. |
| |
| -- Function: int mpfr_prec_round (mpfr_t X, mp_prec_t PREC, mp_rnd_t |
| RND) |
| Round X according to RND with precision PREC, which must be an |
| integer between `MPFR_PREC_MIN' and `MPFR_PREC_MAX' (otherwise the |
| behavior is undefined). If PREC is greater or equal to the |
| precision of X, then new space is allocated for the significand, |
| and it is filled with zeros. Otherwise, the significand is |
| rounded to precision PREC with the given direction. In both cases, |
| the precision of X is changed to PREC. |
| |
| -- Function: int mpfr_round_prec (mpfr_t X, mp_rnd_t RND, mp_prec_t |
| PREC) |
| [This function is obsolete. Please use `mpfr_prec_round' instead.] |
| |
| -- Function: int mpfr_can_round (mpfr_t B, mp_exp_t ERR, mp_rnd_t |
| RND1, mp_rnd_t RND2, mp_prec_t PREC) |
| Assuming B is an approximation of an unknown number X in the |
| direction RND1 with error at most two to the power E(b)-ERR where |
| E(b) is the exponent of B, return a non-zero value if one is able |
| to round correctly X to precision PREC with the direction RND2, |
| and 0 otherwise (including for NaN and Inf). This function *does |
| not modify* its arguments. |
| |
| Note: if one wants to also determine the correct ternary value |
| when rounding B to precision PREC, a useful trick is the following: if (mpfr_can_round (b, err, rnd1, GMP_RNDZ, prec + (rnd2 == GMP_RNDN))) |
| ... |
| Indeed, if RND2 is `GMP_RNDN', this will check if one can round |
| to PREC+1 bits with a directed rounding: if so, one can surely |
| round to nearest to PREC bits, and in addition one can determine |
| the correct ternary value, which would not be the case when B is |
| near from a value exactly representable on PREC bits. |
| |
| -- Function: const char * mpfr_print_rnd_mode (mp_rnd_t RND) |
| Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ) |
| corresponding to the rounding mode RND or a null pointer if RND is |
| an invalid rounding mode. |
| |
| |
| File: mpfr.info, Node: Miscellaneous Functions, Next: Exception Related Functions, Prev: Rounding Related Functions, Up: MPFR Interface |
| |
| 5.12 Miscellaneous Functions |
| ============================ |
| |
| -- Function: void mpfr_nexttoward (mpfr_t X, mpfr_t Y) |
| If X or Y is NaN, set X to NaN. Otherwise, if X is different from |
| Y, replace X by the next floating-point number (with the precision |
| of X and the current exponent range) in the direction of Y, if |
| there is one (the infinite values are seen as the smallest and |
| largest floating-point numbers). If the result is zero, it keeps |
| the same sign. No underflow or overflow is generated. |
| |
| -- Function: void mpfr_nextabove (mpfr_t X) |
| Equivalent to `mpfr_nexttoward' where Y is plus infinity. |
| |
| -- Function: void mpfr_nextbelow (mpfr_t X) |
| Equivalent to `mpfr_nexttoward' where Y is minus infinity. |
| |
| -- Function: int mpfr_min (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Set ROP to the minimum of OP1 and OP2. If OP1 and OP2 are both |
| NaN, then ROP is set to NaN. If OP1 or OP2 is NaN, then ROP is set |
| to the numeric value. If OP1 and OP2 are zeros of different signs, |
| then ROP is set to -0. |
| |
| -- Function: int mpfr_max (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Set ROP to the maximum of OP1 and OP2. If OP1 and OP2 are both |
| NaN, then ROP is set to NaN. If OP1 or OP2 is NaN, then ROP is set |
| to the numeric value. If OP1 and OP2 are zeros of different signs, |
| then ROP is set to +0. |
| |
| -- Function: int mpfr_urandomb (mpfr_t ROP, gmp_randstate_t STATE) |
| Generate a uniformly distributed random float in the interval 0 <= |
| ROP < 1. More precisely, the number can be seen as a float with a |
| random non-normalized significand and exponent 0, which is then |
| normalized (thus if E denotes the exponent after normalization, |
| then the least -E significant bits of the significand are always |
| 0). Return 0, unless the exponent is not in the current exponent |
| range, in which case ROP is set to NaN and a non-zero value is |
| returned (this should never happen in practice, except in very |
| specific cases). The second argument is a `gmp_randstate_t' |
| structure which should be created using the GMP `gmp_randinit' |
| function, see the GMP manual. |
| |
| -- Function: void mpfr_random (mpfr_t ROP) |
| Generate a uniformly distributed random float in the interval 0 <= |
| ROP < 1. |
| |
| This function is deprecated and will be suppressed in the next |
| release; `mpfr_urandomb' should be used instead. |
| |
| -- Function: void mpfr_random2 (mpfr_t ROP, mp_size_t SIZE, mp_exp_t |
| EXP) |
| Generate a random float of at most SIZE limbs, with long strings of |
| zeros and ones in the binary representation. The exponent of the |
| number is in the interval -EXP to EXP. This function is useful for |
| testing functions and algorithms, since this kind of random |
| numbers have proven to be more likely to trigger corner-case bugs. |
| Negative random numbers are generated when SIZE is negative. Put |
| +0 in ROP when size if zero. The internal state of the default |
| pseudorandom number generator is modified by a call to this |
| function (the same one as GMP if MPFR was built using |
| `--with-gmp-build'). |
| |
| This function is deprecated and will be suppressed in the next |
| release. |
| |
| -- Function: mp_exp_t mpfr_get_exp (mpfr_t X) |
| Get the exponent of X, assuming that X is a non-zero ordinary |
| number and the significand is chosen in [1/2,1). The behavior for |
| NaN, infinity or zero is undefined. |
| |
| -- Function: int mpfr_set_exp (mpfr_t X, mp_exp_t E) |
| Set the exponent of X if E is in the current exponent range, and |
| return 0 (even if X is not a non-zero ordinary number); otherwise, |
| return a non-zero value. The significand is assumed to be in |
| [1/2,1). |
| |
| -- Function: int mpfr_signbit (mpfr_t OP) |
| Return a non-zero value iff OP has its sign bit set (i.e. if it is |
| negative, -0, or a NaN whose representation has its sign bit set). |
| |
| -- Function: int mpfr_setsign (mpfr_t ROP, mpfr_t OP, int S, mp_rnd_t |
| RND) |
| Set the value of ROP from OP, rounded toward the given direction |
| RND, then set (resp. clear) its sign bit if S is non-zero (resp. |
| zero), even when OP is a NaN. |
| |
| -- Function: int mpfr_copysign (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Set the value of ROP from OP1, rounded toward the given direction |
| RND, then set its sign bit to that of OP2 (even when OP1 or OP2 is |
| a NaN). This function is equivalent to `mpfr_setsign (ROP, OP1, |
| mpfr_signbit (OP2), RND)'. |
| |
| -- Function: const char * mpfr_get_version (void) |
| Return the MPFR version, as a null-terminated string. |
| |
| -- Macro: MPFR_VERSION |
| -- Macro: MPFR_VERSION_MAJOR |
| -- Macro: MPFR_VERSION_MINOR |
| -- Macro: MPFR_VERSION_PATCHLEVEL |
| -- Macro: MPFR_VERSION_STRING |
| `MPFR_VERSION' is the version of MPFR as a preprocessing constant. |
| `MPFR_VERSION_MAJOR', `MPFR_VERSION_MINOR' and |
| `MPFR_VERSION_PATCHLEVEL' are respectively the major, minor and |
| patch level of MPFR version, as preprocessing constants. |
| `MPFR_VERSION_STRING' is the version (with an optional suffix, used |
| in development and pre-release versions) as a string constant, |
| which can be compared to the result of `mpfr_get_version' to check |
| at run time the header file and library used match: |
| if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING)) |
| fprintf (stderr, "Warning: header and library do not match\n"); |
| Note: Obtaining different strings is not necessarily an error, as |
| in general, a program compiled with some old MPFR version can be |
| dynamically linked with a newer MPFR library version (if allowed |
| by the library versioning system). |
| |
| -- Macro: long MPFR_VERSION_NUM (MAJOR, MINOR, PATCHLEVEL) |
| Create an integer in the same format as used by `MPFR_VERSION' |
| from the given MAJOR, MINOR and PATCHLEVEL. Here is an example of |
| how to check the MPFR version at compile time: |
| #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0))) |
| # error "Wrong MPFR version." |
| #endif |
| |
| -- Function: const char * mpfr_get_patches (void) |
| Return a null-terminated string containing the ids of the patches |
| applied to the MPFR library (contents of the `PATCHES' file), |
| separated by spaces. Note: If the program has been compiled with |
| an older MPFR version and is dynamically linked with a new MPFR |
| library version, the ids of the patches applied to the old |
| (compile-time) MPFR version are not available (however this |
| information should not have much interest in general). |
| |
| |
| File: mpfr.info, Node: Exception Related Functions, Next: Compatibility with MPF, Prev: Miscellaneous Functions, Up: MPFR Interface |
| |
| 5.13 Exception Related Functions |
| ================================ |
| |
| -- Function: mp_exp_t mpfr_get_emin (void) |
| -- Function: mp_exp_t mpfr_get_emax (void) |
| Return the (current) smallest and largest exponents allowed for a |
| floating-point variable. The smallest positive value of a |
| floating-point variable is one half times 2 raised to the smallest |
| exponent and the largest value has the form (1 - epsilon) times 2 |
| raised to the largest exponent. |
| |
| -- Function: int mpfr_set_emin (mp_exp_t EXP) |
| -- Function: int mpfr_set_emax (mp_exp_t EXP) |
| Set the smallest and largest exponents allowed for a |
| floating-point variable. Return a non-zero value when EXP is not |
| in the range accepted by the implementation (in that case the |
| smallest or largest exponent is not changed), and zero otherwise. |
| If the user changes the exponent range, it is her/his |
| responsibility to check that all current floating-point variables |
| are in the new allowed range (for example using |
| `mpfr_check_range'), otherwise the subsequent behavior will be |
| undefined, in the sense of the ISO C standard. |
| |
| -- Function: mp_exp_t mpfr_get_emin_min (void) |
| -- Function: mp_exp_t mpfr_get_emin_max (void) |
| -- Function: mp_exp_t mpfr_get_emax_min (void) |
| -- Function: mp_exp_t mpfr_get_emax_max (void) |
| Return the minimum and maximum of the smallest and largest |
| exponents allowed for `mpfr_set_emin' and `mpfr_set_emax'. These |
| values are implementation dependent; it is possible to create a non |
| portable program by writing `mpfr_set_emax(mpfr_get_emax_max())' |
| and `mpfr_set_emin(mpfr_get_emin_min())' since the values of the |
| smallest and largest exponents become implementation dependent. |
| |
| -- Function: int mpfr_check_range (mpfr_t X, int T, mp_rnd_t RND) |
| This function forces X to be in the current range of acceptable |
| values, T being the current ternary value: negative if X is |
| smaller than the exact value, positive if X is larger than the |
| exact value and zero if X is exact (before the call). It generates |
| an underflow or an overflow if the exponent of X is outside the |
| current allowed range; the value of T may be used to avoid a |
| double rounding. This function returns zero if the rounded result |
| is equal to the exact one, a positive value if the rounded result |
| is larger than the exact one, a negative value if the rounded |
| result is smaller than the exact one. Note that unlike most |
| functions, the result is compared to the exact one, not the input |
| value X, i.e. the ternary value is propagated. |
| |
| Note: If X is an infinity and T is different from zero (i.e., if |
| the rounded result is an inexact infinity), then the overflow flag |
| is set. This is useful because `mpfr_check_range' is typically |
| called (at least in MPFR functions) after restoring the flags that |
| could have been set due to internal computations. |
| |
| -- Function: int mpfr_subnormalize (mpfr_t X, int T, mp_rnd_t RND) |
| This function rounds X emulating subnormal number arithmetic: if X |
| is outside the subnormal exponent range, it just propagates the |
| ternary value T; otherwise, it rounds X to precision |
| `EXP(x)-emin+1' according to rounding mode RND and previous |
| ternary value T, avoiding double rounding problems. More |
| precisely in the subnormal domain, denoting by E the value of |
| `emin', X is rounded in fixed-point arithmetic to an integer |
| multiple of two to the power E-1; as a consequence, 1.5 multiplied |
| by two to the power E-1 when T is zero is rounded to two to the |
| power E with rounding to nearest. |
| |
| `PREC(x)' is not modified by this function. RND and T must be the |
| used rounding mode for computing X and the returned ternary value |
| when computing X. The subnormal exponent range is from `emin' to |
| `emin+PREC(x)-1'. If the result cannot be represented in the |
| current exponent range (due to a too small `emax'), the behavior |
| is undefined. Note that unlike most functions, the result is |
| compared to the exact one, not the input value X, i.e. the ternary |
| value is propagated. This is a preliminary interface. |
| |
| This is an example of how to emulate double IEEE-754 arithmetic |
| using MPFR: |
| |
| { |
| mpfr_t xa, xb; |
| int i; |
| volatile double a, b; |
| |
| mpfr_set_default_prec (53); |
| mpfr_set_emin (-1073); |
| mpfr_set_emax (1024); |
| |
| mpfr_init (xa); mpfr_init (xb); |
| |
| b = 34.3; mpfr_set_d (xb, b, GMP_RNDN); |
| a = 0x1.1235P-1021; mpfr_set_d (xa, a, GMP_RNDN); |
| |
| a /= b; |
| i = mpfr_div (xa, xa, xb, GMP_RNDN); |
| i = mpfr_subnormalize (xa, i, GMP_RNDN); |
| |
| mpfr_clear (xa); mpfr_clear (xb); |
| } |
| |
| Warning: this emulates a double IEEE-754 arithmetic with correct |
| rounding in the subnormal range, which may not be the case for your |
| hardware. |
| |
| -- Function: void mpfr_clear_underflow (void) |
| -- Function: void mpfr_clear_overflow (void) |
| -- Function: void mpfr_clear_nanflag (void) |
| -- Function: void mpfr_clear_inexflag (void) |
| -- Function: void mpfr_clear_erangeflag (void) |
| Clear the underflow, overflow, invalid, inexact and _erange_ flags. |
| |
| -- Function: void mpfr_set_underflow (void) |
| -- Function: void mpfr_set_overflow (void) |
| -- Function: void mpfr_set_nanflag (void) |
| -- Function: void mpfr_set_inexflag (void) |
| -- Function: void mpfr_set_erangeflag (void) |
| Set the underflow, overflow, invalid, inexact and _erange_ flags. |
| |
| -- Function: void mpfr_clear_flags (void) |
| Clear all global flags (underflow, overflow, inexact, invalid, |
| _erange_). |
| |
| -- Function: int mpfr_underflow_p (void) |
| -- Function: int mpfr_overflow_p (void) |
| -- Function: int mpfr_nanflag_p (void) |
| -- Function: int mpfr_inexflag_p (void) |
| -- Function: int mpfr_erangeflag_p (void) |
| Return the corresponding (underflow, overflow, invalid, inexact, |
| _erange_) flag, which is non-zero iff the flag is set. |
| |
| |
| File: mpfr.info, Node: Compatibility with MPF, Next: Custom Interface, Prev: Exception Related Functions, Up: MPFR Interface |
| |
| 5.14 Compatibility With MPF |
| =========================== |
| |
| A header file `mpf2mpfr.h' is included in the distribution of MPFR for |
| compatibility with the GNU MP class MPF. After inserting the following |
| two lines after the `#include <gmp.h>' line, |
| #include <mpfr.h> |
| #include <mpf2mpfr.h> |
| any program written for MPF can be compiled directly with MPFR without |
| any changes. All operations are then performed with the default MPFR |
| rounding mode, which can be reset with `mpfr_set_default_rounding_mode'. |
| |
| Warning: the `mpf_init' and `mpf_init2' functions initialize to |
| zero, whereas the corresponding MPFR functions initialize to NaN: this |
| is useful to detect uninitialized values, but is slightly incompatible |
| with `mpf'. |
| |
| -- Function: void mpfr_set_prec_raw (mpfr_t X, mp_prec_t PREC) |
| Reset the precision of X to be *exactly* PREC bits. The only |
| difference with `mpfr_set_prec' is that PREC is assumed to be |
| small enough so that the significand fits into the current |
| allocated memory space for X. Otherwise the behavior is undefined. |
| |
| -- Function: int mpfr_eq (mpfr_t OP1, mpfr_t OP2, unsigned long int |
| OP3) |
| Return non-zero if OP1 and OP2 are both non-zero ordinary numbers |
| with the same exponent and the same first OP3 bits, both zero, or |
| both infinities of the same sign. Return zero otherwise. This |
| function is defined for compatibility with `mpf'. Do not use it if |
| you want to know whether two numbers are close to each other; for |
| instance, 1.011111 and 1.100000 are currently regarded as |
| different for any value of OP3 larger than 1 (but this may change |
| in the next release). |
| |
| -- Function: void mpfr_reldiff (mpfr_t ROP, mpfr_t OP1, mpfr_t OP2, |
| mp_rnd_t RND) |
| Compute the relative difference between OP1 and OP2 and store the |
| result in ROP. This function does not guarantee the correct |
| rounding on the relative difference; it just computes |
| |OP1-OP2|/OP1, using the rounding mode RND for all operations and |
| the precision of ROP. |
| |
| -- Function: int mpfr_mul_2exp (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| -- Function: int mpfr_div_2exp (mpfr_t ROP, mpfr_t OP1, unsigned long |
| int OP2, mp_rnd_t RND) |
| See `mpfr_mul_2ui' and `mpfr_div_2ui'. These functions are only |
| kept for compatibility with MPF. |
| |
| |
| File: mpfr.info, Node: Custom Interface, Next: Internals, Prev: Compatibility with MPF, Up: MPFR Interface |
| |
| 5.15 Custom Interface |
| ===================== |
| |
| Some applications use a stack to handle the memory and their objects. |
| However, the MPFR memory design is not well suited for such a thing. So |
| that such applications are able to use MPFR, an auxiliary memory |
| interface has been created: the Custom Interface. |
| |
| The following interface allows them to use MPFR in two ways: |
| * Either they directly store the MPFR FP number as a `mpfr_t' on the |
| stack. |
| |
| * Either they store their own representation of a FP number on the |
| stack and construct a new temporary `mpfr_t' each time it is |
| needed. |
| Nothing has to be done to destroy the FP numbers except garbaging |
| the used memory: all the memory stuff (allocating, destroying, |
| garbaging) is kept to the application. |
| |
| Each function in this interface is also implemented as a macro for |
| efficiency reasons: for example `mpfr_custom_init (s, p)' uses the |
| macro, while `(mpfr_custom_init) (s, p)' uses the function. |
| |
| Note 1: MPFR functions may still initialize temporary FP numbers |
| using standard mpfr_init. See Custom Allocation (GNU MP). |
| |
| Note 2: MPFR functions may use the cached functions (mpfr_const_pi |
| for example), even if they are not explicitly called. You have to call |
| `mpfr_free_cache' each time you garbage the memory iff mpfr_init, |
| through GMP Custom Allocation, allocates its memory on the application |
| stack. |
| |
| Note 3: This interface is preliminary. |
| |
| -- Function: size_t mpfr_custom_get_size (mp_prec_t PREC) |
| Return the needed size in bytes to store the significand of a FP |
| number of precision PREC. |
| |
| -- Function: void mpfr_custom_init (void *SIGNIFICAND, mp_prec_t PREC) |
| Initialize a significand of precision PREC. SIGNIFICAND must be |
| an area of `mpfr_custom_get_size (prec)' bytes at least and be |
| suitably aligned for an array of `mp_limb_t'. |
| |
| -- Function: void mpfr_custom_init_set (mpfr_t X, int KIND, mp_exp_t |
| EXP, mp_prec_t PREC, void *SIGNIFICAND) |
| Perform a dummy initialization of a `mpfr_t' and set it to: |
| * if `ABS(kind) == MPFR_NAN_KIND', X is set to NaN; |
| |
| * if `ABS(kind) == MPFR_INF_KIND', X is set to the infinity of |
| sign `sign(kind)'; |
| |
| * if `ABS(kind) == MPFR_ZERO_KIND', X is set to the zero of |
| sign `sign(kind)'; |
| |
| * if `ABS(kind) == MPFR_REGULAR_KIND', X is set to a regular |
| number: `x = sign(kind)*significand*2^exp' |
| In all cases, it uses SIGNIFICAND directly for further computing |
| involving X. It will not allocate anything. A FP number |
| initialized with this function cannot be resized using |
| `mpfr_set_prec', or cleared using `mpfr_clear'! SIGNIFICAND must |
| have been initialized with `mpfr_custom_init' using the same |
| precision PREC. |
| |
| -- Function: int mpfr_custom_get_kind (mpfr_t X) |
| Return the current kind of a `mpfr_t' as used by |
| `mpfr_custom_init_set'. The behavior of this function for any |
| `mpfr_t' not initialized with `mpfr_custom_init_set' is undefined. |
| |
| -- Function: void * mpfr_custom_get_mantissa (mpfr_t X) |
| Return a pointer to the significand used by a `mpfr_t' initialized |
| with `mpfr_custom_init_set'. The behavior of this function for |
| any `mpfr_t' not initialized with `mpfr_custom_init_set' is |
| undefined. |
| |
| -- Function: mp_exp_t mpfr_custom_get_exp (mpfr_t X) |
| Return the exponent of X, assuming that X is a non-zero ordinary |
| number. The return value for NaN, Infinity or Zero is unspecified |
| but does not produce any trap. The behavior of this function for |
| any `mpfr_t' not initialized with `mpfr_custom_init_set' is |
| undefined. |
| |
| -- Function: void mpfr_custom_move (mpfr_t X, void *NEW_POSITION) |
| Inform MPFR that the significand has moved due to a garbage collect |
| and update its new position to `new_position'. However the |
| application has to move the significand and the `mpfr_t' itself. |
| The behavior of this function for any `mpfr_t' not initialized |
| with `mpfr_custom_init_set' is undefined. |
| |
| See the test suite for examples. |
| |
| |
| File: mpfr.info, Node: Internals, Prev: Custom Interface, Up: MPFR Interface |
| |
| 5.16 Internals |
| ============== |
| |
| The following types and functions were mainly designed for the |
| implementation of MPFR, but may be useful for users too. However no |
| upward compatibility is guaranteed. You may need to include |
| `mpfr-impl.h' to use them. |
| |
| The `mpfr_t' type consists of four fields. |
| |
| * The `_mpfr_prec' field is used to store the precision of the |
| variable (in bits); this is not less than `MPFR_PREC_MIN'. |
| |
| * The `_mpfr_sign' field is used to store the sign of the variable. |
| |
| * The `_mpfr_exp' field stores the exponent. An exponent of 0 means |
| a radix point just above the most significant limb. Non-zero |
| values n are a multiplier 2^n relative to that point. A NaN, an |
| infinity and a zero are indicated by a special value of the |
| exponent. |
| |
| * Finally, the `_mpfr_d' is a pointer to the limbs, least |
| significant limbs stored first. The number of limbs in use is |
| controlled by `_mpfr_prec', namely |
| ceil(`_mpfr_prec'/`mp_bits_per_limb'). Non-singular values always |
| have the most significant bit of the most significant limb set to |
| 1. When the precision does not correspond to a whole number of |
| limbs, the excess bits at the low end of the data are zero. |
| |
| |
| |
| File: mpfr.info, Node: Contributors, Next: References, Prev: MPFR Interface, Up: Top |
| |
| Contributors |
| ************ |
| |
| The main developers of MPFR are Guillaume Hanrot, Vincent Lefèvre, |
| Patrick Pélissier, Philippe Théveny and Paul Zimmermann. |
| |
| Sylvie Boldo from ENS-Lyon, France, contributed the functions |
| `mpfr_agm' and `mpfr_log'. Emmanuel Jeandel, from ENS-Lyon too, |
| contributed the generic hypergeometric code, as well as the `mpfr_exp3', |
| a first implementation of the sine and cosine, and improved versions of |
| `mpfr_const_log2' and `mpfr_const_pi'. Mathieu Dutour contributed the |
| functions `mpfr_atan' and `mpfr_asin', and a previous version of |
| `mpfr_gamma'; David Daney contributed the hyperbolic and inverse |
| hyperbolic functions, the base-2 exponential, and the factorial |
| function. Fabrice Rouillier contributed the original version of |
| `mul_ui.c', the `gmp_op.c' file, and helped to the Microsoft Windows |
| porting. Jean-Luc Rémy contributed the `mpfr_zeta' code. Ludovic |
| Meunier helped in the design of the `mpfr_erf' code. Damien Stehlé |
| contributed the `mpfr_get_ld_2exp' function. |
| |
| We would like to thank Jean-Michel Muller and Joris van der Hoeven |
| for very fruitful discussions at the beginning of that project, |
| Torbjörn Granlund and Kevin Ryde for their help about design issues, |
| and Nathalie Revol for her careful reading of a previous version of |
| this documentation. Kevin Ryde did a tremendous job for the |
| portability of MPFR in 2002-2004. |
| |
| The development of the MPFR library would not have been possible |
| without the continuous support of INRIA, and of the LORIA (Nancy, |
| France) and LIP (Lyon, France) laboratories. In particular the main |
| authors were or are members of the PolKA, Spaces, Cacao project-teams |
| at LORIA and of the Arenaire project-team at LIP. This project was |
| started during the Fiable (reliable in French) action supported by |
| INRIA, and continued during the AOC action. The development of MPFR |
| was also supported by a grant (202F0659 00 MPN 121) from the Conseil |
| Régional de Lorraine in 2002, and from INRIA by an "associate engineer" |
| grant (2003-2005) and an "opération de développement logiciel" grant |
| (2007-2009). |
| |
| |
| File: mpfr.info, Node: References, Next: GNU Free Documentation License, Prev: Contributors, Up: Top |
| |
| References |
| ********** |
| |
| * Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick |
| Pélissier and Paul Zimmermann, "MPFR: A Multiple-Precision Binary |
| Floating-Point Library With Correct Rounding", ACM Transactions on |
| Mathematical Software, volume 33, issue 2, article 13, 15 pages, |
| 2007, `http://doi.acm.org/10.1145/1236463.1236468'. |
| |
| * Torbjörn Granlund, "GNU MP: The GNU Multiple Precision Arithmetic |
| Library", version 4.2.2, 2007, `http://gmplib.org'. |
| |
| * IEEE standard for binary floating-point arithmetic, Technical |
| Report ANSI-IEEE Standard 754-1985, New York, 1985. Approved |
| March 21, 1985: IEEE Standards Board; approved July 26, 1985: |
| American National Standards Institute, 18 pages. |
| |
| * Donald E. Knuth, "The Art of Computer Programming", vol 2, |
| "Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981. |
| |
| * Jean-Michel Muller, "Elementary Functions, Algorithms and |
| Implementation", Birkhauser, Boston, 2nd edition, 2006. |
| |
| |
| |
| File: mpfr.info, Node: GNU Free Documentation License, Next: Concept Index, Prev: References, Up: Top |
| |
| Appendix A GNU Free Documentation License |
| ***************************************** |
| |
| Version 1.2, November 2002 |
| |
| Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. |
| 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA |
| |
| Everyone is permitted to copy and distribute verbatim copies |
| of this license document, but changing it is not allowed. |
| |
| 0. PREAMBLE |
| |
| The purpose of this License is to make a manual, textbook, or other |
| functional and useful document "free" in the sense of freedom: to |
| assure everyone the effective freedom to copy and redistribute it, |
| with or without modifying it, either commercially or |
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| |
| This License is a kind of "copyleft", which means that derivative |
| works of the document must themselves be free in the same sense. |
| It complements the GNU General Public License, which is a copyleft |
| license designed for free software. |
| |
| We have designed this License in order to use it for manuals for |
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| of subject matter or whether it is published as a printed book. |
| We recommend this License principally for works whose purpose is |
| instruction or reference. |
| |
| 1. APPLICABILITY AND DEFINITIONS |
| |
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| 4. MODIFICATIONS |
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| E. Add an appropriate copyright notice for your modifications |
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| H. Include an unaltered copy of this License. |
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| I. Preserve the section Entitled "History", Preserve its Title, |
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| 5. COMBINING DOCUMENTS |
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| You may combine the Document with other documents released under |
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| In the combination, you must combine any sections Entitled |
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| 6. COLLECTIONS OF DOCUMENTS |
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| You may make a collection consisting of the Document and other |
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| 7. AGGREGATION WITH INDEPENDENT WORKS |
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| 10. FUTURE REVISIONS OF THIS LICENSE |
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| The Free Software Foundation may publish new, revised versions of |
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| |
| A.1 ADDENDUM: How to use this License for your documents |
| ======================================================== |
| |
| To use this License in a document you have written, include a copy of |
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| Copyright (C) YEAR YOUR NAME. |
| 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, no Front-Cover Texts, and no Back-Cover |
| Texts. A copy of the license is included in the section entitled ``GNU |
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| |
| File: mpfr.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top |
| |
| Concept Index |
| ************* |
| |
| [index] |
| * Menu: |
| |
| * Accuracy: MPFR Interface. (line 28) |
| * Arithmetic functions: Basic Arithmetic Functions. |
| (line 3) |
| * Assignment functions: Assignment Functions. (line 3) |
| * Basic arithmetic functions: Basic Arithmetic Functions. |
| (line 3) |
| * Combined initialization and assignment functions: Combined Initialization and Assignment Functions. |
| (line 3) |
| * Comparison functions: Comparison Functions. (line 3) |
| * Compatibility with MPF: Compatibility with MPF. |
| (line 3) |
| * Conditions for copying MPFR: Copying. (line 6) |
| * Conversion functions: Conversion Functions. (line 3) |
| * Copying conditions: Copying. (line 6) |
| * Custom interface: Custom Interface. (line 3) |
| * Exception related functions: Exception Related Functions. |
| (line 3) |
| * FDL, GNU Free Documentation License: GNU Free Documentation License. |
| (line 6) |
| * Float arithmetic functions: Basic Arithmetic Functions. |
| (line 3) |
| * Float comparisons functions: Comparison Functions. (line 3) |
| * Float functions: MPFR Interface. (line 6) |
| * Float input and output functions: Input and Output Functions. |
| (line 3) |
| * Float output functions: Formatted Output Functions. |
| (line 3) |
| * Floating-point functions: MPFR Interface. (line 6) |
| * Floating-point number: MPFR Basics. (line 52) |
| * GNU Free Documentation License: GNU Free Documentation License. |
| (line 6) |
| * I/O functions <1>: Formatted Output Functions. |
| (line 3) |
| * I/O functions: Input and Output Functions. |
| (line 3) |
| * Initialization functions: Initialization Functions. |
| (line 3) |
| * Input functions: Input and Output Functions. |
| (line 3) |
| * Installation: Installing MPFR. (line 6) |
| * Integer related functions: Integer Related Functions. |
| (line 3) |
| * Internals: Internals. (line 3) |
| * libmpfr: MPFR Basics. (line 32) |
| * Libraries: MPFR Basics. (line 32) |
| * Libtool: MPFR Basics. (line 38) |
| * Limb: MPFR Basics. (line 84) |
| * Linking: MPFR Basics. (line 32) |
| * Miscellaneous float functions: Miscellaneous Functions. |
| (line 3) |
| * mpfr.h: MPFR Basics. (line 9) |
| * Output functions <1>: Formatted Output Functions. |
| (line 3) |
| * Output functions: Input and Output Functions. |
| (line 3) |
| * Precision <1>: MPFR Interface. (line 20) |
| * Precision: MPFR Basics. (line 65) |
| * Reporting bugs: Reporting Bugs. (line 6) |
| * Rounding mode related functions: Rounding Related Functions. |
| (line 3) |
| * Rounding Modes: MPFR Basics. (line 79) |
| * Special functions: Special Functions. (line 3) |
| * stdarg.h: MPFR Basics. (line 22) |
| * stdio.h: MPFR Basics. (line 15) |
| |
| |
| File: mpfr.info, Node: Function Index, Prev: Concept Index, Up: Top |
| |
| Function and Type Index |
| *********************** |
| |
| [index] |
| * Menu: |
| |
| * mp_prec_t: MPFR Basics. (line 65) |
| * mp_rnd_t: MPFR Basics. (line 79) |
| * mpfr_abs: Basic Arithmetic Functions. |
| (line 177) |
| * mpfr_acos: Special Functions. (line 48) |
| * mpfr_acosh: Special Functions. (line 131) |
| * mpfr_add: Basic Arithmetic Functions. |
| (line 8) |
| * mpfr_add_d: Basic Arithmetic Functions. |
| (line 14) |
| * mpfr_add_q: Basic Arithmetic Functions. |
| (line 18) |
| * mpfr_add_si: Basic Arithmetic Functions. |
| (line 12) |
| * mpfr_add_ui: Basic Arithmetic Functions. |
| (line 10) |
| * mpfr_add_z: Basic Arithmetic Functions. |
| (line 16) |
| * mpfr_agm: Special Functions. (line 221) |
| * mpfr_asin: Special Functions. (line 49) |
| * mpfr_asinh: Special Functions. (line 132) |
| * mpfr_asprintf: Formatted Output Functions. |
| (line 171) |
| * mpfr_atan: Special Functions. (line 50) |
| * mpfr_atan2: Special Functions. (line 60) |
| * mpfr_atanh: Special Functions. (line 133) |
| * mpfr_can_round: Rounding Related Functions. |
| (line 29) |
| * mpfr_cbrt: Basic Arithmetic Functions. |
| (line 107) |
| * mpfr_ceil: Integer Related Functions. |
| (line 8) |
| * mpfr_check_range: Exception Related Functions. |
| (line 38) |
| * mpfr_clear: Initialization Functions. |
| (line 31) |
| * mpfr_clear_erangeflag: Exception Related Functions. |
| (line 111) |
| * mpfr_clear_flags: Exception Related Functions. |
| (line 121) |
| * mpfr_clear_inexflag: Exception Related Functions. |
| (line 110) |
| * mpfr_clear_nanflag: Exception Related Functions. |
| (line 109) |
| * mpfr_clear_overflow: Exception Related Functions. |
| (line 108) |
| * mpfr_clear_underflow: Exception Related Functions. |
| (line 107) |
| * mpfr_clears: Initialization Functions. |
| (line 35) |
| * mpfr_cmp: Comparison Functions. |
| (line 7) |
| * mpfr_cmp_d: Comparison Functions. |
| (line 10) |
| * mpfr_cmp_f: Comparison Functions. |
| (line 14) |
| * mpfr_cmp_ld: Comparison Functions. |
| (line 11) |
| * mpfr_cmp_q: Comparison Functions. |
| (line 13) |
| * mpfr_cmp_si: Comparison Functions. |
| (line 9) |
| * mpfr_cmp_si_2exp: Comparison Functions. |
| (line 31) |
| * mpfr_cmp_ui: Comparison Functions. |
| (line 8) |
| * mpfr_cmp_ui_2exp: Comparison Functions. |
| (line 29) |
| * mpfr_cmp_z: Comparison Functions. |
| (line 12) |
| * mpfr_cmpabs: Comparison Functions. |
| (line 35) |
| * mpfr_const_catalan: Special Functions. (line 242) |
| * mpfr_const_euler: Special Functions. (line 241) |
| * mpfr_const_log2: Special Functions. (line 239) |
| * mpfr_const_pi: Special Functions. (line 240) |
| * mpfr_copysign: Miscellaneous Functions. |
| (line 93) |
| * mpfr_cos: Special Functions. (line 29) |
| * mpfr_cosh: Special Functions. (line 111) |
| * mpfr_cot: Special Functions. (line 37) |
| * mpfr_coth: Special Functions. (line 127) |
| * mpfr_csc: Special Functions. (line 36) |
| * mpfr_csch: Special Functions. (line 126) |
| * mpfr_custom_get_exp: Custom Interface. (line 78) |
| * mpfr_custom_get_kind: Custom Interface. (line 67) |
| * mpfr_custom_get_mantissa: Custom Interface. (line 72) |
| * mpfr_custom_get_size: Custom Interface. (line 38) |
| * mpfr_custom_init: Custom Interface. (line 42) |
| * mpfr_custom_init_set: Custom Interface. (line 48) |
| * mpfr_custom_move: Custom Interface. (line 85) |
| * mpfr_d_div: Basic Arithmetic Functions. |
| (line 82) |
| * mpfr_d_sub: Basic Arithmetic Functions. |
| (line 37) |
| * MPFR_DECL_INIT: Initialization Functions. |
| (line 75) |
| * mpfr_dim: Basic Arithmetic Functions. |
| (line 182) |
| * mpfr_div: Basic Arithmetic Functions. |
| (line 72) |
| * mpfr_div_2exp: Compatibility with MPF. |
| (line 49) |
| * mpfr_div_2si: Basic Arithmetic Functions. |
| (line 197) |
| * mpfr_div_2ui: Basic Arithmetic Functions. |
| (line 195) |
| * mpfr_div_d: Basic Arithmetic Functions. |
| (line 84) |
| * mpfr_div_q: Basic Arithmetic Functions. |
| (line 88) |
| * mpfr_div_si: Basic Arithmetic Functions. |
| (line 80) |
| * mpfr_div_ui: Basic Arithmetic Functions. |
| (line 76) |
| * mpfr_div_z: Basic Arithmetic Functions. |
| (line 86) |
| * mpfr_eint: Special Functions. (line 150) |
| * mpfr_eq: Compatibility with MPF. |
| (line 28) |
| * mpfr_equal_p: Comparison Functions. |
| (line 71) |
| * mpfr_erangeflag_p: Exception Related Functions. |
| (line 129) |
| * mpfr_erf: Special Functions. (line 186) |
| * mpfr_erfc: Special Functions. (line 190) |
| * mpfr_exp: Special Functions. (line 23) |
| * mpfr_exp10: Special Functions. (line 25) |
| * mpfr_exp2: Special Functions. (line 24) |
| * mpfr_expm1: Special Functions. (line 146) |
| * mpfr_fac_ui: Special Functions. (line 138) |
| * mpfr_fits_intmax_p: Conversion Functions. |
| (line 113) |
| * mpfr_fits_sint_p: Conversion Functions. |
| (line 110) |
| * mpfr_fits_slong_p: Conversion Functions. |
| (line 108) |
| * mpfr_fits_sshort_p: Conversion Functions. |
| (line 112) |
| * mpfr_fits_uint_p: Conversion Functions. |
| (line 109) |
| * mpfr_fits_uintmax_p: Conversion Functions. |
| (line 114) |
| * mpfr_fits_ulong_p: Conversion Functions. |
| (line 107) |
| * mpfr_fits_ushort_p: Conversion Functions. |
| (line 111) |
| * mpfr_floor: Integer Related Functions. |
| (line 9) |
| * mpfr_fma: Special Functions. (line 213) |
| * mpfr_fmod: Integer Related Functions. |
| (line 63) |
| * mpfr_fms: Special Functions. (line 217) |
| * mpfr_fprintf: Formatted Output Functions. |
| (line 117) |
| * mpfr_frac: Integer Related Functions. |
| (line 48) |
| * mpfr_free_cache: Special Functions. (line 249) |
| * mpfr_free_str: Conversion Functions. |
| (line 100) |
| * mpfr_gamma: Special Functions. (line 162) |
| * mpfr_get_d: Conversion Functions. |
| (line 7) |
| * mpfr_get_d_2exp: Conversion Functions. |
| (line 20) |
| * mpfr_get_decimal64: Conversion Functions. |
| (line 9) |
| * mpfr_get_default_prec: Initialization Functions. |
| (line 109) |
| * mpfr_get_default_rounding_mode: Rounding Related Functions. |
| (line 11) |
| * mpfr_get_emax: Exception Related Functions. |
| (line 8) |
| * mpfr_get_emax_max: Exception Related Functions. |
| (line 30) |
| * mpfr_get_emax_min: Exception Related Functions. |
| (line 29) |
| * mpfr_get_emin: Exception Related Functions. |
| (line 7) |
| * mpfr_get_emin_max: Exception Related Functions. |
| (line 28) |
| * mpfr_get_emin_min: Exception Related Functions. |
| (line 27) |
| * mpfr_get_exp: Miscellaneous Functions. |
| (line 71) |
| * mpfr_get_f: Conversion Functions. |
| (line 55) |
| * mpfr_get_ld: Conversion Functions. |
| (line 8) |
| * mpfr_get_ld_2exp: Conversion Functions. |
| (line 22) |
| * mpfr_get_patches: Miscellaneous Functions. |
| (line 130) |
| * mpfr_get_prec: Initialization Functions. |
| (line 143) |
| * mpfr_get_si: Conversion Functions. |
| (line 31) |
| * mpfr_get_sj: Conversion Functions. |
| (line 33) |
| * mpfr_get_str: Conversion Functions. |
| (line 61) |
| * mpfr_get_ui: Conversion Functions. |
| (line 32) |
| * mpfr_get_uj: Conversion Functions. |
| (line 34) |
| * mpfr_get_version: Miscellaneous Functions. |
| (line 99) |
| * mpfr_get_z: Conversion Functions. |
| (line 51) |
| * mpfr_get_z_exp: Conversion Functions. |
| (line 44) |
| * mpfr_greater_p: Comparison Functions. |
| (line 54) |
| * mpfr_greaterequal_p: Comparison Functions. |
| (line 57) |
| * mpfr_hypot: Special Functions. (line 230) |
| * mpfr_inexflag_p: Exception Related Functions. |
| (line 128) |
| * mpfr_inf_p: Comparison Functions. |
| (line 42) |
| * mpfr_init: Initialization Functions. |
| (line 51) |
| * mpfr_init2: Initialization Functions. |
| (line 11) |
| * mpfr_init_set: Combined Initialization and Assignment Functions. |
| (line 7) |
| * mpfr_init_set_d: Combined Initialization and Assignment Functions. |
| (line 12) |
| * mpfr_init_set_f: Combined Initialization and Assignment Functions. |
| (line 17) |
| * mpfr_init_set_ld: Combined Initialization and Assignment Functions. |
| (line 14) |
| * mpfr_init_set_q: Combined Initialization and Assignment Functions. |
| (line 16) |
| * mpfr_init_set_si: Combined Initialization and Assignment Functions. |
| (line 11) |
| * mpfr_init_set_str: Combined Initialization and Assignment Functions. |
| (line 23) |
| * mpfr_init_set_ui: Combined Initialization and Assignment Functions. |
| (line 9) |
| * mpfr_init_set_z: Combined Initialization and Assignment Functions. |
| (line 15) |
| * mpfr_inits: Initialization Functions. |
| (line 63) |
| * mpfr_inits2: Initialization Functions. |
| (line 23) |
| * mpfr_inp_str: Input and Output Functions. |
| (line 33) |
| * mpfr_integer_p: Integer Related Functions. |
| (line 89) |
| * mpfr_j0: Special Functions. (line 194) |
| * mpfr_j1: Special Functions. (line 195) |
| * mpfr_jn: Special Functions. (line 196) |
| * mpfr_less_p: Comparison Functions. |
| (line 60) |
| * mpfr_lessequal_p: Comparison Functions. |
| (line 63) |
| * mpfr_lessgreater_p: Comparison Functions. |
| (line 66) |
| * mpfr_lgamma: Special Functions. (line 172) |
| * mpfr_li2: Special Functions. (line 157) |
| * mpfr_lngamma: Special Functions. (line 166) |
| * mpfr_log: Special Functions. (line 16) |
| * mpfr_log10: Special Functions. (line 18) |
| * mpfr_log1p: Special Functions. (line 142) |
| * mpfr_log2: Special Functions. (line 17) |
| * mpfr_max: Miscellaneous Functions. |
| (line 29) |
| * mpfr_min: Miscellaneous Functions. |
| (line 22) |
| * mpfr_modf: Integer Related Functions. |
| (line 55) |
| * mpfr_mul: Basic Arithmetic Functions. |
| (line 51) |
| * mpfr_mul_2exp: Compatibility with MPF. |
| (line 47) |
| * mpfr_mul_2si: Basic Arithmetic Functions. |
| (line 190) |
| * mpfr_mul_2ui: Basic Arithmetic Functions. |
| (line 188) |
| * mpfr_mul_d: Basic Arithmetic Functions. |
| (line 57) |
| * mpfr_mul_q: Basic Arithmetic Functions. |
| (line 61) |
| * mpfr_mul_si: Basic Arithmetic Functions. |
| (line 55) |
| * mpfr_mul_ui: Basic Arithmetic Functions. |
| (line 53) |
| * mpfr_mul_z: Basic Arithmetic Functions. |
| (line 59) |
| * mpfr_nan_p: Comparison Functions. |
| (line 41) |
| * mpfr_nanflag_p: Exception Related Functions. |
| (line 127) |
| * mpfr_neg: Basic Arithmetic Functions. |
| (line 173) |
| * mpfr_nextabove: Miscellaneous Functions. |
| (line 15) |
| * mpfr_nextbelow: Miscellaneous Functions. |
| (line 18) |
| * mpfr_nexttoward: Miscellaneous Functions. |
| (line 7) |
| * mpfr_number_p: Comparison Functions. |
| (line 43) |
| * mpfr_out_str: Input and Output Functions. |
| (line 17) |
| * mpfr_overflow_p: Exception Related Functions. |
| (line 126) |
| * mpfr_pow: Basic Arithmetic Functions. |
| (line 116) |
| * mpfr_pow_si: Basic Arithmetic Functions. |
| (line 120) |
| * mpfr_pow_ui: Basic Arithmetic Functions. |
| (line 118) |
| * mpfr_pow_z: Basic Arithmetic Functions. |
| (line 122) |
| * mpfr_prec_round: Rounding Related Functions. |
| (line 15) |
| * mpfr_print_rnd_mode: Rounding Related Functions. |
| (line 46) |
| * mpfr_printf: Formatted Output Functions. |
| (line 130) |
| * mpfr_random: Miscellaneous Functions. |
| (line 48) |
| * mpfr_random2: Miscellaneous Functions. |
| (line 56) |
| * mpfr_rec_sqrt: Basic Arithmetic Functions. |
| (line 102) |
| * mpfr_reldiff: Compatibility with MPF. |
| (line 39) |
| * mpfr_remainder: Integer Related Functions. |
| (line 65) |
| * mpfr_remquo: Integer Related Functions. |
| (line 67) |
| * mpfr_rint: Integer Related Functions. |
| (line 7) |
| * mpfr_rint_ceil: Integer Related Functions. |
| (line 34) |
| * mpfr_rint_floor: Integer Related Functions. |
| (line 35) |
| * mpfr_rint_round: Integer Related Functions. |
| (line 36) |
| * mpfr_rint_trunc: Integer Related Functions. |
| (line 37) |
| * mpfr_root: Basic Arithmetic Functions. |
| (line 109) |
| * mpfr_round: Integer Related Functions. |
| (line 10) |
| * mpfr_round_prec: Rounding Related Functions. |
| (line 25) |
| * mpfr_sec: Special Functions. (line 35) |
| * mpfr_sech: Special Functions. (line 125) |
| * mpfr_set: Assignment Functions. |
| (line 12) |
| * mpfr_set_d: Assignment Functions. |
| (line 18) |
| * mpfr_set_decimal64: Assignment Functions. |
| (line 21) |
| * mpfr_set_default_prec: Initialization Functions. |
| (line 101) |
| * mpfr_set_default_rounding_mode: Rounding Related Functions. |
| (line 7) |
| * mpfr_set_emax: Exception Related Functions. |
| (line 16) |
| * mpfr_set_emin: Exception Related Functions. |
| (line 15) |
| * mpfr_set_erangeflag: Exception Related Functions. |
| (line 118) |
| * mpfr_set_exp: Miscellaneous Functions. |
| (line 76) |
| * mpfr_set_f: Assignment Functions. |
| (line 24) |
| * mpfr_set_inexflag: Exception Related Functions. |
| (line 117) |
| * mpfr_set_inf: Assignment Functions. |
| (line 131) |
| * mpfr_set_ld: Assignment Functions. |
| (line 19) |
| * mpfr_set_nan: Assignment Functions. |
| (line 132) |
| * mpfr_set_nanflag: Exception Related Functions. |
| (line 116) |
| * mpfr_set_overflow: Exception Related Functions. |
| (line 115) |
| * mpfr_set_prec: Initialization Functions. |
| (line 131) |
| * mpfr_set_prec_raw: Compatibility with MPF. |
| (line 21) |
| * mpfr_set_q: Assignment Functions. |
| (line 23) |
| * mpfr_set_si: Assignment Functions. |
| (line 15) |
| * mpfr_set_si_2exp: Assignment Functions. |
| (line 51) |
| * mpfr_set_sj: Assignment Functions. |
| (line 17) |
| * mpfr_set_sj_2exp: Assignment Functions. |
| (line 55) |
| * mpfr_set_str: Assignment Functions. |
| (line 61) |
| * mpfr_set_ui: Assignment Functions. |
| (line 14) |
| * mpfr_set_ui_2exp: Assignment Functions. |
| (line 49) |
| * mpfr_set_uj: Assignment Functions. |
| (line 16) |
| * mpfr_set_uj_2exp: Assignment Functions. |
| (line 53) |
| * mpfr_set_underflow: Exception Related Functions. |
| (line 114) |
| * mpfr_set_z: Assignment Functions. |
| (line 22) |
| * mpfr_setsign: Miscellaneous Functions. |
| (line 87) |
| * mpfr_sgn: Comparison Functions. |
| (line 49) |
| * mpfr_si_div: Basic Arithmetic Functions. |
| (line 78) |
| * mpfr_si_sub: Basic Arithmetic Functions. |
| (line 33) |
| * mpfr_signbit: Miscellaneous Functions. |
| (line 82) |
| * mpfr_sin: Special Functions. (line 30) |
| * mpfr_sin_cos: Special Functions. (line 42) |
| * mpfr_sinh: Special Functions. (line 112) |
| * mpfr_sinh_cosh: Special Functions. (line 118) |
| * mpfr_snprintf: Formatted Output Functions. |
| (line 155) |
| * mpfr_sprintf: Formatted Output Functions. |
| (line 141) |
| * mpfr_sqr: Basic Arithmetic Functions. |
| (line 68) |
| * mpfr_sqrt: Basic Arithmetic Functions. |
| (line 95) |
| * mpfr_sqrt_ui: Basic Arithmetic Functions. |
| (line 97) |
| * mpfr_strtofr: Assignment Functions. |
| (line 72) |
| * mpfr_sub: Basic Arithmetic Functions. |
| (line 27) |
| * mpfr_sub_d: Basic Arithmetic Functions. |
| (line 39) |
| * mpfr_sub_q: Basic Arithmetic Functions. |
| (line 43) |
| * mpfr_sub_si: Basic Arithmetic Functions. |
| (line 35) |
| * mpfr_sub_ui: Basic Arithmetic Functions. |
| (line 31) |
| * mpfr_sub_z: Basic Arithmetic Functions. |
| (line 41) |
| * mpfr_subnormalize: Exception Related Functions. |
| (line 58) |
| * mpfr_sum: Special Functions. (line 258) |
| * mpfr_swap: Assignment Functions. |
| (line 137) |
| * mpfr_t: MPFR Basics. (line 52) |
| * mpfr_tan: Special Functions. (line 31) |
| * mpfr_tanh: Special Functions. (line 113) |
| * mpfr_trunc: Integer Related Functions. |
| (line 11) |
| * mpfr_ui_div: Basic Arithmetic Functions. |
| (line 74) |
| * mpfr_ui_pow: Basic Arithmetic Functions. |
| (line 126) |
| * mpfr_ui_pow_ui: Basic Arithmetic Functions. |
| (line 124) |
| * mpfr_ui_sub: Basic Arithmetic Functions. |
| (line 29) |
| * mpfr_underflow_p: Exception Related Functions. |
| (line 125) |
| * mpfr_unordered_p: Comparison Functions. |
| (line 75) |
| * mpfr_urandomb: Miscellaneous Functions. |
| (line 35) |
| * mpfr_vasprintf: Formatted Output Functions. |
| (line 173) |
| * MPFR_VERSION: Miscellaneous Functions. |
| (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: |