From 4bb85c6d43b42dbc5d14bd87d1fb89bd0fdf2629 Mon Sep 17 00:00:00 2001 From: Aurelien Larcher Date: Mon, 15 Aug 2016 01:41:41 +0200 Subject: [PATCH] Bump mpfr to 3.1.5 --- components/{ => library}/mpfr/Makefile | 47 +- .../{ => library}/mpfr/Solaris/libmpfr-64.pc | 2 +- components/{ => library}/mpfr/Solaris/libmpfr.3 | 3 +- components/{ => library}/mpfr/Solaris/libmpfr.pc | 2 +- components/{ => library}/mpfr/llib-lmpfr | 0 .../mpfr/manifests/sample-manifest.p5m | 16 +- components/library/mpfr/mpfr.license | 839 +++++ .../sample-manifest.p5m => library/mpfr/mpfr.p5m} | 25 +- components/mpfr/Solaris/index.html | 3525 -------------------- components/mpfr/mpfr.license | 1246 ------- components/mpfr/mpfr.p5m | 57 - components/mpfr/resolve.deps | 2 - 12 files changed, 881 insertions(+), 4883 deletions(-) rename components/{ => library}/mpfr/Makefile (79%) rename components/{ => library}/mpfr/Solaris/libmpfr-64.pc (94%) rename components/{ => library}/mpfr/Solaris/libmpfr.3 (91%) rename components/{ => library}/mpfr/Solaris/libmpfr.pc (94%) rename components/{ => library}/mpfr/llib-lmpfr (100%) copy components/{ => library}/mpfr/manifests/sample-manifest.p5m (79%) create mode 100644 components/library/mpfr/mpfr.license rename components/{mpfr/manifests/sample-manifest.p5m => library/mpfr/mpfr.p5m} (62%) delete mode 100644 components/mpfr/Solaris/index.html delete mode 100644 components/mpfr/mpfr.license delete mode 100644 components/mpfr/mpfr.p5m delete mode 100644 components/mpfr/resolve.deps diff --git a/components/mpfr/Makefile b/components/library/mpfr/Makefile similarity index 79% rename from components/mpfr/Makefile rename to components/library/mpfr/Makefile index 332527310..d13ef769d 100644 --- a/components/mpfr/Makefile +++ b/components/library/mpfr/Makefile @@ -20,25 +20,29 @@ # # Copyright (c) 2011, 2012, Oracle and/or its affiliates. All rights reserved. +# Copyright (c) 2016, Aurelien Larcher. All rights reserved. # -include ../../make-rules/shared-macros.mk - -PATH=$(dir $(CC)):/usr/bin:/usr/gnu/bin +include ../../../make-rules/shared-macros.mk COMPONENT_NAME= mpfr -COMPONENT_VERSION= 3.1.2 +COMPONENT_VERSION= 3.1.5 +COMPONENT_SUMMARY= The GNU Multiple Precision with IEEE Rounding Floating-Point Library COMPONENT_PROJECT_URL= http://www.mpfr.org/ +COMPONENT_FMRI= library/mpfr +COMPONENT_CLASSIFICATION=Development/High Performance Computing COMPONENT_SRC= $(COMPONENT_NAME)-$(COMPONENT_VERSION) COMPONENT_ARCHIVE= $(COMPONENT_SRC).tar.bz2 -COMPONENT_ARCHIVE_HASH= \ - sha256:79c73f60af010a30a5c27a955a1d2d01ba095b72537dab0ecaad57f5a7bb1b6b COMPONENT_ARCHIVE_URL= $(COMPONENT_PROJECT_URL)$(COMPONENT_SRC)/$(COMPONENT_ARCHIVE) -COMPONENT_BUGDB= library/libmpfr +COMPONENT_ARCHIVE_HASH= \ + sha256:ca498c1c7a74dd37a576f353312d1e68d490978de4395fa28f1cbd46a364e658 +COMPONENT_LICENSE= LGPLv2.1,GPLv2,FDLv1.2 -include ../../make-rules/prep.mk -include ../../make-rules/configure.mk -include ../../make-rules/ips.mk +include $(WS_MAKE_RULES)/prep.mk +include $(WS_MAKE_RULES)/configure.mk +include $(WS_MAKE_RULES)/ips.mk + +PATH=$(dir $(CC)):/usr/bin:/usr/gnu/bin CLOBBER_PATHS += libmpfr.pc PATCH_LEVEL = 0 @@ -96,30 +100,25 @@ COMPONENT_POST_INSTALL_ACTION = \ $(MKDIR) $(PROTOPKGCONFIGDIR) ; \ $(MKDIR) $(PROTOPKGCONFIGDIR64) ; \ $(GSED) -e "s^\#include ^\#include ^g" \ - $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h > \ - $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h.sed ; \ + $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h > \ + $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h.sed ; \ $(CP) -fp $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h.sed \ - $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h ; \ + $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h ; \ $(RM) -f $(PROTOUSRINCLUDEDIR)/mpfr/mpfr.h.sed ; \ $(GSED) -e "s/MACH64/$(MACH64)/g" \ - $(COMPONENT_DIR)/Solaris/libmpfr-64.pc > $(COMPONENT_DIR)/libmpfr.pc ; \ - $(INSTALL) -m 0644 $(COMPONENT_DIR)/Solaris/index.html \ - $(PROTOUSRSHAREHTMLDIR)/ ; \ + $(COMPONENT_DIR)/Solaris/libmpfr-64.pc > $(COMPONENT_DIR)/libmpfr.pc ; \ $(INSTALL) -m 0644 $(COMPONENT_DIR)/Solaris/libmpfr.pc \ - $(PROTOPKGCONFIGDIR) ; \ + $(PROTOPKGCONFIGDIR) ; \ $(INSTALL) -m 0644 $(COMPONENT_DIR)/libmpfr.pc \ - $(PROTOPKGCONFIGDIR64) ; \ + $(PROTOPKGCONFIGDIR64) ; \ $(INSTALL) -m 0644 $(COMPONENT_DIR)/Solaris/libmpfr.3 \ - $(PROTOUSRSHAREMAN3DIR)/ ) + $(PROTOUSRSHAREMAN3DIR)/ ) -# common targets build: $(BUILD_32_and_64) install: $(INSTALL_32_and_64) test: $(TEST_32_and_64) -BUILD_PKG_DEPENDENCIES = $(BUILD_TOOLS) - -include ../../make-rules/depend.mk - +REQUIRED_PACKAGES += library/gmp +REQUIRED_PACKAGES += system/library diff --git a/components/mpfr/Solaris/libmpfr-64.pc b/components/library/mpfr/Solaris/libmpfr-64.pc similarity index 94% rename from components/mpfr/Solaris/libmpfr-64.pc rename to components/library/mpfr/Solaris/libmpfr-64.pc index 72c2061a4..b588be88b 100644 --- a/components/mpfr/Solaris/libmpfr-64.pc +++ b/components/library/mpfr/Solaris/libmpfr-64.pc @@ -5,6 +5,6 @@ includedir=${prefix}/include/mpfr Name: libmpfr Description: The GNU Multiple Precision Rounding Floating-Point Library -Version: 3.1.2 +Version: 3.1.5 Libs: -L${libdir} -lmpfr Cflags: -I/usr/include/gmp -I${includedir} diff --git a/components/mpfr/Solaris/libmpfr.3 b/components/library/mpfr/Solaris/libmpfr.3 similarity index 91% rename from components/mpfr/Solaris/libmpfr.3 rename to components/library/mpfr/Solaris/libmpfr.3 index a79ee1f1b..030572b90 100644 --- a/components/mpfr/Solaris/libmpfr.3 +++ b/components/library/mpfr/Solaris/libmpfr.3 @@ -3,8 +3,7 @@ .\" Modified for Solaris to to add the Solaris stability classification, .\" and to add a note about source availability. .\" -.\" generic libgd man page for the LibGD Project -.TH libmpfr 3 "12 Nov 2010" "GNU MPFR 2.4.2" "Libraries" +.TH libmpfr 3 "06 Mar 2016" "GNU MPFR 3.1.4" "Libraries" .SH NAME \fBlibmpfr\fP diff --git a/components/mpfr/Solaris/libmpfr.pc b/components/library/mpfr/Solaris/libmpfr.pc similarity index 94% rename from components/mpfr/Solaris/libmpfr.pc rename to components/library/mpfr/Solaris/libmpfr.pc index 7d312e873..519b1203a 100644 --- a/components/mpfr/Solaris/libmpfr.pc +++ b/components/library/mpfr/Solaris/libmpfr.pc @@ -5,6 +5,6 @@ includedir=${prefix}/include/mpfr Name: libmpfr Description: The GNU Multiple Precision Rounding Floating-Point Library -Version: 3.1.2 +Version: 3.1.5 Libs: -L${libdir} -lmpfr Cflags: -I/usr/include/gmp -I${includedir} diff --git a/components/mpfr/llib-lmpfr b/components/library/mpfr/llib-lmpfr similarity index 100% rename from components/mpfr/llib-lmpfr rename to components/library/mpfr/llib-lmpfr diff --git a/components/mpfr/manifests/sample-manifest.p5m b/components/library/mpfr/manifests/sample-manifest.p5m similarity index 79% copy from components/mpfr/manifests/sample-manifest.p5m copy to components/library/mpfr/manifests/sample-manifest.p5m index 07e9d0f62..7ba75d55e 100644 --- a/components/mpfr/manifests/sample-manifest.p5m +++ b/components/library/mpfr/manifests/sample-manifest.p5m @@ -5,12 +5,12 @@ # 1.0 of the CDDL. # # A full copy of the text of the CDDL should have accompanied this -# source. A copy of the CDDL is also available via the Internet at +# source. A copy of the CDDL is also available via the Internet at # http://www.illumos.org/license/CDDL. # # -# Copyright 2016 +# Copyright 2017 # set name=pkg.fmri value=pkg:/$(COMPONENT_FMRI)@$(IPS_COMPONENT_VERSION),$(BUILD_VERSION) @@ -24,13 +24,13 @@ license $(COMPONENT_LICENSE_FILE) license='$(COMPONENT_LICENSE)' file path=usr/include/mpfr/mpf2mpfr.h file path=usr/include/mpfr/mpfr.h -link path=usr/lib/$(MACH64)/libmpfr.so target=libmpfr.so.4.1.2 -link path=usr/lib/$(MACH64)/libmpfr.so.4 target=libmpfr.so.4.1.2 -file path=usr/lib/$(MACH64)/libmpfr.so.4.1.2 +link path=usr/lib/$(MACH64)/libmpfr.so target=libmpfr.so.4.1.5 +link path=usr/lib/$(MACH64)/libmpfr.so.4 target=libmpfr.so.4.1.5 +file path=usr/lib/$(MACH64)/libmpfr.so.4.1.5 file path=usr/lib/$(MACH64)/pkgconfig/libmpfr.pc -link path=usr/lib/libmpfr.so target=libmpfr.so.4.1.2 -link path=usr/lib/libmpfr.so.4 target=libmpfr.so.4.1.2 -file path=usr/lib/libmpfr.so.4.1.2 +link path=usr/lib/libmpfr.so target=libmpfr.so.4.1.5 +link path=usr/lib/libmpfr.so.4 target=libmpfr.so.4.1.5 +file path=usr/lib/libmpfr.so.4.1.5 file path=usr/lib/pkgconfig/libmpfr.pc file path=usr/share/doc/mpfr/AUTHORS file path=usr/share/doc/mpfr/BUGS diff --git a/components/library/mpfr/mpfr.license b/components/library/mpfr/mpfr.license new file mode 100644 index 000000000..b3276d879 --- /dev/null +++ b/components/library/mpfr/mpfr.license @@ -0,0 +1,839 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. diff --git a/components/mpfr/manifests/sample-manifest.p5m b/components/library/mpfr/mpfr.p5m similarity index 62% rename from components/mpfr/manifests/sample-manifest.p5m rename to components/library/mpfr/mpfr.p5m index 07e9d0f62..1dcc4b425 100644 --- a/components/mpfr/manifests/sample-manifest.p5m +++ b/components/library/mpfr/mpfr.p5m @@ -5,12 +5,12 @@ # 1.0 of the CDDL. # # A full copy of the text of the CDDL should have accompanied this -# source. A copy of the CDDL is also available via the Internet at +# source. A copy of the CDDL is also available via the Internet at # http://www.illumos.org/license/CDDL. # # -# Copyright 2016 +# Copyright 2016 Aurelien Larcher # set name=pkg.fmri value=pkg:/$(COMPONENT_FMRI)@$(IPS_COMPONENT_VERSION),$(BUILD_VERSION) @@ -24,27 +24,18 @@ license $(COMPONENT_LICENSE_FILE) license='$(COMPONENT_LICENSE)' file path=usr/include/mpfr/mpf2mpfr.h file path=usr/include/mpfr/mpfr.h -link path=usr/lib/$(MACH64)/libmpfr.so target=libmpfr.so.4.1.2 -link path=usr/lib/$(MACH64)/libmpfr.so.4 target=libmpfr.so.4.1.2 -file path=usr/lib/$(MACH64)/libmpfr.so.4.1.2 +link path=usr/lib/$(MACH64)/libmpfr.so target=libmpfr.so.4.1.5 +link path=usr/lib/$(MACH64)/libmpfr.so.4 target=libmpfr.so.4.1.5 +file path=usr/lib/$(MACH64)/libmpfr.so.4.1.5 file path=usr/lib/$(MACH64)/pkgconfig/libmpfr.pc -link path=usr/lib/libmpfr.so target=libmpfr.so.4.1.2 -link path=usr/lib/libmpfr.so.4 target=libmpfr.so.4.1.2 -file path=usr/lib/libmpfr.so.4.1.2 +link path=usr/lib/libmpfr.so target=libmpfr.so.4.1.5 +link path=usr/lib/libmpfr.so.4 target=libmpfr.so.4.1.5 +file path=usr/lib/libmpfr.so.4.1.5 file path=usr/lib/pkgconfig/libmpfr.pc -file path=usr/share/doc/mpfr/AUTHORS -file path=usr/share/doc/mpfr/BUGS -file path=usr/share/doc/mpfr/COPYING -file path=usr/share/doc/mpfr/COPYING.LESSER -file path=usr/share/doc/mpfr/FAQ.html -file path=usr/share/doc/mpfr/NEWS -file path=usr/share/doc/mpfr/TODO file path=usr/share/doc/mpfr/examples/ReadMe file path=usr/share/doc/mpfr/examples/divworst.c file path=usr/share/doc/mpfr/examples/rndo-add.c file path=usr/share/doc/mpfr/examples/sample.c file path=usr/share/doc/mpfr/examples/version.c -file path=usr/share/doc/mpfr/html/index.html -file path=usr/share/info/dir file path=usr/share/info/mpfr.info file path=usr/share/man/man3/libmpfr.3 diff --git a/components/mpfr/Solaris/index.html b/components/mpfr/Solaris/index.html deleted file mode 100644 index 197412a71..000000000 --- a/components/mpfr/Solaris/index.html +++ /dev/null @@ -1,3525 +0,0 @@ - - -MPFR 2.3.2 - - - - - - - - - - -
-

- -Next: , -Previous: (dir), -Up: (dir) - -
- -

MPFR

- -

This manual documents how to install and use the Multiple Precision -Floating-Point Reliable Library, version 2.3.2. - -

Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 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 GNU Free Documentation License. - 

-
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- - -

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 -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 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 MPFR library are found in the -Lesser General Public License that accompanies the source code. -See the file COPYING.LIB. - -

-

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- - -

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 MPFR Basics. If you need to install the library -yourself, you need to read 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. - -

-

- -Next: , -Previous: 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’. (See 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’. -See Reporting Bugs. -Some bug fixes are available on the -MPFR 2.3.2 web page http://www.mpfr.org/mpfr-2.3.2/. - -

2.4 Getting the Latest Version of MPFR

- -

The latest version of MPFR is available from http://www.mpfr.org/. - -

-

- -Next: , -Previous: 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 2.3.2 web page http://www.mpfr.org/mpfr-2.3.2/ 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 won't 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. - -

-

- -Next: , -Previous: 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>
-
-

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, see GNU Libtool. - - - - - -

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 don't 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 (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 MPFR Interface. - - - - -Example: mpfr_hypot on (NaN,0) gives NaN, but mpfr_hypot -on (NaN,+Inf) gives +Inf (as specified in 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 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). - -

-

- -Next: , -Previous: 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. - -

- -
-

- -Next: , -Previous: 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_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_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. -

- -
-— 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. -

- -
-

- -Next: , -Previous: Initialization Functions, -Up: MPFR Interface - -
- - -

- -

5.2 Assignment Functions

- -

These functions assign new values to already initialized floats -(see 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 doesn't 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 whole 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. - - - - -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 = 36; 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. -

- -
-

- -Next: , -Previous: 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. -

- -
-

- -Next: , -Previous: 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 flag erange 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: -see section “Custom Allocation” in GNU MP. -

- -
-— 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. -

- -
-

- -Next: , -Previous: 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_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)). -

- -
-— 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_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)). -

- -
-— 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_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). -

- -
-— 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_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). -

- -
-— 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_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. -

- -
-

- -Next: , -Previous: 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. -

- -
-

- -Next: , -Previous: 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_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_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 order 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 order 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. -

- -
-

- -Next: , -Previous: 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 argument 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. -

- - - - - -
-

- -Next: , -Previous: Input and Output Functions, -Up: MPFR Interface - -
- - -

- -

5.9 Integer 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_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 remainder of the division of x by y, with -quotient rounded to the nearest integer (ties rounded to even), and -r rounded according to the direction rnd. -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. -These functions are useful for additive argument reduction. -

- -
-— Function: int mpfr_integer_p (mpfr_t op)
-

Return non-zero iff op is an integer. -

- -
-

- -Next: , -Previous: Integer Related Functions, -Up: MPFR Interface - -
- - -

- -

5.10 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. -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. 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; 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’). -

- -
-— 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). -

- -
-

- -Next: , -Previous: Miscellaneous Functions, -Up: MPFR Interface - -
- -

- -

5.11 Rounding Mode 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: 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. -

- -
-

- -Next: , -Previous: Rounding Mode Related Functions, -Up: MPFR Interface - -
- - -

- -

5.12 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. -

- -
-

- -Next: , -Previous: Exception Related Functions, -Up: MPFR Interface - -
- - -

- -

5.13 Advanced Functions

- -

All the given interfaces are preliminary. They might change incompatibly in -future revisions. - -

-— 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 can not 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 compiler constant, your compiler -must support ‘Variable-length automatic arrays’ (standard in ISO C99). -‘GCC 2.95.3’ 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_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). -

- -
-— 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_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);
-     }
-
-
-

- -Next: , -Previous: Advanced 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 regarded as different for any value of op3 -larger than 1. -

- -
-— 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. -

- -
-

- -Next: , -Previous: 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 doesn't -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. - -

-

- -Previous: 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. - -
- - - - - - - - - - - - - - -
-— 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: double mpfr_get_d1 (mpfr_t op)
-

Convert op to a double, using the default MPFR rounding mode -(see function mpfr_set_default_rounding_mode). This function is -obsolete. -

- - - - - - - - - - - - - - - - -
-

- -Next: , -Previous: 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 in -generic.c, 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). - -

-

- -Next: , -Previous: 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. - -
- -
-

- -Next: , -Previous: References, -Up: Top - -
- -

Appendix A GNU Free Documentation License

- -

- - - - -

Version 1.2, November 2002
- -
     Copyright © 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.
-
-
    -
  1. PREAMBLE - -

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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 free -software, because free software needs free documentation: a free -program should come with manuals providing the same freedoms that the -software does. But this License is not limited to software manuals; -it can be used for any textual work, regardless 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. - -

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To prevent this, we have made it clear that any -patent must be licensed for everyone's free use or not licensed at all. - - The precise terms and conditions for copying, distribution and -modification follow. - - GNU GENERAL PUBLIC LICENSE - TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION - - 0. This License applies to any program or other work which contains -a notice placed by the copyright holder saying it may be distributed -under the terms of this General Public License. The "Program", below, -refers to any such program or work, and a "work based on the Program" -means either the Program or any derivative work under copyright law: -that is to say, a work containing the Program or a portion of it, -either verbatim or with modifications and/or translated into another -language. (Hereinafter, translation is included without limitation in -the term "modification".) Each licensee is addressed as "you". - -Activities other than copying, distribution and modification are not -covered by this License; they are outside its scope. The act of -running the Program is not restricted, and the output from the Program -is covered only if its contents constitute a work based on the -Program (independent of having been made by running the Program). -Whether that is true depends on what the Program does. - - 1. You may copy and distribute verbatim copies of the Program's -source code as you receive it, in any medium, provided that you -conspicuously and appropriately publish on each copy an appropriate -copyright notice and disclaimer of warranty; keep intact all the -notices that refer to this License and to the absence of any warranty; -and give any other recipients of the Program a copy of this License -along with the Program. - -You may charge a fee for the physical act of transferring a copy, and -you may at your option offer warranty protection in exchange for a fee. - - 2. You may modify your copy or copies of the Program or any portion -of it, thus forming a work based on the Program, and copy and -distribute such modifications or work under the terms of Section 1 -above, provided that you also meet all of these conditions: - - a) You must cause the modified files to carry prominent notices - stating that you changed the files and the date of any change. - - b) You must cause any work that you distribute or publish, that in - whole or in part contains or is derived from the Program or any - part thereof, to be licensed as a whole at no charge to all third - parties under the terms of this License. - - c) If the modified program normally reads commands interactively - when run, you must cause it, when started running for such - interactive use in the most ordinary way, to print or display an - announcement including an appropriate copyright notice and a - notice that there is no warranty (or else, saying that you provide - a warranty) and that users may redistribute the program under - these conditions, and telling the user how to view a copy of this - License. (Exception: if the Program itself is interactive but - does not normally print such an announcement, your work based on - the Program is not required to print an announcement.) - -These requirements apply to the modified work as a whole. If -identifiable sections of that work are not derived from the Program, -and can be reasonably considered independent and separate works in -themselves, then this License, and its terms, do not apply to those -sections when you distribute them as separate works. But when you -distribute the same sections as part of a whole which is a work based -on the Program, the distribution of the whole must be on the terms of -this License, whose permissions for other licensees extend to the -entire whole, and thus to each and every part regardless of who wrote it. - -Thus, it is not the intent of this section to claim rights or contest -your rights to work written entirely by you; rather, the intent is to -exercise the right to control the distribution of derivative or -collective works based on the Program. - -In addition, mere aggregation of another work not based on the Program -with the Program (or with a work based on the Program) on a volume of -a storage or distribution medium does not bring the other work under -the scope of this License. - - 3. You may copy and distribute the Program (or a work based on it, -under Section 2) in object code or executable form under the terms of -Sections 1 and 2 above provided that you also do one of the following: - - a) Accompany it with the complete corresponding machine-readable - source code, which must be distributed under the terms of Sections - 1 and 2 above on a medium customarily used for software interchange; or, - - b) Accompany it with a written offer, valid for at least three - years, to give any third party, for a charge no more than your - cost of physically performing source distribution, a complete - machine-readable copy of the corresponding source code, to be - distributed under the terms of Sections 1 and 2 above on a medium - customarily used for software interchange; or, - - c) Accompany it with the information you received as to the offer - to distribute corresponding source code. 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Any attempt -otherwise to copy, modify, sublicense or distribute the Program is -void, and will automatically terminate your rights under this License. -However, parties who have received copies, or rights, from you under -this License will not have their licenses terminated so long as such -parties remain in full compliance. - - 5. You are not required to accept this License, since you have not -signed it. However, nothing else grants you permission to modify or -distribute the Program or its derivative works. These actions are -prohibited by law if you do not accept this License. Therefore, by -modifying or distributing the Program (or any work based on the -Program), you indicate your acceptance of this License to do so, and -all its terms and conditions for copying, distributing or modifying -the Program or works based on it. - - 6. Each time you redistribute the Program (or any work based on the -Program), the recipient automatically receives a license from the -original licensor to copy, distribute or modify the Program subject to -these terms and conditions. You may not impose any further -restrictions on the recipients' exercise of the rights granted herein. -You are not responsible for enforcing compliance by third parties to -this License. - - 7. If, as a consequence of a court judgment or allegation of patent -infringement or for any other reason (not limited to patent issues), -conditions are imposed on you (whether by court order, agreement or -otherwise) that contradict the conditions of this License, they do not -excuse you from the conditions of this License. If you cannot -distribute so as to satisfy simultaneously your obligations under this -License and any other pertinent obligations, then as a consequence you -may not distribute the Program at all. For example, if a patent -license would not permit royalty-free redistribution of the Program by -all those who receive copies directly or indirectly through you, then -the only way you could satisfy both it and this License would be to -refrain entirely from distribution of the Program. - -If any portion of this section is held invalid or unenforceable under -any particular circumstance, the balance of the section is intended to -apply and the section as a whole is intended to apply in other -circumstances. - -It is not the purpose of this section to induce you to infringe any -patents or other property right claims or to contest validity of any -such claims; this section has the sole purpose of protecting the -integrity of the free software distribution system, which is -implemented by public license practices. Many people have made -generous contributions to the wide range of software distributed -through that system in reliance on consistent application of that -system; it is up to the author/donor to decide if he or she is willing -to distribute software through any other system and a licensee cannot -impose that choice. - -This section is intended to make thoroughly clear what is believed to -be a consequence of the rest of this License. - - 8. If the distribution and/or use of the Program is restricted in -certain countries either by patents or by copyrighted interfaces, the -original copyright holder who places the Program under this License -may add an explicit geographical distribution limitation excluding -those countries, so that distribution is permitted only in or among -countries not thus excluded. In such case, this License incorporates -the limitation as if written in the body of this License. - - 9. The Free Software Foundation may publish revised and/or new versions -of the General Public License from time to time. Such new versions will -be similar in spirit to the present version, but may differ in detail to -address new problems or concerns. - -Each version is given a distinguishing version number. If the Program -specifies a version number of this License which applies to it and "any -later version", you have the option of following the terms and conditions -either of that version or of any later version published by the Free -Software Foundation. If the Program does not specify a version number of -this License, you may choose any version ever published by the Free Software -Foundation. - - 10. If you wish to incorporate parts of the Program into other free -programs whose distribution conditions are different, write to the author -to ask for permission. For software which is copyrighted by the Free -Software Foundation, write to the Free Software Foundation; we sometimes -make exceptions for this. Our decision will be guided by the two goals -of preserving the free status of all derivatives of our free software and -of promoting the sharing and reuse of software generally. - - NO WARRANTY - - 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY -FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN -OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES -PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED -OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF -MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS -TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE -PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, -REPAIR OR CORRECTION. - - 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING -WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR -REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, -INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING -OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED -TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY -YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER -PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE -POSSIBILITY OF SUCH DAMAGES. - - END OF TERMS AND CONDITIONS - - How to Apply These Terms to Your New Programs - - If you develop a new program, and you want it to be of the greatest -possible use to the public, the best way to achieve this is to make it -free software which everyone can redistribute and change under these terms. - - To do so, attach the following notices to the program. It is safest -to attach them to the start of each source file to most effectively -convey the exclusion of warranty; and each file should have at least -the "copyright" line and a pointer to where the full notice is found. - - - Copyright (C) - - This program is free software; you can redistribute it and/or modify - it under the terms of the GNU General Public License as published by - the Free Software Foundation; either version 2 of the License, or - (at your option) any later version. - - This program is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - GNU General Public License for more details. - - You should have received a copy of the GNU General Public License - along with this program; if not, write to the Free Software - Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA - - -Also add information on how to contact you by electronic and paper mail. - -If the program is interactive, make it output a short notice like this -when it starts in an interactive mode: - - Gnomovision version 69, Copyright (C) year name of author - Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. - This is free software, and you are welcome to redistribute it - under certain conditions; type `show c' for details. - -The hypothetical commands `show w' and `show c' should show the appropriate -parts of the General Public License. Of course, the commands you use may -be called something other than `show w' and `show c'; they could even be -mouse-clicks or menu items--whatever suits your program. - -You should also get your employer (if you work as a programmer) or your -school, if any, to sign a "copyright disclaimer" for the program, if -necessary. Here is a sample; alter the names: - - Yoyodyne, Inc., hereby disclaims all copyright interest in the program - `Gnomovision' (which makes passes at compilers) written by James Hacker. - - , 1 April 1989 - Ty Coon, President of Vice - -This General Public License does not permit incorporating your program into -proprietary programs. If your program is a subroutine library, you may -consider it more useful to permit linking proprietary applications with the -library. If this is what you want to do, use the GNU Library General -Public License instead of this License. - ------------------------------------------------------------------- - - 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 noncommercially. -Secondarily, this License preserves for the author and publisher a way -to get credit for their work, while not being considered responsible -for modifications made by others. - -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 free -software, because free software needs free documentation: a free -program should come with manuals providing the same freedoms that the -software does. But this License is not limited to software manuals; -it can be used for any textual work, regardless 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 - -This License applies to any manual or other work, in any medium, that -contains a notice placed by the copyright holder saying it can be -distributed under the terms of this License. Such a notice grants a -world-wide, royalty-free license, unlimited in duration, to use that -work under the conditions stated herein. The "Document", below, -refers to any such manual or work. Any member of the public is a -licensee, and is addressed as "you". 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A copy that is not "Transparent" is called "Opaque". - -Examples of suitable formats for Transparent copies include plain -ASCII without markup, Texinfo input format, LaTeX input format, SGML -or XML using a publicly available DTD, and standard-conforming simple -HTML, PostScript or PDF designed for human modification. Examples of -transparent image formats include PNG, XCF and JPG. Opaque formats -include proprietary formats that can be read and edited only by -proprietary word processors, SGML or XML for which the DTD and/or -processing tools are not generally available, and the -machine-generated HTML, PostScript or PDF produced by some word -processors for output purposes only. - -The "Title Page" means, for a printed book, the title page itself, -plus such following pages as are needed to hold, legibly, the material -this License requires to appear in the title page. For works in -formats which do not have any title page as such, "Title Page" means -the text near the most prominent appearance of the work's title, -preceding the beginning of the body of the text. - -A section "Entitled XYZ" means a named subunit of the Document whose -title either is precisely XYZ or contains XYZ in parentheses following -text that translates XYZ in another language. (Here XYZ stands for a -specific section name mentioned below, such as "Acknowledgements", -"Dedications", "Endorsements", or "History".) To "Preserve the Title" -of such a section when you modify the Document means that it remains a -section "Entitled XYZ" according to this definition. - -The Document may include Warranty Disclaimers next to the notice which -states that this License applies to the Document. 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MODIFICATIONS - -You may copy and distribute a Modified Version of the Document under -the conditions of sections 2 and 3 above, provided that you release -the Modified Version under precisely this License, with the Modified -Version filling the role of the Document, thus licensing distribution -and modification of the Modified Version to whoever possesses a copy -of it. In addition, you must do these things in the Modified Version: - -A. Use in the Title Page (and on the covers, if any) a title distinct - from that of the Document, and from those of previous versions - (which should, if there were any, be listed in the History section - of the Document). You may use the same title as a previous version - if the original publisher of that version gives permission. -B. List on the Title Page, as authors, one or more persons or entities - responsible for authorship of the modifications in the Modified - Version, together with at least five of the principal authors of the - Document (all of its principal authors, if it has fewer than five), - unless they release you from this requirement. -C. State on the Title page the name of the publisher of the - Modified Version, as the publisher. -D. Preserve all the copyright notices of the Document. -E. Add an appropriate copyright notice for your modifications - adjacent to the other copyright notices. -F. Include, immediately after the copyright notices, a license notice - giving the public permission to use the Modified Version under the - terms of this License, in the form shown in the Addendum below. -G. Preserve in that license notice the full lists of Invariant Sections - and required Cover Texts given in the Document's license notice. -H. Include an unaltered copy of this License. -I. Preserve the section Entitled "History", Preserve its Title, and add - to it an item stating at least the title, year, new authors, and - publisher of the Modified Version as given on the Title Page. If - there is no section Entitled "History" in the Document, create one - stating the title, year, authors, and publisher of the Document as - given on its Title Page, then add an item describing the Modified - Version as stated in the previous sentence. -J. Preserve the network location, if any, given in the Document for - public access to a Transparent copy of the Document, and likewise - the network locations given in the Document for previous versions - it was based on. These may be placed in the "History" section. - You may omit a network location for a work that was published at - least four years before the Document itself, or if the original - publisher of the version it refers to gives permission. -K. For any section Entitled "Acknowledgements" or "Dedications", - Preserve the Title of the section, and preserve in the section all - the substance and tone of each of the contributor acknowledgements - and/or dedications given therein. -L. Preserve all the Invariant Sections of the Document, - unaltered in their text and in their titles. Section numbers - or the equivalent are not considered part of the section titles. -M. Delete any section Entitled "Endorsements". Such a section - may not be included in the Modified Version. -N. Do not retitle any existing section to be Entitled "Endorsements" - or to conflict in title with any Invariant Section. -O. Preserve any Warranty Disclaimers. - -If the Modified Version includes new front-matter sections or -appendices that qualify as Secondary Sections and contain no material -copied from the Document, you may at your option designate some or all -of these sections as invariant. To do this, add their titles to the -list of Invariant Sections in the Modified Version's license notice. -These titles must be distinct from any other section titles. - -You may add a section Entitled "Endorsements", provided it contains -nothing but endorsements of your Modified Version by various -parties--for example, statements of peer review or that the text has -been approved by an organization as the authoritative definition of a -standard. - -You may add a passage of up to five words as a Front-Cover Text, and a -passage of up to 25 words as a Back-Cover Text, to the end of the list -of Cover Texts in the Modified Version. Only one passage of -Front-Cover Text and one of Back-Cover Text may be added by (or -through arrangements made by) any one entity. If the Document already -includes a cover text for the same cover, previously added by you or -by arrangement made by the same entity you are acting on behalf of, -you may not add another; but you may replace the old one, on explicit -permission from the previous publisher that added the old one. - -The author(s) and publisher(s) of the Document do not by this License -give permission to use their names for publicity for or to assert or -imply endorsement of any Modified Version. - - -5. COMBINING DOCUMENTS - -You may combine the Document with other documents released under this -License, under the terms defined in section 4 above for modified -versions, provided that you include in the combination all of the -Invariant Sections of all of the original documents, unmodified, and -list them all as Invariant Sections of your combined work in its -license notice, and that you preserve all their Warranty Disclaimers. - -The combined work need only contain one copy of this License, and -multiple identical Invariant Sections may be replaced with a single -copy. If there are multiple Invariant Sections with the same name but -different contents, make the title of each such section unique by -adding at the end of it, in parentheses, the name of the original -author or publisher of that section if known, or else a unique number. -Make the same adjustment to the section titles in the list of -Invariant Sections in the license notice of the combined work. - -In the combination, you must combine any sections Entitled "History" -in the various original documents, forming one section Entitled -"History"; likewise combine any sections Entitled "Acknowledgements", -and any sections Entitled "Dedications". You must delete all sections -Entitled "Endorsements". - - -6. COLLECTIONS OF DOCUMENTS - -You may make a collection consisting of the Document and other documents -released under this License, and replace the individual copies of this -License in the various documents with a single copy that is included in -the collection, provided that you follow the rules of this License for -verbatim copying of each of the documents in all other respects. - -You may extract a single document from such a collection, and distribute -it individually under this License, provided you insert a copy of this -License into the extracted document, and follow this License in all -other respects regarding verbatim copying of that document. - - -7. AGGREGATION WITH INDEPENDENT WORKS - -A compilation of the Document or its derivatives with other separate -and independent documents or works, in or on a volume of a storage or -distribution medium, is called an "aggregate" if the copyright -resulting from the compilation is not used to limit the legal rights -of the compilation's users beyond what the individual works permit. -When the Document is included in an aggregate, this License does not -apply to the other works in the aggregate which are not themselves -derivative works of the Document. - -If the Cover Text requirement of section 3 is applicable to these -copies of the Document, then if the Document is less than one half of -the entire aggregate, the Document's Cover Texts may be placed on -covers that bracket the Document within the aggregate, or the -electronic equivalent of covers if the Document is in electronic form. -Otherwise they must appear on printed covers that bracket the whole -aggregate. - - -8. TRANSLATION - -Translation is considered a kind of modification, so you may -distribute translations of the Document under the terms of section 4. -Replacing Invariant Sections with translations requires special -permission from their copyright holders, but you may include -translations of some or all Invariant Sections in addition to the -original versions of these Invariant Sections. You may include a -translation of this License, and all the license notices in the -Document, and any Warranty Disclaimers, provided that you also include -the original English version of this License and the original versions -of those notices and disclaimers. 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Such new -versions will be similar in spirit to the present version, but may -differ in detail to address new problems or concerns. See -http://www.gnu.org/copyleft/. - -Each version of the License is given a distinguishing version number. -If the Document specifies that a particular numbered version of this -License "or any later version" applies to it, you have the option of -following the terms and conditions either of that specified version or -of any later version that has been published (not as a draft) by the -Free Software Foundation. If the Document does not specify a version -number of this License, you may choose any version ever published (not -as a draft) by the Free Software Foundation. - - -ADDENDUM: How to use this License for your documents - -To use this License in a document you have written, include a copy of -the License in the document and put the following copyright and -license notices just after the title page: - - 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 - Free Documentation License". - -If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, -replace the "with...Texts." line with this: - - with the Invariant Sections being LIST THEIR TITLES, with the - Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. - -If you have Invariant Sections without Cover Texts, or some other -combination of the three, merge those two alternatives to suit the -situation. - -If your document contains nontrivial examples of program code, we -recommend releasing these examples in parallel under your choice of -free software license, such as the GNU General Public License, -to permit their use in free software. diff --git a/components/mpfr/mpfr.p5m b/components/mpfr/mpfr.p5m deleted file mode 100644 index cca56ba06..000000000 --- a/components/mpfr/mpfr.p5m +++ /dev/null @@ -1,57 +0,0 @@ -# -# CDDL HEADER START -# -# The contents of this file are subject to the terms of the -# Common Development and Distribution License (the "License"). -# You may not use this file except in compliance with the License. -# -# You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE -# or http://www.opensolaris.org/os/licensing. -# See the License for the specific language governing permissions -# and limitations under the License. -# -# When distributing Covered Code, include this CDDL HEADER in each -# file and include the License file at usr/src/OPENSOLARIS.LICENSE. -# If applicable, add the following below this CDDL HEADER, with the -# fields enclosed by brackets "[]" replaced with your own identifying -# information: Portions Copyright [yyyy] [name of copyright owner] -# -# CDDL HEADER END -# -# Copyright (c) 2011, 2013, Oracle and/or its affiliates. All rights reserved. -# - default mangler.man.stability uncommitted> - -set name=pkg.fmri value=pkg:/library/mpfr@$(IPS_COMPONENT_VERSION),$(BUILD_VERSION) -set name=pkg.summary value="GNU MPFR" -set name=pkg.description value="The GNU Multiple Precision with IEEE Rounding Floating-Point Library" -set name=com.oracle.info.description value="GNU MPFR" -set name=info.classification value="org.opensolaris.category.2008:Development/High Performance Computing" -set name=info.upstream-url value=$(COMPONENT_PROJECT_URL) -set name=info.source-url value=$(COMPONENT_ARCHIVE_URL) -set name=org.opensolaris.arc-caseid \ - value=LSARC/2008/655 -set name=org.opensolaris.consolidation value=$(CONSOLIDATION) -# -# -file path=usr/include/mpfr/mpf2mpfr.h -file path=usr/include/mpfr/mpfr.h -file path=usr/lib/libmpfr.so.4.1.2 -file path=usr/lib/$(MACH64)/libmpfr.so.4.1.2 -file path=usr/lib/pkgconfig/libmpfr.pc -file path=usr/lib/$(MACH64)/pkgconfig/libmpfr.pc -file path=usr/share/doc/mpfr/examples/ReadMe -file path=usr/share/doc/mpfr/examples/divworst.c -file path=usr/share/doc/mpfr/examples/rndo-add.c -file path=usr/share/doc/mpfr/examples/sample.c -file path=usr/share/doc/mpfr/examples/version.c -file path=usr/share/doc/mpfr/html/index.html -file path=usr/share/info/mpfr.info -file path=usr/share/man/man3/libmpfr.3 -# -link path=usr/lib/libmpfr.so.4 target=libmpfr.so.4.1.2 -link path=usr/lib/libmpfr.so target=libmpfr.so.4.1.2 -link path=usr/lib/$(MACH64)/libmpfr.so.4 target=libmpfr.so.4.1.2 -link path=usr/lib/$(MACH64)/libmpfr.so target=libmpfr.so.4.1.2 -# -license mpfr.license license="LGPLv2.1, GPLv2, FDLv1.2" diff --git a/components/mpfr/resolve.deps b/components/mpfr/resolve.deps deleted file mode 100644 index ba5334fb6..000000000 --- a/components/mpfr/resolve.deps +++ /dev/null @@ -1,2 +0,0 @@ -library/gmp -system/library -- 2.11.4.GIT