--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/components/gnump/gmp.license Mon May 09 11:36:28 2011 -0700
@@ -0,0 +1,1302 @@
+For the avoidance of doubt, except that if any license choice other than
+GPL or LGPL is available it will apply instead, Oracle elects to use
+only the General Public License version 3 (GPLv3) at this time for any
+software where a choice of GPL license versions is made available with
+the language indicating that GPLv3 or any later version may be used.
+------------------------------------------------------------------
+
+ GNU LESSER GENERAL PUBLIC LICENSE
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+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
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+----------------------------------------------------------------------
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+ GNU GENERAL PUBLIC LICENSE
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+ 11. Patents.
+
+ A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based. The
+work thus licensed is called the contributor's "contributor version".
+
+ A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version. For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+ Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+ In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement). To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+ If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients. "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+ If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+ A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License. You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
+to the third party based on the extent of your activity of conveying
+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
+patent license (a) in connection with copies of the covered work
+conveyed by you (or copies made from those copies), or (b) primarily
+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+ Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+ 12. No Surrender of Others' Freedom.
+
+ If 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 convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all. For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+ 13. Use with the GNU Affero General Public License.
+
+ Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
+combined work, and to convey the resulting work. The terms of this
+License will continue to apply to the part which is the covered work,
+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+ 14. Revised Versions of this License.
+
+ The Free Software Foundation may publish revised and/or new versions of
+the GNU 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 that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation. If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+ If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+ Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+ 15. Disclaimer of Warranty.
+
+ 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.
+
+ 16. Limitation of Liability.
+
+ IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+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.
+
+ 17. Interpretation of Sections 15 and 16.
+
+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ 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
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ 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 3 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, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+ If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+ <program> Copyright (C) <year> <name of author>
+ This program 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, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+ You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+ The GNU 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 Lesser General
+Public License instead of this License. But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+
+-------------------------------------------------------------------------
+
+ GNU Free Documentation License
+ Version 1.3, 3 November 2008
+
+
+ Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
+ <http://fsf.org/>
+ 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". You accept the license if you
+copy, modify or distribute the work in a way requiring permission
+under copyright law.
+
+A "Modified Version" of the Document means any work containing the
+Document or a portion of it, either copied verbatim, or with
+modifications and/or translated into another language.
+
+A "Secondary Section" is a named appendix or a front-matter section of
+the Document that deals exclusively with the relationship of the
+publishers or authors of the Document to the Document's overall
+subject (or to related matters) and contains nothing that could fall
+directly within that overall subject. (Thus, if the Document is in
+part a textbook of mathematics, a Secondary Section may not explain
+any mathematics.) The relationship could be a matter of historical
+connection with the subject or with related matters, or of legal,
+commercial, philosophical, ethical or political position regarding
+them.
+
+The "Invariant Sections" are certain Secondary Sections whose titles
+are designated, as being those of Invariant Sections, in the notice
+that says that the Document is released under this License. If a
+section does not fit the above definition of Secondary then it is not
+allowed to be designated as Invariant. The Document may contain zero
+Invariant Sections. If the Document does not identify any Invariant
+Sections then there are none.
+
+The "Cover Texts" are certain short passages of text that are listed,
+as Front-Cover Texts or Back-Cover Texts, in the notice that says that
+the Document is released under this License. A Front-Cover Text may
+be at most 5 words, and a Back-Cover Text may be at most 25 words.
+
+A "Transparent" copy of the Document means a machine-readable copy,
+represented in a format whose specification is available to the
+general public, that is suitable for revising the document
+straightforwardly with generic text editors or (for images composed of
+pixels) generic paint programs or (for drawings) some widely available
+drawing editor, and that is suitable for input to text formatters or
+for automatic translation to a variety of formats suitable for input
+to text formatters. A copy made in an otherwise Transparent file
+format whose markup, or absence of markup, has been arranged to thwart
+or discourage subsequent modification by readers is not Transparent.
+An image format is not Transparent if used for any substantial amount
+of text. 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.
+
+The "publisher" means any person or entity that distributes copies of
+the Document to the public.
+
+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. These Warranty
+Disclaimers are considered to be included by reference in this
+License, but only as regards disclaiming warranties: any other
+implication that these Warranty Disclaimers may have is void and has
+no effect on the meaning of this License.
+
+2. VERBATIM COPYING
+
+You may copy and distribute the Document in any medium, either
+commercially or noncommercially, provided that this License, the
+copyright notices, and the license notice saying this License applies
+to the Document are reproduced in all copies, and that you add no
+other conditions whatsoever to those of this License. You may not use
+technical measures to obstruct or control the reading or further
+copying of the copies you make or distribute. However, you may accept
+compensation in exchange for copies. If you distribute a large enough
+number of copies you must also follow the conditions in section 3.
+
+You may also lend copies, under the same conditions stated above, and
+you may publicly display copies.
+
+
+3. COPYING IN QUANTITY
+
+If you publish printed copies (or copies in media that commonly have
+printed covers) of the Document, numbering more than 100, and the
+Document's license notice requires Cover Texts, you must enclose the
+copies in covers that carry, clearly and legibly, all these Cover
+Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on
+the back cover. Both covers must also clearly and legibly identify
+you as the publisher of these copies. The front cover must present
+the full title with all words of the title equally prominent and
+visible. You may add other material on the covers in addition.
+Copying with changes limited to the covers, as long as they preserve
+the title of the Document and satisfy these conditions, can be treated
+as verbatim copying in other respects.
+
+If the required texts for either cover are too voluminous to fit
+legibly, you should put the first ones listed (as many as fit
+reasonably) on the actual cover, and continue the rest onto adjacent
+pages.
+
+If you publish or distribute Opaque copies of the Document numbering
+more than 100, you must either include a machine-readable Transparent
+copy along with each Opaque copy, or state in or with each Opaque copy
+a computer-network location from which the general network-using
+public has access to download using public-standard network protocols
+a complete Transparent copy of the Document, free of added material.
+If you use the latter option, you must take reasonably prudent steps,
+when you begin distribution of Opaque copies in quantity, to ensure
+that this Transparent copy will remain thus accessible at the stated
+location until at least one year after the last time you distribute an
+Opaque copy (directly or through your agents or retailers) of that
+edition to the public.
+
+It is requested, but not required, that you contact the authors of the
+Document well before redistributing any large number of copies, to
+give them a chance to provide you with an updated version of the
+Document.
+
+
+4. 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. In case of a disagreement between
+the translation and the original version of this License or a notice
+or disclaimer, the original version will prevail.
+
+If a section in the Document is Entitled "Acknowledgements",
+"Dedications", or "History", the requirement (section 4) to Preserve
+its Title (section 1) will typically require changing the actual
+title.
+
+
+9. TERMINATION
+
+You may not copy, modify, sublicense, or distribute the Document
+except as expressly provided under this License. Any attempt
+otherwise to copy, modify, sublicense, or distribute it is void, and
+will automatically terminate your rights under this License.
+
+However, if you cease all violation of this License, then your license
+from a particular copyright holder is reinstated (a) provisionally,
+unless and until the copyright holder explicitly and finally
+terminates your license, and (b) permanently, if the copyright holder
+fails to notify you of the violation by some reasonable means prior to
+60 days after the cessation.
+
+Moreover, your license from a particular copyright holder is
+reinstated permanently if the copyright holder notifies you of the
+violation by some reasonable means, this is the first time you have
+received notice of violation of this License (for any work) from that
+copyright holder, and you cure the violation prior to 30 days after
+your receipt of the notice.
+
+Termination of your rights under this section does not terminate the
+licenses of parties who have received copies or rights from you under
+this License. If your rights have been terminated and not permanently
+reinstated, receipt of a copy of some or all of the same material does
+not give you any rights to use it.
+
+
+10. FUTURE REVISIONS OF THIS LICENSE
+
+The Free Software Foundation may publish new, revised versions of the
+GNU Free Documentation License from time to time. Such new versions
+will be similar in spirit to the present version, but may differ in
+detail to address new problems or concerns. See
+http://www.gnu.org/copyleft/.
+
+Each version of the License is given a distinguishing version number.
+If the Document specifies that a particular numbered version of this
+License "or any later version" applies to it, you have the option of
+following the terms and conditions either of that specified version or
+of any later version that has been published (not as a draft) by the
+Free Software Foundation. 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. If the Document
+specifies that a proxy can decide which future versions of this
+License can be used, that proxy's public statement of acceptance of a
+version permanently authorizes you to choose that version for the
+Document.
+
+11. RELICENSING
+
+"Massive Multiauthor Collaboration Site" (or "MMC Site") means any
+World Wide Web server that publishes copyrightable works and also
+provides prominent facilities for anybody to edit those works. A
+public wiki that anybody can edit is an example of such a server. A
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+
+"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0
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+"Incorporate" means to publish or republish a Document, in whole or in
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+
+An MMC is "eligible for relicensing" if it is licensed under this
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+(2) were thus incorporated prior to November 1, 2008.
+
+The operator of an MMC Site may republish an MMC contained in the site
+under CC-BY-SA on the same site at any time before August 1, 2009,
+provided the MMC is eligible for relicensing.
+
+
+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 1.3
+ 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
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+If you have Invariant Sections without Cover Texts, or some other
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+
+If your document contains nontrivial examples of program code, we
+recommend releasing these examples in parallel under your choice of
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+to permit their use in free software.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/components/mpfr/Solaris/index.html Mon May 09 11:36:28 2011 -0700
@@ -0,0 +1,3525 @@
+<html lang="en">
+<head>
+<title>MPFR 2.3.2</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="description" content="How to install and use MPFR, a library for reliable multiple precision floating-point arithmetic, version 2.3.2.">
+<meta name="generator" content="makeinfo 4.11">
+<link title="Top" rel="top" href="#Top">
+<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
+<!--
+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 *note GNU Free Documentation License::.-->
+<meta http-equiv="Content-Style-Type" content="text/css">
+<style type="text/css"><!--
+ pre.display { font-family:inherit }
+ pre.format { font-family:inherit }
+ pre.smalldisplay { font-family:inherit; font-size:smaller }
+ pre.smallformat { font-family:inherit; font-size:smaller }
+ pre.smallexample { font-size:smaller }
+ pre.smalllisp { font-size:smaller }
+ span.sc { font-variant:small-caps }
+ span.roman { font-family:serif; font-weight:normal; }
+ span.sansserif { font-family:sans-serif; font-weight:normal; }
+--></style>
+</head>
+<body>
+<div class="node">
+<p><hr>
+<a name="Top"></a>
+Next: <a rel="next" accesskey="n" href="#Copying">Copying</a>,
+Previous: <a rel="previous" accesskey="p" href="#dir">(dir)</a>,
+Up: <a rel="up" accesskey="u" href="#dir">(dir)</a>
+
+</div>
+
+<h2 class="unnumbered">MPFR</h2>
+
+ <p>This manual documents how to install and use the Multiple Precision
+Floating-Point Reliable Library, version 2.3.2.
+
+ <p>Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
+
+ <p>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 <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>.
+ <pre class="sp">
+
+</pre>
+
+<!-- Don't bother with contents for html, the menus seem adequate. -->
+<ul class="menu">
+<li><a accesskey="1" href="#Copying">Copying</a>: MPFR Copying Conditions (LGPL).
+<li><a accesskey="2" href="#Introduction-to-MPFR">Introduction to MPFR</a>: Brief introduction to MPFR.
+<li><a accesskey="3" href="#Installing-MPFR">Installing MPFR</a>: How to configure and compile the MPFR library.
+<li><a accesskey="4" href="#Reporting-Bugs">Reporting Bugs</a>: How to usefully report bugs.
+<li><a accesskey="5" href="#MPFR-Basics">MPFR Basics</a>: What every MPFR user should now.
+<li><a accesskey="6" href="#MPFR-Interface">MPFR Interface</a>: MPFR functions and macros.
+<li><a accesskey="7" href="#Contributors">Contributors</a>
+<li><a accesskey="8" href="#References">References</a>
+<li><a accesskey="9" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>
+<li><a href="#Concept-Index">Concept Index</a>
+<li><a href="#Function-Index">Function Index</a>
+</ul>
+
+<!-- @m{T,N} is $T$ in tex or @math{N} otherwise. This is an easy way to give -->
+<!-- different forms for math in tex and info. Commas in N or T don't work, -->
+<!-- but @C{} can be used instead. \, works in info but not in tex. -->
+<!-- Usage: @GMPabs{x} -->
+<!-- Give either |x| in tex, or abs(x) in info or html. -->
+<!-- Usage: @GMPtimes{} -->
+<!-- Give either \times or the word "times". -->
+<!-- New math operators. -->
+<!-- @abs{} can be used in both tex and info, or just \abs in tex. -->
+<!-- @times{} made available as a "*" in info and html (already works in tex). -->
+<!-- Math operators already available in tex, made available in info too. -->
+<!-- For example @log{} can be used in both tex and info. -->
+<!-- @pom{} definition -->
+<!-- The following macro have been copied from gmp.texi -->
+<!-- Usage: @MPFRpxreftop{info,title} -->
+<!-- Like @pxref{}, but designed for a reference to the top of a document, not -->
+<!-- a particular section. -->
+<!-- The texinfo manual recommends putting a likely section name in references -->
+<!-- like this, eg. "Introduction", but it seems better to just give the title. -->
+<div class="node">
+<p><hr>
+<a name="Copying"></a>
+Next: <a rel="next" accesskey="n" href="#Introduction-to-MPFR">Introduction to MPFR</a>,
+Previous: <a rel="previous" accesskey="p" href="#Top">Top</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="unnumbered">MPFR Copying Conditions</h2>
+
+<p><a name="index-Copying-conditions-1"></a><a name="index-Conditions-for-copying-MPFR-2"></a>
+This library is <dfn>free</dfn>; 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.
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+<div class="node">
+<p><hr>
+<a name="Introduction-to-MPFR"></a>
+Next: <a rel="next" accesskey="n" href="#Installing-MPFR">Installing MPFR</a>,
+Previous: <a rel="previous" accesskey="p" href="#Copying">Copying</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="chapter">1 Introduction to MPFR</h2>
+
+<p>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 <code>mpf</code> class from GNU MP are:
+
+ <ul>
+<li>the MPFR code is portable, i.e. the result of any operation
+does not depend (or should not) on the machine word size
+<code>mp_bits_per_limb</code> (32 or 64 on most machines);
+<li>the precision in bits can be set exactly to any valid value
+for each variable (including very small precision);
+<li>MPFR provides the four rounding modes from the IEEE 754-1985
+standard.
+</ul>
+
+ <p>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., <code>double</code> type in C, with a C
+implementation that rigorously follows Annex F of the ISO C99 standard
+and <code>FP_CONTRACT</code> pragma set to <code>OFF</code>) 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).
+
+ <p>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.
+
+<h3 class="section">1.1 How to Use This Manual</h3>
+
+<p>Everyone should read <a href="#MPFR-Basics">MPFR Basics</a>. If you need to install the library
+yourself, you need to read <a href="#Installing-MPFR">Installing MPFR</a>, too.
+
+ <p>The rest of the manual can be used for later reference, although it is
+probably a good idea to glance through it.
+
+<div class="node">
+<p><hr>
+<a name="Installing-MPFR"></a>
+Next: <a rel="next" accesskey="n" href="#Reporting-Bugs">Reporting Bugs</a>,
+Previous: <a rel="previous" accesskey="p" href="#Introduction-to-MPFR">Introduction to MPFR</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="chapter">2 Installing MPFR</h2>
+
+<p><a name="index-Installation-3"></a>
+
+<h3 class="section">2.1 How to Install</h3>
+
+<p>Here are the steps needed to install the library on Unix systems
+(more details are provided in the <samp><span class="file">INSTALL</span></samp> file):
+
+ <ol type=1 start=1>
+<li>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 ‘<samp><span class="samp">make</span></samp>’ program, plus some other
+standard Unix utility programs.
+
+ <li>In the MPFR build directory, type
+‘<samp><span class="samp">./configure</span></samp>’
+
+ <p>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 <samp><span class="file">INSTALL</span></samp> file).
+
+ <li>‘<samp><span class="samp">make</span></samp>’
+
+ <p>This will compile MPFR, and create a library archive file <samp><span class="file">libmpfr.a</span></samp>.
+A dynamic library may be produced too (see configure).
+
+ <li>‘<samp><span class="samp">make check</span></samp>’
+
+ <p>This will make sure MPFR was built correctly.
+If you get error messages, please
+report this to ‘<samp><span class="samp">[email protected]</span></samp>’. (See <a href="#Reporting-Bugs">Reporting Bugs</a>, for
+information on what to include in useful bug reports.)
+
+ <li>‘<samp><span class="samp">make install</span></samp>’
+
+ <p>This will copy the files <samp><span class="file">mpfr.h</span></samp> and <samp><span class="file">mpf2mpfr.h</span></samp> to the directory
+<samp><span class="file">/usr/local/include</span></samp>, the file <samp><span class="file">libmpfr.a</span></samp> to the directory
+<samp><span class="file">/usr/local/lib</span></samp>, and the file <samp><span class="file">mpfr.info</span></samp> to the directory
+<samp><span class="file">/usr/local/share/info</span></samp> (or if you passed the ‘<samp><span class="samp">--prefix</span></samp>’ option to
+ <samp><span class="file">configure</span></samp>, using the prefix directory given as argument to
+‘<samp><span class="samp">--prefix</span></samp>’ instead of <samp><span class="file">/usr/local</span></samp>).
+ </ol>
+
+<h3 class="section">2.2 Other `make' Targets</h3>
+
+<p>There are some other useful make targets:
+
+ <ul>
+<li>‘<samp><span class="samp">mpfr.info</span></samp>’ or ‘<samp><span class="samp">info</span></samp>’
+
+ <p>Create an info version of the manual, in <samp><span class="file">mpfr.info</span></samp>.
+
+ <li>‘<samp><span class="samp">mpfr.pdf</span></samp>’ or ‘<samp><span class="samp">pdf</span></samp>’
+
+ <p>Create a PDF version of the manual, in <samp><span class="file">mpfr.pdf</span></samp>.
+
+ <li>‘<samp><span class="samp">mpfr.dvi</span></samp>’ or ‘<samp><span class="samp">dvi</span></samp>’
+
+ <p>Create a DVI version of the manual, in <samp><span class="file">mpfr.dvi</span></samp>.
+
+ <li>‘<samp><span class="samp">mpfr.ps</span></samp>’ or ‘<samp><span class="samp">ps</span></samp>’
+
+ <p>Create a Postscript version of the manual, in <samp><span class="file">mpfr.ps</span></samp>.
+
+ <li>‘<samp><span class="samp">mpfr.html</span></samp>’ or ‘<samp><span class="samp">html</span></samp>’
+
+ <p>Create a HTML version of the manual, in several pages in the directory
+<samp><span class="file">mpfr.html</span></samp>; if you want only one output HTML file, then type
+‘<samp><span class="samp">makeinfo --html --no-split mpfr.texi</span></samp>’ instead.
+
+ <li>‘<samp><span class="samp">clean</span></samp>’
+
+ <p>Delete all object files and archive files, but not the configuration files.
+
+ <li>‘<samp><span class="samp">distclean</span></samp>’
+
+ <p>Delete all files not included in the distribution.
+
+ <li>‘<samp><span class="samp">uninstall</span></samp>’
+
+ <p>Delete all files copied by ‘<samp><span class="samp">make install</span></samp>’.
+</ul>
+
+<h3 class="section">2.3 Build Problems</h3>
+
+<p>In case of problem, please read the <samp><span class="file">INSTALL</span></samp> 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
+<a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>.
+
+<!-- Warning! Do not split "MPFR ... @url{...}" across several lines -->
+<!-- as this needs to be updated with update-version. -->
+ <p>Please report problems to ‘<samp><span class="samp">[email protected]</span></samp>’.
+See <a href="#Reporting-Bugs">Reporting Bugs</a>.
+Some bug fixes are available on the
+MPFR 2.3.2 web page <a href="http://www.mpfr.org/mpfr-2.3.2/">http://www.mpfr.org/mpfr-2.3.2/</a>.
+
+<h3 class="section">2.4 Getting the Latest Version of MPFR</h3>
+
+<p>The latest version of MPFR is available from <a href="http://www.mpfr.org/">http://www.mpfr.org/</a>.
+
+<div class="node">
+<p><hr>
+<a name="Reporting-Bugs"></a>
+Next: <a rel="next" accesskey="n" href="#MPFR-Basics">MPFR Basics</a>,
+Previous: <a rel="previous" accesskey="p" href="#Installing-MPFR">Installing MPFR</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="chapter">3 Reporting Bugs</h2>
+
+<p><a name="index-Reporting-bugs-4"></a>
+<!-- Warning! Do not split "MPFR ... @url{...}" across several lines -->
+<!-- as this needs to be updated with update-version. -->
+If you think you have found a bug in the MPFR library, first have a look
+on the MPFR 2.3.2 web page <a href="http://www.mpfr.org/mpfr-2.3.2/">http://www.mpfr.org/mpfr-2.3.2/</a> and the
+FAQ <a href="http://www.mpfr.org/faq.html">http://www.mpfr.org/faq.html</a>:
+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.
+
+ <p>There are a few things you should think about when you put your bug report
+together.
+
+ <p>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.
+
+ <p>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.
+
+ <p>Please include compiler version information in your bug report. This can
+be extracted using ‘<samp><span class="samp">cc -V</span></samp>’ on some machines, or, if you're using gcc,
+‘<samp><span class="samp">gcc -v</span></samp>’. Also, include the output from ‘<samp><span class="samp">uname -a</span></samp>’ and the MPFR
+version (the GMP version may be useful too).
+
+ <p>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).
+
+ <p>Send your bug report to: ‘<samp><span class="samp">[email protected]</span></samp>’.
+
+ <p>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.
+
+<div class="node">
+<p><hr>
+<a name="MPFR-Basics"></a>
+Next: <a rel="next" accesskey="n" href="#MPFR-Interface">MPFR Interface</a>,
+Previous: <a rel="previous" accesskey="p" href="#Reporting-Bugs">Reporting Bugs</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="chapter">4 MPFR Basics</h2>
+
+<h3 class="section">4.1 Headers and Libraries</h3>
+
+<p><a name="index-g_t_0040file_007bmpfr_002eh_007d-5"></a>All declarations needed to use MPFR are collected in the include file
+<samp><span class="file">mpfr.h</span></samp>. It is designed to work with both C and C++ compilers.
+You should include that file in any program using the MPFR library:
+
+<pre class="example"> #include <mpfr.h>
+</pre>
+ <p><a name="index-g_t_0040code_007bstdio_002eh_007d-6"></a>Note however that prototypes for MPFR functions with <code>FILE *</code> parameters
+are provided only if <code><stdio.h></code> is included too (before <samp><span class="file">mpfr.h</span></samp>).
+
+<pre class="example"> #include <stdio.h>
+ #include <mpfr.h>
+</pre>
+ <p>You can avoid the use of MPFR macros encapsulating functions by defining
+the ‘<samp><span class="samp">MPFR_USE_NO_MACRO</span></samp>’ macro before <samp><span class="file">mpfr.h</span></samp> 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.
+
+ <p><a name="index-Libraries-7"></a><a name="index-Linking-8"></a><a name="index-g_t_0040code_007blibmpfr_007d-9"></a>All programs using MPFR must link against both <samp><span class="file">libmpfr</span></samp> and
+<samp><span class="file">libgmp</span></samp> libraries. On a typical Unix-like system this can be
+done with ‘<samp><span class="samp">-lmpfr -lgmp</span></samp>’ (in that order), for example
+
+<pre class="example"> gcc myprogram.c -lmpfr -lgmp
+</pre>
+ <p><a name="index-Libtool-10"></a>MPFR is built using Libtool and an application can use that to link if
+desired, see <cite>GNU Libtool</cite>.
+<!-- Note: Do not try the above cross reference without moving mpfr.info -->
+<!-- into some "safe" place first. Due to a poor design, "info" will not -->
+<!-- find the correct libtool info file because of the "libtool" script -->
+<!-- in MPFR's directory! -->
+
+ <p>If MPFR has been installed to a non-standard location, then it may be
+necessary to set up environment variables such as ‘<samp><span class="samp">C_INCLUDE_PATH</span></samp>’
+and ‘<samp><span class="samp">LIBRARY_PATH</span></samp>’, or use ‘<samp><span class="samp">-I</span></samp>’ and ‘<samp><span class="samp">-L</span></samp>’ 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.,
+‘<samp><span class="samp">LD_LIBRARY_PATH</span></samp>’) on some systems. Please read the <samp><span class="file">INSTALL</span></samp>
+file for additional information.
+
+<h3 class="section">4.2 Nomenclature and Types</h3>
+
+<p><a name="index-Floating_002dpoint-number-11"></a><a name="index-g_t_0040code_007bmpfr_005ft_007d-12"></a>A <dfn>floating-point number</dfn> or <dfn>float</dfn> for short, is an arbitrary
+precision significand (also called mantissa) with a limited precision
+exponent. The C data type
+for such objects is <code>mpfr_t</code> (internally defined as a one-element
+array of a structure, and <code>mpfr_ptr</code> 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.
+
+ <p><a name="index-Precision-13"></a><a name="index-g_t_0040code_007bmp_005fprec_005ft_007d-14"></a>The <dfn>precision</dfn> is the number of bits used to represent the significand
+of a floating-point number;
+the corresponding C data type is <code>mp_prec_t</code>.
+The precision can be any integer between <code>MPFR_PREC_MIN</code> and
+<code>MPFR_PREC_MAX</code>. In the current implementation, <code>MPFR_PREC_MIN</code>
+is equal to 2.
+
+ <p>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 <code>MPFR_PREC_MAX</code>,
+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).
+
+ <p><a name="index-Rounding-Modes-15"></a><a name="index-g_t_0040code_007bmp_005frnd_005ft_007d-16"></a>The <dfn>rounding mode</dfn> 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 <code>mp_rnd_t</code>.
+
+ <p><a name="index-Limb-17"></a><!-- @tindex @code{mp_limb_t} -->
+A <dfn>limb</dfn> 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 <code>mp_limb_t</code>.
+
+<h3 class="section">4.3 Function Classes</h3>
+
+<p>There is only one class of functions in the MPFR library:
+
+ <ol type=1 start=1>
+<li>Functions for floating-point arithmetic, with names beginning with
+<code>mpfr_</code>. The associated type is <code>mpfr_t</code>.
+ </ol>
+
+<h3 class="section">4.4 MPFR Variable Conventions</h3>
+
+<p>As a general rule, all MPFR functions expect output arguments before input
+arguments. This notation is based on an analogy with the assignment operator.
+
+ <p>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,
+<code>mpfr_mul</code>, can be used like this: <code>mpfr_mul (x, x, x, rnd_mode)</code>.
+This
+computes the square of <var>x</var> with rounding mode <code>rnd_mode</code>
+and puts the result back in <var>x</var>.
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+<h3 class="section">4.5 Rounding Modes</h3>
+
+<p>The following four rounding modes are supported:
+
+ <ul>
+<li><code>GMP_RNDN</code>: round to nearest
+<li><code>GMP_RNDZ</code>: round toward zero
+<li><code>GMP_RNDU</code>: round toward plus infinity
+<li><code>GMP_RNDD</code>: round toward minus infinity
+</ul>
+
+ <p>The ‘<samp><span class="samp">round to nearest</span></samp>’ 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 <dfn>drift</dfn> phenomenon mentioned by Knuth in volume 2
+of The Art of Computer Programming (Section 4.2.2).
+
+ <p>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 <code>int</code>, called the
+<dfn>ternary value</dfn>. 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).
+
+ <p>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).
+<!-- Since subnormals are not supported, we must take into account the ulp of -->
+<!-- the rounded result, not the one of the exact result, for full generality. -->
+
+ <p>Unless documented otherwise, functions returning an <code>int</code> 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 <code>GMP_RNDU</code> 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 <code>int</code>.
+
+ <p>Unless documented otherwise, functions returning a <code>1</code>
+(or any other value specified in this manual)
+for special cases (like <code>acos(0)</code>) should return an overflow or
+an underflow if <code>1</code> is not representable in the current exponent range.
+
+<h3 class="section">4.6 Floating-Point Values on Special Numbers</h3>
+
+<p>This section specifies the floating-point values (of type <code>mpfr_t</code>)
+returned by MPFR functions. For functions returning several values (like
+<code>mpfr_sin_cos</code>), the rules apply to each result separately.
+
+ <p>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).
+
+ <p>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 (<a href="#MPFR-Interface">MPFR Interface</a>).
+
+ <p>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: <code>mpfr_hypot</code> on (+Inf,0) gives +Inf. But <code>mpfr_pow</code>
+cannot be defined on (1,+Inf) using this rule, as one can find
+sequences (<var>x</var>_<var>n</var>,<var>y</var>_<var>n</var>) such that
+<var>x</var>_<var>n</var> goes to 1, <var>y</var>_<var>n</var> goes to +Inf
+and <var>x</var>_<var>n</var> to the <var>y</var>_<var>n</var> goes to any
+positive value when <var>n</var> goes to the infinity.
+
+ <p>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., <code>mpfr_log</code> on
+−0), the behavior must be specified in the description of the
+MPFR function.
+
+ <p>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: <code>mpfr_sin</code> on +0 gives +0.
+
+ <p>When the input point is not in the closure of the domain of the function,
+the result is NaN. Example: <code>mpfr_sqrt</code> on −17 gives NaN.
+
+ <p>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 <a href="#MPFR-Interface">MPFR Interface</a>.
+<!-- Said otherwise, if such a case is not specified, this is a bug, thus -->
+<!-- we may change the returned value after documenting it without having -->
+<!-- to change the libtool interface number (this would have more drawbacks -->
+<!-- that advantages in practice), like for any bug fix. -->
+Example: <code>mpfr_hypot</code> on (NaN,0) gives NaN, but <code>mpfr_hypot</code>
+on (NaN,+Inf) gives +Inf (as specified in <a href="#Special-Functions">Special Functions</a>),
+since for any finite input <var>x</var>, <code>mpfr_hypot</code> on (<var>x</var>,+Inf)
+gives +Inf.
+
+<h3 class="section">4.7 Exceptions</h3>
+
+<p>MPFR supports 5 exception types:
+
+ <ul>
+<li>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.
+
+ <p>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
+<var>e</var>−4, where <var>e</var> 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 <var>e</var>−1. With the underflow
+before rounding, such a function call would yield an underflow, as
+<var>e</var>−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 <var>e</var>, which is
+representable in the current exponent range. As a consequence, this will
+not yield an underflow in MPFR.
+
+ <li>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.
+
+ <li>NaN:
+A NaN exception occurs when the result of a function is a NaN.
+<!-- NaN is defined above. So, we don't say anything more. -->
+
+ <li>Inexact:
+An inexact exception occurs when the result of a function cannot be
+represented exactly and must be rounded.
+
+ <li>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 <code>mpfr_cmp</code> or in a
+conversion to an integer).
+
+ </ul>
+
+ <p>MPFR has a global flag for each exception, which can be cleared, set
+or tested by functions described in <a href="#Exception-Related-Functions">Exception Related Functions</a>.
+
+ <p>Differences with the ISO C99 standard:
+
+ <ul>
+<li>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.
+
+ <li>An invalid exception in C corresponds to either a NaN exception or
+a range error in MPFR.
+
+ </ul>
+
+<h3 class="section">4.8 Memory Handling</h3>
+
+<p>MPFR functions may create caches, e.g. when computing constants such
+as Pi, either because the user has called a function like
+<code>mpfr_const_pi</code> directly or because such a function was called
+internally by the MPFR library itself to compute some other function.
+
+ <p>At any time, the user can free the various caches with
+<code>mpfr_free_cache</code>. It is strongly advised to do that before
+terminating a thread, or before exiting when using tools like
+‘<samp><span class="samp">valgrind</span></samp>’ (to avoid memory leaks being reported).
+
+ <p>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).
+
+<div class="node">
+<p><hr>
+<a name="MPFR-Interface"></a>
+Next: <a rel="next" accesskey="n" href="#Contributors">Contributors</a>,
+Previous: <a rel="previous" accesskey="p" href="#MPFR-Basics">MPFR Basics</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="chapter">5 MPFR Interface</h2>
+
+<p><a name="index-Floating_002dpoint-functions-18"></a><a name="index-Float-functions-19"></a>
+The floating-point functions expect arguments of type <code>mpfr_t</code>.
+
+ <p>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
+<code>mpfr_</code>.
+
+ <p>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).
+
+ <p><a name="index-Precision-20"></a>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.
+
+ <p><a name="index-Accuracy-21"></a>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.
+
+ <p>The value of the standard C macro <code>errno</code> may be set to non-zero by
+any MPFR function or macro, whether or not there is an error.
+
+<ul class="menu">
+<li><a accesskey="1" href="#Initialization-Functions">Initialization Functions</a>
+<li><a accesskey="2" href="#Assignment-Functions">Assignment Functions</a>
+<li><a accesskey="3" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>
+<li><a accesskey="4" href="#Conversion-Functions">Conversion Functions</a>
+<li><a accesskey="5" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>
+<li><a accesskey="6" href="#Comparison-Functions">Comparison Functions</a>
+<li><a accesskey="7" href="#Special-Functions">Special Functions</a>
+<li><a accesskey="8" href="#Input-and-Output-Functions">Input and Output Functions</a>
+<li><a accesskey="9" href="#Integer-Related-Functions">Integer Related Functions</a>
+<li><a href="#Miscellaneous-Functions">Miscellaneous Functions</a>
+<li><a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>
+<li><a href="#Exception-Related-Functions">Exception Related Functions</a>
+<li><a href="#Advanced-Functions">Advanced Functions</a>
+<li><a href="#Compatibility-with-MPF">Compatibility with MPF</a>
+<li><a href="#Custom-Interface">Custom Interface</a>
+<li><a href="#Internals">Internals</a>
+</ul>
+
+<div class="node">
+<p><hr>
+<a name="Initialization-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Assignment-Functions">Assignment Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Initialization-functions-22"></a>
+
+<h3 class="section">5.1 Initialization Functions</h3>
+
+<p>An <code>mpfr_t</code> object must be initialized before storing the first value in
+it. The functions <code>mpfr_init</code> and <code>mpfr_init2</code> are used for that
+purpose.
+
+<div class="defun">
+— Function: void <b>mpfr_init2</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005finit2-23"></a></var><br>
+<blockquote><p>Initialize <var>x</var>, set its precision to be <strong>exactly</strong>
+<var>prec</var> bits and its value to NaN. (Warning: the corresponding
+<code>mpf</code> functions initialize to zero instead.)
+
+ <p>Normally, a variable should be initialized once only or at
+least be cleared, using <code>mpfr_clear</code>, between initializations.
+To change the precision of a variable which has already been initialized,
+use <code>mpfr_set_prec</code>.
+The precision <var>prec</var> must be an integer between <code>MPFR_PREC_MIN</code> and
+<code>MPFR_PREC_MAX</code> (otherwise the behavior is undefined).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_clear</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fclear-24"></a></var><br>
+<blockquote><p>Free the space occupied by <var>x</var>. Make sure to call this function for all
+<code>mpfr_t</code> variables when you are done with them.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_init</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005finit-25"></a></var><br>
+<blockquote><p>Initialize <var>x</var> and set its value to NaN.
+
+ <p>Normally, a variable should be initialized once only
+or at least be cleared, using <code>mpfr_clear</code>, between initializations. The
+precision of <var>x</var> is the default precision, which can be changed
+by a call to <code>mpfr_set_default_prec</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_set_default_prec</b> (<var>mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fdefault_005fprec-26"></a></var><br>
+<blockquote><p>Set the default precision to be <strong>exactly</strong> <var>prec</var> bits. The
+precision of a variable means the number of bits used to store its significand.
+All
+subsequent calls to <code>mpfr_init</code> 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 <code>MPFR_PREC_MIN</code> and
+<code>MPFR_PREC_MAX</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_prec_t <b>mpfr_get_default_prec</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fdefault_005fprec-27"></a></var><br>
+<blockquote><p>Return the default MPFR precision in bits.
+</p></blockquote></div>
+
+ <p>Here is an example on how to initialize floating-point variables:
+
+<pre class="example"> {
+ mpfr_t x, y;
+ mpfr_init (x); /* use default precision */
+ mpfr_init2 (y, 256); /* precision <em>exactly</em> 256 bits */
+ ...
+ /* When the program is about to exit, do ... */
+ mpfr_clear (x);
+ mpfr_clear (y);
+ mpfr_free_cache ();
+ }
+</pre>
+ <p>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.
+
+<div class="defun">
+— Function: void <b>mpfr_set_prec</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fprec-28"></a></var><br>
+<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits,
+and set its value to NaN.
+The previous value stored in <var>x</var> is lost. It is equivalent to
+a call to <code>mpfr_clear(x)</code> followed by a call to
+<code>mpfr_init2(x, prec)</code>, but more efficient as no allocation is done in
+case the current allocated space for the significand of <var>x</var> is enough.
+The precision <var>prec</var> can be any integer between <code>MPFR_PREC_MIN</code> and
+<code>MPFR_PREC_MAX</code>.
+
+ <p>In case you want to keep the previous value stored in <var>x</var>,
+use <code>mpfr_prec_round</code> instead.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_prec_t <b>mpfr_get_prec</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fget_005fprec-29"></a></var><br>
+<blockquote><p>Return the precision actually used for assignments of <var>x</var>, i.e. the
+number of bits used to store its significand.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Assignment-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Initialization-Functions">Initialization Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Assignment-functions-30"></a>
+
+<h3 class="section">5.2 Assignment Functions</h3>
+
+<p>These functions assign new values to already initialized floats
+(see <a href="#Initialization-Functions">Initialization Functions</a>). When using any functions using
+<code>intmax_t</code>, you must include <code><stdint.h></code> or <code><inttypes.h></code>
+before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define prototypes for
+these functions.
+
+<div class="defun">
+— Function: int <b>mpfr_set</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset-31"></a></var><br>
+— Function: int <b>mpfr_set_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fui-32"></a></var><br>
+— Function: int <b>mpfr_set_si</b> (<var>mpfr_t rop, long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsi-33"></a></var><br>
+— Function: int <b>mpfr_set_uj</b> (<var>mpfr_t rop, uintmax_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fuj-34"></a></var><br>
+— Function: int <b>mpfr_set_sj</b> (<var>mpfr_t rop, intmax_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsj-35"></a></var><br>
+— Function: int <b>mpfr_set_d</b> (<var>mpfr_t rop, double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fd-36"></a></var><br>
+— Function: int <b>mpfr_set_ld</b> (<var>mpfr_t rop, long double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fld-37"></a></var><br>
+— Function: int <b>mpfr_set_decimal64</b> (<var>mpfr_t rop, _Decimal64 op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fdecimal64-38"></a></var><br>
+— Function: int <b>mpfr_set_z</b> (<var>mpfr_t rop, mpz_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fz-39"></a></var><br>
+— Function: int <b>mpfr_set_q</b> (<var>mpfr_t rop, mpq_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fq-40"></a></var><br>
+— Function: int <b>mpfr_set_f</b> (<var>mpfr_t rop, mpf_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005ff-41"></a></var><br>
+<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded
+toward the given direction <var>rnd</var>.
+Note that the input 0 is converted to +0 by <code>mpfr_set_ui</code>,
+<code>mpfr_set_si</code>, <code>mpfr_set_sj</code>, <code>mpfr_set_uj</code>,
+<code>mpfr_set_z</code>, <code>mpfr_set_q</code> and
+<code>mpfr_set_f</code>, regardless of the rounding mode.
+If the system doesn't support the IEEE-754 standard, <code>mpfr_set_d</code>,
+<code>mpfr_set_ld</code> and
+<code>mpfr_set_decimal64</code> might not preserve the signed zeros.
+The <code>mpfr_set_decimal64</code> function is built only with the configure
+option ‘<samp><span class="samp">--enable-decimal-float</span></samp>’, which also requires
+‘<samp><span class="samp">--with-gmp-build</span></samp>’, and when the compiler or
+system provides the ‘<samp><span class="samp">_Decimal64</span></samp>’ data type
+(GCC version 4.2.0 is known to support this data type,
+but only when configured with ‘<samp><span class="samp">--enable-decimal-float</span></samp>’ too).
+<code>mpfr_set_q</code> might not be able to work if the numerator (or the
+denominator) can not be representable as a <code>mpfr_t</code>.
+
+ <p>Note: If you want to store a floating-point constant to a <code>mpfr_t</code>,
+you should use <code>mpfr_set_str</code> (or one of the MPFR constant functions,
+such as <code>mpfr_const_pi</code> for Pi) instead of <code>mpfr_set_d</code>,
+<code>mpfr_set_ld</code> or <code>mpfr_set_decimal64</code>.
+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.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_set_ui_2exp</b> (<var>mpfr_t rop, unsigned long int op, mp_exp_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fui_005f2exp-42"></a></var><br>
+— Function: int <b>mpfr_set_si_2exp</b> (<var>mpfr_t rop, long int op, mp_exp_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsi_005f2exp-43"></a></var><br>
+— Function: int <b>mpfr_set_uj_2exp</b> (<var>mpfr_t rop, uintmax_t op, intmax_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fuj_005f2exp-44"></a></var><br>
+— Function: int <b>mpfr_set_sj_2exp</b> (<var>mpfr_t rop, intmax_t op, intmax_t e, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fsj_005f2exp-45"></a></var><br>
+<blockquote><p>Set the value of <var>rop</var> from <var>op</var> multiplied by
+two to the power <var>e</var>, rounded toward the given direction <var>rnd</var>.
+Note that the input 0 is converted to +0.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_set_str</b> (<var>mpfr_t rop, const char *s, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fstr-46"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the whole string <var>s</var> in base <var>base</var>,
+rounded in the direction <var>rnd</var>.
+See the documentation of <code>mpfr_strtofr</code> for a detailed description
+of the valid string formats.
+<!-- Additionally, special values -->
+<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, -->
+<!-- all case insensitive, without leading whitespace and possibly followed by -->
+<!-- other characters, are accepted too (it may change). -->
+This function returns 0 if the entire string up to the final null character
+is a valid number in base <var>base</var>; otherwise it returns −1, and
+<var>rop</var> may have changed.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_strtofr</b> (<var>mpfr_t rop, const char *nptr, char **endptr, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fstrtofr-47"></a></var><br>
+<blockquote>
+ <p>Read a floating-point number from a string <var>nptr</var> in base <var>base</var>,
+rounded in the direction <var>rnd</var>; <var>base</var> must be either 0 (to
+detect the base, as described below) or a number from 2 to 36 (otherwise
+the behavior is undefined). If <var>nptr</var> starts with valid data, the
+result is stored in <var>rop</var> and <code>*</code><var>endptr</var> points to the
+character just after the valid data (if <var>endptr</var> is not a null pointer);
+otherwise <var>rop</var> is set to zero and the value of <var>nptr</var> is stored
+in the location referenced by <var>endptr</var> (if <var>endptr</var> is not a null
+pointer). The usual ternary value is returned.
+
+ <p>Parsing follows the standard C <code>strtod</code> function with some extensions.
+Case is ignored. After optional leading whitespace, one has a subject
+sequence consisting of an optional sign (<code>+</code> or <code>-</code>), 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.
+
+ <p>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 <code>a</code> = 10, <code>b</code> = 11,
+<small class="dots">...</small>, <code>z</code> = 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 <code>e</code> or <code>E</code> for bases up to 10, or
+<code>@</code> in any base; it indicates a multiplication by a power of the
+base. In bases 2 and 16, the exponent prefix can also be <code>p</code> or
+<code>P</code>, 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 <code>0b</code> or <code>0B</code>, and
+in base 16, it can start with <code>0x</code> or <code>0X</code>.
+
+ <p>If the argument <var>base</var> is 0, then the base is automatically detected
+as follows. If the significand starts with <code>0b</code> or <code>0B</code>, base 2
+is assumed. If the significand starts with <code>0x</code> or <code>0X</code>, base 16
+is assumed. Otherwise base 10 is assumed.
+
+ <p>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 <code>0b</code>, <code>0B</code>, <code>0x</code> or <code>0X</code>
+is not followed by a binary/hexadecimal digit, then the subject sequence
+stops at the character <code>0</code>.
+
+ <p>Special data (for infinities and NaN) can be <code>@inf@</code> or
+<code>@nan@(n-char-sequence)</code>, and if <var>base</var> <= 16,
+it can also be <code>infinity</code>, <code>inf</code>, <code>nan</code> or
+<code>nan(n-char-sequence)</code>, all case insensitive.
+A <code>n-char-sequence</code> is a non-empty string containing only digits,
+Latin letters and the underscore (0, 1, 2, <small class="dots">...</small>, 9, a, b, <small class="dots">...</small>, z,
+A, B, <small class="dots">...</small>, Z, _). Note: one has an optional sign for all data, even
+NaN.
+
+ </blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_set_inf</b> (<var>mpfr_t x, int sign</var>)<var><a name="index-mpfr_005fset_005finf-48"></a></var><br>
+— Function: void <b>mpfr_set_nan</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fset_005fnan-49"></a></var><br>
+<blockquote><p>Set the variable <var>x</var> to infinity or NaN (Not-a-Number) respectively.
+In <code>mpfr_set_inf</code>, <var>x</var> is set to plus infinity iff <var>sign</var> is
+nonnegative.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_swap</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fswap-50"></a></var><br>
+<blockquote><p>Swap the values <var>x</var> and <var>y</var> efficiently. Warning: the
+precisions are exchanged too; in case the precisions are different,
+<code>mpfr_swap</code> is thus not equivalent to three <code>mpfr_set</code> calls
+using a third auxiliary variable.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Combined-Initialization-and-Assignment-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Conversion-Functions">Conversion Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Assignment-Functions">Assignment Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Combined-initialization-and-assignment-functions-51"></a>
+
+<h3 class="section">5.3 Combined Initialization and Assignment Functions</h3>
+
+<div class="defun">
+— Macro: int <b>mpfr_init_set</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset-52"></a></var><br>
+— Macro: int <b>mpfr_init_set_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fui-53"></a></var><br>
+— Macro: int <b>mpfr_init_set_si</b> (<var>mpfr_t rop, signed long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fsi-54"></a></var><br>
+— Macro: int <b>mpfr_init_set_d</b> (<var>mpfr_t rop, double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fd-55"></a></var><br>
+— Macro: int <b>mpfr_init_set_ld</b> (<var>mpfr_t rop, long double op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fld-56"></a></var><br>
+— Macro: int <b>mpfr_init_set_z</b> (<var>mpfr_t rop, mpz_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fz-57"></a></var><br>
+— Macro: int <b>mpfr_init_set_q</b> (<var>mpfr_t rop, mpq_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fq-58"></a></var><br>
+— Macro: int <b>mpfr_init_set_f</b> (<var>mpfr_t rop, mpf_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005ff-59"></a></var><br>
+<blockquote><p>Initialize <var>rop</var> and set its value from <var>op</var>, rounded in the direction
+<var>rnd</var>.
+The precision of <var>rop</var> will be taken from the active default precision,
+as set by <code>mpfr_set_default_prec</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_init_set_str</b> (<var>mpfr_t x, const char *s, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finit_005fset_005fstr-60"></a></var><br>
+<blockquote><p>Initialize <var>x</var> and set its value from
+the string <var>s</var> in base <var>base</var>,
+rounded in the direction <var>rnd</var>.
+See <code>mpfr_set_str</code>.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Conversion-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Conversion-functions-61"></a>
+
+<h3 class="section">5.4 Conversion Functions</h3>
+
+<div class="defun">
+— Function: double <b>mpfr_get_d</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fd-62"></a></var><br>
+— Function: long double <b>mpfr_get_ld</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fld-63"></a></var><br>
+— Function: _Decimal64 <b>mpfr_get_decimal64</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fdecimal64-64"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a <code>double</code> (respectively <code>_Decimal64</code> or
+<code>long double</code>), using the rounding mode <var>rnd</var>.
+If <var>op</var> is NaN, some fixed NaN (either quiet or signaling) or the result
+of 0.0/0.0 is returned. If <var>op</var> is �Inf, an infinity of the same
+sign or the result of �1.0/0.0 is returned. If <var>op</var> is zero, these
+functions return a zero, trying to preserve its sign, if possible.
+The <code>mpfr_get_decimal64</code> function is built only under some conditions:
+see the documentation of <code>mpfr_set_decimal64</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: double <b>mpfr_get_d_2exp</b> (<var>long *exp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fd_005f2exp-65"></a></var><br>
+— Function: long double <b>mpfr_get_ld_2exp</b> (<var>long *exp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fld_005f2exp-66"></a></var><br>
+<blockquote><p>Return <var>d</var> and set <var>exp</var> such that 0.5<=abs(<var>d</var>)<1
+and <var>d</var> times 2 raised to <var>exp</var> equals
+<var>op</var> rounded to double (resp. long double)
+precision, using the given rounding mode.
+<!-- See ISO C standard, frexp function. -->
+If <var>op</var> is zero, then a zero of the same sign (or an unsigned zero,
+if the implementation does not have signed zeros) is returned, and
+<var>exp</var> is set to 0.
+If <var>op</var> is NaN or an infinity, then the corresponding double precision
+(resp. long-double precision)
+value is returned, and <var>exp</var> is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: long <b>mpfr_get_si</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fsi-67"></a></var><br>
+— Function: unsigned long <b>mpfr_get_ui</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fui-68"></a></var><br>
+— Function: intmax_t <b>mpfr_get_sj</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fsj-69"></a></var><br>
+— Function: uintmax_t <b>mpfr_get_uj</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fuj-70"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a <code>long</code>, an <code>unsigned long</code>,
+an <code>intmax_t</code> or an <code>uintmax_t</code> (respectively) after rounding
+it with respect to <var>rnd</var>.
+If <var>op</var> is NaN, the result is undefined.
+If <var>op</var> 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 <code>mpfr_fits_slong_p</code>, <code>mpfr_fits_ulong_p</code>,
+<code>mpfr_fits_intmax_p</code> and <code>mpfr_fits_uintmax_p</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_exp_t <b>mpfr_get_z_exp</b> (<var>mpz_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fget_005fz_005fexp-71"></a></var><br>
+<blockquote><p>Put the scaled significand of <var>op</var> (regarded as an integer, with the
+precision of <var>op</var>) into <var>rop</var>, and return the exponent <var>exp</var>
+(which may be outside the current exponent range) such that <var>op</var>
+exactly equals
+<var>rop</var> multiplied by two exponent <var>exp</var>.
+If the exponent is not representable in the <code>mp_exp_t</code> type, the
+behavior is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_get_z</b> (<var>mpz_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fz-72"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a <code>mpz_t</code>, after rounding it with respect to
+<var>rnd</var>. If <var>op</var> is NaN or Inf, the result is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_get_f</b> (<var>mpf_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005ff-73"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a <code>mpf_t</code>, after rounding it with respect to
+<var>rnd</var>. Return zero iff no error occurred,
+in particular a non-zero value is returned if
+<var>op</var> is NaN or Inf, which do not exist in <code>mpf</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: char * <b>mpfr_get_str</b> (<var>char *str, mp_exp_t *expptr, int b, size_t n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fget_005fstr-74"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a string of digits in base <var>b</var>, with rounding in
+the direction <var>rnd</var>, where <var>n</var> is either zero (see below) or the
+number of significant digits; in the latter case, <var>n</var> must be greater
+or equal to 2. The base may vary from 2 to 36.
+
+ <p>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 <var>expptr</var>.
+If <var>rnd</var> is to nearest, and <var>op</var> 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).
+
+ <p>If <var>n</var> 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 <var>op</var>.
+More precisely, in most cases, the chosen precision of <var>str</var> is
+the minimal precision depending on <var>n</var> and <var>b</var> only that
+satisfies the above property, i.e.,
+m = 1 + ceil(<var>n</var>*log(2)/log(<var>b</var>)),
+but in some very rare cases, it might be m+1.
+
+ <p>If <var>str</var> 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 <code>mpfr_free_str</code>.
+
+ <p>If <var>str</var> is not a null pointer, it should point to a block of storage
+large enough for the significand, i.e., at least <code>max(</code><var>n</var><code> + 2, 7)</code>.
+The extra two bytes are for a possible minus sign, and for the terminating null
+character.
+
+ <p>If the input number is an ordinary number, the exponent is written through
+the pointer <var>expptr</var> (the current minimal exponent for 0).
+
+ <p>A pointer to the string is returned, unless there is an error, in which
+case a null pointer is returned.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_free_str</b> (<var>char *str</var>)<var><a name="index-mpfr_005ffree_005fstr-75"></a></var><br>
+<blockquote><p>Free a string allocated by <code>mpfr_get_str</code> using the current unallocation
+function (preliminary interface).
+The block is assumed to be <code>strlen(</code><var>str</var><code>)+1</code> bytes.
+For more information about how it is done:
+see section “Custom Allocation” in <cite>GNU MP</cite>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_fits_ulong_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fulong_005fp-76"></a></var><br>
+— Function: int <b>mpfr_fits_slong_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fslong_005fp-77"></a></var><br>
+— Function: int <b>mpfr_fits_uint_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fuint_005fp-78"></a></var><br>
+— Function: int <b>mpfr_fits_sint_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fsint_005fp-79"></a></var><br>
+— Function: int <b>mpfr_fits_ushort_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fushort_005fp-80"></a></var><br>
+— Function: int <b>mpfr_fits_sshort_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fsshort_005fp-81"></a></var><br>
+— Function: int <b>mpfr_fits_intmax_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fintmax_005fp-82"></a></var><br>
+— Function: int <b>mpfr_fits_uintmax_p</b> (<var>mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffits_005fuintmax_005fp-83"></a></var><br>
+<blockquote><p>Return non-zero if <var>op</var> would fit in the respective C data type, when
+rounded to an integer in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Basic-Arithmetic-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Comparison-Functions">Comparison Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Conversion-Functions">Conversion Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Basic-arithmetic-functions-84"></a><a name="index-Float-arithmetic-functions-85"></a><a name="index-Arithmetic-functions-86"></a>
+
+<h3 class="section">5.5 Basic Arithmetic Functions</h3>
+
+<div class="defun">
+— Function: int <b>mpfr_add</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd-87"></a></var><br>
+— Function: int <b>mpfr_add_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fui-88"></a></var><br>
+— Function: int <b>mpfr_add_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fsi-89"></a></var><br>
+— Function: int <b>mpfr_add_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fz-90"></a></var><br>
+— Function: int <b>mpfr_add_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fadd_005fq-91"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> + <var>op2</var> rounded in the direction
+<var>rnd</var>. For types having no signed zero, it is considered unsigned
+(i.e. (+0) + 0 = (+0) and (−0) + 0 = (−0)).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sub</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub-92"></a></var><br>
+— Function: int <b>mpfr_ui_sub</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fsub-93"></a></var><br>
+— Function: int <b>mpfr_sub_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fui-94"></a></var><br>
+— Function: int <b>mpfr_si_sub</b> (<var>mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsi_005fsub-95"></a></var><br>
+— Function: int <b>mpfr_sub_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fsi-96"></a></var><br>
+— Function: int <b>mpfr_sub_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fz-97"></a></var><br>
+— Function: int <b>mpfr_sub_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsub_005fq-98"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> - <var>op2</var> rounded in the direction
+<var>rnd</var>. 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)).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_mul</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul-99"></a></var><br>
+— Function: int <b>mpfr_mul_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fui-100"></a></var><br>
+— Function: int <b>mpfr_mul_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fsi-101"></a></var><br>
+— Function: int <b>mpfr_mul_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fz-102"></a></var><br>
+— Function: int <b>mpfr_mul_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005fq-103"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> times <var>op2</var> rounded in the
+direction <var>rnd</var>.
+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).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sqr</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqr-104"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the square of <var>op</var>
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_div</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv-105"></a></var><br>
+— Function: int <b>mpfr_ui_div</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fdiv-106"></a></var><br>
+— Function: int <b>mpfr_div_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fui-107"></a></var><br>
+— Function: int <b>mpfr_si_div</b> (<var>mpfr_t rop, long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsi_005fdiv-108"></a></var><br>
+— Function: int <b>mpfr_div_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fsi-109"></a></var><br>
+— Function: int <b>mpfr_div_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fz-110"></a></var><br>
+— Function: int <b>mpfr_div_q</b> (<var>mpfr_t rop, mpfr_t op1, mpq_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005fq-111"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var>/<var>op2</var> rounded in the direction <var>rnd</var>.
+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).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sqrt</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqrt-112"></a></var><br>
+— Function: int <b>mpfr_sqrt_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsqrt_005fui-113"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the square root of <var>op</var>
+rounded in the direction <var>rnd</var>. Return −0 if <var>op</var> is
+−0 (to be consistent with the IEEE 754-1985 standard).
+Set <var>rop</var> to NaN if <var>op</var> is negative.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_cbrt</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcbrt-114"></a></var><br>
+— Function: int <b>mpfr_root</b> (<var>mpfr_t rop, mpfr_t op, unsigned long int k, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005froot-115"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the cubic root (resp. the <var>k</var>th root)
+of <var>op</var> rounded in the direction <var>rnd</var>.
+An odd (resp. even) root of a negative number (including −Inf)
+returns a negative number (resp. NaN).
+The <var>k</var>th root of −0 is defined to be −0,
+whatever the parity of <var>k</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_pow</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow-116"></a></var><br>
+— Function: int <b>mpfr_pow_ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fui-117"></a></var><br>
+— Function: int <b>mpfr_pow_si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fsi-118"></a></var><br>
+— Function: int <b>mpfr_pow_z</b> (<var>mpfr_t rop, mpfr_t op1, mpz_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fpow_005fz-119"></a></var><br>
+— Function: int <b>mpfr_ui_pow_ui</b> (<var>mpfr_t rop, unsigned long int op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fpow_005fui-120"></a></var><br>
+— Function: int <b>mpfr_ui_pow</b> (<var>mpfr_t rop, unsigned long int op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fui_005fpow-121"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> raised to <var>op2</var>,
+rounded in the direction <var>rnd</var>.
+Special values are currently handled as described in the ISO C99 standard
+for the <code>pow</code> function (note this may change in future versions):
+ <ul>
+<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus infinity for <var>y</var> a negative odd integer.
+<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> negative and not an odd integer.
+<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus or minus zero for <var>y</var> a positive odd integer.
+<li><code>pow(�0, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> positive and not an odd integer.
+<li><code>pow(-1, �Inf)</code> returns 1.
+<li><code>pow(+1, </code><var>y</var><code>)</code> returns 1 for any <var>y</var>, even a NaN.
+<li><code>pow(</code><var>x</var><code>, �0)</code> returns 1 for any <var>x</var>, even a NaN.
+<li><code>pow(</code><var>x</var><code>, </code><var>y</var><code>)</code> returns NaN for finite negative <var>x</var> and finite non-integer <var>y</var>.
+<li><code>pow(</code><var>x</var><code>, -Inf)</code> returns plus infinity for 0 < abs(x) < 1, and plus zero for abs(x) > 1.
+<li><code>pow(</code><var>x</var><code>, +Inf)</code> returns plus zero for 0 < abs(x) < 1, and plus infinity for abs(x) > 1.
+<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus zero for <var>y</var> a negative odd integer.
+<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> negative and not an odd integer.
+<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns minus infinity for <var>y</var> a positive odd integer.
+<li><code>pow(-Inf, </code><var>y</var><code>)</code> returns plus infinity for <var>y</var> positive and not an odd integer.
+<li><code>pow(+Inf, </code><var>y</var><code>)</code> returns plus zero for <var>y</var> negative, and plus infinity for <var>y</var> positive.
+</ul>
+ </p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_neg</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fneg-122"></a></var><br>
+<blockquote><p>Set <var>rop</var> to -<var>op</var> rounded in the direction <var>rnd</var>.
+Just changes the sign if <var>rop</var> and <var>op</var> are the same variable.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_abs</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fabs-123"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the absolute value of <var>op</var>,
+rounded in the direction <var>rnd</var>.
+Just changes the sign if <var>rop</var> and <var>op</var> are the same variable.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_dim</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdim-124"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the positive difference of <var>op1</var> and <var>op2</var>, i.e.,
+<var>op1</var> - <var>op2</var> rounded in the direction <var>rnd</var>
+if <var>op1</var> > <var>op2</var>, and +0 otherwise.
+Returns NaN when <var>op1</var> or <var>op2</var> is NaN.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_mul_2ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2ui-125"></a></var><br>
+— Function: int <b>mpfr_mul_2si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2si-126"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> times 2 raised
+to <var>op2</var>
+rounded in the direction <var>rnd</var>. Just increases the exponent by <var>op2</var>
+when <var>rop</var> and <var>op1</var> are identical.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_div_2ui</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2ui-127"></a></var><br>
+— Function: int <b>mpfr_div_2si</b> (<var>mpfr_t rop, mpfr_t op1, long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2si-128"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op1</var> divided by 2 raised
+to <var>op2</var>
+rounded in the direction <var>rnd</var>. Just decreases the exponent by <var>op2</var>
+when <var>rop</var> and <var>op1</var> are identical.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Comparison-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Special-Functions">Special Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Float-comparisons-functions-129"></a><a name="index-Comparison-functions-130"></a>
+
+<h3 class="section">5.6 Comparison Functions</h3>
+
+<div class="defun">
+— Function: int <b>mpfr_cmp</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmp-131"></a></var><br>
+— Function: int <b>mpfr_cmp_ui</b> (<var>mpfr_t op1, unsigned long int op2</var>)<var><a name="index-mpfr_005fcmp_005fui-132"></a></var><br>
+— Function: int <b>mpfr_cmp_si</b> (<var>mpfr_t op1, signed long int op2</var>)<var><a name="index-mpfr_005fcmp_005fsi-133"></a></var><br>
+— Function: int <b>mpfr_cmp_d</b> (<var>mpfr_t op1, double op2</var>)<var><a name="index-mpfr_005fcmp_005fd-134"></a></var><br>
+— Function: int <b>mpfr_cmp_ld</b> (<var>mpfr_t op1, long double op2</var>)<var><a name="index-mpfr_005fcmp_005fld-135"></a></var><br>
+— Function: int <b>mpfr_cmp_z</b> (<var>mpfr_t op1, mpz_t op2</var>)<var><a name="index-mpfr_005fcmp_005fz-136"></a></var><br>
+— Function: int <b>mpfr_cmp_q</b> (<var>mpfr_t op1, mpq_t op2</var>)<var><a name="index-mpfr_005fcmp_005fq-137"></a></var><br>
+— Function: int <b>mpfr_cmp_f</b> (<var>mpfr_t op1, mpf_t op2</var>)<var><a name="index-mpfr_005fcmp_005ff-138"></a></var><br>
+<blockquote><p>Compare <var>op1</var> and <var>op2</var>. Return a positive value if <var>op1</var> >
+<var>op2</var>, zero if <var>op1</var> = <var>op2</var>, and a negative value if
+<var>op1</var> < <var>op2</var>.
+Both <var>op1</var> and <var>op2</var> are considered to their full own precision,
+which may differ.
+If one of the operands is NaN, set the erange flag and return zero.
+
+ <p>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., <code>mpfr_equal_p</code> 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).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_cmp_ui_2exp</b> (<var>mpfr_t op1, unsigned long int op2, mp_exp_t e</var>)<var><a name="index-mpfr_005fcmp_005fui_005f2exp-139"></a></var><br>
+— Function: int <b>mpfr_cmp_si_2exp</b> (<var>mpfr_t op1, long int op2, mp_exp_t e</var>)<var><a name="index-mpfr_005fcmp_005fsi_005f2exp-140"></a></var><br>
+<blockquote><p>Compare <var>op1</var> and <var>op2</var> multiplied by two to
+the power <var>e</var>. Similar as above.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_cmpabs</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fcmpabs-141"></a></var><br>
+<blockquote><p>Compare |<var>op1</var>| and |<var>op2</var>|. Return a positive value if
+|<var>op1</var>| > |<var>op2</var>|, zero if |<var>op1</var>| = |<var>op2</var>|, and
+a negative value if |<var>op1</var>| < |<var>op2</var>|.
+If one of the operands is NaN, set the erange flag and return zero.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_nan_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnan_005fp-142"></a></var><br>
+— Function: int <b>mpfr_inf_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finf_005fp-143"></a></var><br>
+— Function: int <b>mpfr_number_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fnumber_005fp-144"></a></var><br>
+— Function: int <b>mpfr_zero_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fzero_005fp-145"></a></var><br>
+<blockquote><p>Return non-zero if <var>op</var> is respectively NaN, an infinity, an ordinary
+number (i.e. neither NaN nor an infinity) or zero. Return zero otherwise.
+</p></blockquote></div>
+
+<div class="defun">
+— Macro: int <b>mpfr_sgn</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsgn-146"></a></var><br>
+<blockquote><p>Return a positive value if <var>op</var> > 0, zero if <var>op</var> = 0,
+and a negative value if <var>op</var> < 0.
+If the operand is NaN, set the erange flag and return zero.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_greater_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fgreater_005fp-147"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> > <var>op2</var>, zero otherwise.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_greaterequal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fgreaterequal_005fp-148"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> >= <var>op2</var>, zero otherwise.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_less_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fless_005fp-149"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var>, zero otherwise.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_lessequal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005flessequal_005fp-150"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> <= <var>op2</var>, zero otherwise.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_lessgreater_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005flessgreater_005fp-151"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> < <var>op2</var> or
+<var>op1</var> > <var>op2</var> (i.e. neither <var>op1</var>, nor <var>op2</var> is
+NaN, and <var>op1</var> <> <var>op2</var>), zero otherwise (i.e. <var>op1</var>
+and/or <var>op2</var> are NaN, or <var>op1</var> = <var>op2</var>).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_equal_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005fequal_005fp-152"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> = <var>op2</var>, zero otherwise
+(i.e. <var>op1</var> and/or <var>op2</var> are NaN, or
+<var>op1</var> <> <var>op2</var>).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_unordered_p</b> (<var>mpfr_t op1, mpfr_t op2</var>)<var><a name="index-mpfr_005funordered_005fp-153"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> or <var>op2</var> is a NaN (i.e. they cannot be
+compared), zero otherwise.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Special-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Input-and-Output-Functions">Input and Output Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Comparison-Functions">Comparison Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+ <p><a name="index-Special-functions-154"></a>
+
+<h3 class="section">5.7 Special Functions</h3>
+
+<p>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.
+
+ <p>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.
+
+<div class="defun">
+— Function: int <b>mpfr_log</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog-155"></a></var><br>
+— Function: int <b>mpfr_log2</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog2-156"></a></var><br>
+— Function: int <b>mpfr_log10</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog10-157"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the natural logarithm of <var>op</var>,
+log2(<var>op</var>) or
+log10(<var>op</var>), respectively,
+rounded in the direction <var>rnd</var>.
+Return −Inf if <var>op</var> is −0 (i.e. the sign of the zero
+has no influence on the result).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_exp</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp-158"></a></var><br>
+— Function: int <b>mpfr_exp2</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp2-159"></a></var><br>
+— Function: int <b>mpfr_exp10</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexp10-160"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var>,
+ to 2 power of <var>op</var>
+or to 10 power of <var>op</var>, respectively,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_cos</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcos-161"></a></var><br>
+— Function: int <b>mpfr_sin</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsin-162"></a></var><br>
+— Function: int <b>mpfr_tan</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ftan-163"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the cosine of <var>op</var>, sine of <var>op</var>,
+tangent of <var>op</var>, rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sec</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsec-164"></a></var><br>
+— Function: int <b>mpfr_csc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcsc-165"></a></var><br>
+— Function: int <b>mpfr_cot</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcot-166"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the secant of <var>op</var>, cosecant of <var>op</var>,
+cotangent of <var>op</var>, rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sin_cos</b> (<var>mpfr_t sop, mpfr_t cop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsin_005fcos-167"></a></var><br>
+<blockquote><p>Set simultaneously <var>sop</var> to the sine of <var>op</var> and
+ <var>cop</var> to the cosine of <var>op</var>,
+rounded in the direction <var>rnd</var> with the corresponding precisions of
+<var>sop</var> and <var>cop</var>, which must be different variables.
+Return 0 iff both results are exact.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_acos</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005facos-168"></a></var><br>
+— Function: int <b>mpfr_asin</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fasin-169"></a></var><br>
+— Function: int <b>mpfr_atan</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatan-170"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the arc-cosine, arc-sine or arc-tangent of <var>op</var>,
+rounded in the direction <var>rnd</var>.
+Note that since <code>acos(-1)</code> returns the floating-point number closest to
+Pi according to the given rounding mode, this number might not be
+in the output range 0 <= <var>rop</var> < \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 <code>asin(-1)</code>, <code>asin(1)</code>, <code>atan(-Inf)</code>,
+<code>atan(+Inf)</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_atan2</b> (<var>mpfr_t rop, mpfr_t y, mpfr_t x, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatan2-171"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the arc-tangent2 of <var>y</var> and <var>x</var>,
+rounded in the direction <var>rnd</var>:
+if <code>x > 0</code>, <code>atan2(y, x) = atan (y/x)</code>;
+if <code>x < 0</code>, <code>atan2(y, x) = sign(y)*(Pi - atan (abs(y/x)))</code>.
+As for <code>atan</code>, in case the exact mathematical result is +Pi or
+-Pi, its rounded result might be outside the function output range.
+
+ <p><code>atan2(y, 0)</code> does not raise any floating-point exception.
+Special values are currently handled as described in the ISO C99 standard
+for the <code>atan2</code> function (note this may change in future versions):
+ <ul>
+<li><code>atan2(+0, -0)</code> returns +Pi.
+<li><code>atan2(-0, -0)</code> returns -Pi.
+<li><code>atan2(+0, +0)</code> returns +0.
+<li><code>atan2(-0, +0)</code> returns −0.
+<li><code>atan2(+0, x)</code> returns +Pi for x < 0.
+<li><code>atan2(-0, x)</code> returns -Pi for x < 0.
+<li><code>atan2(+0, x)</code> returns +0 for x > 0.
+<li><code>atan2(-0, x)</code> returns −0 for x > 0.
+<li><code>atan2(y, 0)</code> returns -Pi/2 for y < 0.
+<li><code>atan2(y, 0)</code> returns +Pi/2 for y > 0.
+<li><code>atan2(+Inf, -Inf)</code> returns +3*Pi/4.
+<li><code>atan2(-Inf, -Inf)</code> returns -3*Pi/4.
+<li><code>atan2(+Inf, +Inf)</code> returns +Pi/4.
+<li><code>atan2(-Inf, +Inf)</code> returns -Pi/4.
+<li><code>atan2(+Inf, x)</code> returns +Pi/2 for finite x.
+<li><code>atan2(-Inf, x)</code> returns -Pi/2 for finite x.
+<li><code>atan2(y, -Inf)</code> returns +Pi for finite y > 0.
+<li><code>atan2(y, -Inf)</code> returns -Pi for finite y < 0.
+<li><code>atan2(y, +Inf)</code> returns +0 for finite y > 0.
+<li><code>atan2(y, +Inf)</code> returns −0 for finite y < 0.
+</ul>
+ </p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_cosh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcosh-172"></a></var><br>
+— Function: int <b>mpfr_sinh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsinh-173"></a></var><br>
+— Function: int <b>mpfr_tanh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ftanh-174"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the hyperbolic cosine, sine or tangent of <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sech</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsech-175"></a></var><br>
+— Function: int <b>mpfr_csch</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcsch-176"></a></var><br>
+— Function: int <b>mpfr_coth</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcoth-177"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the hyperbolic secant of <var>op</var>, cosecant of <var>op</var>,
+cotangent of <var>op</var>, rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_acosh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005facosh-178"></a></var><br>
+— Function: int <b>mpfr_asinh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fasinh-179"></a></var><br>
+— Function: int <b>mpfr_atanh</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fatanh-180"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the inverse hyperbolic cosine, sine or tangent of <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_fac_ui</b> (<var>mpfr_t rop, unsigned long int op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffac_005fui-181"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the factorial of the <code>unsigned long int</code> <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_log1p</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flog1p-182"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the logarithm of one plus <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_expm1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fexpm1-183"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the exponential of <var>op</var> minus one,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_eint</b> (<var>mpfr_t y, mpfr_t x, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005feint-184"></a></var><br>
+<blockquote><p>Set <var>y</var> to the exponential integral of <var>x</var>,
+rounded in the direction <var>rnd</var>.
+For positive <var>x</var>,
+the exponential integral is the sum of Euler's constant, of the logarithm
+of <var>x</var>, and of the sum for k from 1 to infinity of
+<var>x</var> to the power k, divided by k and factorial(k).
+For negative <var>x</var>, the returned value is NaN.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_gamma</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fgamma-185"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the Gamma function on <var>op</var>, rounded in the
+direction <var>rnd</var>. When <var>op</var> is a negative integer, NaN is returned.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_lngamma</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flngamma-186"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the logarithm of the Gamma function on <var>op</var>,
+rounded in the direction <var>rnd</var>.
+When −2<var>k</var>−1 <= <var>x</var> <= −2<var>k</var>,
+<var>k</var> being a non-negative integer, NaN is returned.
+See also <code>mpfr_lgamma</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_lgamma</b> (<var>mpfr_t rop, int *signp, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005flgamma-187"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the logarithm of the absolute value of the
+Gamma function on <var>op</var>, rounded in the direction <var>rnd</var>. The sign
+(1 or −1) of Gamma(<var>op</var>) is returned in the object pointed to
+by <var>signp</var>. When <var>op</var> is an infinity or a non-positive integer,
++Inf is returned. When <var>op</var> is NaN, −Inf or a negative integer,
+*<var>signp</var> is undefined, and when <var>op</var> is �0, *<var>signp</var> is
+the sign of the zero.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_zeta</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fzeta-188"></a></var><br>
+— Function: int <b>mpfr_zeta_ui</b> (<var>mpfr_t rop, unsigned long op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fzeta_005fui-189"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the Riemann Zeta function on <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_erf</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ferf-190"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the error function on <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_erfc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ferfc-191"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the complementary error function on <var>op</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_j0</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fj0-192"></a></var><br>
+— Function: int <b>mpfr_j1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fj1-193"></a></var><br>
+— Function: int <b>mpfr_jn</b> (<var>mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fjn-194"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the first order Bessel function of order 0, 1
+and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is
+NaN, <var>rop</var> is always set to NaN. When <var>op</var> is plus or minus Infinity,
+<var>rop</var> is set to +0. When <var>op</var> is zero, and <var>n</var> is not zero,
+<var>rop</var> is +0 or −0 depending on the parity and sign of <var>n</var>,
+and the sign of <var>op</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_y0</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fy0-195"></a></var><br>
+— Function: int <b>mpfr_y1</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fy1-196"></a></var><br>
+— Function: int <b>mpfr_yn</b> (<var>mpfr_t rop, long n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fyn-197"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the value of the second order Bessel function of order 0, 1
+and <var>n</var> on <var>op</var>, rounded in the direction <var>rnd</var>. When <var>op</var> is
+NaN or negative,
+<var>rop</var> is always set to NaN. When <var>op</var> is +Inf,
+<var>rop</var> is +0. When <var>op</var> is zero,
+<var>rop</var> is +Inf or −Inf depending on the parity and sign of <var>n</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_fma</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffma-198"></a></var><br>
+<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) + <var>op3</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_fms</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_t op3, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffms-199"></a></var><br>
+<blockquote><p>Set <var>rop</var> to (<var>op1</var> times <var>op2</var>) - <var>op3</var>,
+rounded in the direction <var>rnd</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_agm</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fagm-200"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the arithmetic-geometric mean of <var>op1</var> and <var>op2</var>,
+rounded in the direction <var>rnd</var>.
+The arithmetic-geometric mean is the common limit of the sequences
+u[n] and v[n], where u[0]=<var>op1</var>, v[0]=<var>op2</var>, 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.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_hypot</b> (<var>mpfr_t rop, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fhypot-201"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the Euclidean norm of <var>x</var> and <var>y</var>,
+i.e. the square root of the sum of the squares of <var>x</var> and <var>y</var>,
+rounded in the direction <var>rnd</var>.
+Special values are currently handled as described in Section F.9.4.3 of
+the ISO C99 standard, for the <code>hypot</code> function (note this may change
+in future versions): If <var>x</var> or <var>y</var> is an infinity, then plus
+infinity is returned in <var>rop</var>, even if the other number is NaN.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_const_log2</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005flog2-202"></a></var><br>
+— Function: int <b>mpfr_const_pi</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005fpi-203"></a></var><br>
+— Function: int <b>mpfr_const_euler</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005feuler-204"></a></var><br>
+— Function: int <b>mpfr_const_catalan</b> (<var>mpfr_t rop, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fconst_005fcatalan-205"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the logarithm of 2, the value of Pi,
+of Euler's constant 0.577<small class="dots">...</small>, of Catalan's constant 0.915<small class="dots">...</small>,
+respectively, rounded in the direction
+<var>rnd</var>. These functions cache the computed values to avoid other
+calculations if a lower or equal precision is requested. To free these caches,
+use <code>mpfr_free_cache</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_free_cache</b> (<var>void</var>)<var><a name="index-mpfr_005ffree_005fcache-206"></a></var><br>
+<blockquote><p>Free various caches used by MPFR internally, in particular the
+caches used by the functions computing constants (currently
+<code>mpfr_const_log2</code>, <code>mpfr_const_pi</code>,
+<code>mpfr_const_euler</code> and <code>mpfr_const_catalan</code>).
+You should call this function before terminating a thread, even if you did
+not call these functions directly (they could have been called internally).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_sum</b> (<var>mpfr_t rop, mpfr_ptr const tab</var>[]<var>, unsigned long n, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsum-207"></a></var><br>
+<blockquote><p>Set <var>ret</var> to the sum of all elements of <var>tab</var> whose size is <var>n</var>,
+rounded in the direction <var>rnd</var>. Warning, <var>tab</var> is a table of pointers
+to mpfr_t, not a table of mpfr_t (preliminary interface). The returned
+<code>int</code> 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.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Input-and-Output-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Integer-Related-Functions">Integer Related Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Special-Functions">Special Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Float-input-and-output-functions-208"></a><a name="index-Input-functions-209"></a><a name="index-Output-functions-210"></a><a name="index-I_002fO-functions-211"></a>
+
+<h3 class="section">5.8 Input and Output Functions</h3>
+
+<p>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 <var>stream</var> argument to any of
+these functions will make them read from <code>stdin</code> and write to
+<code>stdout</code>, respectively.
+
+ <p>When using any of these functions, you must include the <code><stdio.h></code>
+standard header before <samp><span class="file">mpfr.h</span></samp>, to allow <samp><span class="file">mpfr.h</span></samp> to define
+prototypes for these functions.
+
+<div class="defun">
+— Function: size_t <b>mpfr_out_str</b> (<var>FILE *stream, int base, size_t n, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fout_005fstr-212"></a></var><br>
+<blockquote><p>Output <var>op</var> on stream <var>stream</var>, as a string of digits in
+base <var>base</var>, rounded in the direction <var>rnd</var>.
+The base may vary from 2 to 36. Print <var>n</var> significant digits exactly,
+or if <var>n</var> is 0, enough digits so that <var>op</var> can be read back
+exactly (see <code>mpfr_get_str</code>).
+
+ <p>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 ‘<samp><span class="samp">eNNN</span></samp>’,
+are printed. If <var>base</var> is greater than 10, ‘<samp><span class="samp">@</span></samp>’ will be used
+instead of ‘<samp><span class="samp">e</span></samp>’ as exponent delimiter.
+
+ <p>Return the number of bytes written, or if an error occurred, return 0.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: size_t <b>mpfr_inp_str</b> (<var>mpfr_t rop, FILE *stream, int base, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005finp_005fstr-213"></a></var><br>
+<blockquote><p>Input a string in base <var>base</var> from stream <var>stream</var>,
+rounded in the direction <var>rnd</var>, and put the
+read float in <var>rop</var>.
+<!-- The argument @var{base} must be in the range 2 to 36. -->
+
+ <!-- The string is of the form @samp{M@@N} or, if the -->
+ <!-- base is 10 or less, alternatively @samp{MeN} or @samp{MEN}, or, if the base -->
+ <!-- is 16, alternatively @samp{MpB} or @samp{MPB}. -->
+ <!-- @samp{M} is the significand in the specified base, @samp{N} is the exponent -->
+ <!-- written in decimal for the specified base, and in base 16, @samp{B} is the -->
+ <!-- binary exponent written in decimal (i.e.@: it indicates the power of 2 by -->
+ <!-- which the significand is to be scaled). -->
+ <p>This function reads a word (defined as a sequence of characters between
+whitespace) and parses it using <code>mpfr_set_str</code> (it may change).
+See the documentation of <code>mpfr_strtofr</code> for a detailed description
+of the valid string formats.
+<!-- Special values can be read as follows (the case does not matter): -->
+<!-- @code{@@NaN@@}, @code{@@Inf@@}, @code{+@@Inf@@} and @code{-@@Inf@@}, -->
+<!-- possibly followed by other characters; if the base is smaller or equal -->
+<!-- to 16, the following strings are accepted too: @code{NaN}, @code{Inf}, -->
+<!-- @code{+Inf} and @code{-Inf}. -->
+
+ <p>Return the number of bytes read, or if an error occurred, return 0.
+</p></blockquote></div>
+
+<!-- @deftypefun void mpfr_inp_raw (mpfr_t @var{float}, FILE *@var{stream}) -->
+<!-- Input from stdio stream @var{stream} in the format written by -->
+<!-- @code{mpfr_out_raw}, and put the result in @var{float}. -->
+<!-- @end deftypefun -->
+<div class="node">
+<p><hr>
+<a name="Integer-Related-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Miscellaneous-Functions">Miscellaneous Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Input-and-Output-Functions">Input and Output Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Integer-related-functions-214"></a>
+
+<h3 class="section">5.9 Integer Related Functions</h3>
+
+<div class="defun">
+— Function: int <b>mpfr_rint</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint-215"></a></var><br>
+— Function: int <b>mpfr_ceil</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fceil-216"></a></var><br>
+— Function: int <b>mpfr_floor</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ffloor-217"></a></var><br>
+— Function: int <b>mpfr_round</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005fround-218"></a></var><br>
+— Function: int <b>mpfr_trunc</b> (<var>mpfr_t rop, mpfr_t op</var>)<var><a name="index-mpfr_005ftrunc-219"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
+<code>mpfr_rint</code> rounds to the nearest representable integer in the
+given rounding mode, <code>mpfr_ceil</code> rounds
+to the next higher or equal representable integer, <code>mpfr_floor</code> to
+the next lower or equal representable integer, <code>mpfr_round</code> to the
+nearest representable integer, rounding halfway cases away from zero,
+and <code>mpfr_trunc</code> to the next representable integer toward zero.
+
+ <p>The returned value is zero when the result is exact, positive when it is
+greater than the original value of <var>op</var>, and negative when it is smaller.
+More precisely, the returned value is 0 when <var>op</var> is an integer
+representable in <var>rop</var>, 1 or −1 when <var>op</var> is an integer
+that is not representable in <var>rop</var>, 2 or −2 when <var>op</var> is
+not an integer.
+
+ <p>Note that <code>mpfr_round</code> is different from <code>mpfr_rint</code> 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 <code>mpfr_round</code> to 4 (100
+in binary) in 2-bit precision, though <code>round(4.5)</code> is equal to 5 and
+5 (101 in binary) is rounded to 6 (110 in binary) in 2-bit precision.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_rint_ceil</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005fceil-220"></a></var><br>
+— Function: int <b>mpfr_rint_floor</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005ffloor-221"></a></var><br>
+— Function: int <b>mpfr_rint_round</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005fround-222"></a></var><br>
+— Function: int <b>mpfr_rint_trunc</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005frint_005ftrunc-223"></a></var><br>
+<blockquote><p>Set <var>rop</var> to <var>op</var> rounded to an integer.
+<code>mpfr_rint_ceil</code> rounds to the next higher or equal integer,
+<code>mpfr_rint_floor</code> to the next lower or equal integer,
+<code>mpfr_rint_round</code> to the nearest integer, rounding halfway cases away
+from zero, and <code>mpfr_rint_trunc</code> to the next integer toward zero.
+If the result is not representable, it is rounded in the direction <var>rnd</var>.
+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).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_frac</b> (<var>mpfr_t rop, mpfr_t op, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005ffrac-224"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the fractional part of <var>op</var>, having the same sign as
+<var>op</var>, rounded in the direction <var>rnd</var> (unlike in <code>mpfr_rint</code>,
+<var>rnd</var> affects only how the exact fractional part is rounded, not how
+the fractional part is generated).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_remainder</b> (<var>mpfr_t r, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fremainder-225"></a></var><br>
+— Function: int <b>mpfr_remquo</b> (<var>mpfr_t r, long* q, mpfr_t x, mpfr_t y, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fremquo-226"></a></var><br>
+<blockquote><p>Set <var>r</var> to the remainder of the division of <var>x</var> by <var>y</var>, with
+quotient rounded to the nearest integer (ties rounded to even), and
+<var>r</var> rounded according to the direction <var>rnd</var>.
+If <var>r</var> is zero, it has the sign of <var>x</var>.
+The return value is the ternary value corresponding to <var>r</var>.
+Additionally, <code>mpfr_remquo</code> stores
+the low significant bits from the quotient in <var>*q</var>
+(more precisely the number of bits in a <code>long</code> minus one),
+with the sign of <var>x</var> divided by <var>y</var>
+(except if those low bits are all zero, in which case zero is returned).
+Note that <var>x</var> may be so large in magnitude relative to <var>y</var> that an
+exact representation of the quotient is not practical.
+These functions are useful for additive argument reduction.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_integer_p</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005finteger_005fp-227"></a></var><br>
+<blockquote><p>Return non-zero iff <var>op</var> is an integer.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Miscellaneous-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Integer-Related-Functions">Integer Related Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Miscellaneous-float-functions-228"></a>
+
+<h3 class="section">5.10 Miscellaneous Functions</h3>
+
+<div class="defun">
+— Function: void <b>mpfr_nexttoward</b> (<var>mpfr_t x, mpfr_t y</var>)<var><a name="index-mpfr_005fnexttoward-229"></a></var><br>
+<blockquote><p>If <var>x</var> or <var>y</var> is NaN, set <var>x</var> to NaN. Otherwise, if <var>x</var>
+is different from <var>y</var>, replace <var>x</var> by the next floating-point
+number (with the precision of <var>x</var> and the current exponent range)
+in the direction of <var>y</var>, 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.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_nextabove</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextabove-230"></a></var><br>
+<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is plus infinity.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_nextbelow</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fnextbelow-231"></a></var><br>
+<blockquote><p>Equivalent to <code>mpfr_nexttoward</code> where <var>y</var> is minus infinity.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_min</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmin-232"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the minimum of <var>op1</var> and <var>op2</var>. If <var>op1</var>
+and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var>
+or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If
+<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var>
+is set to −0.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_max</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmax-233"></a></var><br>
+<blockquote><p>Set <var>rop</var> to the maximum of <var>op1</var> and <var>op2</var>. If <var>op1</var>
+and <var>op2</var> are both NaN, then <var>rop</var> is set to NaN. If <var>op1</var>
+or <var>op2</var> is NaN, then <var>rop</var> is set to the numeric value. If
+<var>op1</var> and <var>op2</var> are zeros of different signs, then <var>rop</var>
+is set to +0.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_urandomb</b> (<var>mpfr_t rop, gmp_randstate_t state</var>)<var><a name="index-mpfr_005furandomb-234"></a></var><br>
+<blockquote><p>Generate a uniformly distributed random float in the interval
+0 <= <var>rop</var> < 1.
+Return 0, unless the exponent is not in the current exponent range, in
+which case <var>rop</var> is set to NaN and a non-zero value is returned. The
+second argument is a <code>gmp_randstate_t</code> structure which should be
+created using the GMP <code>gmp_randinit</code> function, see the GMP manual.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_random</b> (<var>mpfr_t rop</var>)<var><a name="index-mpfr_005frandom-235"></a></var><br>
+<blockquote><p>Generate a uniformly distributed random float in the interval
+0 <= <var>rop</var> < 1.
+This function is deprecated; <code>mpfr_urandomb</code> should be used instead.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_random2</b> (<var>mpfr_t rop, mp_size_t size, mp_exp_t exp</var>)<var><a name="index-mpfr_005frandom2-236"></a></var><br>
+<blockquote><p>Generate a random float of at most <var>size</var> limbs, with long strings of
+zeros and ones in the binary representation. The exponent of the number is in
+the interval −<var>exp</var> to <var>exp</var>.
+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 <var>size</var> is negative.
+Put +0 in <var>rop</var> 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 ‘<samp><span class="samp">--with-gmp-build</span></samp>’).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_exp_t <b>mpfr_get_exp</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fget_005fexp-237"></a></var><br>
+<blockquote><p>Get the exponent of <var>x</var>, assuming that <var>x</var> is a non-zero ordinary
+number and the significand is chosen in [1/2,1). The behavior for NaN,
+infinity or zero is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_set_exp</b> (<var>mpfr_t x, mp_exp_t e</var>)<var><a name="index-mpfr_005fset_005fexp-238"></a></var><br>
+<blockquote><p>Set the exponent of <var>x</var> if <var>e</var> is in the current exponent range,
+and return 0 (even if <var>x</var> is not a non-zero ordinary number);
+otherwise, return a non-zero value.
+The significand is assumed to be in [1/2,1).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_signbit</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fsignbit-239"></a></var><br>
+<blockquote><p>Return a non-zero value iff <var>op</var> has its sign bit set (i.e. if it is
+negative, −0, or a NaN whose representation has its sign bit set).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_setsign</b> (<var>mpfr_t rop, mpfr_t op, int s, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsetsign-240"></a></var><br>
+<blockquote><p>Set the value of <var>rop</var> from <var>op</var>, rounded toward the given
+direction <var>rnd</var>, then set (resp. clear) its sign bit if <var>s</var>
+is non-zero (resp. zero), even when <var>op</var> is a NaN.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_copysign</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcopysign-241"></a></var><br>
+<blockquote><p>Set the value of <var>rop</var> from <var>op1</var>, rounded toward the given
+direction <var>rnd</var>, then set its sign bit to that of <var>op2</var> (even
+when <var>op1</var> or <var>op2</var> is a NaN). This function is equivalent to
+<code>mpfr_setsign (</code><var>rop</var><code>, </code><var>op1</var><code>, mpfr_signbit (</code><var>op2</var><code>), </code><var>rnd</var><code>)</code>.
+</p></blockquote></div>
+
+<!-- By definition, a C string is always null-terminated, so that we -->
+<!-- could just say "string" or "null-terminated character array", -->
+<!-- but "null-terminated string" is not an error and probably better -->
+<!-- for most users. -->
+<div class="defun">
+— Function: const char * <b>mpfr_get_version</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fversion-242"></a></var><br>
+<blockquote><p>Return the MPFR version, as a null-terminated string.
+</p></blockquote></div>
+
+<div class="defun">
+— Macro: <b>MPFR_VERSION</b><var><a name="index-MPFR_005fVERSION-243"></a></var><br>
+— Macro: <b>MPFR_VERSION_MAJOR</b><var><a name="index-MPFR_005fVERSION_005fMAJOR-244"></a></var><br>
+— Macro: <b>MPFR_VERSION_MINOR</b><var><a name="index-MPFR_005fVERSION_005fMINOR-245"></a></var><br>
+— Macro: <b>MPFR_VERSION_PATCHLEVEL</b><var><a name="index-MPFR_005fVERSION_005fPATCHLEVEL-246"></a></var><br>
+— Macro: <b>MPFR_VERSION_STRING</b><var><a name="index-MPFR_005fVERSION_005fSTRING-247"></a></var><br>
+<blockquote><p><code>MPFR_VERSION</code> is the version of MPFR as a preprocessing constant.
+<code>MPFR_VERSION_MAJOR</code>, <code>MPFR_VERSION_MINOR</code> and
+<code>MPFR_VERSION_PATCHLEVEL</code> are respectively the major, minor and patch
+level of MPFR version, as preprocessing constants.
+<code>MPFR_VERSION_STRING</code> 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 <code>mpfr_get_version</code> to check at run time
+the header file and library used match:
+ <pre class="example"> if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING))
+ fprintf (stderr, "Warning: header and library do not match\n");
+</pre>
+ <p>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).
+</p></blockquote></div>
+
+<div class="defun">
+— Macro: long <b>MPFR_VERSION_NUM</b> (<var>major, minor, patchlevel</var>)<var><a name="index-MPFR_005fVERSION_005fNUM-248"></a></var><br>
+<blockquote><p>Create an integer in the same format as used by <code>MPFR_VERSION</code> from the
+given <var>major</var>, <var>minor</var> and <var>patchlevel</var>.
+Here is an example of how to check the MPFR version at compile time:
+ <pre class="example"> #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0)))
+ # error "Wrong MPFR version."
+ #endif
+</pre>
+ </blockquote></div>
+
+<div class="defun">
+— Function: const char * <b>mpfr_get_patches</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fpatches-249"></a></var><br>
+<blockquote><p>Return a null-terminated string containing the ids of the patches applied to
+the MPFR library (contents of the <samp><span class="file">PATCHES</span></samp> 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).
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Rounding-Mode-Related-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Exception-Related-Functions">Exception Related Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Miscellaneous-Functions">Miscellaneous Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+ <p><a name="index-Rounding-mode-related-functions-250"></a>
+
+<h3 class="section">5.11 Rounding Mode Related Functions</h3>
+
+<div class="defun">
+— Function: void <b>mpfr_set_default_rounding_mode</b> (<var>mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fset_005fdefault_005frounding_005fmode-251"></a></var><br>
+<blockquote><p>Set the default rounding mode to <var>rnd</var>.
+The default rounding mode is to nearest initially.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_rnd_t <b>mpfr_get_default_rounding_mode</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005fdefault_005frounding_005fmode-252"></a></var><br>
+<blockquote><p>Get the default rounding mode.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_prec_round</b> (<var>mpfr_t x, mp_prec_t prec, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fprec_005fround-253"></a></var><br>
+<blockquote><p>Round <var>x</var> according to <var>rnd</var> with precision <var>prec</var>, which
+must be an integer between <code>MPFR_PREC_MIN</code> and <code>MPFR_PREC_MAX</code>
+(otherwise the behavior is undefined).
+If <var>prec</var> is greater or equal to the precision of <var>x</var>, then new
+space is allocated for the significand, and it is filled with zeros.
+Otherwise, the significand is rounded to precision <var>prec</var> with the given
+direction. In both cases, the precision of <var>x</var> is changed to <var>prec</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_round_prec</b> (<var>mpfr_t x, mp_rnd_t rnd, mp_prec_t prec</var>)<var><a name="index-mpfr_005fround_005fprec-254"></a></var><br>
+<blockquote><p>[This function is obsolete. Please use <code>mpfr_prec_round</code> instead.]
+</p></blockquote></div>
+
+<div class="defun">
+— Function: const char * <b>mpfr_print_rnd_mode</b> (<var>mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fprint_005frnd_005fmode-255"></a></var><br>
+<blockquote><p>Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ)
+corresponding to the rounding mode <var>rnd</var> or a null pointer if
+<var>rnd</var> is an invalid rounding mode.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Exception-Related-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Advanced-Functions">Advanced Functions</a>,
+Previous: <a rel="previous" accesskey="p" href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Exception-related-functions-256"></a>
+
+<h3 class="section">5.12 Exception Related Functions</h3>
+
+<div class="defun">
+— Function: mp_exp_t <b>mpfr_get_emin</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin-257"></a></var><br>
+— Function: mp_exp_t <b>mpfr_get_emax</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax-258"></a></var><br>
+<blockquote><p>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.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_set_emin</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femin-259"></a></var><br>
+— Function: int <b>mpfr_set_emax</b> (<var>mp_exp_t exp</var>)<var><a name="index-mpfr_005fset_005femax-260"></a></var><br>
+<blockquote><p>Set the smallest and largest exponents allowed for a floating-point variable.
+Return a non-zero value when <var>exp</var> 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 <code>mpfr_check_range</code>), otherwise the subsequent
+behavior will be undefined, in the sense of the ISO C standard.
+<!-- It is also her/his responsibility to check that @m {emin <= emax}. -->
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_exp_t <b>mpfr_get_emin_min</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin_005fmin-261"></a></var><br>
+— Function: mp_exp_t <b>mpfr_get_emin_max</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femin_005fmax-262"></a></var><br>
+— Function: mp_exp_t <b>mpfr_get_emax_min</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax_005fmin-263"></a></var><br>
+— Function: mp_exp_t <b>mpfr_get_emax_max</b> (<var>void</var>)<var><a name="index-mpfr_005fget_005femax_005fmax-264"></a></var><br>
+<blockquote><p>Return the minimum and maximum of the smallest and largest exponents
+allowed for <code>mpfr_set_emin</code> and <code>mpfr_set_emax</code>. These values
+are implementation dependent; it is possible to create a non
+portable program by writing <code>mpfr_set_emax(mpfr_get_emax_max())</code>
+and <code>mpfr_set_emin(mpfr_get_emin_min())</code> since the values
+of the smallest and largest exponents become implementation dependent.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_check_range</b> (<var>mpfr_t x, int t, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fcheck_005frange-265"></a></var><br>
+<blockquote><p>This function forces <var>x</var> to be in the current range of acceptable
+values, <var>t</var> being the current ternary value: negative if <var>x</var>
+is smaller than the exact value, positive if <var>x</var> is larger than
+the exact value and zero if <var>x</var> is exact (before the call). It
+generates an underflow or an overflow if the exponent of <var>x</var> is
+outside the current allowed range; the value of <var>t</var> 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 <var>x</var>,
+i.e. the ternary value is propagated.
+
+ <p>Note: If <var>x</var> is an infinity and <var>t</var> is different from zero (i.e.,
+if the rounded result is an inexact infinity), then the overflow flag is
+set. This is useful because <code>mpfr_check_range</code> is typically called
+(at least in MPFR functions) after restoring the flags that could have
+been set due to internal computations.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_subnormalize</b> (<var>mpfr_t x, int t, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fsubnormalize-266"></a></var><br>
+<blockquote><p>This function rounds <var>x</var> emulating subnormal number arithmetic:
+if <var>x</var> is outside the subnormal exponent range, it just propagates the
+ternary value <var>t</var>; otherwise, it rounds <var>x</var> to precision
+<code>EXP(x)-emin+1</code> according to rounding mode <var>rnd</var> and previous
+ternary value <var>t</var>, avoiding double rounding problems.
+More precisely in the subnormal domain, denoting by <var>e</var> the value of
+<code>emin</code>, <var>x</var> is rounded in fixed-point
+arithmetic to an integer multiple of two to the power
+<var>e</var>−1; as a consequence, 1.5 multiplied by two to the power <var>e</var>−1 when <var>t</var> is zero
+is rounded to two to the power <var>e</var> with rounding to nearest.
+
+ <p><code>PREC(x)</code> is not modified by this function.
+<var>rnd</var> and <var>t</var> must be the used rounding mode for computing <var>x</var>
+and the returned ternary value when computing <var>x</var>.
+The subnormal exponent range is from <code>emin</code> to <code>emin+PREC(x)-1</code>.
+If the result cannot be represented in the current exponent range
+(due to a too small <code>emax</code>), the behavior is undefined.
+Note that unlike most functions, the result is compared to the exact one,
+not the input value <var>x</var>, i.e. the ternary value is propagated.
+This is a preliminary interface.
+</p></blockquote></div>
+
+ <p>This is an example of how to emulate double IEEE-754 arithmetic
+using MPFR:
+
+<pre class="example"> {
+ 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);
+ }
+</pre>
+ <p>Warning: this emulates a double IEEE-754 arithmetic with correct rounding
+in the subnormal range, which may not be the case for your hardware.
+
+<div class="defun">
+— Function: void <b>mpfr_clear_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005funderflow-267"></a></var><br>
+— Function: void <b>mpfr_clear_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005foverflow-268"></a></var><br>
+— Function: void <b>mpfr_clear_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fnanflag-269"></a></var><br>
+— Function: void <b>mpfr_clear_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005finexflag-270"></a></var><br>
+— Function: void <b>mpfr_clear_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005ferangeflag-271"></a></var><br>
+<blockquote><p>Clear the underflow, overflow, invalid, inexact and erange flags.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_set_underflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005funderflow-272"></a></var><br>
+— Function: void <b>mpfr_set_overflow</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005foverflow-273"></a></var><br>
+— Function: void <b>mpfr_set_nanflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005fnanflag-274"></a></var><br>
+— Function: void <b>mpfr_set_inexflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005finexflag-275"></a></var><br>
+— Function: void <b>mpfr_set_erangeflag</b> (<var>void</var>)<var><a name="index-mpfr_005fset_005ferangeflag-276"></a></var><br>
+<blockquote><p>Set the underflow, overflow, invalid, inexact and erange flags.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_clear_flags</b> (<var>void</var>)<var><a name="index-mpfr_005fclear_005fflags-277"></a></var><br>
+<blockquote><p>Clear all global flags (underflow, overflow, inexact, invalid, erange).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_underflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005funderflow_005fp-278"></a></var><br>
+— Function: int <b>mpfr_overflow_p</b> (<var>void</var>)<var><a name="index-mpfr_005foverflow_005fp-279"></a></var><br>
+— Function: int <b>mpfr_nanflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005fnanflag_005fp-280"></a></var><br>
+— Function: int <b>mpfr_inexflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005finexflag_005fp-281"></a></var><br>
+— Function: int <b>mpfr_erangeflag_p</b> (<var>void</var>)<var><a name="index-mpfr_005ferangeflag_005fp-282"></a></var><br>
+<blockquote><p>Return the corresponding (underflow, overflow, invalid, inexact, erange)
+flag, which is non-zero iff the flag is set.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Advanced-Functions"></a>
+Next: <a rel="next" accesskey="n" href="#Compatibility-with-MPF">Compatibility with MPF</a>,
+Previous: <a rel="previous" accesskey="p" href="#Exception-Related-Functions">Exception Related Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+ <p><a name="index-Advanced-functions-283"></a>
+
+<h3 class="section">5.13 Advanced Functions</h3>
+
+<p>All the given interfaces are preliminary. They might change incompatibly in
+future revisions.
+
+<div class="defun">
+— Macro: <b>MPFR_DECL_INIT</b> (<var>name, prec</var>)<var><a name="index-MPFR_005fDECL_005fINIT-284"></a></var><br>
+<blockquote><p>This macro declares <var>name</var> as an automatic variable of type <code>mpfr_t</code>,
+initializes it and sets its precision to be <strong>exactly</strong> <var>prec</var> bits
+and its value to NaN. <var>name</var> must be a valid identifier.
+You must use this macro in the declaration section.
+This macro is much faster than using <code>mpfr_init2</code> but has some
+drawbacks:
+
+ <ul>
+<li>You <strong>must not</strong> call <code>mpfr_clear</code> with variables
+created with this macro (The storage is allocated at the point of declaration
+and deallocated when the brace-level is exited.).
+<li>You <strong>can not</strong> change their precision.
+<li>You <strong>should not</strong> create variables with huge precision with this macro.
+<li>Your compiler must support ‘<samp><span class="samp">Non-Constant Initializers</span></samp>’ (standard
+in C++ and ISO C99) and ‘<samp><span class="samp">Token Pasting</span></samp>’
+(standard in ISO C89). If <var>prec</var> is not a compiler constant, your compiler
+must support ‘<samp><span class="samp">Variable-length automatic arrays</span></samp>’ (standard in ISO C99).
+‘<samp><span class="samp">GCC 2.95.3</span></samp>’ supports all these features. If you compile your program
+with gcc in c89 mode and with ‘<samp><span class="samp">-pedantic</span></samp>’, you may want to define the
+<code>MPFR_USE_EXTENSION</code> macro to avoid warnings due to the
+<code>MPFR_DECL_INIT</code> implementation.
+</ul>
+ </p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_inits</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005finits-285"></a></var><br>
+<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>,
+set their precision to be the default precision and their value to NaN.
+See <code>mpfr_init</code> for more details.
+The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
+(or equivalently <code>mpfr_ptr</code>).
+It begins from <var>x</var>. It ends when it encounters a null pointer (whose
+type must also be <code>mpfr_ptr</code>).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_inits2</b> (<var>mp_prec_t prec, mpfr_t x, ...</var>)<var><a name="index-mpfr_005finits2-286"></a></var><br>
+<blockquote><p>Initialize all the <code>mpfr_t</code> variables of the given <code>va_list</code>,
+set their precision to be <strong>exactly</strong>
+<var>prec</var> bits and their value to NaN.
+See <code>mpfr_init2</code> for more details.
+The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
+(or equivalently <code>mpfr_ptr</code>).
+It begins from <var>x</var>. It ends when it encounters a null pointer (whose
+type must also be <code>mpfr_ptr</code>).
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_clears</b> (<var>mpfr_t x, ...</var>)<var><a name="index-mpfr_005fclears-287"></a></var><br>
+<blockquote><p>Free the space occupied by all the <code>mpfr_t</code> variables of the given
+<code>va_list</code>. See <code>mpfr_clear</code> for more details.
+The <code>va_list</code> is assumed to be composed only of type <code>mpfr_t</code>
+(or equivalently <code>mpfr_ptr</code>).
+It begins from <var>x</var>. It ends when it encounters a null pointer (whose
+type must also be <code>mpfr_ptr</code>).
+</p></blockquote></div>
+
+ <p>Here is an example of how to use multiple initialization functions:
+
+<pre class="example"> {
+ 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);
+ }
+</pre>
+ <div class="node">
+<p><hr>
+<a name="Compatibility-with-MPF"></a>
+Next: <a rel="next" accesskey="n" href="#Custom-Interface">Custom Interface</a>,
+Previous: <a rel="previous" accesskey="p" href="#Advanced-Functions">Advanced Functions</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+ <p><a name="index-Compatibility-with-MPF-288"></a>
+
+<h3 class="section">5.14 Compatibility With MPF</h3>
+
+<p>A header file <samp><span class="file">mpf2mpfr.h</span></samp> is included in the distribution of MPFR for
+compatibility with the GNU MP class MPF.
+After inserting the following two lines after the <code>#include <gmp.h></code>
+line,
+<pre class="verbatim">
+#include <mpfr.h>
+#include <mpf2mpfr.h>
+</pre>
+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 <code>mpfr_set_default_rounding_mode</code>.
+
+ <p>Warning: the <code>mpf_init</code> and <code>mpf_init2</code> functions initialize
+to zero, whereas the corresponding MPFR functions initialize to NaN:
+this is useful to detect uninitialized values, but is slightly incompatible
+with <code>mpf</code>.
+
+<div class="defun">
+— Function: void <b>mpfr_set_prec_raw</b> (<var>mpfr_t x, mp_prec_t prec</var>)<var><a name="index-mpfr_005fset_005fprec_005fraw-289"></a></var><br>
+<blockquote><p>Reset the precision of <var>x</var> to be <strong>exactly</strong> <var>prec</var> bits.
+The only difference with <code>mpfr_set_prec</code> is that <var>prec</var> is assumed to
+be small enough so that the significand fits into the current allocated memory
+space for <var>x</var>. Otherwise the behavior is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_eq</b> (<var>mpfr_t op1, mpfr_t op2, unsigned long int op3</var>)<var><a name="index-mpfr_005feq-290"></a></var><br>
+<blockquote><p>Return non-zero if <var>op1</var> and <var>op2</var> are both non-zero ordinary
+numbers with the same exponent and the same first <var>op3</var> bits, both
+zero, or both infinities of the same sign. Return zero otherwise. This
+function is defined for compatibility with <code>mpf</code>. 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 <var>op3</var>
+larger than 1.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_reldiff</b> (<var>mpfr_t rop, mpfr_t op1, mpfr_t op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005freldiff-291"></a></var><br>
+<blockquote><p>Compute the relative difference between <var>op1</var> and <var>op2</var>
+and store the result in <var>rop</var>.
+This function does not guarantee the correct rounding on the relative
+difference; it just computes |<var>op1</var>-<var>op2</var>|/<var>op1</var>, using the
+rounding mode <var>rnd</var> for all operations and the precision of <var>rop</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_mul_2exp</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fmul_005f2exp-292"></a></var><br>
+— Function: int <b>mpfr_div_2exp</b> (<var>mpfr_t rop, mpfr_t op1, unsigned long int op2, mp_rnd_t rnd</var>)<var><a name="index-mpfr_005fdiv_005f2exp-293"></a></var><br>
+<blockquote><p>See <code>mpfr_mul_2ui</code> and <code>mpfr_div_2ui</code>. These functions are only kept
+for compatibility with MPF.
+</p></blockquote></div>
+
+<div class="node">
+<p><hr>
+<a name="Custom-Interface"></a>
+Next: <a rel="next" accesskey="n" href="#Internals">Internals</a>,
+Previous: <a rel="previous" accesskey="p" href="#Compatibility-with-MPF">Compatibility with MPF</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+ <p><a name="index-Custom-interface-294"></a>
+
+<h3 class="section">5.15 Custom Interface</h3>
+
+<p>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.
+
+ <p>The following interface allows them to use MPFR in two ways:
+ <ul>
+<li>Either they directly store the MPFR FP number as a <code>mpfr_t</code>
+on the stack.
+<li>Either they store their own representation of a FP number on the
+stack and construct a new temporary <code>mpfr_t</code> each time it is needed.
+</ul>
+ 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.
+
+ <p>Each function in this interface is also implemented as a macro for
+efficiency reasons: for example <code>mpfr_custom_init (s, p)</code>
+uses the macro, while <code>(mpfr_custom_init) (s, p)</code> uses the function.
+
+ <p>Note 1: MPFR functions may still initialize temporary FP numbers
+using standard mpfr_init. See Custom Allocation (GNU MP).
+
+ <p>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
+<code>mpfr_free_cache</code> each time you garbage the memory iff mpfr_init, through
+GMP Custom Allocation, allocates its memory on the application stack.
+
+ <p>Note 3: This interface is preliminary.
+
+<div class="defun">
+— Function: size_t <b>mpfr_custom_get_size</b> (<var>mp_prec_t prec</var>)<var><a name="index-mpfr_005fcustom_005fget_005fsize-295"></a></var><br>
+<blockquote><p>Return the needed size in bytes to store the significand of a FP number
+of precision <var>prec</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_custom_init</b> (<var>void *significand, mp_prec_t prec</var>)<var><a name="index-mpfr_005fcustom_005finit-296"></a></var><br>
+<blockquote><p>Initialize a significand of precision <var>prec</var>.
+<var>significand</var> must be an area of <code>mpfr_custom_get_size (prec)</code> bytes
+at least and be suitably aligned for an array of <code>mp_limb_t</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_custom_init_set</b> (<var>mpfr_t x, int kind, mp_exp_t exp, mp_prec_t prec, void *significand</var>)<var><a name="index-mpfr_005fcustom_005finit_005fset-297"></a></var><br>
+<blockquote><p>Perform a dummy initialization of a <code>mpfr_t</code> and set it to:
+ <ul>
+<li>if <code>ABS(kind) == MPFR_NAN_KIND</code>, <var>x</var> is set to NaN;
+<li>if <code>ABS(kind) == MPFR_INF_KIND</code>, <var>x</var> is set to the infinity
+of sign <code>sign(kind)</code>;
+<li>if <code>ABS(kind) == MPFR_ZERO_KIND</code>, <var>x</var> is set to the zero of
+sign <code>sign(kind)</code>;
+<li>if <code>ABS(kind) == MPFR_REGULAR_KIND</code>, <var>x</var> is set to a regular
+number: <code>x = sign(kind)*significand*2^exp</code>
+</ul>
+ In all cases, it uses <var>significand</var> directly for further computing
+involving <var>x</var>. It will not allocate anything.
+A FP number initialized with this function cannot be resized using
+<code>mpfr_set_prec</code>, or cleared using <code>mpfr_clear</code>!
+<var>significand</var> must have been initialized with <code>mpfr_custom_init</code>
+using the same precision <var>prec</var>.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: int <b>mpfr_custom_get_kind</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fkind-298"></a></var><br>
+<blockquote><p>Return the current kind of a <code>mpfr_t</code> as used by
+<code>mpfr_custom_init_set</code>.
+The behavior of this function for any <code>mpfr_t</code> not initialized
+with <code>mpfr_custom_init_set</code> is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void * <b>mpfr_custom_get_mantissa</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fmantissa-299"></a></var><br>
+<blockquote><p>Return a pointer to the significand used by a <code>mpfr_t</code> initialized with
+<code>mpfr_custom_init_set</code>.
+The behavior of this function for any <code>mpfr_t</code> not initialized
+with <code>mpfr_custom_init_set</code> is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: mp_exp_t <b>mpfr_custom_get_exp</b> (<var>mpfr_t x</var>)<var><a name="index-mpfr_005fcustom_005fget_005fexp-300"></a></var><br>
+<blockquote><p>Return the exponent of <var>x</var>, assuming that <var>x</var> 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 <code>mpfr_t</code> not initialized
+with <code>mpfr_custom_init_set</code> is undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: void <b>mpfr_custom_move</b> (<var>mpfr_t x, void *new_position</var>)<var><a name="index-mpfr_005fcustom_005fmove-301"></a></var><br>
+<blockquote><p>Inform MPFR that the significand has moved due to a garbage collect
+and update its new position to <code>new_position</code>.
+However the application has to move the significand and the <code>mpfr_t</code>
+itself.
+The behavior of this function for any <code>mpfr_t</code> not initialized
+with <code>mpfr_custom_init_set</code> is undefined.
+</p></blockquote></div>
+
+ <p>See the test suite for examples.
+
+<div class="node">
+<p><hr>
+<a name="Internals"></a>
+Previous: <a rel="previous" accesskey="p" href="#Custom-Interface">Custom Interface</a>,
+Up: <a rel="up" accesskey="u" href="#MPFR-Interface">MPFR Interface</a>
+
+</div>
+
+ <p><a name="index-Internals-302"></a>
+
+<h3 class="section">5.16 Internals</h3>
+
+<p>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 <samp><span class="file">mpfr-impl.h</span></samp> to use them.
+
+ <p>The <code>mpfr_t</code> type consists of four fields.
+
+ <ul>
+<li>The <code>_mpfr_prec</code> field is used to store the precision of
+the variable (in bits); this is not less than <code>MPFR_PREC_MIN</code>.
+
+ <li>The <code>_mpfr_sign</code> field is used to store the sign of the variable.
+
+ <li>The <code>_mpfr_exp</code> 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.
+
+ <li>Finally, the <code>_mpfr_d</code> is a pointer to the limbs, least
+significant limbs stored first.
+The number of limbs in use is controlled by <code>_mpfr_prec</code>, namely
+ceil(<code>_mpfr_prec</code>/<code>mp_bits_per_limb</code>).
+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.
+
+ </ul>
+
+<!-- @deftypefun int mpfr_add_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) -->
+<!-- Add one unit in last place (ulp) to @var{x} if @var{x} is finite -->
+<!-- and positive, subtract one ulp if @var{x} is finite and negative; -->
+<!-- otherwise, @var{x} is not changed. -->
+<!-- The return value is zero unless an overflow occurs, in which case the -->
+<!-- @code{mpfr_add_one_ulp} function behaves like a conventional addition. -->
+<!-- @end deftypefun -->
+<!-- @deftypefun int mpfr_sub_one_ulp (mpfr_t @var{x}, mp_rnd_t @var{rnd}) -->
+<!-- Subtract one ulp to @var{x} if @var{x} is finite and positive, add one -->
+<!-- ulp if @var{x} is finite and negative; otherwise, @var{x} is not changed. -->
+<!-- The return value is zero unless an underflow occurs, in which case the -->
+<!-- @code{mpfr_sub_one_ulp} function behaves like a conventional subtraction. -->
+<!-- @end deftypefun -->
+<div class="defun">
+— Function: int <b>mpfr_can_round</b> (<var>mpfr_t b, mp_exp_t err, mp_rnd_t rnd1, mp_rnd_t rnd2, mp_prec_t prec</var>)<var><a name="index-mpfr_005fcan_005fround-303"></a></var><br>
+<blockquote><p>Assuming <var>b</var> is an approximation of an unknown number
+<var>x</var> in the direction <var>rnd1</var> with error at most two to the power
+E(b)-<var>err</var> where E(b) is the exponent of <var>b</var>, return a non-zero
+value if one is able to round correctly <var>x</var> to precision
+<var>prec</var> with the direction <var>rnd2</var>,
+and 0 otherwise (including for NaN and Inf).
+This function <strong>does not modify</strong> its arguments.
+
+ <p>Note: if one wants to also determine the correct ternary value when rounding
+<var>b</var> to precision <var>prec</var>, a useful trick is the following:
+<pre class="verbatim">
+ if (mpfr_can_round (b, err, rnd1, GMP_RNDZ, prec + (rnd2 == GMP_RNDN)))
+ ...
+</pre>
+Indeed, if <var>rnd2</var> is <code>GMP_RNDN</code>, this will check if one can
+round to <var>prec</var>+1 bits with a directed rounding:
+if so, one can surely round to nearest to <var>prec</var> bits,
+and in addition one can determine the correct ternary value, which would not
+be the case when <var>b</var> is near from a value exactly representable on
+<var>prec</var> bits.
+</p></blockquote></div>
+
+<div class="defun">
+— Function: double <b>mpfr_get_d1</b> (<var>mpfr_t op</var>)<var><a name="index-mpfr_005fget_005fd1-304"></a></var><br>
+<blockquote><p>Convert <var>op</var> to a <code>double</code>, using the default MPFR rounding mode
+(see function <code>mpfr_set_default_rounding_mode</code>). This function is
+obsolete.
+</p></blockquote></div>
+
+<!-- @deftypefun void mpfr_set_str_binary (mpfr_t @var{x}, const char *@var{s}) -->
+<!-- Set @var{x} to the value of the binary number in string @var{s}, which has to -->
+<!-- be of the -->
+<!-- form +/-xxxx.xxxxxxEyy. The exponent is read in decimal, but is interpreted -->
+<!-- as the power of two to be multiplied by the significand. -->
+<!-- The significand length of @var{s} has to be less or equal to the precision -->
+<!-- of @var{x}, otherwise an error occurs. -->
+<!-- If @var{s} starts with @code{N}, it is interpreted as NaN (Not-a-Number); -->
+<!-- if it starts with @code{I} after the sign, it is interpreted as infinity, -->
+<!-- with the corresponding sign. -->
+<!-- @end deftypefun -->
+<!-- @deftypefun void mpfr_print_binary (mpfr_t @var{float}) -->
+<!-- Output @var{float} on stdout -->
+<!-- in raw binary format (the exponent is written in decimal, yet). -->
+<!-- @end deftypefun -->
+<div class="node">
+<p><hr>
+<a name="Contributors"></a>
+Next: <a rel="next" accesskey="n" href="#References">References</a>,
+Previous: <a rel="previous" accesskey="p" href="#MPFR-Interface">MPFR Interface</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="unnumbered">Contributors</h2>
+
+<p>The main developers of MPFR are Guillaume Hanrot, Vincent Lefèvre,
+Patrick Pélissier, Philippe Théveny and Paul Zimmermann.
+
+ <p>Sylvie Boldo from ENS-Lyon, France,
+contributed the functions <code>mpfr_agm</code> and <code>mpfr_log</code>.
+Emmanuel Jeandel, from ENS-Lyon too,
+contributed the generic hypergeometric code in
+<code>generic.c</code>, as well as the <code>mpfr_exp3</code>,
+a first implementation of the sine and cosine,
+and improved versions of
+<code>mpfr_const_log2</code> and <code>mpfr_const_pi</code>.
+Mathieu Dutour contributed the functions <code>mpfr_atan</code> and <code>mpfr_asin</code>,
+and a previous version of <code>mpfr_gamma</code>;
+David Daney contributed the hyperbolic and inverse hyperbolic functions,
+the base-2 exponential, and the factorial function. Fabrice Rouillier
+contributed the original version of <samp><span class="file">mul_ui.c</span></samp>, the <samp><span class="file">gmp_op.c</span></samp>
+file, and helped to the Microsoft Windows porting.
+Jean-Luc Rémy contributed the <code>mpfr_zeta</code> code.
+Ludovic Meunier helped in the design of the <code>mpfr_erf</code> code.
+Damien Stehlé contributed the <code>mpfr_get_ld_2exp</code> function.
+
+ <p>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.
+
+ <p>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).
+
+<div class="node">
+<p><hr>
+<a name="References"></a>
+Next: <a rel="next" accesskey="n" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>,
+Previous: <a rel="previous" accesskey="p" href="#Contributors">Contributors</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="unnumbered">References</h2>
+
+ <ul>
+<li>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,
+<a href="http://doi.acm.org/10.1145/1236463.1236468">http://doi.acm.org/10.1145/1236463.1236468</a>.
+
+ <li>Torbjörn Granlund, "GNU MP: The GNU Multiple Precision Arithmetic Library",
+ version 4.2.2, 2007, <a href="http://gmplib.org">http://gmplib.org</a>.
+
+ <li>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.
+
+ <li>Donald E. Knuth, "The Art of Computer Programming", vol 2,
+"Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
+
+ <li>Jean-Michel Muller, "Elementary Functions, Algorithms and Implementation",
+Birkhauser, Boston, 2nd edition, 2006.
+
+</ul>
+
+<div class="node">
+<p><hr>
+<a name="GNU-Free-Documentation-License"></a>
+Next: <a rel="next" accesskey="n" href="#Concept-Index">Concept Index</a>,
+Previous: <a rel="previous" accesskey="p" href="#References">References</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<h2 class="appendix">Appendix A GNU Free Documentation License</h2>
+
+<p><a name="index-GNU-Free-Documentation-License-305"></a>
+
+<!-- MPFR tweak: Have this in mpfr.texi to help texinfo-mode -->
+<!-- @node GNU Free Documentation License -->
+<!-- @appendixsec GNU Free Documentation License -->
+ <p><a name="index-FDL_002c-GNU-Free-Documentation-License-306"></a><div align="center">Version 1.2, November 2002</div>
+
+<pre class="display"> 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.
+</pre>
+ <ol type=1 start=0>
+<li>PREAMBLE
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+unless they release you from this requirement.
+
+ <li>State on the Title page the name of the publisher of the
+Modified Version, as the publisher.
+
+ <li>Preserve all the copyright notices of the Document.
+
+ <li>Add an appropriate copyright notice for your modifications
+adjacent to the other copyright notices.
+
+ <li>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.
+
+ <li>Preserve in that license notice the full lists of Invariant Sections
+and required Cover Texts given in the Document's license notice.
+
+ <li>Include an unaltered copy of this License.
+
+ <li>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.
+
+ <li>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.
+
+ <li>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.
+
+ <li>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.
+
+ <li>Delete any section Entitled “Endorsements”. Such a section
+may not be included in the Modified Version.
+
+ <li>Do not retitle any existing section to be Entitled “Endorsements” or
+to conflict in title with any Invariant Section.
+
+ <li>Preserve any Warranty Disclaimers.
+ </ol>
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.
+
+ <li>COMBINING DOCUMENTS
+
+ <p>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.
+
+ <p>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.
+
+ <p>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.”
+
+ <li>COLLECTIONS OF DOCUMENTS
+
+ <p>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.
+
+ <p>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.
+
+ <li>AGGREGATION WITH INDEPENDENT WORKS
+
+ <p>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.
+
+ <p>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.
+
+ <li>TRANSLATION
+
+ <p>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. In case of a disagreement between
+the translation and the original version of this License or a notice
+or disclaimer, the original version will prevail.
+
+ <p>If a section in the Document is Entitled “Acknowledgements”,
+“Dedications”, or “History”, the requirement (section 4) to Preserve
+its Title (section 1) will typically require changing the actual
+title.
+
+ <li>TERMINATION
+
+ <p>You may not copy, modify, sublicense, or distribute the Document except
+as expressly provided for under this License. Any other attempt to
+copy, modify, sublicense or distribute the Document 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.
+
+ <li>FUTURE REVISIONS OF THIS LICENSE
+
+ <p>The Free Software Foundation may publish new, revised versions
+of the GNU Free Documentation License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns. See
+<a href="http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</a>.
+
+ <p>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.
+ </ol>
+
+<!-- MPFR tweak: Use @appendixsec -->
+<!-- @appendixsubsec ADDENDUM: How to use this License for your documents -->
+<h3 class="appendixsec">A.1 ADDENDUM: How to use this License for your documents</h3>
+
+<p>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:
+
+<pre class="smallexample"> Copyright (C) <var>year</var> <var>your name</var>.
+ 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''.
+</pre>
+ <p>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
+replace the “with...Texts.” line with this:
+
+<pre class="smallexample"> with the Invariant Sections being <var>list their titles</var>, with
+ the Front-Cover Texts being <var>list</var>, and with the Back-Cover Texts
+ being <var>list</var>.
+</pre>
+ <p>If you have Invariant Sections without Cover Texts, or some other
+combination of the three, merge those two alternatives to suit the
+situation.
+
+ <p>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.
+
+<!-- Local Variables: -->
+<!-- ispell-local-pdict: "ispell-dict" -->
+<!-- End: -->
+<div class="node">
+<p><hr>
+<a name="Concept-Index"></a>
+Next: <a rel="next" accesskey="n" href="#Function-Index">Function Index</a>,
+Previous: <a rel="previous" accesskey="p" href="#GNU-Free-Documentation-License">GNU Free Documentation License</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="unnumbered">Concept Index</h2>
+
+<ul class="index-cp" compact>
+<li><a href="#index-Accuracy-21">Accuracy</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
+<li><a href="#index-Advanced-functions-283">Advanced functions</a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
+<li><a href="#index-Arithmetic-functions-86">Arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-Assignment-functions-30">Assignment functions</a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-Basic-arithmetic-functions-84">Basic arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-Combined-initialization-and-assignment-functions-51">Combined initialization and assignment functions</a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-Comparison-functions-130">Comparison functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-Compatibility-with-MPF-288">Compatibility with MPF</a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-Conditions-for-copying-MPFR-2">Conditions for copying MPFR</a>: <a href="#Copying">Copying</a></li>
+<li><a href="#index-Conversion-functions-61">Conversion functions</a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-Copying-conditions-1">Copying conditions</a>: <a href="#Copying">Copying</a></li>
+<li><a href="#index-Custom-interface-294">Custom interface</a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-Exception-related-functions-256">Exception related functions</a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-FDL_002c-GNU-Free-Documentation-License-306">FDL, GNU Free Documentation License</a>: <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a></li>
+<li><a href="#index-Float-arithmetic-functions-85">Float arithmetic functions</a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-Float-comparisons-functions-129">Float comparisons functions</a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-Float-functions-19">Float functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
+<li><a href="#index-Float-input-and-output-functions-208">Float input and output functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-Floating_002dpoint-functions-18">Floating-point functions</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
+<li><a href="#index-Floating_002dpoint-number-11">Floating-point number</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-GNU-Free-Documentation-License-305">GNU Free Documentation License</a>: <a href="#GNU-Free-Documentation-License">GNU Free Documentation License</a></li>
+<li><a href="#index-I_002fO-functions-211">I/O functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-Initialization-functions-22">Initialization functions</a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-Input-functions-209">Input functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-Installation-3">Installation</a>: <a href="#Installing-MPFR">Installing MPFR</a></li>
+<li><a href="#index-Integer-related-functions-214">Integer related functions</a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-Internals-302">Internals</a>: <a href="#Internals">Internals</a></li>
+<li><a href="#index-g_t_0040code_007blibmpfr_007d-9"><code>libmpfr</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Libraries-7">Libraries</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Libtool-10">Libtool</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Limb-17">Limb</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Linking-8">Linking</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Miscellaneous-float-functions-228">Miscellaneous float functions</a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-g_t_0040file_007bmpfr_002eh_007d-5"><samp><span class="file">mpfr.h</span></samp></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Output-functions-210">Output functions</a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-Precision-20">Precision</a>: <a href="#MPFR-Interface">MPFR Interface</a></li>
+<li><a href="#index-Precision-13">Precision</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Reporting-bugs-4">Reporting bugs</a>: <a href="#Reporting-Bugs">Reporting Bugs</a></li>
+<li><a href="#index-Rounding-mode-related-functions-250">Rounding mode related functions</a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-Rounding-Modes-15">Rounding Modes</a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-Special-functions-154">Special functions</a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-g_t_0040code_007bstdio_002eh_007d-6"><code>stdio.h</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+</ul><div class="node">
+<p><hr>
+<a name="Function-Index"></a>
+Previous: <a rel="previous" accesskey="p" href="#Concept-Index">Concept Index</a>,
+Up: <a rel="up" accesskey="u" href="#Top">Top</a>
+
+</div>
+
+<!-- node-name, next, previous, up -->
+<h2 class="unnumbered">Function and Type Index</h2>
+
+
+
+<ul class="index-fn" compact>
+<li><a href="#index-g_t_0040code_007bmp_005fprec_005ft_007d-14"><code>mp_prec_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-g_t_0040code_007bmp_005frnd_005ft_007d-16"><code>mp_rnd_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-mpfr_005fabs-123"><code>mpfr_abs</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005facos-168"><code>mpfr_acos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005facosh-178"><code>mpfr_acosh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fadd-87"><code>mpfr_add</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fadd_005fq-91"><code>mpfr_add_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fadd_005fsi-89"><code>mpfr_add_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fadd_005fui-88"><code>mpfr_add_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fadd_005fz-90"><code>mpfr_add_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fagm-200"><code>mpfr_agm</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fasin-169"><code>mpfr_asin</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fasinh-179"><code>mpfr_asinh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fatan-170"><code>mpfr_atan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fatan2-171"><code>mpfr_atan2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fatanh-180"><code>mpfr_atanh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcan_005fround-303"><code>mpfr_can_round</code></a>: <a href="#Internals">Internals</a></li>
+<li><a href="#index-mpfr_005fcbrt-114"><code>mpfr_cbrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fceil-216"><code>mpfr_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005fcheck_005frange-265"><code>mpfr_check_range</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear-24"><code>mpfr_clear</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005ferangeflag-271"><code>mpfr_clear_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005fflags-277"><code>mpfr_clear_flags</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005finexflag-270"><code>mpfr_clear_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005fnanflag-269"><code>mpfr_clear_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005foverflow-268"><code>mpfr_clear_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclear_005funderflow-267"><code>mpfr_clear_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fclears-287"><code>mpfr_clears</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
+<li><a href="#index-mpfr_005fcmp-131"><code>mpfr_cmp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fd-134"><code>mpfr_cmp_d</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005ff-138"><code>mpfr_cmp_f</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fld-135"><code>mpfr_cmp_ld</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fq-137"><code>mpfr_cmp_q</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fsi-133"><code>mpfr_cmp_si</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fsi_005f2exp-140"><code>mpfr_cmp_si_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fui-132"><code>mpfr_cmp_ui</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fui_005f2exp-139"><code>mpfr_cmp_ui_2exp</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmp_005fz-136"><code>mpfr_cmp_z</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fcmpabs-141"><code>mpfr_cmpabs</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fconst_005fcatalan-205"><code>mpfr_const_catalan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fconst_005feuler-204"><code>mpfr_const_euler</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fconst_005flog2-202"><code>mpfr_const_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fconst_005fpi-203"><code>mpfr_const_pi</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcopysign-241"><code>mpfr_copysign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fcos-161"><code>mpfr_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcosh-172"><code>mpfr_cosh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcot-166"><code>mpfr_cot</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcoth-177"><code>mpfr_coth</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcsc-165"><code>mpfr_csc</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcsch-176"><code>mpfr_csch</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fcustom_005fget_005fexp-300"><code>mpfr_custom_get_exp</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005fget_005fkind-298"><code>mpfr_custom_get_kind</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005fget_005fmantissa-299"><code>mpfr_custom_get_mantissa</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005fget_005fsize-295"><code>mpfr_custom_get_size</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005finit-296"><code>mpfr_custom_init</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005finit_005fset-297"><code>mpfr_custom_init_set</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-mpfr_005fcustom_005fmove-301"><code>mpfr_custom_move</code></a>: <a href="#Custom-Interface">Custom Interface</a></li>
+<li><a href="#index-MPFR_005fDECL_005fINIT-284"><code>MPFR_DECL_INIT</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
+<li><a href="#index-mpfr_005fdim-124"><code>mpfr_dim</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv-105"><code>mpfr_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005f2exp-293"><code>mpfr_div_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-mpfr_005fdiv_005f2si-128"><code>mpfr_div_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005f2ui-127"><code>mpfr_div_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005fq-111"><code>mpfr_div_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005fsi-109"><code>mpfr_div_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005fui-107"><code>mpfr_div_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fdiv_005fz-110"><code>mpfr_div_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005feint-184"><code>mpfr_eint</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005feq-290"><code>mpfr_eq</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-mpfr_005fequal_005fp-152"><code>mpfr_equal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005ferangeflag_005fp-282"><code>mpfr_erangeflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005ferf-190"><code>mpfr_erf</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ferfc-191"><code>mpfr_erfc</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fexp-158"><code>mpfr_exp</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fexp10-160"><code>mpfr_exp10</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fexp2-159"><code>mpfr_exp2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fexpm1-183"><code>mpfr_expm1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ffac_005fui-181"><code>mpfr_fac_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fintmax_005fp-82"><code>mpfr_fits_intmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fsint_005fp-79"><code>mpfr_fits_sint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fslong_005fp-77"><code>mpfr_fits_slong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fsshort_005fp-81"><code>mpfr_fits_sshort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fuint_005fp-78"><code>mpfr_fits_uint_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fuintmax_005fp-83"><code>mpfr_fits_uintmax_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fulong_005fp-76"><code>mpfr_fits_ulong_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffits_005fushort_005fp-80"><code>mpfr_fits_ushort_p</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005ffloor-217"><code>mpfr_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005ffma-198"><code>mpfr_fma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ffms-199"><code>mpfr_fms</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ffrac-224"><code>mpfr_frac</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005ffree_005fcache-206"><code>mpfr_free_cache</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ffree_005fstr-75"><code>mpfr_free_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fgamma-185"><code>mpfr_gamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fd-62"><code>mpfr_get_d</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fd1-304"><code>mpfr_get_d1</code></a>: <a href="#Internals">Internals</a></li>
+<li><a href="#index-mpfr_005fget_005fd_005f2exp-65"><code>mpfr_get_d_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fdecimal64-64"><code>mpfr_get_decimal64</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fdefault_005fprec-27"><code>mpfr_get_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fdefault_005frounding_005fmode-252"><code>mpfr_get_default_rounding_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femax-258"><code>mpfr_get_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femax_005fmax-264"><code>mpfr_get_emax_max</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femax_005fmin-263"><code>mpfr_get_emax_min</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femin-257"><code>mpfr_get_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femin_005fmax-262"><code>mpfr_get_emin_max</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005femin_005fmin-261"><code>mpfr_get_emin_min</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fexp-237"><code>mpfr_get_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fget_005ff-73"><code>mpfr_get_f</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fld-63"><code>mpfr_get_ld</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fld_005f2exp-66"><code>mpfr_get_ld_2exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fpatches-249"><code>mpfr_get_patches</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fprec-29"><code>mpfr_get_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fsi-67"><code>mpfr_get_si</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fsj-69"><code>mpfr_get_sj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fstr-74"><code>mpfr_get_str</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fui-68"><code>mpfr_get_ui</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fuj-70"><code>mpfr_get_uj</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fversion-242"><code>mpfr_get_version</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fz-72"><code>mpfr_get_z</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fget_005fz_005fexp-71"><code>mpfr_get_z_exp</code></a>: <a href="#Conversion-Functions">Conversion Functions</a></li>
+<li><a href="#index-mpfr_005fgreater_005fp-147"><code>mpfr_greater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fgreaterequal_005fp-148"><code>mpfr_greaterequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fhypot-201"><code>mpfr_hypot</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005finexflag_005fp-281"><code>mpfr_inexflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005finf_005fp-143"><code>mpfr_inf_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005finit-25"><code>mpfr_init</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005finit2-23"><code>mpfr_init2</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset-52"><code>mpfr_init_set</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fd-55"><code>mpfr_init_set_d</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005ff-59"><code>mpfr_init_set_f</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fld-56"><code>mpfr_init_set_ld</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fq-58"><code>mpfr_init_set_q</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fsi-54"><code>mpfr_init_set_si</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fstr-60"><code>mpfr_init_set_str</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fui-53"><code>mpfr_init_set_ui</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finit_005fset_005fz-57"><code>mpfr_init_set_z</code></a>: <a href="#Combined-Initialization-and-Assignment-Functions">Combined Initialization and Assignment Functions</a></li>
+<li><a href="#index-mpfr_005finits-285"><code>mpfr_inits</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
+<li><a href="#index-mpfr_005finits2-286"><code>mpfr_inits2</code></a>: <a href="#Advanced-Functions">Advanced Functions</a></li>
+<li><a href="#index-mpfr_005finp_005fstr-213"><code>mpfr_inp_str</code></a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-mpfr_005finteger_005fp-227"><code>mpfr_integer_p</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005fj0-192"><code>mpfr_j0</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fj1-193"><code>mpfr_j1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fjn-194"><code>mpfr_jn</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fless_005fp-149"><code>mpfr_less_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005flessequal_005fp-150"><code>mpfr_lessequal_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005flessgreater_005fp-151"><code>mpfr_lessgreater_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005flgamma-187"><code>mpfr_lgamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005flngamma-186"><code>mpfr_lngamma</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005flog-155"><code>mpfr_log</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005flog10-157"><code>mpfr_log10</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005flog1p-182"><code>mpfr_log1p</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005flog2-156"><code>mpfr_log2</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fmax-233"><code>mpfr_max</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fmin-232"><code>mpfr_min</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fmul-99"><code>mpfr_mul</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005f2exp-292"><code>mpfr_mul_2exp</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-mpfr_005fmul_005f2si-126"><code>mpfr_mul_2si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005f2ui-125"><code>mpfr_mul_2ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005fq-103"><code>mpfr_mul_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005fsi-101"><code>mpfr_mul_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005fui-100"><code>mpfr_mul_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fmul_005fz-102"><code>mpfr_mul_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fnan_005fp-142"><code>mpfr_nan_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fnanflag_005fp-280"><code>mpfr_nanflag_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fneg-122"><code>mpfr_neg</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fnextabove-230"><code>mpfr_nextabove</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fnextbelow-231"><code>mpfr_nextbelow</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fnexttoward-229"><code>mpfr_nexttoward</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fnumber_005fp-144"><code>mpfr_number_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fout_005fstr-212"><code>mpfr_out_str</code></a>: <a href="#Input-and-Output-Functions">Input and Output Functions</a></li>
+<li><a href="#index-mpfr_005foverflow_005fp-279"><code>mpfr_overflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fpow-116"><code>mpfr_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fpow_005fsi-118"><code>mpfr_pow_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fpow_005fui-117"><code>mpfr_pow_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fpow_005fz-119"><code>mpfr_pow_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fprec_005fround-253"><code>mpfr_prec_round</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-mpfr_005fprint_005frnd_005fmode-255"><code>mpfr_print_rnd_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-mpfr_005frandom-235"><code>mpfr_random</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005frandom2-236"><code>mpfr_random2</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005freldiff-291"><code>mpfr_reldiff</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-mpfr_005fremainder-225"><code>mpfr_remainder</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005fremquo-226"><code>mpfr_remquo</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005frint-215"><code>mpfr_rint</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005frint_005fceil-220"><code>mpfr_rint_ceil</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005frint_005ffloor-221"><code>mpfr_rint_floor</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005frint_005fround-222"><code>mpfr_rint_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005frint_005ftrunc-223"><code>mpfr_rint_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005froot-115"><code>mpfr_root</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fround-218"><code>mpfr_round</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005fround_005fprec-254"><code>mpfr_round_prec</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-mpfr_005fsec-164"><code>mpfr_sec</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fsech-175"><code>mpfr_sech</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fset-31"><code>mpfr_set</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fd-36"><code>mpfr_set_d</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fdecimal64-38"><code>mpfr_set_decimal64</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fdefault_005fprec-26"><code>mpfr_set_default_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fdefault_005frounding_005fmode-251"><code>mpfr_set_default_rounding_mode</code></a>: <a href="#Rounding-Mode-Related-Functions">Rounding Mode Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005femax-260"><code>mpfr_set_emax</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005femin-259"><code>mpfr_set_emin</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005ferangeflag-276"><code>mpfr_set_erangeflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fexp-238"><code>mpfr_set_exp</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fset_005ff-41"><code>mpfr_set_f</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005finexflag-275"><code>mpfr_set_inexflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005finf-48"><code>mpfr_set_inf</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fld-37"><code>mpfr_set_ld</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fnan-49"><code>mpfr_set_nan</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fnanflag-274"><code>mpfr_set_nanflag</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005foverflow-273"><code>mpfr_set_overflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fprec-28"><code>mpfr_set_prec</code></a>: <a href="#Initialization-Functions">Initialization Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fprec_005fraw-289"><code>mpfr_set_prec_raw</code></a>: <a href="#Compatibility-with-MPF">Compatibility with MPF</a></li>
+<li><a href="#index-mpfr_005fset_005fq-40"><code>mpfr_set_q</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fsi-33"><code>mpfr_set_si</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fsi_005f2exp-43"><code>mpfr_set_si_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fsj-35"><code>mpfr_set_sj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fsj_005f2exp-45"><code>mpfr_set_sj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fstr-46"><code>mpfr_set_str</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fui-32"><code>mpfr_set_ui</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fui_005f2exp-42"><code>mpfr_set_ui_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fuj-34"><code>mpfr_set_uj</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fuj_005f2exp-44"><code>mpfr_set_uj_2exp</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fset_005funderflow-272"><code>mpfr_set_underflow</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fset_005fz-39"><code>mpfr_set_z</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fsetsign-240"><code>mpfr_setsign</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fsgn-146"><code>mpfr_sgn</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fsi_005fdiv-108"><code>mpfr_si_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsi_005fsub-95"><code>mpfr_si_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsignbit-239"><code>mpfr_signbit</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fsin-162"><code>mpfr_sin</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fsin_005fcos-167"><code>mpfr_sin_cos</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fsinh-173"><code>mpfr_sinh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fsqr-104"><code>mpfr_sqr</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsqrt-112"><code>mpfr_sqrt</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsqrt_005fui-113"><code>mpfr_sqrt_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fstrtofr-47"><code>mpfr_strtofr</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-mpfr_005fsub-92"><code>mpfr_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsub_005fq-98"><code>mpfr_sub_q</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsub_005fsi-96"><code>mpfr_sub_si</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsub_005fui-94"><code>mpfr_sub_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsub_005fz-97"><code>mpfr_sub_z</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fsubnormalize-266"><code>mpfr_subnormalize</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005fsum-207"><code>mpfr_sum</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fswap-50"><code>mpfr_swap</code></a>: <a href="#Assignment-Functions">Assignment Functions</a></li>
+<li><a href="#index-g_t_0040code_007bmpfr_005ft_007d-12"><code>mpfr_t</code></a>: <a href="#MPFR-Basics">MPFR Basics</a></li>
+<li><a href="#index-mpfr_005ftan-163"><code>mpfr_tan</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ftanh-174"><code>mpfr_tanh</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005ftrunc-219"><code>mpfr_trunc</code></a>: <a href="#Integer-Related-Functions">Integer Related Functions</a></li>
+<li><a href="#index-mpfr_005fui_005fdiv-106"><code>mpfr_ui_div</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fui_005fpow-121"><code>mpfr_ui_pow</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fui_005fpow_005fui-120"><code>mpfr_ui_pow_ui</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005fui_005fsub-93"><code>mpfr_ui_sub</code></a>: <a href="#Basic-Arithmetic-Functions">Basic Arithmetic Functions</a></li>
+<li><a href="#index-mpfr_005funderflow_005fp-278"><code>mpfr_underflow_p</code></a>: <a href="#Exception-Related-Functions">Exception Related Functions</a></li>
+<li><a href="#index-mpfr_005funordered_005fp-153"><code>mpfr_unordered_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005furandomb-234"><code>mpfr_urandomb</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION-243"><code>MPFR_VERSION</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION_005fMAJOR-244"><code>MPFR_VERSION_MAJOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION_005fMINOR-245"><code>MPFR_VERSION_MINOR</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION_005fNUM-248"><code>MPFR_VERSION_NUM</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION_005fPATCHLEVEL-246"><code>MPFR_VERSION_PATCHLEVEL</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-MPFR_005fVERSION_005fSTRING-247"><code>MPFR_VERSION_STRING</code></a>: <a href="#Miscellaneous-Functions">Miscellaneous Functions</a></li>
+<li><a href="#index-mpfr_005fy0-195"><code>mpfr_y0</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fy1-196"><code>mpfr_y1</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fyn-197"><code>mpfr_yn</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fzero_005fp-145"><code>mpfr_zero_p</code></a>: <a href="#Comparison-Functions">Comparison Functions</a></li>
+<li><a href="#index-mpfr_005fzeta-188"><code>mpfr_zeta</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+<li><a href="#index-mpfr_005fzeta_005fui-189"><code>mpfr_zeta_ui</code></a>: <a href="#Special-Functions">Special Functions</a></li>
+ </ul></body></html>
+
+<!--
+
+Local Variables:
+coding: iso-8859-1
+End:
+
+-->
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/components/mpfr/mpfr.license Mon May 09 11:36:28 2011 -0700
@@ -0,0 +1,857 @@
+Oracle elects to use only the GNU Lesser General Public License version
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+where a choice of LGPL/GPL license versions are made available with the
+language indicating that LGPLv2.1/GPLv2 or any later version may be
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+unspecified. Unless specifically stated otherwise, where a choice
+exists between another license and either the GPL or the LGPL, Oracle
+chooses the other license.
+------------------------------------------------------------------
+
+ GNU LESSER GENERAL PUBLIC LICENSE
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+
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+
+ NO WARRANTY
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+WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
+EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR
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+
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+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Libraries
+
+ If you develop a new library, and you want it to be of the greatest
+possible use to the public, we recommend making it free software that
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+
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+"copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the library's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; 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.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the library, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the
+ library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+
+ <signature of Ty Coon>, 1 April 1990
+ Ty Coon, President of Vice
+
+That's all there is to it!
+
+---------------------------------------------------------------------
+
+
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
+ Everyone is permitted to copy and distribute verbatim copies
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+
+ Preamble
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+ The licenses for most software are designed to take away your
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+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
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+ 0. This License applies to any program or other work which contains
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+ 4. You may not copy, modify, sublicense, or distribute the Program
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+However, parties who have received copies, or rights, from you under
+this License will not have their licenses terminated so long as such
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+ 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
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+You are not responsible for enforcing compliance by third parties to
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+
+ 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.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ 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.
+
+ <signature of Ty Coon>, 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.
+