2009-07-24 08:24:26 -04:00
|
|
|
|
This is mpir.info, produced by makeinfo version 4.13 from mpir.texi.
|
2009-02-12 09:17:32 -05:00
|
|
|
|
|
2009-03-15 11:51:47 -04:00
|
|
|
|
This manual describes how to install and use MPIR, the Multiple
|
2009-08-12 23:07:39 -04:00
|
|
|
|
Precision Integers and Rationals library, version 1.2.0.
|
2009-02-12 09:17:32 -05:00
|
|
|
|
|
|
|
|
|
|
Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,
|
|
|
|
|
|
2001, 2002, 2003, 2004, 2005, 2006 Free Software Foundation, Inc.
|
|
|
|
|
|
|
|
|
|
|
|
Copyright 2008 William Hart
|
|
|
|
|
|
|
|
|
|
|
|
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 the Front-Cover Texts being "A GNU
|
|
|
|
|
|
Manual", and with the Back-Cover Texts being "You have freedom to copy
|
|
|
|
|
|
and modify this GNU Manual, like GNU software". A copy of the license
|
2009-03-15 11:51:47 -04:00
|
|
|
|
is included in *note GNU Free Documentation License::.
|
2009-02-12 09:17:32 -05:00
|
|
|
|
|
|
|
|
|
|
INFO-DIR-SECTION GNU libraries
|
|
|
|
|
|
START-INFO-DIR-ENTRY
|
|
|
|
|
|
* mpir: (mpir). MPIR Multiple Precision Integers and Rationals Library.
|
|
|
|
|
|
END-INFO-DIR-ENTRY
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Indirect:
|
2009-08-12 23:07:39 -04:00
|
|
|
|
mpir.info-1: 990
|
2009-08-19 11:51:45 -04:00
|
|
|
|
mpir.info-2: 300378
|
2009-02-12 09:17:32 -05:00
|
|
|
|
|
|
|
|
|
|
Tag Table:
|
|
|
|
|
|
(Indirect)
|
2009-08-12 23:07:39 -04:00
|
|
|
|
Node: Top990
|
|
|
|
|
|
Node: Copying3235
|
|
|
|
|
|
Node: Introduction to MPIR5080
|
|
|
|
|
|
Node: Installing MPIR7501
|
|
|
|
|
|
Node: Build Options8637
|
|
|
|
|
|
Node: ABI and ISA24945
|
|
|
|
|
|
Node: Notes for Package Builds34372
|
|
|
|
|
|
Node: Notes for Particular Systems37490
|
|
|
|
|
|
Node: Known Build Problems44244
|
|
|
|
|
|
Node: Performance optimization47794
|
|
|
|
|
|
Node: MPIR Basics48929
|
|
|
|
|
|
Node: Headers and Libraries49583
|
|
|
|
|
|
Node: Nomenclature and Types51038
|
|
|
|
|
|
Node: Function Classes52749
|
|
|
|
|
|
Node: Variable Conventions54287
|
|
|
|
|
|
Node: Parameter Conventions55816
|
|
|
|
|
|
Node: Memory Management57880
|
|
|
|
|
|
Node: Reentrancy59012
|
|
|
|
|
|
Node: Useful Macros and Constants60449
|
|
|
|
|
|
Node: Compatibility with older versions61795
|
|
|
|
|
|
Node: Demonstration Programs62638
|
|
|
|
|
|
Node: Efficiency64509
|
|
|
|
|
|
Node: Debugging72139
|
|
|
|
|
|
Node: Profiling78708
|
|
|
|
|
|
Node: Autoconf82742
|
|
|
|
|
|
Node: Emacs84616
|
|
|
|
|
|
Node: Reporting Bugs85225
|
|
|
|
|
|
Node: Integer Functions87792
|
|
|
|
|
|
Node: Initializing Integers88571
|
|
|
|
|
|
Node: Assigning Integers90243
|
|
|
|
|
|
Node: Simultaneous Integer Init & Assign91831
|
|
|
|
|
|
Node: Converting Integers93458
|
|
|
|
|
|
Node: Integer Arithmetic96111
|
|
|
|
|
|
Node: Integer Division97714
|
|
|
|
|
|
Node: Integer Exponentiation104143
|
|
|
|
|
|
Node: Integer Roots105005
|
|
|
|
|
|
Node: Number Theoretic Functions106680
|
2009-08-17 07:53:22 -04:00
|
|
|
|
Node: Integer Comparisons113411
|
|
|
|
|
|
Node: Integer Logic and Bit Fiddling114790
|
|
|
|
|
|
Node: I/O of Integers117404
|
|
|
|
|
|
Node: Integer Random Numbers120019
|
|
|
|
|
|
Node: Integer Import and Export121795
|
|
|
|
|
|
Node: Miscellaneous Integer Functions125800
|
|
|
|
|
|
Node: Integer Special Functions127661
|
2009-08-19 11:51:45 -04:00
|
|
|
|
Node: Rational Number Functions130832
|
|
|
|
|
|
Node: Initializing Rationals132027
|
|
|
|
|
|
Node: Rational Conversions134273
|
|
|
|
|
|
Node: Rational Arithmetic136005
|
|
|
|
|
|
Node: Comparing Rationals137342
|
|
|
|
|
|
Node: Applying Integer Functions138710
|
|
|
|
|
|
Node: I/O of Rationals140194
|
|
|
|
|
|
Node: Floating-point Functions142057
|
|
|
|
|
|
Node: Initializing Floats144945
|
|
|
|
|
|
Node: Assigning Floats148643
|
|
|
|
|
|
Node: Simultaneous Float Init & Assign151211
|
|
|
|
|
|
Node: Converting Floats152741
|
|
|
|
|
|
Node: Float Arithmetic155702
|
|
|
|
|
|
Node: Float Comparison157748
|
|
|
|
|
|
Node: I/O of Floats159100
|
|
|
|
|
|
Node: Miscellaneous Float Functions161426
|
|
|
|
|
|
Node: Low-level Functions163327
|
|
|
|
|
|
Node: Random Number Functions183766
|
|
|
|
|
|
Node: Random State Initialization184836
|
|
|
|
|
|
Node: Random State Seeding186899
|
|
|
|
|
|
Node: Random State Miscellaneous188289
|
|
|
|
|
|
Node: Formatted Output188931
|
|
|
|
|
|
Node: Formatted Output Strings189177
|
|
|
|
|
|
Node: Formatted Output Functions194417
|
|
|
|
|
|
Node: C++ Formatted Output198494
|
|
|
|
|
|
Node: Formatted Input201181
|
|
|
|
|
|
Node: Formatted Input Strings201418
|
|
|
|
|
|
Node: Formatted Input Functions206080
|
|
|
|
|
|
Node: C++ Formatted Input209053
|
|
|
|
|
|
Node: C++ Class Interface210961
|
|
|
|
|
|
Node: C++ Interface General211966
|
|
|
|
|
|
Node: C++ Interface Integers215049
|
|
|
|
|
|
Node: C++ Interface Rationals218483
|
|
|
|
|
|
Node: C++ Interface Floats222162
|
|
|
|
|
|
Node: C++ Interface Random Numbers227457
|
|
|
|
|
|
Node: C++ Interface Limitations229587
|
|
|
|
|
|
Node: BSD Compatible Functions232433
|
|
|
|
|
|
Node: Custom Allocation232651
|
|
|
|
|
|
Node: Language Bindings236843
|
|
|
|
|
|
Node: Algorithms240859
|
|
|
|
|
|
Node: Multiplication Algorithms241564
|
|
|
|
|
|
Node: Basecase Multiplication242499
|
|
|
|
|
|
Node: Karatsuba Multiplication244411
|
|
|
|
|
|
Node: Toom 3-Way Multiplication248041
|
|
|
|
|
|
Node: FFT Multiplication254450
|
|
|
|
|
|
Node: Other Multiplication259788
|
|
|
|
|
|
Node: Division Algorithms262274
|
|
|
|
|
|
Node: Single Limb Division262622
|
|
|
|
|
|
Node: Basecase Division265542
|
|
|
|
|
|
Node: Divide and Conquer Division266746
|
|
|
|
|
|
Node: Exact Division268984
|
|
|
|
|
|
Node: Exact Remainder272152
|
|
|
|
|
|
Node: Small Quotient Division274445
|
|
|
|
|
|
Node: Greatest Common Divisor Algorithms276044
|
|
|
|
|
|
Node: Binary GCD276318
|
|
|
|
|
|
Node: Accelerated GCD278997
|
|
|
|
|
|
Node: Extended GCD280796
|
|
|
|
|
|
Node: Jacobi Symbol282467
|
|
|
|
|
|
Node: Powering Algorithms283384
|
|
|
|
|
|
Node: Normal Powering Algorithm283648
|
|
|
|
|
|
Node: Modular Powering Algorithm284177
|
|
|
|
|
|
Node: Root Extraction Algorithms285241
|
|
|
|
|
|
Node: Square Root Algorithm285557
|
|
|
|
|
|
Node: Nth Root Algorithm287700
|
|
|
|
|
|
Node: Perfect Square Algorithm288486
|
|
|
|
|
|
Node: Perfect Power Algorithm290573
|
|
|
|
|
|
Node: Radix Conversion Algorithms291195
|
|
|
|
|
|
Node: Binary to Radix291572
|
|
|
|
|
|
Node: Radix to Binary295503
|
|
|
|
|
|
Node: Other Algorithms297435
|
|
|
|
|
|
Node: Prime Testing Algorithm297789
|
|
|
|
|
|
Node: Factorial Algorithm298974
|
|
|
|
|
|
Node: Binomial Coefficients Algorithm300378
|
|
|
|
|
|
Node: Fibonacci Numbers Algorithm301273
|
|
|
|
|
|
Node: Lucas Numbers Algorithm303749
|
|
|
|
|
|
Node: Random Number Algorithms304471
|
|
|
|
|
|
Node: Assembler Coding306595
|
|
|
|
|
|
Node: Assembler Code Organisation307572
|
|
|
|
|
|
Node: Assembler Basics308545
|
|
|
|
|
|
Node: Assembler Carry Propagation309704
|
|
|
|
|
|
Node: Assembler Cache Handling311542
|
|
|
|
|
|
Node: Assembler Functional Units313710
|
|
|
|
|
|
Node: Assembler Floating Point315331
|
|
|
|
|
|
Node: Assembler SIMD Instructions319114
|
|
|
|
|
|
Node: Assembler Software Pipelining320103
|
|
|
|
|
|
Node: Assembler Loop Unrolling321171
|
|
|
|
|
|
Node: Assembler Writing Guide323391
|
|
|
|
|
|
Node: Internals326161
|
|
|
|
|
|
Node: Integer Internals326675
|
|
|
|
|
|
Node: Rational Internals328932
|
|
|
|
|
|
Node: Float Internals330172
|
|
|
|
|
|
Node: Raw Output Internals337500
|
|
|
|
|
|
Node: C++ Interface Internals338695
|
|
|
|
|
|
Node: Contributors341994
|
|
|
|
|
|
Node: References346928
|
|
|
|
|
|
Node: GNU Free Documentation License351984
|
|
|
|
|
|
Node: Concept Index374431
|
|
|
|
|
|
Node: Function Index420429
|
2009-02-12 09:17:32 -05:00
|
|
|
|
|
|
|
|
|
|
End Tag Table
|
