Annotation of OpenXM/src/kan96xx/gmp-2.0.2/gmp.texi, Revision 1.1
1.1 ! maekawa 1: \input texinfo @c -*-texinfo-*-
! 2: @c %**start of header
! 3: @setfilename gmp.info
! 4: @settitle GNU MP 2.0.2
! 5: @synindex tp fn
! 6: @iftex
! 7: @afourpaper
! 8: @end iftex
! 9: @comment %**end of header
! 10:
! 11: @ifinfo
! 12: @format
! 13: START-INFO-DIR-ENTRY
! 14: * gmp: (gmp.info). GNU Multiple Precision Arithmetic Library.
! 15: END-INFO-DIR-ENTRY
! 16: @end format
! 17: @end ifinfo
! 18:
! 19: @c smallbook
! 20:
! 21: @iftex
! 22: @finalout
! 23: @end iftex
! 24:
! 25: @c Note: the edition number is listed in *three* places; please update
! 26: @c all three. Also, update the month and year where appropriate.
! 27:
! 28: @c ==> Update edition number for settitle and subtitle, and in the
! 29: @c ==> following paragraph; update date, too.
! 30:
! 31:
! 32: @ifinfo
! 33: This file documents GNU MP, a library for arbitrary-precision arithmetic.
! 34:
! 35: Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
! 36:
! 37: Permission is granted to make and distribute verbatim copies of
! 38: this manual provided the copyright notice and this permission notice
! 39: are preserved on all copies.
! 40:
! 41: @ignore
! 42: Permission is granted to process this file through TeX and print the
! 43: results, provided the printed document carries copying permission
! 44: notice identical to this one except for the removal of this paragraph
! 45: (this paragraph not being relevant to the printed manual).
! 46:
! 47: @end ignore
! 48: Permission is granted to copy and distribute modified versions of this
! 49: manual under the conditions for verbatim copying, provided that the entire
! 50: resulting derived work is distributed under the terms of a permission
! 51: notice identical to this one.
! 52:
! 53: Permission is granted to copy and distribute translations of this manual
! 54: into another language, under the above conditions for modified versions,
! 55: except that this permission notice may be stated in a translation approved
! 56: by the Foundation.
! 57: @end ifinfo
! 58:
! 59: @setchapternewpage on
! 60: @titlepage
! 61: @c use the new format for titles
! 62:
! 63: @title GNU MP
! 64: @subtitle The GNU Multiple Precision Arithmetic Library
! 65: @subtitle Edition 2.0.2
! 66: @subtitle June 1996
! 67:
! 68: @author by Torbj@"orn Granlund, TMG Datakonsult
! 69:
! 70: @c Include the Distribution inside the titlepage so
! 71: @c that headings are turned off.
! 72:
! 73: @tex
! 74: \global\parindent=0pt
! 75: \global\parskip=8pt
! 76: \global\baselineskip=13pt
! 77: @end tex
! 78:
! 79: @page
! 80: @vskip 0pt plus 1filll
! 81: Copyright @copyright{} 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
! 82:
! 83: @sp 2
! 84:
! 85: Published by the Free Software Foundation @*
! 86: 59 Temple Place - Suite 330 @*
! 87: Boston, MA 02111-1307, USA @*
! 88:
! 89: Permission is granted to make and distribute verbatim copies of
! 90: this manual provided the copyright notice and this permission notice
! 91: are preserved on all copies.
! 92:
! 93: Permission is granted to copy and distribute modified versions of this
! 94: manual under the conditions for verbatim copying, provided that the entire
! 95: resulting derived work is distributed under the terms of a permission
! 96: notice identical to this one.
! 97:
! 98: Permission is granted to copy and distribute translations of this manual
! 99: into another language, under the above conditions for modified versions,
! 100: except that this permission notice may be stated in a translation approved
! 101: by the Foundation.
! 102: @end titlepage
! 103: @headings double
! 104:
! 105: @ifinfo
! 106: @node Top, Copying, (dir), (dir)
! 107:
! 108: @top GNU MP
! 109:
! 110: This manual documents how to install and use the GNU multiple precision
! 111: arithmetic library, version 2.0.2.
! 112:
! 113: @end ifinfo
! 114:
! 115: @menu
! 116: * Copying:: GMP Copying Conditions (LGPL).
! 117: * Introduction to MP:: Brief introduction to GNU MP.
! 118: * Installing MP:: How to configure and compile the MP library.
! 119: * MP Basics:: What every MP user should now.
! 120: * Reporting Bugs:: How to usefully report bugs.
! 121: * Integer Functions:: Functions for arithmetic on signed integers.
! 122: * Rational Number Functions:: Functions for arithmetic on rational numbers.
! 123: * Floating-point Functions:: Functions for arithmetic on floats.
! 124: * Low-level Functions:: Fast functions for natural numbers.
! 125: * BSD Compatible Functions:: All functions found in BSD MP.
! 126: * Custom Allocation:: How to customize the internal allocation.
! 127:
! 128: * Contributors::
! 129: * References::
! 130: * Concept Index::
! 131: * Function Index::
! 132: @end menu
! 133:
! 134: @node Copying, Introduction to MP, Top, Top
! 135: @comment node-name, next, previous, up
! 136: @unnumbered GNU MP Copying Conditions
! 137: @cindex Copying conditions
! 138: @cindex Conditions for copying GNU MP
! 139:
! 140: This library is @dfn{free}; this means that everyone is free to use it and
! 141: free to redistribute it on a free basis. The library is not in the public
! 142: domain; it is copyrighted and there are restrictions on its distribution, but
! 143: these restrictions are designed to permit everything that a good cooperating
! 144: citizen would want to do. What is not allowed is to try to prevent others
! 145: from further sharing any version of this library that they might get from
! 146: you.@refill
! 147:
! 148: Specifically, we want to make sure that you have the right to give away copies
! 149: of the library, that you receive source code or else can get it if you want
! 150: it, that you can change this library or use pieces of it in new free programs,
! 151: and that you know you can do these things.@refill
! 152:
! 153: To make sure that everyone has such rights, we have to forbid you to deprive
! 154: anyone else of these rights. For example, if you distribute copies of the GNU
! 155: MP library, you must give the recipients all the rights that you have. You
! 156: must make sure that they, too, receive or can get the source code. And you
! 157: must tell them their rights.@refill
! 158:
! 159: Also, for our own protection, we must make certain that everyone finds out
! 160: that there is no warranty for the GNU MP library. If it is modified by
! 161: someone else and passed on, we want their recipients to know that what they
! 162: have is not what we distributed, so that any problems introduced by others
! 163: will not reflect on our reputation.@refill
! 164:
! 165: The precise conditions of the license for the GNU MP library are found in the
! 166: Library General Public License that accompany the source code.@refill
! 167:
! 168: @node Introduction to MP, Installing MP, Copying, Top
! 169: @comment node-name, next, previous, up
! 170: @chapter Introduction to GNU MP
! 171:
! 172:
! 173: GNU MP is a portable library written in C for arbitrary precision arithmetic
! 174: on integers, rational numbers, and floating-point numbers. It aims to provide
! 175: the fastest possible arithmetic for all applications that need higher
! 176: precision than is directly supported by the basic C types.
! 177:
! 178: Many applications use just a few hundred bits of precision; but some
! 179: applications may need thousands or even millions of bits. MP is designed to
! 180: give good performance for both, by choosing algorithms based on the sizes of
! 181: the operands, and by carefully keeping the overhead at a minimum.
! 182:
! 183: The speed of MP is achieved by using fullwords as the basic arithmetic type,
! 184: by using sophisticated algorithms, by including carefully optimized assembly
! 185: code for the most common inner loops for many different CPUs, and by a general
! 186: emphasis on speed (as opposed to simplicity or elegance).
! 187:
! 188: There is carefully optimized assembly code for these CPUs: DEC Alpha, Amd
! 189: 29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, Intel i960, Motorola
! 190: MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC, National
! 191: NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, generic SPARCv8,
! 192: and DEC VAX. Some optimizations also for ARM, Clipper, IBM ROMP (RT), and
! 193: Pyramid AP/XP.
! 194:
! 195: This version of MP is released under a more liberal license than previous
! 196: versions. It is now permitted to link MP to non-free programs, as long as MP
! 197: source code is provided when distributing the non-free program.
! 198:
! 199:
! 200: @section How to use this Manual
! 201:
! 202: Everyone should read @ref{MP Basics}. If you need to install the library
! 203: yourself, you need to read @ref{Installing MP}, too.
! 204:
! 205: The rest of the manual can be used for later reference, although it is
! 206: probably a good idea to glance through it.
! 207:
! 208:
! 209: @node Installing MP, MP Basics, Introduction to MP, Top
! 210: @comment node-name, next, previous, up
! 211: @chapter Installing MP
! 212: @cindex Installation
! 213:
! 214: To build MP, you first have to configure it for your CPU and operating system.
! 215: You need a C compiler, preferably GCC, but any reasonable compiler should
! 216: work. And you need a standard Unix @samp{make} program, plus some other
! 217: standard Unix utility programs.
! 218:
! 219: (If you're on an MS-DOS machine, your can build MP using @file{make.bat}. It
! 220: requires that djgpp is installed. It does not require configuration, nor is
! 221: @samp{make} needed; @file{make.bat} both configures and builds the library.)
! 222:
! 223: Here are the steps needed to install the library on Unix systems:
! 224:
! 225: @enumerate
! 226: @item
! 227: In most cases, @samp{./configure --target=cpu-vendor-os}, should work both for
! 228: native and cross-compilation. If you get error messages, your machine might
! 229: not be supported.
! 230:
! 231: If you want to compile in a separate object directory, cd to that directory,
! 232: and prefix the configure command with the path to the MP source directory.
! 233: Not all @samp{make} programs have the necessary features to support this. In
! 234: particular, SunOS and Slowaris @samp{make} have bugs that makes them unable to
! 235: build from a separate object directory. Use GNU @samp{make} instead.
! 236:
! 237: In addition to the standard cpu-vendor-os tuples, MP recognizes sparc8 and
! 238: supersparc as valid CPU names. Specifying these CPU names for relevant
! 239: systems will improve performance significantly.
! 240:
! 241: In general, if you want a library that runs as fast as possible, you should
! 242: make sure you configure MP for the exact CPU type your system uses.
! 243:
! 244: If you have @code{gcc} in your @code{PATH}, it will be used by default. To
! 245: override this, pass @samp{-with-gcc=no} to @file{configure}.
! 246:
! 247: @item
! 248: @samp{make}
! 249:
! 250: This will compile MP, and create a library archive file @file{libgmp.a} in the
! 251: working directory.
! 252:
! 253: @item
! 254: @samp{make check}
! 255:
! 256: This will make sure MP was built correctly. If you get error messages, please
! 257: report this to @samp{bug-gmp@@prep.ai.mit.edu}. (@xref{Reporting Bugs}, for
! 258: information on what to include in useful bug reports.)
! 259:
! 260: @item
! 261: @samp{make install}
! 262:
! 263: This will copy the file @file{gmp.h} and @file{libgmp.a}, as well as the info
! 264: files, to @file{/usr/local} (or if you passed the @samp{--prefix} option to
! 265: @file{configure}, to the directory given as argument to @samp{--prefix}).
! 266: @end enumerate
! 267:
! 268: @noindent
! 269: If you wish to build and install the BSD MP compatible functions, use
! 270: @samp{make libmp.a} and @samp{make install-bsdmp}.
! 271:
! 272: There are some other useful make targets:
! 273:
! 274: @itemize @bullet
! 275: @item
! 276: @samp{doc}
! 277:
! 278: Create a DVI version of the manual, in @file{gmp.dvi} and a set of info files,
! 279: in @file{gmp.info}, @file{gmp.info-1}, @file{gmp.info-2}, etc.
! 280:
! 281: @item
! 282: @samp{ps}
! 283:
! 284: Create a Postscript version of the manual, in @file{gmp.ps}.
! 285:
! 286: @item
! 287: @samp{html}
! 288:
! 289: Create a HTML version of the manual, in @file{gmp.html}.
! 290:
! 291: @item
! 292: @samp{clean}
! 293:
! 294: Delete all object files and archive files, but not the configuration files.
! 295:
! 296: @item
! 297: @samp{distclean}
! 298:
! 299: Delete all files not included in the distribution.
! 300:
! 301: @item
! 302: @samp{uninstall}
! 303:
! 304: Delete all files copied by @samp{make install}.
! 305: @end itemize
! 306:
! 307:
! 308: @section Known Build Problems
! 309:
! 310: GCC 2.7.2 (as well as 2.6.3) for the RS/6000 and PowerPC can not be used to
! 311: compile MP, due to a bug in GCC. If you want to use GCC for these machines,
! 312: you need to apply the patch below to GCC, or use a later version of the
! 313: compiler.
! 314:
! 315: If you are on a Sequent Symmetry, use the GNU assembler instead of the
! 316: system's assembler, since the latter has serious bugs.
! 317:
! 318: The system compiler on NeXT is a massacred and old gcc, even if the compiler
! 319: calls itself @file{cc}. This compiler cannot be used to build MP. You need
! 320: to get a real gcc, and install that before you compile MP. (NeXT might have
! 321: fixed this in newer releases of their system.)
! 322:
! 323: The system C compiler under SunOS 4 has a bug that makes it miscompile
! 324: mpq/get_d.c. This will make @samp{make check} fail.
! 325:
! 326: Please report other problems to @samp{bug-gmp@@prep.ai.mit.edu}.
! 327: @xref{Reporting Bugs}.
! 328:
! 329:
! 330: Patch to apply to GCC 2.6.3 and 2.7.2:
! 331:
! 332: @example
! 333: *** config/rs6000/rs6000.md Sun Feb 11 08:22:11 1996
! 334: --- config/rs6000/rs6000.md.new Sun Feb 18 03:33:37 1996
! 335: ***************
! 336: *** 920,926 ****
! 337: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
! 338: (not:SI (match_dup 1)))]
! 339: ""
! 340: ! "nor. %0,%2,%1"
! 341: [(set_attr "type" "compare")])
! 342:
! 343: (define_insn ""
! 344: --- 920,926 ----
! 345: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
! 346: (not:SI (match_dup 1)))]
! 347: ""
! 348: ! "nor. %0,%1,%1"
! 349: [(set_attr "type" "compare")])
! 350:
! 351: (define_insn ""
! 352: @end example
! 353:
! 354: @node MP Basics, Reporting Bugs, Installing MP, Top
! 355: @comment node-name, next, previous, up
! 356: @chapter MP Basics
! 357:
! 358:
! 359: @cindex @file{gmp.h}
! 360: All declarations needed to use MP are collected in the include file
! 361: @file{gmp.h}. It is designed to work with both C and C++ compilers.
! 362:
! 363:
! 364: @section Nomenclature and Types
! 365:
! 366: @cindex Integer
! 367: @tindex @code{mpz_t}
! 368: @noindent
! 369: In this manual, @dfn{integer} usually means a multiple precision integer, as
! 370: defined by the MP library. The C data type for such integers is @code{mpz_t}.
! 371: Here are some examples of how to declare such integers:
! 372:
! 373: @example
! 374: mpz_t sum;
! 375:
! 376: struct foo @{ mpz_t x, y; @};
! 377:
! 378: mpz_t vec[20];
! 379: @end example
! 380:
! 381: @cindex Rational number
! 382: @tindex @code{mpq_t}
! 383: @noindent
! 384: @dfn{Rational number} means a multiple precision fraction. The C data type
! 385: for these fractions is @code{mpq_t}. For example:
! 386:
! 387: @example
! 388: mpq_t quotient;
! 389: @end example
! 390:
! 391: @cindex Floating-point number
! 392: @tindex @code{mpf_t}
! 393: @noindent
! 394: @dfn{Floating point number} or @dfn{Float} for short, is an arbitrary precision
! 395: mantissa with an limited precision exponent. The C data type for such objects
! 396: is @code{mpf_t}.
! 397:
! 398: @cindex Limb
! 399: @tindex @code{mp_limb_t}
! 400: @noindent
! 401: A @dfn{limb} means the part of a multi-precision number that fits in a single
! 402: word. (We chose this word because a limb of the human body is analogous to a
! 403: digit, only larger, and containing several digits.) Normally a limb contains
! 404: 32 or 64 bits. The C data type for a limb is @code{mp_limb_t}.
! 405:
! 406:
! 407: @section Function Classes
! 408:
! 409: There are six classes of functions in the MP library:
! 410:
! 411: @enumerate
! 412: @item
! 413: Functions for signed integer arithmetic, with names beginning with
! 414: @code{mpz_}. The associated type is @code{mpz_t}. There are about 100
! 415: functions in this class.
! 416:
! 417: @item
! 418: Functions for rational number arithmetic, with names beginning with
! 419: @code{mpq_}. The associated type is @code{mpq_t}. There are about 20
! 420: functions in this class, but the functions in the previous class can be used
! 421: for performing arithmetic on the numerator and denominator separately.
! 422:
! 423: @item
! 424: Functions for floating-point arithmetic, with names beginning with
! 425: @code{mpf_}. The associated type is @code{mpf_t}. There are about 50
! 426: functions is this class.
! 427:
! 428: @item
! 429: Functions compatible with Berkeley MP, such as @code{itom}, @code{madd}, and
! 430: @code{mult}. The associated type is @code{MINT}.
! 431:
! 432: @item
! 433: Fast low-level functions that operate on natural numbers. These are used by
! 434: the functions in the preceding groups, and you can also call them directly
! 435: from very time-critical user programs. These functions' names begin with
! 436: @code{mpn_}. There are about 30 (hard-to-use) functions in this class.
! 437:
! 438: The associated type is array of @code{mp_limb_t}.
! 439:
! 440: @item
! 441: Miscellaneous functions. Functions for setting up custom allocation.
! 442: @end enumerate
! 443:
! 444:
! 445: @section MP Variable Conventions
! 446:
! 447: As a general rule, all MP functions expect output arguments before input
! 448: arguments. This notation is based on an analogy with the assignment operator.
! 449: (The BSD MP compatibility functions disobey this rule, having the output
! 450: argument(s) last.)
! 451:
! 452: MP allows you to use the same variable for both input and output in the same
! 453: expression. For example, the main function for integer multiplication,
! 454: @code{mpz_mul}, can be used like this: @code{mpz_mul (x, x, x)}. This
! 455: computes the square of @var{x} and puts the result back in @var{x}.
! 456:
! 457: Before you can assign to an MP variable, you need to initialize it by calling
! 458: one of the special initialization functions. When you're done with a
! 459: variable, you need to clear it out, using one of the functions for that
! 460: purpose. Which function to use depends on the type of variable. See the
! 461: chapters on integer functions, rational number functions, and floating-point
! 462: functions for details.
! 463:
! 464: A variable should only be initialized once, or at least cleared out between
! 465: each initialization. After a variable has been initialized, it may be
! 466: assigned to any number of times.
! 467:
! 468: For efficiency reasons, avoid to initialize and clear out a variable in loops.
! 469: Instead, initialize it before entering the loop, and clear it out after the
! 470: loop has exited.
! 471:
! 472: You don't need to be concerned about allocating additional space for MP
! 473: variables. All functions in MP automatically allocate additional space when a
! 474: variable does not already have enough space. They do not, however, reduce the
! 475: space when a smaller number is stored in the object. Most of the time, this
! 476: policy is best, since it avoids frequent re-allocation.
! 477:
! 478:
! 479: @section Useful Macros and Constants
! 480:
! 481: @deftypevr {Global Constant} {const int} mp_bits_per_limb
! 482: The number of bits per limb.
! 483: @end deftypevr
! 484:
! 485: @defmac __GNU_MP_VERSION
! 486: @defmacx __GNU_MP_VERSION_MINOR
! 487: The major and minor MP version, respectively, as integers.
! 488: @end defmac
! 489:
! 490: @section Compatibility with Version 1.x
! 491:
! 492: This version of MP is upward compatible with previous versions of MP, with a
! 493: few exceptions.
! 494:
! 495: @enumerate
! 496: @item Integer division functions round the result differently. The old
! 497: functions (@code{mpz_div}, @code{mpz_divmod}, @code{mpz_mdiv},
! 498: @code{mpz_mdivmod}, etc) now all use floor rounding (i.e., they round the
! 499: quotient to @minus{}infinity). There are a lot of new functions for integer
! 500: division, giving the user better control over the rounding.
! 501:
! 502: @item The function @code{mpz_mod} now compute the true @strong{mod} function.
! 503:
! 504: @item The functions @code{mpz_powm} and @code{mpz_powm_ui} now use
! 505: @strong{mod} for reduction.
! 506:
! 507: @item The assignment functions for rational numbers do no longer canonicalize
! 508: their results. In the case a non-canonical result could arise from an
! 509: assignment, the user need to insert an explicit call to
! 510: @code{mpq_canonicalize}. This change was made for efficiency.
! 511:
! 512: @item Output generated by @code{mpz_out_raw} in this release cannot be read
! 513: by @code{mpz_inp_raw} in previous releases. This change was made for making
! 514: the file format truly portable between machines with different word sizes.
! 515:
! 516: @item Several @code{mpn} functions have changed. But they were intentionally
! 517: undocumented in previous releases.
! 518:
! 519: @item The functions @code{mpz_cmp_ui}, @code{mpz_cmp_si}, and @code{mpq_cmp_ui}
! 520: are now implementated as macros, and thereby sometimes evaluate their
! 521: arguments multiple times.
! 522:
! 523: @item The functions @code{mpz_pow_ui} and @code{mpz_ui_pow_ui} now yield 1
! 524: for 0^0. (In version 1, they yielded 0.)
! 525:
! 526: @end enumerate
! 527:
! 528:
! 529: @section Getting the Latest Version of MP
! 530:
! 531: The latest version of the MP library is available by anonymous ftp from
! 532: from @samp{prep.ai.mit.edu}. The file name is
! 533: @file{/pub/gnu/gmp-M.N.tar.gz}. Many sites around the world mirror
! 534: @samp{prep}; please use a mirror site near you.
! 535:
! 536: @node Reporting Bugs, Integer Functions, MP Basics, Top
! 537: @comment node-name, next, previous, up
! 538: @chapter Reporting Bugs
! 539: @cindex Reporting bugs
! 540:
! 541: If you think you have found a bug in the MP library, please investigate it and
! 542: report it. We have made this library available to you, and it is not to ask
! 543: too much from you, to ask you to report the bugs that you find.
! 544:
! 545: There are a few things you should think about when you put your bug report
! 546: together.
! 547:
! 548: You have to send us a test case that makes it possible for us to reproduce the
! 549: bug. Include instructions on how to run the test case.
! 550:
! 551: You also have to explain what is wrong; if you get a crash, or if the results
! 552: printed are incorrect and in that case, in what way.
! 553:
! 554: It is not uncommon that an observed problem is actually due to a bug in the
! 555: compiler used when building MP; the MP code tends to explore interesting
! 556: corners in compilers. Therefore, please include compiler version information
! 557: in your bug report. This can be extracted using @samp{what `which cc`}, or,
! 558: if you're using gcc, @samp{gcc -v}. Also, include the output from @samp{uname
! 559: -a}.
! 560:
! 561: If your bug report is good, we will do our best to help you to get a corrected
! 562: version of the library; if the bug report is poor, we won't do anything about
! 563: it (aside of chiding you to send better bug reports).
! 564:
! 565: Send your bug report to: @samp{bug-gmp@@prep.ai.mit.edu}.
! 566:
! 567: If you think something in this manual is unclear, or downright incorrect, or if
! 568: the language needs to be improved, please send a note to the same address.
! 569:
! 570:
! 571: @node Integer Functions, Rational Number Functions, Reporting Bugs, Top
! 572: @comment node-name, next, previous, up
! 573: @chapter Integer Functions
! 574: @cindex Integer functions
! 575:
! 576: This chapter describes the MP functions for performing integer arithmetic.
! 577: These functions start with the prefix @code{mpz_}.
! 578:
! 579: Arbitrary precision integers are stored in objects of type @code{mpz_t}.
! 580:
! 581: @menu
! 582: * Initializing Integers::
! 583: * Assigning Integers::
! 584: * Simultaneous Integer Init & Assign::
! 585: * Converting Integers::
! 586: * Integer Arithmetic::
! 587: * Comparison Functions::
! 588: * Integer Logic and Bit Fiddling::
! 589: * I/O of Integers::
! 590: * Miscellaneous Integer Functions::
! 591: @end menu
! 592:
! 593: @node Initializing Integers, Assigning Integers, , Integer Functions
! 594: @comment node-name, next, previous, up
! 595: @section Initialization and Assignment Functions
! 596:
! 597: The functions for integer arithmetic assume that all integer objects are
! 598: initialized. You do that by calling the function @code{mpz_init}.
! 599:
! 600: @deftypefun void mpz_init (mpz_t @var{integer})
! 601: Initialize @var{integer} with limb space and set the initial numeric value to
! 602: 0. Each variable should normally only be initialized once, or at least cleared
! 603: out (using @code{mpz_clear}) between each initialization.
! 604: @end deftypefun
! 605:
! 606: Here is an example of using @code{mpz_init}:
! 607:
! 608: @example
! 609: @{
! 610: mpz_t integ;
! 611: mpz_init (integ);
! 612: @dots{}
! 613: mpz_add (integ, @dots{});
! 614: @dots{}
! 615: mpz_sub (integ, @dots{});
! 616:
! 617: /* Unless the program is about to exit, do ... */
! 618: mpz_clear (integ);
! 619: @}
! 620: @end example
! 621:
! 622: @noindent
! 623: As you can see, you can store new values any number of times, once an
! 624: object is initialized.
! 625:
! 626: @deftypefun void mpz_clear (mpz_t @var{integer})
! 627: Free the limb space occupied by @var{integer}. Make sure to call this
! 628: function for all @code{mpz_t} variables when you are done with them.
! 629: @end deftypefun
! 630:
! 631: @deftypefun {void *} _mpz_realloc (mpz_t @var{integer}, mp_size_t @var{new_alloc})
! 632: Change the limb space allocation to @var{new_alloc} limbs. This function is
! 633: not normally called from user code, but it can be used to give memory back to
! 634: the heap, or to increase the space of a variable to avoid repeated automatic
! 635: re-allocation.
! 636: @end deftypefun
! 637:
! 638: @deftypefun void mpz_array_init (mpz_t @var{integer_array}[], size_t @var{array_size}, mp_size_t @var{fixed_num_bits})
! 639: Allocate @strong{fixed} limb space for all @var{array_size} integers in
! 640: @var{integer_array}. The fixed allocation for each integer in the array is
! 641: enough to store @var{fixed_num_bits}. If the fixed space will be insufficient
! 642: for storing the result of a subsequent calculation, the result is
! 643: unpredictable.
! 644:
! 645: This function is useful for decreasing the working set for some algorithms
! 646: that use large integer arrays.
! 647:
! 648: There is no way to de-allocate the storage allocated by this function.
! 649: Don't call @code{mpz_clear}!
! 650: @end deftypefun
! 651:
! 652:
! 653: @node Assigning Integers, Simultaneous Integer Init & Assign, Initializing Integers, Integer Functions
! 654: @comment node-name, next, previous, up
! 655: @subsection Assignment Functions
! 656: @cindex Integer assignment functions
! 657:
! 658: These functions assign new values to already initialized integers
! 659: (@pxref{Initializing Integers}).
! 660:
! 661: @deftypefun void mpz_set (mpz_t @var{rop}, mpz_t @var{op})
! 662: @deftypefunx void mpz_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 663: @deftypefunx void mpz_set_si (mpz_t @var{rop}, signed long int @var{op})
! 664: @deftypefunx void mpz_set_d (mpz_t @var{rop}, double @var{op})
! 665: @deftypefunx void mpz_set_q (mpz_t @var{rop}, mpq_t @var{op})
! 666: @deftypefunx void mpz_set_f (mpz_t @var{rop}, mpf_t @var{op})
! 667: Set the value of @var{rop} from @var{op}.
! 668: @end deftypefun
! 669:
! 670: @deftypefun int mpz_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
! 671: Set the value of @var{rop} from @var{str}, a '\0'-terminated C string in base
! 672: @var{base}. White space is allowed in the string, and is simply ignored. The
! 673: base may vary from 2 to 36. If @var{base} is 0, the actual base is determined
! 674: from the leading characters: if the first two characters are `0x' or `0X',
! 675: hexadecimal is assumed, otherwise if the first character is `0', octal is
! 676: assumed, otherwise decimal is assumed.
! 677:
! 678: This function returns 0 if the entire string up to the '\0' is a valid
! 679: number in base @var{base}. Otherwise it returns @minus{}1.
! 680: @end deftypefun
! 681:
! 682:
! 683: @node Simultaneous Integer Init & Assign, Converting Integers, Assigning Integers, Integer Functions
! 684: @comment node-name, next, previous, up
! 685: @subsection Combined Initialization and Assignment Functions
! 686: @cindex Initialization and assignment functions
! 687:
! 688: For convenience, MP provides a parallel series of initialize-and-set functions
! 689: which initialize the output and then store the value there. These functions'
! 690: names have the form @code{mpz_init_set@dots{}}
! 691:
! 692: Here is an example of using one:
! 693:
! 694: @example
! 695: @{
! 696: mpz_t pie;
! 697: mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10);
! 698: @dots{}
! 699: mpz_sub (pie, @dots{});
! 700: @dots{}
! 701: mpz_clear (pie);
! 702: @}
! 703: @end example
! 704:
! 705: @noindent
! 706: Once the integer has been initialized by any of the @code{mpz_init_set@dots{}}
! 707: functions, it can be used as the source or destination operand for the ordinary
! 708: integer functions. Don't use an initialize-and-set function on a variable
! 709: already initialized!
! 710:
! 711: @deftypefun void mpz_init_set (mpz_t @var{rop}, mpz_t @var{op})
! 712: @deftypefunx void mpz_init_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 713: @deftypefunx void mpz_init_set_si (mpz_t @var{rop}, signed long int @var{op})
! 714: @deftypefunx void mpz_init_set_d (mpz_t @var{rop}, double @var{op})
! 715: Initialize @var{rop} with limb space and set the initial numeric value from
! 716: @var{op}.
! 717: @end deftypefun
! 718:
! 719: @deftypefun int mpz_init_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
! 720: Initialize @var{rop} and set its value like @code{mpz_set_str} (see its
! 721: documentation above for details).
! 722:
! 723: If the string is a correct base @var{base} number, the function returns 0;
! 724: if an error occurs it returns @minus{}1. @var{rop} is initialized even if
! 725: an error occurs. (I.e., you have to call @code{mpz_clear} for it.)
! 726: @end deftypefun
! 727:
! 728:
! 729: @node Converting Integers, Integer Arithmetic, Simultaneous Integer Init & Assign, Integer Functions
! 730: @comment node-name, next, previous, up
! 731: @section Conversion Functions
! 732: @cindex Integer conversion functions
! 733: @cindex Conversion functions
! 734:
! 735: This section describes functions for converting arbitrary precision integers
! 736: to standard C types. Functions for converting @emph{to} arbitrary
! 737: precision integers are described in @ref{Assigning Integers} and @ref{I/O of
! 738: Integers}.
! 739:
! 740: @deftypefun {unsigned long int} mpz_get_ui (mpz_t @var{op})
! 741: Return the least significant part from @var{op}. This function combined
! 742: with @* @code{mpz_tdiv_q_2exp(@dots{}, @var{op}, CHAR_BIT*sizeof(unsigned
! 743: long int))} can be used to extract the limbs of an integer.
! 744: @end deftypefun
! 745:
! 746: @deftypefun {signed long int} mpz_get_si (mpz_t @var{op})
! 747: If @var{op} fits into a @code{signed long int} return the value of @var{op}.
! 748: Otherwise return the least significant part of @var{op}, with the same sign
! 749: as @var{op}.
! 750:
! 751: If @var{op} is too large to fit in a @code{signed long int}, the returned
! 752: result is probably not very useful. @c To find out if the value will fit, use
! 753: @c the function @code{mpz_fits_si}.
! 754: @end deftypefun
! 755:
! 756: @deftypefun double mpz_get_d (mpz_t @var{op})
! 757: Convert @var{op} to a double.
! 758: @end deftypefun
! 759:
! 760: @deftypefun {char *} mpz_get_str (char *@var{str}, int @var{base}, mpz_t @var{op})
! 761: Convert @var{op} to a string of digits in base @var{base}. The base may vary
! 762: from 2 to 36.
! 763:
! 764: If @var{str} is NULL, space for the result string is allocated using the
! 765: default allocation function, and a pointer to the string is returned.
! 766:
! 767: If @var{str} is not NULL, it should point to a block of storage enough large
! 768: for the result. To find out the right amount of space to provide for
! 769: @var{str}, use @code{mpz_sizeinbase (@var{op}, @var{base}) + 2}. The two
! 770: extra bytes are for a possible minus sign, and for the terminating null
! 771: character.
! 772: @end deftypefun
! 773:
! 774:
! 775: @node Integer Arithmetic, Comparison Functions, Converting Integers, Integer Functions
! 776: @comment node-name, next, previous, up
! 777: @section Arithmetic Functions
! 778: @cindex Integer arithmetic functions
! 779: @cindex Arithmetic functions
! 780:
! 781: @deftypefun void mpz_add (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 782: @deftypefunx void mpz_add_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 783: @ifinfo
! 784: Set @var{rop} to @var{op1} + @var{op2}.
! 785: @end ifinfo
! 786: @iftex
! 787: @tex
! 788: Set @var{rop} to $@var{op1} + @var{op2}$.
! 789: @end tex
! 790: @end iftex
! 791: @end deftypefun
! 792:
! 793: @deftypefun void mpz_sub (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 794: @deftypefunx void mpz_sub_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 795: Set @var{rop} to @var{op1} @minus{} @var{op2}.
! 796: @end deftypefun
! 797:
! 798: @deftypefun void mpz_mul (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 799: @deftypefunx void mpz_mul_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 800: @ifinfo
! 801: Set @var{rop} to @var{op1} times @var{op2}.
! 802: @end ifinfo
! 803: @iftex
! 804: @tex
! 805: Set @var{rop} to $@var{op1} \times @var{op2}$.
! 806: @end tex
! 807: @end iftex
! 808: @end deftypefun
! 809:
! 810: @deftypefun void mpz_mul_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 811: @ifinfo
! 812: Set @var{rop} to @var{op1} times 2 raised to @var{op2}. This operation can
! 813: also be defined as a left shift, @var{op2} steps.
! 814: @end ifinfo
! 815: @iftex
! 816: @tex
! 817: Set @var{rop} to $@var{op1} \times 2^{op2}$. This operation can also be
! 818: defined as a left shift, @var{op2} steps.
! 819: @end tex
! 820: @end iftex
! 821: @end deftypefun
! 822:
! 823: @deftypefun void mpz_neg (mpz_t @var{rop}, mpz_t @var{op})
! 824: Set @var{rop} to @minus{}@var{op}.
! 825: @end deftypefun
! 826:
! 827: @deftypefun void mpz_abs (mpz_t @var{rop}, mpz_t @var{op})
! 828: Set @var{rop} to the absolute value of @var{op}.
! 829: @end deftypefun
! 830:
! 831: @deftypefun void mpz_fac_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 832: Set @var{rop} to @var{op}!, the factorial of @var{op}.
! 833: @end deftypefun
! 834:
! 835: @subsection Division functions
! 836:
! 837: Division is undefined if the divisor is zero, and passing a zero divisor to
! 838: the divide or modulo functions, as well passing a zero mod argument to the
! 839: @code{mpz_powm} and @code{mpz_powm_ui} functions, will make these functions
! 840: intentionally divide by zero. This gives the user the possibility to handle
! 841: arithmetic exceptions in these functions in the same manner as other
! 842: arithmetic exceptions.
! 843:
! 844: There are three main groups of division functions:
! 845: @itemize @bullet
! 846: @item
! 847: Functions that truncate the quotient towards 0. The names of these
! 848: functions start with @code{mpz_tdiv}. The @samp{t} in the name is short for
! 849: @samp{truncate}.
! 850: @item
! 851: Functions that round the quotient towards @minus{}infinity. The names of
! 852: these routines start with @code{mpz_fdiv}. The @samp{f} in the name is
! 853: short for @samp{floor}.
! 854: @item
! 855: Functions that round the quotient towards +infinity. The names of
! 856: these routines start with @code{mpz_cdiv}. The @samp{c} in the name is
! 857: short for @samp{ceil}.
! 858: @end itemize
! 859:
! 860: For each rounding mode, there are a couple of variants. Here @samp{q} means
! 861: that the quotient is computed, while @samp{r} means that the remainder is
! 862: computed. Functions that compute both the quotient and remainder have
! 863: @samp{qr} in the name.
! 864:
! 865: @deftypefun void mpz_tdiv_q (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 866: @deftypefunx void mpz_tdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 867: Set @var{rop} to [@var{op1}/@var{op2}]. The quotient is truncated towards
! 868: 0.
! 869: @end deftypefun
! 870:
! 871: @deftypefun void mpz_tdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 872: @deftypefunx void mpz_tdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 873: Set @var{rop} to (@var{op1} - [@var{op1}/@var{op2}] * @var{op2}).
! 874: Unless the remainder is zero, it has the same sign as the dividend.
! 875: @end deftypefun
! 876:
! 877: @deftypefun void mpz_tdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 878: @deftypefunx void mpz_tdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
! 879: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 880: remainder in @var{rop2}. The quotient is rounded towards 0. Unless the
! 881: remainder is zero, it has the same sign as the dividend.
! 882:
! 883: If @var{rop1} and @var{rop2} are the same variable, the results are
! 884: undefined.
! 885: @end deftypefun
! 886:
! 887: @deftypefun void mpz_fdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
! 888: @deftypefunx void mpz_fdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 889: @ifinfo
! 890: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
! 891: @minus{}infinity.
! 892: @end ifinfo
! 893: @iftex
! 894: @tex
! 895: Set @var{rop} to $\lfloor@var{op1}/@var{op2}\rfloor$. (I.e., round
! 896: the quotient towards $-\infty$.)
! 897: @end tex
! 898: @end iftex
! 899: @end deftypefun
! 900:
! 901: @deftypefun void mpz_fdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 902: @deftypefunx {unsigned long int} mpz_fdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 903: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
! 904: the remainder is zero, it has the same sign as the divisor.
! 905:
! 906: For @code{mpz_fdiv_r_ui} the remainder is small enough to fit in an
! 907: @code{unsigned long int}, and is therefore returned.
! 908: @end deftypefun
! 909:
! 910: @deftypefun void mpz_fdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 911: @deftypefunx {unsigned long int} mpz_fdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
! 912: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 913: remainder in @var{rop2}. The quotient is rounded towards @minus{}infinity.
! 914: Unless the remainder is zero, it has the same sign as the divisor.
! 915:
! 916: For @code{mpz_fdiv_qr_ui} the remainder is small enough to fit in an
! 917: @code{unsigned long int}, and is therefore returned.
! 918:
! 919: If @var{rop1} and @var{rop2} are the same variable, the results are
! 920: undefined.
! 921: @end deftypefun
! 922:
! 923: @deftypefun {unsigned long int} mpz_fdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 924: This function is similar to @code{mpz_fdiv_r_ui}, but the remainder is only
! 925: returned; it is not stored anywhere.
! 926: @end deftypefun
! 927:
! 928: @deftypefun void mpz_cdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
! 929: @deftypefunx void mpz_cdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 930: @ifinfo
! 931: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
! 932: +infinity.
! 933: @end ifinfo
! 934: @iftex
! 935: @tex
! 936: Set @var{rop} to $\lceil@var{op1}/@var{op2}\rceil$. (I.e., round the
! 937: quotient towards $+\infty$.)
! 938: @end tex
! 939: @end iftex
! 940: @end deftypefun
! 941:
! 942: @deftypefun void mpz_cdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 943: @deftypefunx {unsigned long int} mpz_cdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 944: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
! 945: the remainder is zero, it has the opposite sign as the divisor.
! 946:
! 947: For @code{mpz_cdiv_r_ui} the negated remainder is small enough to fit in an
! 948: @code{unsigned long int}, and it is therefore returned.
! 949: @end deftypefun
! 950:
! 951: @deftypefun void mpz_cdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 952: @deftypefunx {unsigned long int} mpz_cdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
! 953: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 954: remainder in @var{rop2}. The quotient is rounded towards +infinity. Unless
! 955: the remainder is zero, it has the opposite sign as the divisor.
! 956:
! 957: For @code{mpz_cdiv_qr_ui} the negated remainder is small enough to fit in an
! 958: @code{unsigned long int}, and it is therefore returned.
! 959:
! 960: If @var{rop1} and @var{rop2} are the same variable, the results are
! 961: undefined.
! 962: @end deftypefun
! 963:
! 964: @deftypefun {unsigned long int} mpz_cdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 965: Return the negated remainder, similar to @code{mpz_cdiv_r_ui}. (The
! 966: difference is that this function doesn't store the remainder anywhere.)
! 967: @end deftypefun
! 968:
! 969: @deftypefun void mpz_mod (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 970: @deftypefunx {unsigned long int} mpz_mod_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 971: Set @var{rop} to @var{op1} @code{mod} @var{op2}. The sign of the divisor is
! 972: ignored, and the result is always non-negative.
! 973:
! 974: For @code{mpz_mod_ui} the remainder is small enough to fit in an
! 975: @code{unsigned long int}, and is therefore returned.
! 976: @end deftypefun
! 977:
! 978: @deftypefun void mpz_divexact (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 979: Set @var{rop} to @var{op1}/@var{op2}. This function produces correct
! 980: results only when it is known in advance that @var{op2} divides
! 981: @var{op1}.
! 982:
! 983: Since mpz_divexact is much faster than any of the other routines that produce
! 984: the quotient (@pxref{References} Jebelean), it is the best choice for
! 985: instances in which exact division is known to occur, such as reducing a
! 986: rational to lowest terms.
! 987: @end deftypefun
! 988:
! 989: @deftypefun void mpz_tdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 990: @ifinfo
! 991: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
! 992: rounded towards 0.
! 993: @end ifinfo
! 994: @iftex
! 995: @tex
! 996: Set @var{rop} to $@var{op1}/2^{op2}$. The quotient is rounded towards 0.
! 997: @end tex
! 998: @end iftex
! 999: @end deftypefun
! 1000:
! 1001: @deftypefun void mpz_tdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 1002: @ifinfo
! 1003: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
! 1004: @var{rop}. Unless it is zero, @var{rop} will have the same sign as @var{op1}.
! 1005: @end ifinfo
! 1006: @iftex
! 1007: @tex
! 1008: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. Unless it is
! 1009: zero, @var{rop} will have the same sign as @var{op1}.
! 1010: @end tex
! 1011: @end iftex
! 1012: @end deftypefun
! 1013:
! 1014: @deftypefun void mpz_fdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 1015: @ifinfo
! 1016: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
! 1017: rounded towards @minus{}infinity.
! 1018: @end ifinfo
! 1019: @iftex
! 1020: @tex
! 1021: Set @var{rop} to $\lfloor@var{op1}/2^{op2}\rfloor$. The quotient is rounded
! 1022: towards $-\infty$.
! 1023: @end tex
! 1024: @end iftex
! 1025: @end deftypefun
! 1026:
! 1027: @deftypefun void mpz_fdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 1028: @ifinfo
! 1029: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
! 1030: @var{rop}. The sign of @var{rop} will always be positive.
! 1031: @end ifinfo
! 1032: @iftex
! 1033: @tex
! 1034: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. The sign of
! 1035: @var{rop} will always be positive.
! 1036: @end tex
! 1037: @end iftex
! 1038:
! 1039: This operation can also be defined as masking of the @var{op2} least
! 1040: significant bits.
! 1041: @end deftypefun
! 1042:
! 1043: @subsection Exponentialization Functions
! 1044:
! 1045: @deftypefun void mpz_powm (mpz_t @var{rop}, mpz_t @var{base}, mpz_t @var{exp}, mpz_t @var{mod})
! 1046: @deftypefunx void mpz_powm_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp}, mpz_t @var{mod})
! 1047: Set @var{rop} to (@var{base} raised to @var{exp}) @code{mod} @var{mod}. If
! 1048: @var{exp} is negative, the result is undefined.
! 1049: @end deftypefun
! 1050:
! 1051: @deftypefun void mpz_pow_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp})
! 1052: @deftypefunx void mpz_ui_pow_ui (mpz_t @var{rop}, unsigned long int @var{base}, unsigned long int @var{exp})
! 1053: Set @var{rop} to @var{base} raised to @var{exp}.
! 1054: @ifinfo
! 1055: The case of 0^0 yields 1.
! 1056: @end ifinfo
! 1057: @iftex
! 1058: @tex
! 1059: The case of $0^0$ yields 1.
! 1060: @end tex
! 1061: @end iftex
! 1062: @end deftypefun
! 1063:
! 1064: @subsection Square Root Functions
! 1065:
! 1066: @deftypefun void mpz_sqrt (mpz_t @var{rop}, mpz_t @var{op})
! 1067: @ifinfo
! 1068: Set @var{rop} to the truncated integer part of the square root of
! 1069: @var{op}.
! 1070: @end ifinfo
! 1071: @iftex
! 1072: @tex
! 1073: Set @var{rop} to $\lfloor\sqrt{@var{op}}\rfloor$, the truncated integer
! 1074: part of the square root of @var{op}.
! 1075: @end tex
! 1076: @end iftex
! 1077: @end deftypefun
! 1078:
! 1079: @deftypefun void mpz_sqrtrem (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op})
! 1080: @ifinfo
! 1081: Set @var{rop1} to the truncated integer part of the square root of @var{op},
! 1082: like @code{mpz_sqrt}. Set @var{rop2} to
! 1083: @var{op}@minus{}@var{rop1}*@var{rop1},
! 1084: @end ifinfo
! 1085: @iftex
! 1086: @tex
! 1087: Set @var{rop1} to $\lfloor\sqrt{@var{op}}\rfloor$, like @code{mpz_sqrt}.
! 1088: Set @var{rop2} to $(@var{op} - @var{rop1}^2)$,
! 1089: @end tex
! 1090: @end iftex
! 1091: (i.e., zero if @var{op} is a perfect square).
! 1092:
! 1093: If @var{rop1} and @var{rop2} are the same variable, the results are
! 1094: undefined.
! 1095: @end deftypefun
! 1096:
! 1097: @deftypefun int mpz_perfect_square_p (mpz_t @var{op})
! 1098: Return non-zero if @var{op} is a perfect square, i.e., if the square root of
! 1099: @var{op} is an integer. Return zero otherwise.
! 1100: @end deftypefun
! 1101:
! 1102: @subsection Number Theoretic Functions
! 1103:
! 1104: @deftypefun int mpz_probab_prime_p (mpz_t @var{op}, int @var{reps})
! 1105: @ifinfo
! 1106: If this function returns 0, @var{op} is definitely not prime. If it returns
! 1107: 1, then @var{op} is `probably' prime. The probability of a false positive is
! 1108: (1/4)**@var{reps}.
! 1109: @end ifinfo
! 1110: @iftex
! 1111: @tex
! 1112: If this function returns 0, @var{op} is definitely not prime. If it returns
! 1113: 1, then @var{op} is `probably' prime. The probability of a false positive is
! 1114: $(1/4)^{{reps}}$.
! 1115: @end tex
! 1116: @end iftex
! 1117: A reasonable value of reps is 25.
! 1118:
! 1119: An implementation of the probabilistic primality test found in Seminumerical
! 1120: Algorithms (@pxref{References} Knuth).
! 1121: @end deftypefun
! 1122:
! 1123: @deftypefun void mpz_gcd (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1124: Set @var{rop} to the greatest common divisor of @var{op1} and @var{op2}.
! 1125: @end deftypefun
! 1126:
! 1127: @deftypefun {unsigned long int} mpz_gcd_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 1128: Compute the greatest common divisor of @var{op1} and @var{op2}. If
! 1129: @var{rop} is not NULL, store the result there.
! 1130:
! 1131: If the result is small enough to fit in an @code{unsigned long int}, it is
! 1132: returned. If the result does not fit, 0 is returned, and the result is equal
! 1133: to the argument @var{op1}. Note that the result will always fit if @var{op2}
! 1134: is non-zero.
! 1135: @end deftypefun
! 1136:
! 1137: @deftypefun void mpz_gcdext (mpz_t @var{g}, mpz_t @var{s}, mpz_t @var{t}, mpz_t @var{a}, mpz_t @var{b})
! 1138: Compute @var{g}, @var{s}, and @var{t}, such that @var{a}@var{s} +
! 1139: @var{b}@var{t} = @var{g} = @code{gcd} (@var{a}, @var{b}). If @var{t} is
! 1140: NULL, that argument is not computed.
! 1141: @end deftypefun
! 1142:
! 1143: @deftypefun int mpz_invert (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1144: Compute the inverse of @var{op1} modulo @var{op2} and put the result in
! 1145: @var{rop}. Return non-zero if an inverse exist, zero otherwise. When the
! 1146: function returns zero, do not assume anything about the value in @var{rop}.
! 1147: @end deftypefun
! 1148:
! 1149: @deftypefun int mpz_jacobi (mpz_t @var{op1}, mpz_t @var{op2})
! 1150: @deftypefunx int mpz_legendre (mpz_t @var{op1}, mpz_t @var{op2})
! 1151: Compute the Jacobi and Legendre symbols, respectively.
! 1152: @end deftypefun
! 1153:
! 1154: @need 2000
! 1155: @node Comparison Functions, Integer Logic and Bit Fiddling, Integer Arithmetic, Integer Functions
! 1156: @comment node-name, next, previous, up
! 1157: @section Comparison Functions
! 1158:
! 1159: @deftypefun int mpz_cmp (mpz_t @var{op1}, mpz_t @var{op2})
! 1160: @ifinfo
! 1161: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1162: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1163: @var{op2}.
! 1164: @end ifinfo
! 1165: @iftex
! 1166: @tex
! 1167: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1168: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1169: < @var{op2}$.
! 1170: @end tex
! 1171: @end iftex
! 1172: @end deftypefun
! 1173:
! 1174: @deftypefn Macro int mpz_cmp_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 1175: @deftypefnx Macro int mpz_cmp_si (mpz_t @var{op1}, signed long int @var{op2})
! 1176: @ifinfo
! 1177: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1178: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1179: @var{op2}.
! 1180: @end ifinfo
! 1181: @iftex
! 1182: @tex
! 1183: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1184: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1185: < @var{op2}$.
! 1186: @end tex
! 1187: @end iftex
! 1188:
! 1189: These functions are actually implemented as macros. They evaluate their
! 1190: arguments multiple times.
! 1191: @end deftypefn
! 1192:
! 1193: @deftypefn Macro int mpz_sgn (mpz_t @var{op})
! 1194: @ifinfo
! 1195: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
! 1196: @end ifinfo
! 1197: @iftex
! 1198: @tex
! 1199: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1200: @end tex
! 1201: @end iftex
! 1202:
! 1203: This function is actually implemented as a macro. It evaluates its
! 1204: arguments multiple times.
! 1205: @end deftypefn
! 1206:
! 1207: @node Integer Logic and Bit Fiddling, I/O of Integers, Comparison Functions, Integer Functions
! 1208: @comment node-name, next, previous, up
! 1209: @section Logical and Bit Manipulation Functions
! 1210: @cindex Logical functions
! 1211: @cindex Bit manipulation functions
! 1212:
! 1213: These functions behave as if two's complement arithmetic were used (although
! 1214: sign-magnitude is used by the actual implementation).
! 1215:
! 1216: @deftypefun void mpz_and (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1217: Set @var{rop} to @var{op1} logical-and @var{op2}.
! 1218: @end deftypefun
! 1219:
! 1220: @deftypefun void mpz_ior (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1221: Set @var{rop} to @var{op1} inclusive-or @var{op2}.
! 1222: @end deftypefun
! 1223:
! 1224: @c @deftypefun void mpz_xor (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1225: @c Set @var{rop} to @var{op1} exclusive-or @var{op2}.
! 1226: @c @end deftypefun
! 1227:
! 1228: @deftypefun void mpz_com (mpz_t @var{rop}, mpz_t @var{op})
! 1229: Set @var{rop} to the one's complement of @var{op}.
! 1230: @end deftypefun
! 1231:
! 1232: @deftypefun {unsigned long int} mpz_popcount (mpz_t @var{op})
! 1233: For non-negative numbers, return the population count of @var{op}. For
! 1234: negative numbers, return the largest possible value (@var{MAX_ULONG}).
! 1235: @end deftypefun
! 1236:
! 1237: @deftypefun {unsigned long int} mpz_hamdist (mpz_t @var{op1}, mpz_t @var{op2})
! 1238: If @var{op1} and @var{op2} are both non-negative, return the hamming distance
! 1239: between the two operands. Otherwise, return the largest possible value
! 1240: (@var{MAX_ULONG}).
! 1241:
! 1242: It is possible to extend this function to return a useful value when the
! 1243: operands are both negative, but the current implementation returns
! 1244: @var{MAX_ULONG} in this case. @strong{Do not depend on this behavior, since
! 1245: it will change in future versions of the library.}
! 1246: @end deftypefun
! 1247:
! 1248: @deftypefun {unsigned long int} mpz_scan0 (mpz_t @var{op}, unsigned long int @var{starting_bit})
! 1249: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
! 1250: bits, until the first clear bit is found. Return the index of the found bit.
! 1251: @end deftypefun
! 1252:
! 1253: @deftypefun {unsigned long int} mpz_scan1 (mpz_t @var{op}, unsigned long int @var{starting_bit})
! 1254: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
! 1255: bits, until the first set bit is found. Return the index of the found bit.
! 1256: @end deftypefun
! 1257:
! 1258: @deftypefun void mpz_setbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
! 1259: Set bit @var{bit_index} in @var{op1}.
! 1260: @end deftypefun
! 1261:
! 1262: @deftypefun void mpz_clrbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
! 1263: Clear bit @var{bit_index} in @var{op1}.
! 1264: @end deftypefun
! 1265:
! 1266: @node I/O of Integers, Miscellaneous Integer Functions, Integer Logic and Bit Fiddling, Integer Functions
! 1267: @comment node-name, next, previous, up
! 1268: @section Input and Output Functions
! 1269: @cindex Integer input and output functions
! 1270: @cindex Input functions
! 1271: @cindex Output functions
! 1272: @cindex I/O functions
! 1273:
! 1274: Functions that perform input from a stdio stream, and functions that output to
! 1275: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
! 1276: these functions will make them read from @code{stdin} and write to
! 1277: @code{stdout}, respectively.
! 1278:
! 1279: When using any of these functions, it is a good idea to include @file{stdio.h}
! 1280: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
! 1281: for these functions.
! 1282:
! 1283: @deftypefun size_t mpz_out_str (FILE *@var{stream}, int @var{base}, mpz_t @var{op})
! 1284: Output @var{op} on stdio stream @var{stream}, as a string of digits in base
! 1285: @var{base}. The base may vary from 2 to 36.
! 1286:
! 1287: Return the number of bytes written, or if an error occurred, return 0.
! 1288: @end deftypefun
! 1289:
! 1290: @deftypefun size_t mpz_inp_str (mpz_t @var{rop}, FILE *@var{stream}, int @var{base})
! 1291: Input a possibly white-space preceded string in base @var{base} from stdio
! 1292: stream @var{stream}, and put the read integer in @var{rop}. The base may vary
! 1293: from 2 to 36. If @var{base} is 0, the actual base is determined from the
! 1294: leading characters: if the first two characters are `0x' or `0X', hexadecimal
! 1295: is assumed, otherwise if the first character is `0', octal is assumed,
! 1296: otherwise decimal is assumed.
! 1297:
! 1298: Return the number of bytes read, or if an error occurred, return 0.
! 1299: @end deftypefun
! 1300:
! 1301: @deftypefun size_t mpz_out_raw (FILE *@var{stream}, mpz_t @var{op})
! 1302: Output @var{op} on stdio stream @var{stream}, in raw binary format. The
! 1303: integer is written in a portable format, with 4 bytes of size information, and
! 1304: that many bytes of limbs. Both the size and the limbs are written in
! 1305: decreasing significance order (i.e., in big-endian).
! 1306:
! 1307: The output can be read with @code{mpz_inp_raw}.
! 1308:
! 1309: Return the number of bytes written, or if an error occurred, return 0.
! 1310:
! 1311: The output of this can not be read by @code{mpz_inp_raw} from GMP 1, because
! 1312: of changes necessary for compatibility between 32-bit and 64-bit machines.
! 1313: @end deftypefun
! 1314:
! 1315: @deftypefun size_t mpz_inp_raw (mpz_t @var{rop}, FILE *@var{stream})
! 1316: Input from stdio stream @var{stream} in the format written by
! 1317: @code{mpz_out_raw}, and put the result in @var{rop}. Return the number of
! 1318: bytes read, or if an error occurred, return 0.
! 1319:
! 1320: This routine can read the output from @code{mpz_out_raw} also from GMP 1, in
! 1321: spite of changes necessary for compatibility between 32-bit and 64-bit
! 1322: machines.
! 1323: @end deftypefun
! 1324:
! 1325:
! 1326: @need 2000
! 1327: @node Miscellaneous Integer Functions,, I/O of Integers, Integer Functions
! 1328: @comment node-name, next, previous, up
! 1329: @section Miscellaneous Functions
! 1330: @cindex Miscellaneous integer functions
! 1331:
! 1332: @deftypefun void mpz_random (mpz_t @var{rop}, mp_size_t @var{max_size})
! 1333: Generate a random integer of at most @var{max_size} limbs. The generated
! 1334: random number doesn't satisfy any particular requirements of randomness.
! 1335: Negative random numbers are generated when @var{max_size} is negative.
! 1336: @end deftypefun
! 1337:
! 1338: @deftypefun void mpz_random2 (mpz_t @var{rop}, mp_size_t @var{max_size})
! 1339: Generate a random integer of at most @var{max_size} limbs, with long strings
! 1340: of zeros and ones in the binary representation. Useful for testing functions
! 1341: and algorithms, since this kind of random numbers have proven to be more
! 1342: likely to trigger corner-case bugs. Negative random numbers are generated
! 1343: when @var{max_size} is negative.
! 1344: @end deftypefun
! 1345:
! 1346: @deftypefun size_t mpz_size (mpz_t @var{op})
! 1347: Return the size of @var{op} measured in number of limbs. If @var{op} is zero,
! 1348: the returned value will be zero.
! 1349: @c (@xref{Nomenclature}, for an explanation of the concept @dfn{limb}.)
! 1350:
! 1351: @strong{This function is obsolete. It will disappear from future MP
! 1352: releases.}
! 1353: @end deftypefun
! 1354:
! 1355: @deftypefun size_t mpz_sizeinbase (mpz_t @var{op}, int @var{base})
! 1356: Return the size of @var{op} measured in number of digits in base @var{base}.
! 1357: The base may vary from 2 to 36. The returned value will be exact or 1 too
! 1358: big. If @var{base} is a power of 2, the returned value will always be exact.
! 1359:
! 1360: This function is useful in order to allocate the right amount of space before
! 1361: converting @var{op} to a string. The right amount of allocation is normally
! 1362: two more than the value returned by @code{mpz_sizeinbase} (one extra for a
! 1363: minus sign and one for the terminating '\0').
! 1364: @end deftypefun
! 1365:
! 1366:
! 1367: @node Rational Number Functions, Floating-point Functions, Integer Functions, Top
! 1368: @comment node-name, next, previous, up
! 1369: @chapter Rational Number Functions
! 1370: @cindex Rational number functions
! 1371:
! 1372: This chapter describes the MP functions for performing arithmetic on rational
! 1373: numbers. These functions start with the prefix @code{mpq_}.
! 1374:
! 1375: Rational numbers are stored in objects of type @code{mpq_t}.
! 1376:
! 1377: All rational arithmetic functions assume operands have a canonical form, and
! 1378: canonicalize their result. The canonical from means that the denominator and
! 1379: the numerator have no common factors, and that the denominator is positive.
! 1380: Zero has the unique representation 0/1.
! 1381:
! 1382: Pure assignment functions do not canonicalize the assigned variable. It is
! 1383: the responsibility of the user to canonicalize the assigned variable before
! 1384: any arithmetic operations are performed on that variable. @strong{Note that
! 1385: this is an incompatible change from version 1 of the library.}
! 1386:
! 1387: @deftypefun void mpq_canonicalize (mpq_t @var{op})
! 1388: Remove any factors that are common to the numerator and denominator of
! 1389: @var{op}, and make the denominator positive.
! 1390: @end deftypefun
! 1391:
! 1392: @menu
! 1393: * Initializing Rationals::
! 1394: * Assigning Rationals::
! 1395: * Simultaneous Integer Init & Assign::
! 1396: * Comparing Rationals::
! 1397: * Applying Integer Functions::
! 1398: * Miscellaneous Rational Functions::
! 1399: @end menu
! 1400:
! 1401: @node Initializing Rationals, Assigning Rationals, Rational Number Functions, Rational Number Functions
! 1402: @comment node-name, next, previous, up
! 1403: @section Initialization and Assignment Functions
! 1404:
! 1405: @deftypefun void mpq_init (mpq_t @var{dest_rational})
! 1406: Initialize @var{dest_rational} and set it to 0/1. Each variable should
! 1407: normally only be initialized once, or at least cleared out (using the function
! 1408: @code{mpq_clear}) between each initialization.
! 1409: @end deftypefun
! 1410:
! 1411: @deftypefun void mpq_clear (mpq_t @var{rational_number})
! 1412: Free the space occupied by @var{rational_number}. Make sure to call this
! 1413: function for all @code{mpq_t} variables when you are done with them.
! 1414: @end deftypefun
! 1415:
! 1416: @deftypefun void mpq_set (mpq_t @var{rop}, mpq_t @var{op})
! 1417: @deftypefunx void mpq_set_z (mpq_t @var{rop}, mpz_t @var{op})
! 1418: Assign @var{rop} from @var{op}.
! 1419: @end deftypefun
! 1420:
! 1421: @deftypefun void mpq_set_ui (mpq_t @var{rop}, unsigned long int @var{op1}, unsigned long int @var{op2})
! 1422: @deftypefunx void mpq_set_si (mpq_t @var{rop}, signed long int @var{op1}, unsigned long int @var{op2})
! 1423: Set the value of @var{rop} to @var{op1}/@var{op2}. Note that if @var{op1} and
! 1424: @var{op2} have common factors, @var{rop} has to be passed to
! 1425: @code{mpq_canonicalize} before any operations are performed on @var{rop}.
! 1426: @end deftypefun
! 1427:
! 1428: @node Assigning Rationals, Comparing Rationals, Initializing Rationals, Rational Number Functions
! 1429: @comment node-name, next, previous, up
! 1430: @section Arithmetic Functions
! 1431:
! 1432: @deftypefun void mpq_add (mpq_t @var{sum}, mpq_t @var{addend1}, mpq_t @var{addend2})
! 1433: Set @var{sum} to @var{addend1} + @var{addend2}.
! 1434: @end deftypefun
! 1435:
! 1436: @deftypefun void mpq_sub (mpq_t @var{difference}, mpq_t @var{minuend}, mpq_t @var{subtrahend})
! 1437: Set @var{difference} to @var{minuend} @minus{} @var{subtrahend}.
! 1438: @end deftypefun
! 1439:
! 1440: @deftypefun void mpq_mul (mpq_t @var{product}, mpq_t @var{multiplier}, mpq_t @var{multiplicand})
! 1441: @ifinfo
! 1442: Set @var{product} to @var{multiplier} times @var{multiplicand}.
! 1443: @end ifinfo
! 1444: @iftex
! 1445: @tex
! 1446: Set @var{product} to $@var{multiplier} \times @var{multiplicand}$.
! 1447: @end tex
! 1448: @end iftex
! 1449: @end deftypefun
! 1450:
! 1451: @deftypefun void mpq_div (mpq_t @var{quotient}, mpq_t @var{dividend}, mpq_t @var{divisor})
! 1452: Set @var{quotient} to @var{dividend}/@var{divisor}.
! 1453: @end deftypefun
! 1454:
! 1455: @deftypefun void mpq_neg (mpq_t @var{negated_operand}, mpq_t @var{operand})
! 1456: Set @var{negated_operand} to @minus{}@var{operand}.
! 1457: @end deftypefun
! 1458:
! 1459: @deftypefun void mpq_inv (mpq_t @var{inverted_number}, mpq_t @var{number})
! 1460: Set @var{inverted_number} to 1/@var{number}. If the new denominator is
! 1461: zero, this routine will divide by zero.
! 1462: @end deftypefun
! 1463:
! 1464: @node Comparing Rationals, Applying Integer Functions, Assigning Rationals, Rational Number Functions
! 1465: @comment node-name, next, previous, up
! 1466: @section Comparison Functions
! 1467:
! 1468: @deftypefun int mpq_cmp (mpq_t @var{op1}, mpq_t @var{op2})
! 1469: @ifinfo
! 1470: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1471: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1472: @var{op2}.
! 1473: @end ifinfo
! 1474: @iftex
! 1475: @tex
! 1476: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1477: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1478: < @var{op2}$.
! 1479: @end tex
! 1480: @end iftex
! 1481:
! 1482: To determine if two rationals are equal, @code{mpq_equal} is faster than
! 1483: @code{mpq_cmp}.
! 1484: @end deftypefun
! 1485:
! 1486: @deftypefn Macro int mpq_cmp_ui (mpq_t @var{op1}, unsigned long int @var{num2}, unsigned long int @var{den2})
! 1487: @ifinfo
! 1488: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
! 1489: @var{op1} > @var{num2}/@var{den2}, zero if @var{op1} = @var{num2}/@var{den2},
! 1490: and a negative value if @var{op1} < @var{num2}/@var{den2}.
! 1491: @end ifinfo
! 1492: @iftex
! 1493: @tex
! 1494: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
! 1495: $@var{op1} > @var{num2}/@var{den2}$, zero if $@var{op1} =
! 1496: @var{num2}/@var{den2}$, and a negative value if $@var{op1} <
! 1497: @var{num2}/@var{den2}$.
! 1498: @end tex
! 1499: @end iftex
! 1500:
! 1501: This routine allows that @var{num2} and @var{den2} have common factors.
! 1502:
! 1503: This function is actually implemented as a macro. It evaluates its
! 1504: arguments multiple times.
! 1505: @end deftypefn
! 1506:
! 1507: @deftypefn Macro int mpq_sgn (mpq_t @var{op})
! 1508: @ifinfo
! 1509: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
! 1510: @end ifinfo
! 1511: @iftex
! 1512: @tex
! 1513: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1514: @end tex
! 1515: @end iftex
! 1516:
! 1517: This function is actually implemented as a macro. It evaluates its
! 1518: arguments multiple times.
! 1519: @end deftypefn
! 1520:
! 1521: @deftypefun int mpq_equal (mpq_t @var{op1}, mpq_t @var{op2})
! 1522: Return non-zero if @var{op1} and @var{op2} are equal, zero if they are
! 1523: non-equal. Although @code{mpq_cmp} can be used for the same purpose, this
! 1524: function is much faster.
! 1525: @end deftypefun
! 1526:
! 1527: @node Applying Integer Functions, Miscellaneous Rational Functions, Comparing Rationals, Rational Number Functions
! 1528: @comment node-name, next, previous, up
! 1529: @section Applying Integer Functions to Rationals
! 1530:
! 1531: The set of @code{mpq} functions is quite small. In particular, there are no
! 1532: functions for either input or output. But there are two macros that allow us
! 1533: to apply any @code{mpz} function on the numerator or denominator of a rational
! 1534: number. If these macros are used to assign to the rational number,
! 1535: @code{mpq_canonicalize} normally need to be called afterwards.
! 1536:
! 1537: @deftypefn Macro mpz_t mpq_numref (mpq_t @var{op})
! 1538: @deftypefnx Macro mpz_t mpq_denref (mpq_t @var{op})
! 1539: Return a reference to the numerator and denominator of @var{op}, respectively.
! 1540: The @code{mpz} functions can be used on the result of these macros.
! 1541: @end deftypefn
! 1542:
! 1543: @need 2000
! 1544: @node Miscellaneous Rational Functions, , Applying Integer Functions, Rational Number Functions
! 1545: @comment node-name, next, previous, up
! 1546: @section Miscellaneous Functions
! 1547:
! 1548: @deftypefun double mpq_get_d (mpq_t @var{op})
! 1549: Convert @var{op} to a double.
! 1550: @end deftypefun
! 1551:
! 1552: These functions assign between either the numerator or denominator of a
! 1553: rational, and an integer. Instead of using these functions, it is preferable
! 1554: to use the more general mechanisms @code{mpq_numref} and @code{mpq_denref},
! 1555: together with @code{mpz_set}.
! 1556:
! 1557: @deftypefun void mpq_set_num (mpq_t @var{rational}, mpz_t @var{numerator})
! 1558: Copy @var{numerator} to the numerator of @var{rational}. When this risks to
! 1559: make the numerator and denominator of @var{rational} have common factors, you
! 1560: have to pass @var{rational} to @code{mpq_canonicalize} before any operations
! 1561: are performed on @var{rational}.
! 1562:
! 1563: This function is equivalent to
! 1564: @code{mpz_set (mpq_numref (@var{rational}), @var{numerator})}.
! 1565: @end deftypefun
! 1566:
! 1567: @deftypefun void mpq_set_den (mpq_t @var{rational}, mpz_t @var{denominator})
! 1568: Copy @var{denominator} to the denominator of @var{rational}. When this risks
! 1569: to make the numerator and denominator of @var{rational} have common factors,
! 1570: or if the denominator might be negative, you have to pass @var{rational} to
! 1571: @code{mpq_canonicalize} before any operations are performed on @var{rational}.
! 1572:
! 1573: @strong{In version 1 of the library, negative denominators were handled by
! 1574: copying the sign to the numerator. That is no longer done.}
! 1575:
! 1576: This function is equivalent to
! 1577: @code{mpz_set (mpq_denref (@var{rational}), @var{denominators})}.
! 1578: @end deftypefun
! 1579:
! 1580: @deftypefun void mpq_get_num (mpz_t @var{numerator}, mpq_t @var{rational})
! 1581: Copy the numerator of @var{rational} to the integer @var{numerator}, to
! 1582: prepare for integer operations on the numerator.
! 1583:
! 1584: This function is equivalent to
! 1585: @code{mpz_set (@var{numerator}, mpq_numref (@var{rational}))}.
! 1586: @end deftypefun
! 1587:
! 1588: @deftypefun void mpq_get_den (mpz_t @var{denominator}, mpq_t @var{rational})
! 1589: Copy the denominator of @var{rational} to the integer @var{denominator}, to
! 1590: prepare for integer operations on the denominator.
! 1591:
! 1592: This function is equivalent to
! 1593: @code{mpz_set (@var{denominator}, mpq_denref (@var{rational}))}.
! 1594: @end deftypefun
! 1595:
! 1596:
! 1597: @node Floating-point Functions, Low-level Functions, Rational Number Functions, Top
! 1598: @comment node-name, next, previous, up
! 1599: @chapter Floating-point Functions
! 1600: @cindex Floating-point functions
! 1601: @cindex Float functions
! 1602:
! 1603: This is a description of the @emph{preliminary} interface for floating-point
! 1604: arithmetic in GNU MP 2.
! 1605:
! 1606: The floating-point functions expect arguments of type @code{mpf_t}.
! 1607:
! 1608: The MP floating-point functions have an interface that is similar to the MP
! 1609: integer functions. The function prefix for floating-point operations is
! 1610: @code{mpf_}.
! 1611:
! 1612: There is one significant characteristic of floating-point numbers that has
! 1613: motivated a difference between this function class and other MP function
! 1614: classes: the inherent inexactness of floating point arithmetic. The user has
! 1615: to specify the precision of each variable. A computation that assigns a
! 1616: variable will take place with the precision of the assigned variable; the
! 1617: precision of variables used as input is ignored.
! 1618:
! 1619: @cindex User-defined precision
! 1620: The precision of a calculation is defined as follows: Compute the requested
! 1621: operation exactly (with ``infinite precision''), and truncate the result to
! 1622: the destination variable precision. Even if the user has asked for a very
! 1623: high precision, MP will not calculate with superfluous digits. For example,
! 1624: if two low-precision numbers of nearly equal magnitude are added, the
! 1625: precision of the result will be limited to what is required to represent the
! 1626: result accurately.
! 1627:
! 1628: The MP floating-point functions are @emph{not} intended as a smooth extension
! 1629: to the IEEE P754 arithmetic. Specifically, the results obtained on one
! 1630: computer often differs from the results obtained on a computer with a
! 1631: different word size.
! 1632:
! 1633: @menu
! 1634: * Initializing Floats::
! 1635: * Assigning Floats::
! 1636: * Simultaneous Float Init & Assign::
! 1637: * Converting Floats::
! 1638: * Float Arithmetic::
! 1639: * Float Comparison::
! 1640: * I/O of Floats::
! 1641: * Miscellaneous Float Functions::
! 1642: @end menu
! 1643:
! 1644: @node Initializing Floats, Assigning Floats, , Floating-point Functions
! 1645: @comment node-name, next, previous, up
! 1646: @section Initialization and Assignment Functions
! 1647:
! 1648: @deftypefun void mpf_set_default_prec (unsigned long int @var{prec})
! 1649: Set the default precision to be @strong{at least} @var{prec} bits. All
! 1650: subsequent calls to @code{mpf_init} will use this precision, but previously
! 1651: initialized variables are unaffected.
! 1652: @end deftypefun
! 1653:
! 1654: An @code{mpf_t} object must be initialized before storing the first value in
! 1655: it. The functions @code{mpf_init} and @code{mpf_init2} are used for that
! 1656: purpose.
! 1657:
! 1658: @deftypefun void mpf_init (mpf_t @var{x})
! 1659: Initialize @var{x} to 0. Normally, a variable should be initialized once only
! 1660: or at least be cleared, using @code{mpf_clear}, between initializations. The
! 1661: precision of @var{x} is undefined unless a default precision has already been
! 1662: established by a call to @code{mpf_set_default_prec}.
! 1663: @end deftypefun
! 1664:
! 1665: @deftypefun void mpf_init2 (mpf_t @var{x}, unsigned long int @var{prec})
! 1666: Initialize @var{x} to 0 and set its precision to be @strong{at least}
! 1667: @var{prec} bits. Normally, a variable should be initialized once only or at
! 1668: least be cleared, using @code{mpf_clear}, between initializations.
! 1669: @end deftypefun
! 1670:
! 1671: @deftypefun void mpf_clear (mpf_t @var{x})
! 1672: Free the space occupied by @var{x}. Make sure to call this function for all
! 1673: @code{mpf_t} variables when you are done with them.
! 1674: @end deftypefun
! 1675:
! 1676: @need 2000
! 1677: Here is an example on how to initialize floating-point variables:
! 1678: @example
! 1679: @{
! 1680: mpf_t x, y;
! 1681: mpf_init (x); /* use default precision */
! 1682: mpf_init2 (y, 256); /* precision @emph{at least} 256 bits */
! 1683: @dots{}
! 1684: /* Unless the program is about to exit, do ... */
! 1685: mpf_clear (x);
! 1686: mpf_clear (y);
! 1687: @}
! 1688: @end example
! 1689:
! 1690: The following three functions are useful for changing the precision during a
! 1691: calculation. A typical use would be for adjusting the precision gradually in
! 1692: iterative algorithms like Newton-Raphson, making the computation precision
! 1693: closely match the actual accurate part of the numbers.
! 1694:
! 1695: @deftypefun void mpf_set_prec (mpf_t @var{rop}, unsigned long int @var{prec})
! 1696: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits.
! 1697: Since changing the precision involves calls to @code{realloc}, this routine
! 1698: should not be called in a tight loop.
! 1699: @end deftypefun
! 1700:
! 1701: @deftypefun {unsigned long int} mpf_get_prec (mpf_t @var{op})
! 1702: Return the precision actually used for assignments of @var{op}.
! 1703: @end deftypefun
! 1704:
! 1705: @deftypefun void mpf_set_prec_raw (mpf_t @var{rop}, unsigned long int @var{prec})
! 1706: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits. This
! 1707: is a low-level function that does not change the allocation. The @var{prec}
! 1708: argument must not be larger that the precision previously returned by
! 1709: @code{mpf_get_prec}. It is crucial that the precision of @var{rop} is
! 1710: ultimately reset to exactly the value returned by @code{mpf_get_prec}.
! 1711: @end deftypefun
! 1712:
! 1713:
! 1714: @node Assigning Floats, Simultaneous Float Init & Assign, Initializing Floats, Floating-point Functions
! 1715: @comment node-name, next, previous, up
! 1716: @subsection Assignment Functions
! 1717: @cindex Float assignment functions
! 1718:
! 1719: These functions assign new values to already initialized floats
! 1720: (@pxref{Initializing Floats}).
! 1721:
! 1722: @deftypefun void mpf_set (mpf_t @var{rop}, mpf_t @var{op})
! 1723: @deftypefunx void mpf_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1724: @deftypefunx void mpf_set_si (mpf_t @var{rop}, signed long int @var{op})
! 1725: @deftypefunx void mpf_set_d (mpf_t @var{rop}, double @var{op})
! 1726: @deftypefunx void mpf_set_z (mpf_t @var{rop}, mpz_t @var{op})
! 1727: @deftypefunx void mpf_set_q (mpf_t @var{rop}, mpq_t @var{op})
! 1728: Set the value of @var{rop} from @var{op}.
! 1729: @end deftypefun
! 1730:
! 1731: @deftypefun int mpf_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
! 1732: Set the value of @var{rop} from the string in @var{str}. The string is of the
! 1733: form @samp{M@@N} or, if the base is 10 or less, alternatively @samp{MeN}.
! 1734: @samp{M} is the mantissa and @samp{N} is the exponent. The mantissa is always
! 1735: in the specified base. The exponent is either in the specified base or, if
! 1736: @var{base} is negative, in decimal.
! 1737:
! 1738: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
! 1739: @minus{}2. Negative values are used to specify that the exponent is in
! 1740: decimal.
! 1741:
! 1742: Unlike the corresponding @code{mpz} function, the base will not be determined
! 1743: from the leading characters of the string if @var{base} is 0. This is so that
! 1744: numbers like @samp{0.23} are not interpreted as octal.
! 1745:
! 1746: White space is allowed in the string, and is simply ignored.
! 1747:
! 1748: This function returns 0 if the entire string up to the '\0' is a valid number
! 1749: in base @var{base}. Otherwise it returns @minus{}1.
! 1750: @end deftypefun
! 1751:
! 1752:
! 1753: @node Simultaneous Float Init & Assign, Converting Floats, Assigning Floats, Floating-point Functions
! 1754: @comment node-name, next, previous, up
! 1755: @subsection Combined Initialization and Assignment Functions
! 1756: @cindex Initialization and assignment functions
! 1757:
! 1758: For convenience, MP provides a parallel series of initialize-and-set functions
! 1759: which initialize the output and then store the value there. These functions'
! 1760: names have the form @code{mpf_init_set@dots{}}
! 1761:
! 1762: Once the float has been initialized by any of the @code{mpf_init_set@dots{}}
! 1763: functions, it can be used as the source or destination operand for the ordinary
! 1764: float functions. Don't use an initialize-and-set function on a variable
! 1765: already initialized!
! 1766:
! 1767: @deftypefun void mpf_init_set (mpf_t @var{rop}, mpf_t @var{op})
! 1768: @deftypefunx void mpf_init_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1769: @deftypefunx void mpf_init_set_si (mpf_t @var{rop}, signed long int @var{op})
! 1770: @deftypefunx void mpf_init_set_d (mpf_t @var{rop}, double @var{op})
! 1771: Initialize @var{rop} and set its value from @var{op}.
! 1772:
! 1773: The precision of @var{rop} will be taken from the active default precision, as
! 1774: set by @code{mpf_set_default_prec}.
! 1775: @end deftypefun
! 1776:
! 1777: @deftypefun int mpf_init_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
! 1778: Initialize @var{rop} and set its value from the string in @var{str}. See
! 1779: @code{mpf_set_str} above for details on the assignment operation.
! 1780:
! 1781: Note that @var{rop} is initialized even if an error occurs. (I.e., you have to
! 1782: call @code{mpf_clear} for it.)
! 1783:
! 1784: The precision of @var{rop} will be taken from the active default precision, as
! 1785: set by @code{mpf_set_default_prec}.
! 1786: @end deftypefun
! 1787:
! 1788:
! 1789: @node Converting Floats, Float Arithmetic, Simultaneous Float Init & Assign, Floating-point Functions
! 1790: @comment node-name, next, previous, up
! 1791: @section Conversion Functions
! 1792: @cindex Conversion functions
! 1793:
! 1794: @deftypefun double mpf_get_d (mpf_t @var{op})
! 1795: Convert @var{op} to a double.
! 1796: @end deftypefun
! 1797:
! 1798: @deftypefun {char *} mpf_get_str (char *@var{str}, mp_exp_t *@var{expptr}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
! 1799: Convert @var{op} to a string of digits in base @var{base}. The base may vary
! 1800: from 2 to 36. Generate at most @var{n_digits} significant digits, or if
! 1801: @var{n_digits} is 0, the maximum number of digits accurately representable by
! 1802: @var{op}.
! 1803:
! 1804: If @var{str} is NULL, space for the mantissa is allocated using the default
! 1805: allocation function, and a pointer to the string is returned.
! 1806:
! 1807: If @var{str} is not NULL, it should point to a block of storage enough large
! 1808: for the mantissa, i.e., @var{n_digits} + 2. The two extra bytes are for a
! 1809: possible minus sign, and for the terminating null character.
! 1810:
! 1811: The exponent is written through the pointer @var{expptr}.
! 1812:
! 1813: If @var{n_digits} is 0, the maximum number of digits meaningfully achievable
! 1814: from the precision of @var{op} will be generated. Note that the space
! 1815: requirements for @var{str} in this case will be impossible for the user to
! 1816: predetermine. Therefore, you need to pass NULL for the string argument
! 1817: whenever @var{n_digits} is 0.
! 1818:
! 1819: The generated string is a fraction, with an implicit radix point immediately
! 1820: to the left of the first digit. For example, the number 3.1416 would be
! 1821: returned as "31416" in the string and 1 written at @var{expptr}.
! 1822: @end deftypefun
! 1823:
! 1824:
! 1825: @node Float Arithmetic, Float Comparison, Converting Floats, Floating-point Functions
! 1826: @comment node-name, next, previous, up
! 1827: @section Arithmetic Functions
! 1828: @cindex Float arithmetic functions
! 1829: @cindex Arithmetic functions
! 1830:
! 1831: @deftypefun void mpf_add (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1832: @deftypefunx void mpf_add_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1833: @ifinfo
! 1834: Set @var{rop} to @var{op1} + @var{op2}.
! 1835: @end ifinfo
! 1836: @iftex
! 1837: @tex
! 1838: Set @var{rop} to $@var{op1} + @var{op2}$.
! 1839: @end tex
! 1840: @end iftex
! 1841: @end deftypefun
! 1842:
! 1843: @deftypefun void mpf_sub (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1844: @deftypefunx void mpf_ui_sub (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
! 1845: @deftypefunx void mpf_sub_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1846: Set @var{rop} to @var{op1} @minus{} @var{op2}.
! 1847: @end deftypefun
! 1848:
! 1849: @deftypefun void mpf_mul (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1850: @deftypefunx void mpf_mul_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1851: @ifinfo
! 1852: Set @var{rop} to @var{op1} times @var{op2}.
! 1853: @end ifinfo
! 1854: @iftex
! 1855: @tex
! 1856: Set @var{rop} to $@var{op1} \times @var{op2}$.
! 1857: @end tex
! 1858: @end iftex
! 1859: @end deftypefun
! 1860:
! 1861: Division is undefined if the divisor is zero, and passing a zero divisor to
! 1862: the divide functions will make these functions intentionally divide by zero.
! 1863: This gives the user the possibility to handle arithmetic exceptions in these
! 1864: functions in the same manner as other arithmetic exceptions.
! 1865:
! 1866: @deftypefun void mpf_div (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1867: @deftypefunx void mpf_ui_div (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
! 1868: @deftypefunx void mpf_div_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1869: Set @var{rop} to @var{op1}/@var{op2}.
! 1870: @end deftypefun
! 1871:
! 1872: @deftypefun void mpf_sqrt (mpf_t @var{rop}, mpf_t @var{op})
! 1873: @deftypefunx void mpf_sqrt_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1874: @ifinfo
! 1875: Set @var{rop} to the square root of @var{op}.
! 1876: @end ifinfo
! 1877: @iftex
! 1878: @tex
! 1879: Set @var{rop} to $\sqrt{@var{op}}$.
! 1880: @end tex
! 1881: @end iftex
! 1882: @end deftypefun
! 1883:
! 1884: @c @deftypefun void mpf_pow_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1885: @c Set @var{rop} to @var{op1} raised to @var{op2}.
! 1886: @c @end deftypefun
! 1887:
! 1888: @deftypefun void mpf_neg (mpf_t @var{rop}, mpf_t @var{op})
! 1889: Set @var{rop} to @minus{}@var{op}.
! 1890: @end deftypefun
! 1891:
! 1892: @deftypefun void mpf_abs (mpf_t @var{rop}, mpf_t @var{op})
! 1893: Set @var{rop} to the absolute value of @var{op}.
! 1894: @end deftypefun
! 1895:
! 1896: @deftypefun void mpf_mul_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1897: @ifinfo
! 1898: Set @var{rop} to @var{op1} times 2 raised to @var{op2}.
! 1899: @end ifinfo
! 1900: @iftex
! 1901: @tex
! 1902: Set @var{rop} to $@var{op1} \times 2^{op2}$.
! 1903: @end tex
! 1904: @end iftex
! 1905: @end deftypefun
! 1906:
! 1907: @deftypefun void mpf_div_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1908: @ifinfo
! 1909: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.
! 1910: @end ifinfo
! 1911: @iftex
! 1912: @tex
! 1913: Set @var{rop} to $@var{op1}/2^{op2}$.
! 1914: @end tex
! 1915: @end iftex
! 1916: @end deftypefun
! 1917:
! 1918: @node Float Comparison, I/O of Floats, Float Arithmetic, Floating-point Functions
! 1919: @comment node-name, next, previous, up
! 1920: @section Comparison Functions
! 1921: @cindex Float comparisons functions
! 1922: @cindex Comparison functions
! 1923:
! 1924: @deftypefun int mpf_cmp (mpf_t @var{op1}, mpf_t @var{op2})
! 1925: @deftypefunx int mpf_cmp_ui (mpf_t @var{op1}, unsigned long int @var{op2})
! 1926: @deftypefunx int mpf_cmp_si (mpf_t @var{op1}, signed long int @var{op2})
! 1927: @ifinfo
! 1928: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1929: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1930: @var{op2}.
! 1931: @end ifinfo
! 1932: @iftex
! 1933: @tex
! 1934: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1935: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1936: < @var{op2}$.
! 1937: @end tex
! 1938: @end iftex
! 1939: @end deftypefun
! 1940:
! 1941: @deftypefun int mpf_eq (mpf_t @var{op1}, mpf_t @var{op2}, unsigned long int op3)
! 1942: Return non-zero if the first @var{op3} bits of @var{op1} and @var{op2} are
! 1943: equal, zero otherwise. I.e., test of @var{op1} and @var{op2} are
! 1944: approximately equal.
! 1945: @end deftypefun
! 1946:
! 1947: @deftypefun void mpf_reldiff (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1948: Compute the relative difference between @var{op1} and @var{op2} and store the
! 1949: result in @var{rop}.
! 1950: @end deftypefun
! 1951:
! 1952: @deftypefn Macro int mpf_sgn (mpf_t @var{op})
! 1953: @ifinfo
! 1954: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
! 1955: @end ifinfo
! 1956: @iftex
! 1957: @tex
! 1958: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1959: @end tex
! 1960: @end iftex
! 1961:
! 1962: This function is actually implemented as a macro. It evaluates its
! 1963: arguments multiple times.
! 1964: @end deftypefn
! 1965:
! 1966: @node I/O of Floats, Miscellaneous Float Functions, Float Comparison, Floating-point Functions
! 1967: @comment node-name, next, previous, up
! 1968: @section Input and Output Functions
! 1969: @cindex Float input and output functions
! 1970: @cindex Input functions
! 1971: @cindex Output functions
! 1972: @cindex I/O functions
! 1973:
! 1974: Functions that perform input from a stdio stream, and functions that output to
! 1975: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
! 1976: these functions will make them read from @code{stdin} and write to
! 1977: @code{stdout}, respectively.
! 1978:
! 1979: When using any of these functions, it is a good idea to include @file{stdio.h}
! 1980: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
! 1981: for these functions.
! 1982:
! 1983: @deftypefun size_t mpf_out_str (FILE *@var{stream}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
! 1984: Output @var{op} on stdio stream @var{stream}, as a string of digits in
! 1985: base @var{base}. The base may vary from 2 to 36. Print at most
! 1986: @var{n_digits} significant digits, or if @var{n_digits} is 0, the maximum
! 1987: number of digits accurately representable by @var{op}.
! 1988:
! 1989: In addition to the significant digits, a leading @samp{0.} and a
! 1990: trailing exponent, in the form @samp{eNNN}, are printed. If @var{base}
! 1991: is greater than 10, @samp{@@} will be used instead of @samp{e} as
! 1992: exponent delimiter.
! 1993:
! 1994: Return the number of bytes written, or if an error occurred, return 0.
! 1995: @end deftypefun
! 1996:
! 1997: @deftypefun size_t mpf_inp_str (mpf_t @var{rop}, FILE *@var{stream}, int @var{base})
! 1998: Input a string in base @var{base} from stdio stream @var{stream}, and put the
! 1999: read float in @var{rop}. The string is of the form @samp{M@@N} or, if the
! 2000: base is 10 or less, alternatively @samp{MeN}. @samp{M} is the mantissa and
! 2001: @samp{N} is the exponent. The mantissa is always in the specified base. The
! 2002: exponent is either in the specified base or, if @var{base} is negative, in
! 2003: decimal.
! 2004:
! 2005: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
! 2006: @minus{}2. Negative values are used to specify that the exponent is in
! 2007: decimal.
! 2008:
! 2009: Unlike the corresponding @code{mpz} function, the base will not be determined
! 2010: from the leading characters of the string if @var{base} is 0. This is so that
! 2011: numbers like @samp{0.23} are not interpreted as octal.
! 2012:
! 2013: Return the number of bytes read, or if an error occurred, return 0.
! 2014: @end deftypefun
! 2015:
! 2016: @c @deftypefun void mpf_out_raw (FILE *@var{stream}, mpf_t @var{float})
! 2017: @c Output @var{float} on stdio stream @var{stream}, in raw binary
! 2018: @c format. The float is written in a portable format, with 4 bytes of
! 2019: @c size information, and that many bytes of limbs. Both the size and the
! 2020: @c limbs are written in decreasing significance order.
! 2021: @c @end deftypefun
! 2022:
! 2023: @c @deftypefun void mpf_inp_raw (mpf_t @var{float}, FILE *@var{stream})
! 2024: @c Input from stdio stream @var{stream} in the format written by
! 2025: @c @code{mpf_out_raw}, and put the result in @var{float}.
! 2026: @c @end deftypefun
! 2027:
! 2028:
! 2029: @node Miscellaneous Float Functions, , I/O of Floats, Floating-point Functions
! 2030: @comment node-name, next, previous, up
! 2031: @section Miscellaneous Functions
! 2032: @cindex Miscellaneous float functions
! 2033:
! 2034: @deftypefun void mpf_random2 (mpf_t @var{rop}, mp_size_t @var{max_size}, mp_exp_t @var{max_exp})
! 2035: Generate a random float of at most @var{max_size} limbs, with long strings of
! 2036: zeros and ones in the binary representation. The exponent of the number is in
! 2037: the interval @minus{}@var{exp} to @var{exp}. This function is useful for
! 2038: testing functions and algorithms, since this kind of random numbers have
! 2039: proven to be more likely to trigger corner-case bugs. Negative random numbers
! 2040: are generated when @var{max_size} is negative.
! 2041: @end deftypefun
! 2042:
! 2043: @c @deftypefun size_t mpf_size (mpf_t @var{op})
! 2044: @c Return the size of @var{op} measured in number of limbs. If @var{op} is
! 2045: @c zero, the returned value will be zero. (@xref{Nomenclature}, for an
! 2046: @c explanation of the concept @dfn{limb}.)
! 2047: @c
! 2048: @c @strong{This function is obsolete. It will disappear from future MP
! 2049: @c releases.}
! 2050: @c @end deftypefun
! 2051:
! 2052: @node Low-level Functions, BSD Compatible Functions, Floating-point Functions, Top
! 2053: @comment node-name, next, previous, up
! 2054: @chapter Low-level Functions
! 2055: @cindex Low-level functions
! 2056:
! 2057: This chapter describes low-level MP functions, used to implement the high-level
! 2058: MP functions, but also intended for time-critical user code.
! 2059:
! 2060: These functions start with the prefix @code{mpn_}.
! 2061:
! 2062: @c 1. Some of these function clobber input operands.
! 2063: @c
! 2064:
! 2065: The @code{mpn} functions are designed to be as fast as possible, @strong{not}
! 2066: to provide a coherent calling interface. The different functions have somewhat
! 2067: similar interfaces, but there are variations that make them hard to use. These
! 2068: functions do as little as possible apart from the real multiple precision
! 2069: computation, so that no time is spent on things that not all callers need.
! 2070:
! 2071: A source operand is specified by a pointer to the least significant limb and a
! 2072: limb count. A destination operand is specified by just a pointer. It is the
! 2073: responsibility of the caller to ensure that the destination has enough space
! 2074: for storing the result.
! 2075:
! 2076: With this way of specifying operands, it is possible to perform computations
! 2077: on subranges of an argument, and store the result into a subrange of a
! 2078: destination.
! 2079:
! 2080: A common requirement for all functions is that each source area needs at least
! 2081: one limb. No size argument may be zero.
! 2082:
! 2083: The @code{mpn} functions is the base for the implementation of the @code{mpz_},
! 2084: @code{mpf_}, and @code{mpq_} functions.
! 2085:
! 2086: This example adds the number beginning at @var{src1_ptr} and the number
! 2087: beginning at @var{src2_ptr} and writes the sum at @var{dest_ptr}. All areas
! 2088: have @var{size} limbs.
! 2089:
! 2090: @example
! 2091: cy = mpn_add_n (dest_ptr, src1_ptr, src2_ptr, size)
! 2092: @end example
! 2093:
! 2094: @noindent
! 2095: In the notation used here, a source operand is identified by the pointer to
! 2096: the least significant limb, and the limb count in braces. For example,
! 2097: @{s1_ptr, s1_size@}.
! 2098:
! 2099: @deftypefun mp_limb_t mpn_add_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
! 2100: Add @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@}, and
! 2101: write the @var{size} least significant limbs of the result to @var{dest_ptr}.
! 2102: Return carry, either 0 or 1.
! 2103:
! 2104: This is the lowest-level function for addition. It is the preferred function
! 2105: for addition, since it is written in assembly for most targets. For addition
! 2106: of a variable to itself (i.e., @var{src1_ptr} equals @var{src2_ptr}, use
! 2107: @code{mpn_lshift} with a count of 1 for optimal speed.
! 2108: @end deftypefun
! 2109:
! 2110: @deftypefun mp_limb_t mpn_add_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
! 2111: Add @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
! 2112: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
! 2113: carry, either 0 or 1.
! 2114: @end deftypefun
! 2115:
! 2116: @deftypefun mp_limb_t mpn_add (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
! 2117: Add @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
! 2118: @var{src2_size}@}, and write the @var{src1_size} least significant limbs of
! 2119: the result to @var{dest_ptr}. Return carry, either 0 or 1.
! 2120:
! 2121: This function requires that @var{src1_size} is greater than or equal to
! 2122: @var{src2_size}.
! 2123: @end deftypefun
! 2124:
! 2125: @deftypefun mp_limb_t mpn_sub_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
! 2126: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
! 2127: @var{size}@}, and write the @var{size} least significant limbs of the result
! 2128: to @var{dest_ptr}. Return borrow, either 0 or 1.
! 2129:
! 2130: This is the lowest-level function for subtraction. It is the preferred
! 2131: function for subtraction, since it is written in assembly for most targets.
! 2132: @end deftypefun
! 2133:
! 2134: @deftypefun mp_limb_t mpn_sub_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
! 2135: Subtract @var{src2_limb} from @{@var{src1_ptr}, @var{size}@}, and write the
! 2136: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
! 2137: borrow, either 0 or 1.
! 2138: @end deftypefun
! 2139:
! 2140: @deftypefun mp_limb_t mpn_sub (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
! 2141: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
! 2142: @var{src1_size}@}, and write the @var{src1_size} least significant limbs of
! 2143: the result to @var{dest_ptr}. Return borrow, either 0 or 1.
! 2144:
! 2145: This function requires that @var{src1_size} is greater than or equal to
! 2146: @var{src2_size}.
! 2147: @end deftypefun
! 2148:
! 2149: @deftypefun void mpn_mul_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
! 2150: Multiply @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@},
! 2151: and write the @strong{entire} result to @var{dest_ptr}.
! 2152:
! 2153: The destination has to have space for 2@var{size} limbs, even if the
! 2154: significant result might be one limb smaller.
! 2155: @end deftypefun
! 2156:
! 2157: @deftypefun mp_limb_t mpn_mul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
! 2158: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
! 2159: @var{size} least significant limbs of the product to @var{dest_ptr}. Return
! 2160: the most significant limb of the product.
! 2161:
! 2162: This is a low-level function that is a building block for general
! 2163: multiplication as well as other operations in MP. It is written in assembly
! 2164: for most targets.
! 2165:
! 2166: Don't call this function if @var{src2_limb} is a power of 2; use
! 2167: @code{mpn_lshift} with a count equal to the logarithm of @var{src2_limb}
! 2168: instead, for optimal speed.
! 2169: @end deftypefun
! 2170:
! 2171: @deftypefun mp_limb_t mpn_addmul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
! 2172: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and add the
! 2173: @var{size} least significant limbs of the product to @{@var{dest_ptr},
! 2174: @var{size}@} and write the result to @var{dest_ptr} @var{dest_ptr}. Return
! 2175: the most significant limb of the product, plus carry-out from the addition.
! 2176:
! 2177: This is a low-level function that is a building block for general
! 2178: multiplication as well as other operations in MP. It is written in assembly
! 2179: for most targets.
! 2180: @end deftypefun
! 2181:
! 2182: @deftypefun mp_limb_t mpn_submul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
! 2183: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and subtract the
! 2184: @var{size} least significant limbs of the product from @{@var{dest_ptr},
! 2185: @var{size}@} and write the result to @var{dest_ptr}. Return the most
! 2186: significant limb of the product, minus borrow-out from the subtraction.
! 2187:
! 2188: This is a low-level function that is a building block for general
! 2189: multiplication and division as well as other operations in MP. It is written
! 2190: in assembly for most targets.
! 2191: @end deftypefun
! 2192:
! 2193: @deftypefun mp_limb_t mpn_mul (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
! 2194: Multiply @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
! 2195: @var{src2_size}@}, and write the result to @var{dest_ptr}. Return the most
! 2196: significant limb of the result.
! 2197:
! 2198: The destination has to have space for @var{src1_size} + @var{src1_size}
! 2199: limbs, even if the result might be one limb smaller.
! 2200:
! 2201: This function requires that @var{src1_size} is greater than or equal to
! 2202: @var{src2_size}. The destination must be distinct from either input operands.
! 2203: @end deftypefun
! 2204:
! 2205: @deftypefun mp_size_t mpn_divrem (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
! 2206: Divide @{@var{rs2p}, @var{rs2size}@} by @{@var{s3p}, @var{s3size}@}, and
! 2207: write the quotient at @var{r1p}, with the exception of the most significant
! 2208: limb, which is returned. The remainder replaces the dividend at @var{rs2p}.
! 2209:
! 2210: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
! 2211: and stored after the integral limbs. For most usages, @var{xsize} will be
! 2212: zero.
! 2213:
! 2214: It is required that @var{rs2size} is greater than or equal to @var{s3size}.
! 2215: It is required that the most significant bit of the divisor is set.
! 2216:
! 2217: If the quotient is not needed, pass @var{rs2p} + @var{s3size} as @var{r1p}.
! 2218: Aside from that special case, no overlap between arguments is permitted.
! 2219:
! 2220: Return the most significant limb of the quotient, either 0 or 1.
! 2221:
! 2222: The area at @var{r1p} needs to be @var{rs2size} @minus{} @var{s3size} +
! 2223: @var{xsize} limbs large.
! 2224: @end deftypefun
! 2225:
! 2226: @deftypefun mp_limb_t mpn_divrem_1 (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
! 2227: Divide @{@var{s2p}, @var{s2size}@} by @var{s3limb}, and write the quotient
! 2228: at @var{r1p}. Return the remainder.
! 2229:
! 2230: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
! 2231: and stored after the integral limbs. For most usages, @var{xsize} will be
! 2232: zero.
! 2233:
! 2234: The areas at @var{r1p} and @var{s2p} have to be identical or completely
! 2235: separate, not partially overlapping.
! 2236: @end deftypefun
! 2237:
! 2238: @deftypefun mp_size_t mpn_divmod (mp_limb_t * @var{r1p}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
! 2239: @strong{This interface is obsolete. It will disappear from future releases.
! 2240: Use @code{mpn_divrem} in its stead.}
! 2241: @end deftypefun
! 2242:
! 2243: @deftypefun mp_limb_t mpn_divmod_1 (mp_limb_t * @var{r1p}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
! 2244: @strong{This interface is obsolete. It will disappear from future releases.
! 2245: Use @code{mpn_divrem_1} in its stead.}
! 2246: @end deftypefun
! 2247:
! 2248: @deftypefun mp_limb_t mpn_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb})
! 2249: Divide @{@var{s1p}, @var{s1size}@} by @var{s2limb}, and return the remainder.
! 2250: @end deftypefun
! 2251:
! 2252: @deftypefun mp_limb_t mpn_preinv_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb}, mp_limb_t @var{s3limb})
! 2253: @strong{This interface is obsolete. It will disappear from future releases.
! 2254: Use @code{mpn_mod_1} in its stead.}
! 2255: @end deftypefun
! 2256:
! 2257: @deftypefun mp_limb_t mpn_bdivmod (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, const mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, unsigned long int @var{d})
! 2258: The function puts the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
! 2259: @var{q} =
! 2260: @{@var{s1p}, @var{s1size}@}/@{@var{s2p}, @var{s2size}@}
! 2261: mod 2^@var{d}
! 2262: at @var{dest_ptr},
! 2263: and returns the high @var{d} mod @var{BITS_PER_MP_LIMB} bits of @var{q}.
! 2264:
! 2265: @{@var{s1p}, @var{s1size}@} - @var{q} * @{@var{s2p}, @var{s2size}@}
! 2266: mod 2^(@var{s1size}*@var{BITS_PER_MP_LIMB})
! 2267: is placed at @var{s1p}.
! 2268: Since the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
! 2269: this difference are zero, it is possible to overwrite the low limbs at
! 2270: @var{s1p} with this difference,
! 2271: provided @var{dest_ptr} <= @var{s1p}.
! 2272:
! 2273: This function requires that @var{s1size} * @var{BITS_PER_MP_LIMB} >= @var{D},
! 2274: and that @{@var{s2p}, @var{s2size}@} is odd.
! 2275:
! 2276: @strong{This interface is preliminary. It might change incompatibly in
! 2277: future revisions.}
! 2278: @end deftypefun
! 2279:
! 2280: @deftypefun mp_limb_t mpn_lshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
! 2281: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the left, and
! 2282: write the @var{src_size} least significant limbs of the result to
! 2283: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
! 2284: n-bit machine. The bits shifted out to the left are returned.
! 2285:
! 2286: Overlapping of the destination space and the source space is allowed in this
! 2287: function, provided @var{dest_ptr} >= @var{src_ptr}.
! 2288:
! 2289: This function is written in assembly for most targets.
! 2290: @end deftypefun
! 2291:
! 2292: @deftypefun mp_limp_t mpn_rshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
! 2293: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the right, and
! 2294: write the @var{src_size} most significant limbs of the result to
! 2295: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
! 2296: n-bit machine. The bits shifted out to the right are returned.
! 2297:
! 2298: Overlapping of the destination space and the source space is allowed in this
! 2299: function, provided @var{dest_ptr} <= @var{src_ptr}.
! 2300:
! 2301: This function is written in assembly for most targets.
! 2302: @end deftypefun
! 2303:
! 2304: @deftypefun int mpn_cmp (const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
! 2305: Compare @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@} and
! 2306: return a positive value if src1 > src2, 0 of they are equal, and a negative
! 2307: value if src1 < src2.
! 2308: @end deftypefun
! 2309:
! 2310: @deftypefun mp_size_t mpn_gcd (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
! 2311: Puts at @var{dest_ptr} the greatest common divisor of @{@var{src1_ptr},
! 2312: @var{src1_size}@} and @{@var{src2_ptr}, @var{src2_size}@}; both source
! 2313: operands are destroyed by the operation. The size in limbs of the greatest
! 2314: common divisor is returned.
! 2315:
! 2316: @{@var{src1_ptr}, @var{src1_size}@} must be odd, and @{@var{src2_ptr},
! 2317: @var{src2_size}@} must have at least as many bits as @{@var{src1_ptr},
! 2318: @var{src1_size}@}.
! 2319:
! 2320: @strong{This interface is preliminary. It might change incompatibly in
! 2321: future revisions.}
! 2322: @end deftypefun
! 2323:
! 2324: @deftypefun mp_limb_t mpn_gcd_1 (const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t @var{src2_limb})
! 2325: Return the greatest common divisor of @{@var{src1_ptr}, @var{src1_size}@}
! 2326: and @var{src2_limb}, where @var{src2_limb} (as well as @var{src1_size})
! 2327: must be different from 0.
! 2328: @end deftypefun
! 2329:
! 2330: @deftypefun mp_size_t mpn_gcdext (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size})
! 2331: Puts at @var{r1p} the greatest common divisor of @{@var{s1p}, @var{s1size}@}
! 2332: and @{@var{s2p}, @var{s2size}@}. The first cofactor is written at
! 2333: @var{r2p}. Both source operands are destroyed by the operation. The size
! 2334: in limbs of the greatest common divisor is returned.
! 2335:
! 2336: @strong{This interface is preliminary. It might change incompatibly in
! 2337: future revisions.}
! 2338: @end deftypefun
! 2339:
! 2340: @deftypefun mp_size_t mpn_sqrtrem (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, const mp_limb_t * @var{sp}, mp_size_t @var{size})
! 2341: Compute the square root of @{@var{sp}, @var{size}@} and put the result at
! 2342: @var{r1p}. Write the remainder at @var{r2p}, unless @var{r2p} is NULL.
! 2343:
! 2344: Return the size of the remainder, whether @var{r2p} was NULL or non-NULL.
! 2345: Iff the operand was a perfect square, the return value will be 0.
! 2346:
! 2347: The areas at @var{r1p} and @var{sp} have to be distinct. The areas at
! 2348: @var{r2p} and @var{sp} have to be identical or completely separate, not
! 2349: partially overlapping.
! 2350:
! 2351: @ifinfo
! 2352: The area at @var{r1p} needs to have space for ceil(@var{size}/2) limbs.
! 2353: @end ifinfo
! 2354: @iftex
! 2355: @tex
! 2356: The area at @var{r1p} needs to have space for $\lceil@var{size}/2\rceil$ limbs.
! 2357: @end tex
! 2358: @end iftex
! 2359: The area at @var{r2p} needs to be @var{size} limbs large.
! 2360:
! 2361: @strong{This interface is preliminary. It might change incompatibly in
! 2362: future revisions.}
! 2363: @end deftypefun
! 2364:
! 2365: @deftypefun mp_size_t mpn_get_str (unsigned char *@var{str}, int @var{base}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size})
! 2366: Convert @{@var{s1p}, @var{s1size}@} to a raw unsigned char array in base
! 2367: @var{base}. The string is not in ASCII; to convert it to printable format,
! 2368: add the ASCII codes for @samp{0} or @samp{A}, depending on the base and
! 2369: range. There may be leading zeros in the string.
! 2370:
! 2371: The area at @var{s1p} is clobbered.
! 2372:
! 2373: Return the number of characters in @var{str}.
! 2374:
! 2375: The area at @var{str} has to have space for the largest possible number
! 2376: represented by a @var{s1size} long limb array, plus one extra character.
! 2377: @end deftypefun
! 2378:
! 2379: @deftypefun mp_size_t mpn_set_str (mp_limb_t * @var{r1p}, const char *@var{str}, size_t {strsize}, int @var{base})
! 2380: Convert the raw unsigned char array at @var{str} of length @var{strsize} to
! 2381: a limb array @{@var{s1p}, @var{s1size}@}. The base of @var{str} is
! 2382: @var{base}.
! 2383:
! 2384: Return the number of limbs stored in @var{r1p}.
! 2385: @end deftypefun
! 2386:
! 2387: @deftypefun {unsigned long int} mpn_scan0 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
! 2388: Scan @var{s1p} from bit position @var{bit} for the next clear bit.
! 2389:
! 2390: It is required that there be a clear bit within the area at @var{s1p} at or
! 2391: beyond bit position @var{bit}, so that the function has something to return.
! 2392:
! 2393: @strong{This interface is preliminary. It might change incompatibly in
! 2394: future revisions.}
! 2395: @end deftypefun
! 2396:
! 2397: @deftypefun {unsigned long int} mpn_scan1 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
! 2398: Scan @var{s1p} from bit position @var{bit} for the next set bit.
! 2399:
! 2400: It is required that there be a set bit within the area at @var{s1p} at or
! 2401: beyond bit position @var{bit}, so that the function has something to return.
! 2402:
! 2403: @strong{This interface is preliminary. It might change incompatibly in
! 2404: future revisions.}
! 2405: @end deftypefun
! 2406:
! 2407: @deftypefun void mpn_random2 (mp_limb_t * @var{r1p}, mp_size_t @var{r1size})
! 2408: Generate a random number of length @var{r1size} with long strings of zeros
! 2409: and ones in the binary representation, and store it at @var{r1p}.
! 2410:
! 2411: The generated random numbers are intended for testing the correctness of the
! 2412: implementation of the @code{mpn} routines.
! 2413: @end deftypefun
! 2414:
! 2415: @deftypefun {unsigned long int} mpn_popcount (const mp_limb_t * @var{s1p}, unsigned long int @var{size})
! 2416: Count the number of set bits in @{@var{s1p}, @var{size}@}.
! 2417: @end deftypefun
! 2418:
! 2419: @deftypefun {unsigned long int} mpn_hamdist (const mp_limb_t * @var{s1p}, const mp_limb_t * @var{s2p}, unsigned long int @var{size})
! 2420: Compute the hamming distance between @{@var{s1p}, @var{size}@} and
! 2421: @{@var{s2p}, @var{size}@}.
! 2422: @end deftypefun
! 2423:
! 2424: @deftypefun int mpn_perfect_square_p (const mp_limb_t * @var{s1p}, mp_size_t @var{size})
! 2425: Return non-zero iff @{@var{s1p}, @var{size}@} is a perfect square.
! 2426: @end deftypefun
! 2427:
! 2428:
! 2429: @node BSD Compatible Functions, Custom Allocation, Low-level Functions, Top
! 2430: @comment node-name, next, previous, up
! 2431: @chapter Berkeley MP Compatible Functions
! 2432: @cindex BSD MP compatible functions
! 2433:
! 2434: These functions are intended to be fully compatible with the Berkeley MP
! 2435: library which is available on many BSD derived U*ix systems.
! 2436:
! 2437: The original Berkeley MP library has a usage restriction: you cannot use the
! 2438: same variable as both source and destination in a single function call. The
! 2439: compatible functions in GNU MP do not share this restriction---inputs and
! 2440: outputs may overlap.
! 2441:
! 2442: It is not recommended that new programs are written using these functions.
! 2443: Apart from the incomplete set of functions, the interface for initializing
! 2444: @code{MINT} objects is more error prone, and the @code{pow} function collides
! 2445: with @code{pow} in @file{libm.a}.
! 2446:
! 2447: @cindex @file{mp.h}
! 2448: Include the header @file{mp.h} to get the definition of the necessary types
! 2449: and functions. If you are on a BSD derived system, make sure to include GNU
! 2450: @file{mp.h} if you are going to link the GNU @file{libmp.a} to you program.
! 2451: This means that you probably need to give the -I<dir> option to the compiler,
! 2452: where <dir> is the directory where you have GNU @file{mp.h}.
! 2453:
! 2454: @deftypefun {MINT *} itom (signed short int @var{initial_value})
! 2455: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
! 2456: Initialize the integer to @var{initial_value}. Return a pointer to the
! 2457: @code{MINT} object.
! 2458: @end deftypefun
! 2459:
! 2460: @deftypefun {MINT *} xtom (char *@var{initial_value})
! 2461: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
! 2462: Initialize the integer from @var{initial_value}, a hexadecimal, '\0'-terminate
! 2463: C string. Return a pointer to the @code{MINT} object.
! 2464: @end deftypefun
! 2465:
! 2466: @deftypefun void move (MINT *@var{src}, MINT *@var{dest})
! 2467: Set @var{dest} to @var{src} by copying. Both variables must be previously
! 2468: initialized.
! 2469: @end deftypefun
! 2470:
! 2471: @deftypefun void madd (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2472: Add @var{src_1} and @var{src_2} and put the sum in @var{destination}.
! 2473: @end deftypefun
! 2474:
! 2475: @deftypefun void msub (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2476: Subtract @var{src_2} from @var{src_1} and put the difference in
! 2477: @var{destination}.
! 2478: @end deftypefun
! 2479:
! 2480: @deftypefun void mult (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2481: Multiply @var{src_1} and @var{src_2} and put the product in
! 2482: @var{destination}.
! 2483: @end deftypefun
! 2484:
! 2485: @deftypefun void mdiv (MINT *@var{dividend}, MINT *@var{divisor}, MINT *@var{quotient}, MINT *@var{remainder})
! 2486: @deftypefunx void sdiv (MINT *@var{dividend}, signed short int @var{divisor}, MINT *@var{quotient}, signed short int *@var{remainder})
! 2487: Set @var{quotient} to @var{dividend}/@var{divisor}, and @var{remainder} to
! 2488: @var{dividend} mod @var{divisor}. The quotient is rounded towards zero; the
! 2489: remainder has the same sign as the dividend unless it is zero.
! 2490:
! 2491: Some implementations of these functions work differently---or not at all---for
! 2492: negative arguments.
! 2493: @end deftypefun
! 2494:
! 2495: @deftypefun void msqrt (MINT *@var{operand}, MINT *@var{root}, MINT *@var{remainder})
! 2496: @ifinfo
! 2497: Set @var{root} to the truncated integer part of the square root of
! 2498: @var{operand}. Set @var{remainder} to
! 2499: @var{operand}@minus{}@var{root}*@var{root},
! 2500: @end ifinfo
! 2501: @iftex
! 2502: @tex
! 2503: Set @var{root} to $\lfloor\sqrt{@var{operand}}\rfloor$, like
! 2504: @code{mpz_sqrt}. Set @var{remainder} to $(operand - root^2)$,
! 2505: @end tex
! 2506: @end iftex
! 2507: (i.e., zero if @var{operand} is a perfect square).
! 2508:
! 2509: If @var{root} and @var{remainder} are the same variable, the results are
! 2510: undefined.
! 2511: @end deftypefun
! 2512:
! 2513: @deftypefun void pow (MINT *@var{base}, MINT *@var{exp}, MINT *@var{mod}, MINT *@var{dest})
! 2514: Set @var{dest} to (@var{base} raised to @var{exp}) modulo @var{mod}.
! 2515: @end deftypefun
! 2516:
! 2517: @deftypefun void rpow (MINT *@var{base}, signed short int @var{exp}, MINT *@var{dest})
! 2518: Set @var{dest} to @var{base} raised to @var{exp}.
! 2519: @end deftypefun
! 2520:
! 2521: @deftypefun void gcd (MINT *@var{operand1}, MINT *@var{operand2}, MINT *@var{res})
! 2522: Set @var{res} to the greatest common divisor of @var{operand1} and
! 2523: @var{operand2}.
! 2524: @end deftypefun
! 2525:
! 2526: @deftypefun int mcmp (MINT *@var{operand1}, MINT *@var{operand2})
! 2527: Compare @var{operand1} and @var{operand2}. Return a positive value if
! 2528: @var{operand1} > @var{operand2}, zero if @var{operand1} =
! 2529: @var{operand2}, and a negative value if @var{operand1} < @var{operand2}.
! 2530: @end deftypefun
! 2531:
! 2532: @deftypefun void min (MINT *@var{dest})
! 2533: Input a decimal string from @code{stdin}, and put the read integer in
! 2534: @var{dest}. SPC and TAB are allowed in the number string, and are ignored.
! 2535: @end deftypefun
! 2536:
! 2537: @deftypefun void mout (MINT *@var{src})
! 2538: Output @var{src} to @code{stdout}, as a decimal string. Also output a newline.
! 2539: @end deftypefun
! 2540:
! 2541: @deftypefun {char *} mtox (MINT *@var{operand})
! 2542: Convert @var{operand} to a hexadecimal string, and return a pointer to the
! 2543: string. The returned string is allocated using the default memory allocation
! 2544: function, @code{malloc} by default.
! 2545: @end deftypefun
! 2546:
! 2547: @deftypefun void mfree (MINT *@var{operand})
! 2548: De-allocate, the space used by @var{operand}. @strong{This function should
! 2549: only be passed a value returned by @code{itom} or @code{xtom}.}
! 2550: @end deftypefun
! 2551:
! 2552: @node Custom Allocation, Contributors, BSD Compatible Functions, Top
! 2553: @comment node-name, next, previous, up
! 2554: @chapter Custom Allocation
! 2555:
! 2556: By default, the MP functions use @code{malloc}, @code{realloc}, and
! 2557: @code{free} for memory allocation. If @code{malloc} or @code{realloc} fails,
! 2558: the MP library terminates execution after printing a fatal error message to
! 2559: standard error.
! 2560:
! 2561: For some applications, you may wish to allocate memory in other ways, or you
! 2562: may not want to have a fatal error when there is no more memory available. To
! 2563: accomplish this, you can specify alternative memory allocation functions.
! 2564:
! 2565: @deftypefun void mp_set_memory_functions (@* void *(*@var{alloc_func_ptr}) (size_t), @* void *(*@var{realloc_func_ptr}) (void *, size_t, size_t), @* void (*@var{free_func_ptr}) (void *, size_t))
! 2566: Replace the current allocation functions from the arguments. If an argument
! 2567: is NULL, the corresponding default function is retained.
! 2568:
! 2569: @strong{Make sure to call this function in such a way that there are no active
! 2570: MP objects that were allocated using the previously active allocation
! 2571: function! Usually, that means that you have to call this function before any
! 2572: other MP function.}
! 2573: @end deftypefun
! 2574:
! 2575: The functions you supply should fit the following declarations:
! 2576:
! 2577: @deftypefun {void *} allocate_function (size_t @var{alloc_size})
! 2578: This function should return a pointer to newly allocated space with at least
! 2579: @var{alloc_size} storage units.
! 2580: @end deftypefun
! 2581:
! 2582: @deftypefun {void *} reallocate_function (void *@var{ptr}, size_t @var{old_size}, size_t @var{new_size})
! 2583: This function should return a pointer to newly allocated space of at least
! 2584: @var{new_size} storage units, after copying at least the first @var{old_size}
! 2585: storage units from @var{ptr}. It should also de-allocate the space at
! 2586: @var{ptr}.
! 2587:
! 2588: You can assume that the space at @var{ptr} was formerly returned from
! 2589: @code{allocate_function} or @code{reallocate_function}, for a request for
! 2590: @var{old_size} storage units.
! 2591: @end deftypefun
! 2592:
! 2593: @deftypefun void deallocate_function (void *@var{ptr}, size_t @var{size})
! 2594: De-allocate the space pointed to by @var{ptr}.
! 2595:
! 2596: You can assume that the space at @var{ptr} was formerly returned from
! 2597: @code{allocate_function} or @code{reallocate_function}, for a request for
! 2598: @var{size} storage units.
! 2599: @end deftypefun
! 2600:
! 2601: (A @dfn{storage unit} is the unit in which the @code{sizeof} operator returns
! 2602: the size of an object, normally an 8 bit byte.)
! 2603:
! 2604:
! 2605: @node Contributors, References, Custom Allocation, Top
! 2606: @comment node-name, next, previous, up
! 2607: @unnumbered Contributors
! 2608:
! 2609: I would like to thank Gunnar Sjoedin and Hans Riesel for their help with
! 2610: mathematical problems, Richard Stallman for his help with design issues and
! 2611: for revising the first version of this manual, Brian Beuning and Doug Lea for
! 2612: their testing of early versions of the library.
! 2613:
! 2614: John Amanatides of York University in Canada contributed the function
! 2615: @code{mpz_probab_prime_p}.
! 2616:
! 2617: Paul Zimmermann of Inria sparked the development of GMP 2, with his
! 2618: comparisons between bignum packages.
! 2619:
! 2620: Ken Weber (Kent State University, Universidade Federal do Rio Grande do Sul)
! 2621: contributed @code{mpz_gcd}, @code{mpz_divexact}, @code{mpn_gcd}, and
! 2622: @code{mpn_bdivmod}, partially supported by CNPq (Brazil) grant 301314194-2.
! 2623:
! 2624: Per Bothner of Cygnus Support helped to set up MP to use Cygnus' configure.
! 2625: He has also made valuable suggestions and tested numerous intermediary
! 2626: releases.
! 2627:
! 2628: Joachim Hollman was involved in the design of the @code{mpf} interface, and in
! 2629: the @code{mpz} design revisions for version 2.
! 2630:
! 2631: Bennet Yee contributed the functions @code{mpz_jacobi} and
! 2632: @code{mpz_legendre}.
! 2633:
! 2634: Andreas Schwab contributed the files @file{mpn/m68k/lshift.S} and
! 2635: @file{mpn/m68k/rshift.S}.
! 2636:
! 2637: The development of floating point functions of GNU MP 2, were supported in
! 2638: part by the ESPRIT-BRA (Basic Research Activities) 6846 project POSSO
! 2639: (POlynomial System SOlving).
! 2640:
! 2641: GNU MP 2 was finished and released by TMG Datakonsult, Sodermannagatan 5, 116
! 2642: 23 STOCKHOLM, SWEDEN, in cooperation with the IDA Center for Computing
! 2643: Sciences, USA.
! 2644:
! 2645:
! 2646: @node References, , Contributors, Top
! 2647: @comment node-name, next, previous, up
! 2648: @unnumbered References
! 2649:
! 2650: @itemize @bullet
! 2651:
! 2652: @item
! 2653: Donald E. Knuth, "The Art of Computer Programming", vol 2,
! 2654: "Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
! 2655:
! 2656: @item
! 2657: John D. Lipson, "Elements of Algebra and Algebraic Computing",
! 2658: The Benjamin Cummings Publishing Company Inc, 1981.
! 2659:
! 2660: @item
! 2661: Richard M. Stallman, "Using and Porting GCC", Free Software Foundation,
! 2662: 1995.
! 2663:
! 2664: @item
! 2665: Peter L. Montgomery, "Modular Multiplication Without Trial Division", in
! 2666: Mathematics of Computation, volume 44, number 170, April 1985.
! 2667:
! 2668: @item
! 2669: Torbjorn Granlund and Peter L. Montgomery, "Division by Invariant
! 2670: Integers using Multiplication", in Proceedings of the SIGPLAN
! 2671: PLDI'94 Conference, June 1994.
! 2672:
! 2673: @item
! 2674: Tudor Jebelean,
! 2675: "An algorithm for exact division",
! 2676: Journal of Symbolic Computation,
! 2677: v. 15, 1993, pp. 169-180.
! 2678:
! 2679: @item
! 2680: Kenneth Weber, "The accelerated integer GCD algorithm",
! 2681: ACM Transactions on Mathematical Software,
! 2682: v. 21 (March), 1995, pp. 111-122.
! 2683: @end itemize
! 2684:
! 2685: @node Concept Index, , , Top
! 2686: @comment node-name, next, previous, up
! 2687: @unnumbered Concept Index
! 2688: @printindex cp
! 2689:
! 2690: @node Function Index, , , Top
! 2691: @comment node-name, next, previous, up
! 2692: @unnumbered Function and Type Index
! 2693: @printindex fn
! 2694:
! 2695:
! 2696: @contents
! 2697: @bye
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