Annotation of OpenXM/src/kan96xx/gmp-2.0.2/gmp.info, Revision 1.1
1.1 ! maekawa 1: Info file: gmp.info, -*-Text-*-
! 2: produced by `texinfo-format-buffer'
! 3: from file `gmp.texi'
! 4: using `texinfmt.el' version 2.32 of 19 November 1993.
! 5:
! 6:
! 7: START-INFO-DIR-ENTRY
! 8: * gmp: (gmp.info). GNU Multiple Precision Arithmetic Library.
! 9: END-INFO-DIR-ENTRY
! 10:
! 11:
! 12:
! 13:
! 14:
! 15:
! 16: This file documents GNU MP, a library for arbitrary-precision
! 17: arithmetic.
! 18:
! 19: Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation,
! 20: Inc.
! 21:
! 22: Permission is granted to make and distribute verbatim copies of this
! 23: manual provided the copyright notice and this permission notice are
! 24: preserved on all copies.
! 25:
! 26: Permission is granted to copy and distribute modified versions of this
! 27: manual under the conditions for verbatim copying, provided that the
! 28: entire resulting derived work is distributed under the terms of a
! 29: permission notice identical to this one.
! 30:
! 31: Permission is granted to copy and distribute translations of this manual
! 32: into another language, under the above conditions for modified versions,
! 33: except that this permission notice may be stated in a translation
! 34: approved by the Foundation.
! 35:
! 36:
! 37:
! 38: File: gmp.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir)
! 39:
! 40:
! 41: GNU MP
! 42: ******
! 43:
! 44: This manual documents how to install and use the GNU multiple precision
! 45: arithmetic library, version 2.0.2.
! 46:
! 47:
! 48: * Menu:
! 49:
! 50: * Copying:: GMP Copying Conditions (LGPL).
! 51: * Introduction to MP:: Brief introduction to GNU MP.
! 52: * Installing MP:: How to configure and compile the MP library.
! 53: * MP Basics:: What every MP user should now.
! 54: * Reporting Bugs:: How to usefully report bugs.
! 55: * Integer Functions:: Functions for arithmetic on signed integers.
! 56: * Rational Number Functions:: Functions for arithmetic on rational numbers.
! 57: * Floating-point Functions:: Functions for arithmetic on floats.
! 58: * Low-level Functions:: Fast functions for natural numbers.
! 59: * BSD Compatible Functions:: All functions found in BSD MP.
! 60: * Custom Allocation:: How to customize the internal allocation.
! 61:
! 62: * Contributors::
! 63: * References::
! 64: * Concept Index::
! 65: * Function Index::
! 66:
! 67:
! 68: File: gmp.info, Node: Copying, Next: Introduction to MP, Prev: Top, Up: Top
! 69:
! 70: GNU MP Copying Conditions
! 71: *************************
! 72:
! 73: This library is "free"; this means that everyone is free to use it and
! 74: free to redistribute it on a free basis. The library is not in the
! 75: public domain; it is copyrighted and there are restrictions on its
! 76: distribution, but these restrictions are designed to permit everything
! 77: that a good cooperating citizen would want to do. What is not allowed
! 78: is to try to prevent others from further sharing any version of this
! 79: library that they might get from you.
! 80:
! 81: Specifically, we want to make sure that you have the right to give away
! 82: copies of the library, that you receive source code or else can get it
! 83: if you want it, that you can change this library or use pieces of it in
! 84: new free programs, and that you know you can do these things.
! 85:
! 86: To make sure that everyone has such rights, we have to forbid you to
! 87: deprive anyone else of these rights. For example, if you distribute
! 88: copies of the GNU MP library, you must give the recipients all the
! 89: rights that you have. You must make sure that they, too, receive or can
! 90: get the source code. And you must tell them their rights.
! 91:
! 92: Also, for our own protection, we must make certain that everyone finds
! 93: out that there is no warranty for the GNU MP library. If it is modified
! 94: by someone else and passed on, we want their recipients to know that
! 95: what they have is not what we distributed, so that any problems
! 96: introduced by others will not reflect on our reputation.
! 97:
! 98: The precise conditions of the license for the GNU MP library are found
! 99: in the Library General Public License that accompany the source code.
! 100:
! 101:
! 102: File: gmp.info, Node: Introduction to MP, Next: Installing MP, Prev: Copying, Up: Top
! 103:
! 104: Introduction to GNU MP
! 105: **********************
! 106:
! 107:
! 108: GNU MP is a portable library written in C for arbitrary precision
! 109: arithmetic on integers, rational numbers, and floating-point numbers.
! 110: It aims to provide the fastest possible arithmetic for all applications
! 111: that need higher precision than is directly supported by the basic C
! 112: types.
! 113:
! 114: Many applications use just a few hundred bits of precision; but some
! 115: applications may need thousands or even millions of bits. MP is
! 116: designed to give good performance for both, by choosing algorithms based
! 117: on the sizes of the operands, and by carefully keeping the overhead at a
! 118: minimum.
! 119:
! 120: The speed of MP is achieved by using fullwords as the basic arithmetic
! 121: type, by using sophisticated algorithms, by including carefully
! 122: optimized assembly code for the most common inner loops for many
! 123: different CPUs, and by a general emphasis on speed (as opposed to
! 124: simplicity or elegance).
! 125:
! 126: There is carefully optimized assembly code for these CPUs: DEC Alpha,
! 127: Amd 29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, Intel i960,
! 128: Motorola MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC,
! 129: National NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC,
! 130: generic SPARCv8, and DEC VAX. Some optimizations also for ARM, Clipper,
! 131: IBM ROMP (RT), and Pyramid AP/XP.
! 132:
! 133: This version of MP is released under a more liberal license than
! 134: previous versions. It is now permitted to link MP to non-free programs,
! 135: as long as MP source code is provided when distributing the non-free
! 136: program.
! 137:
! 138:
! 139:
! 140: How to use this Manual
! 141: ======================
! 142:
! 143: Everyone should read *Note MP Basics::. If you need to install the
! 144: library yourself, you need to read *Note Installing MP::, too.
! 145:
! 146: The rest of the manual can be used for later reference, although it is
! 147: probably a good idea to glance through it.
! 148:
! 149:
! 150:
! 151: File: gmp.info, Node: Installing MP, Next: MP Basics, Prev: Introduction to MP, Up: Top
! 152:
! 153: Installing MP
! 154: *************
! 155:
! 156: To build MP, you first have to configure it for your CPU and operating
! 157: system. You need a C compiler, preferably GCC, but any reasonable
! 158: compiler should work. And you need a standard Unix `make' program, plus
! 159: some other standard Unix utility programs.
! 160:
! 161: (If you're on an MS-DOS machine, your can build MP using `make.bat'. It
! 162: requires that djgpp is installed. It does not require configuration,
! 163: nor is `make' needed; `make.bat' both configures and builds the
! 164: library.)
! 165:
! 166: Here are the steps needed to install the library on Unix systems:
! 167:
! 168: 1. In most cases, `./configure --target=cpu-vendor-os', should work
! 169: both for native and cross-compilation. If you get error messages,
! 170: your machine might not be supported.
! 171:
! 172: If you want to compile in a separate object directory, cd to that
! 173: directory, and prefix the configure command with the path to the MP
! 174: source directory. Not all `make' programs have the necessary
! 175: features to support this. In particular, SunOS and Slowaris `make'
! 176: have bugs that makes them unable to build from a separate object
! 177: directory. Use GNU `make' instead.
! 178:
! 179: In addition to the standard cpu-vendor-os tuples, MP recognizes
! 180: sparc8 and supersparc as valid CPU names. Specifying these CPU
! 181: names for relevant systems will improve performance significantly.
! 182:
! 183: In general, if you want a library that runs as fast as possible,
! 184: you should make sure you configure MP for the exact CPU type your
! 185: system uses.
! 186:
! 187: If you have `gcc' in your `PATH', it will be used by default. To
! 188: override this, pass `-with-gcc=no' to `configure'.
! 189:
! 190: 2. `make'
! 191:
! 192: This will compile MP, and create a library archive file `libgmp.a'
! 193: in the working directory.
! 194:
! 195: 3. `make check'
! 196:
! 197: This will make sure MP was built correctly. If you get error
! 198: messages, please report this to `bug-gmp@prep.ai.mit.edu'. (*Note
! 199: Reporting Bugs::, for information on what to include in useful bug
! 200: reports.)
! 201:
! 202: 4. `make install'
! 203:
! 204: This will copy the file `gmp.h' and `libgmp.a', as well as the info
! 205: files, to `/usr/local' (or if you passed the `--prefix' option to
! 206: `configure', to the directory given as argument to `--prefix').
! 207:
! 208: If you wish to build and install the BSD MP compatible functions, use
! 209: `make libmp.a' and `make install-bsdmp'.
! 210:
! 211: There are some other useful make targets:
! 212:
! 213: * `doc'
! 214:
! 215: Create a DVI version of the manual, in `gmp.dvi' and a set of info
! 216: files, in `gmp.info', `gmp.info-1', `gmp.info-2', etc.
! 217:
! 218: * `ps'
! 219:
! 220: Create a Postscript version of the manual, in `gmp.ps'.
! 221:
! 222: * `html'
! 223:
! 224: Create a HTML version of the manual, in `gmp.html'.
! 225:
! 226: * `clean'
! 227:
! 228: Delete all object files and archive files, but not the
! 229: configuration files.
! 230:
! 231: * `distclean'
! 232:
! 233: Delete all files not included in the distribution.
! 234:
! 235: * `uninstall'
! 236:
! 237: Delete all files copied by `make install'.
! 238:
! 239:
! 240:
! 241: Known Build Problems
! 242: ====================
! 243:
! 244: GCC 2.7.2 (as well as 2.6.3) for the RS/6000 and PowerPC can not be used
! 245: to compile MP, due to a bug in GCC. If you want to use GCC for these
! 246: machines, you need to apply the patch below to GCC, or use a later
! 247: version of the compiler.
! 248:
! 249: If you are on a Sequent Symmetry, use the GNU assembler instead of the
! 250: system's assembler, since the latter has serious bugs.
! 251:
! 252: The system compiler on NeXT is a massacred and old gcc, even if the
! 253: compiler calls itself `cc'. This compiler cannot be used to build MP.
! 254: You need to get a real gcc, and install that before you compile MP.
! 255: (NeXT might have fixed this in newer releases of their system.)
! 256:
! 257: The system C compiler under SunOS 4 has a bug that makes it miscompile
! 258: mpq/get_d.c. This will make `make check' fail.
! 259:
! 260: Please report other problems to `bug-gmp@prep.ai.mit.edu'.
! 261: *Note Reporting Bugs::.
! 262:
! 263:
! 264: Patch to apply to GCC 2.6.3 and 2.7.2:
! 265:
! 266: *** config/rs6000/rs6000.md Sun Feb 11 08:22:11 1996
! 267: --- config/rs6000/rs6000.md.new Sun Feb 18 03:33:37 1996
! 268: ***************
! 269: *** 920,926 ****
! 270: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
! 271: (not:SI (match_dup 1)))]
! 272: ""
! 273: ! "nor. %0,%2,%1"
! 274: [(set_attr "type" "compare")])
! 275:
! 276: (define_insn ""
! 277: --- 920,926 ----
! 278: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
! 279: (not:SI (match_dup 1)))]
! 280: ""
! 281: ! "nor. %0,%1,%1"
! 282: [(set_attr "type" "compare")])
! 283:
! 284: (define_insn ""
! 285:
! 286:
! 287: File: gmp.info, Node: MP Basics, Next: Reporting Bugs, Prev: Installing MP, Up: Top
! 288:
! 289: MP Basics
! 290: *********
! 291:
! 292:
! 293: All declarations needed to use MP are collected in the include file
! 294: `gmp.h'. It is designed to work with both C and C++ compilers.
! 295:
! 296:
! 297:
! 298: Nomenclature and Types
! 299: ======================
! 300:
! 301: In this manual, "integer" usually means a multiple precision integer, as
! 302: defined by the MP library. The C data type for such integers is
! 303: `mpz_t'. Here are some examples of how to declare such integers:
! 304:
! 305: mpz_t sum;
! 306:
! 307: struct foo { mpz_t x, y; };
! 308:
! 309: mpz_t vec[20];
! 310:
! 311: "Rational number" means a multiple precision fraction. The C data type
! 312: for these fractions is `mpq_t'. For example:
! 313:
! 314: mpq_t quotient;
! 315:
! 316: "Floating point number" or "Float" for short, is an arbitrary precision
! 317: mantissa with an limited precision exponent. The C data type for such
! 318: objects is `mpf_t'.
! 319:
! 320: A "limb" means the part of a multi-precision number that fits in a
! 321: single word. (We chose this word because a limb of the human body is
! 322: analogous to a digit, only larger, and containing several digits.)
! 323: Normally a limb contains 32 or 64 bits. The C data type for a limb is
! 324: `mp_limb_t'.
! 325:
! 326:
! 327:
! 328: Function Classes
! 329: ================
! 330:
! 331: There are six classes of functions in the MP library:
! 332:
! 333: 1. Functions for signed integer arithmetic, with names beginning with
! 334: `mpz_'. The associated type is `mpz_t'. There are about 100
! 335: functions in this class.
! 336:
! 337: 2. Functions for rational number arithmetic, with names beginning with
! 338: `mpq_'. The associated type is `mpq_t'. There are about 20
! 339: functions in this class, but the functions in the previous class
! 340: can be used for performing arithmetic on the numerator and
! 341: denominator separately.
! 342:
! 343: 3. Functions for floating-point arithmetic, with names beginning with
! 344: `mpf_'. The associated type is `mpf_t'. There are about 50
! 345: functions is this class.
! 346:
! 347: 4. Functions compatible with Berkeley MP, such as `itom', `madd', and
! 348: `mult'. The associated type is `MINT'.
! 349:
! 350: 5. Fast low-level functions that operate on natural numbers. These
! 351: are used by the functions in the preceding groups, and you can also
! 352: call them directly from very time-critical user programs. These
! 353: functions' names begin with `mpn_'. There are about 30
! 354: (hard-to-use) functions in this class.
! 355:
! 356: The associated type is array of `mp_limb_t'.
! 357:
! 358: 6. Miscellaneous functions. Functions for setting up custom
! 359: allocation.
! 360:
! 361:
! 362:
! 363: MP Variable Conventions
! 364: =======================
! 365:
! 366: As a general rule, all MP functions expect output arguments before input
! 367: arguments. This notation is based on an analogy with the assignment
! 368: operator. (The BSD MP compatibility functions disobey this rule, having
! 369: the output argument(s) last.)
! 370:
! 371: MP allows you to use the same variable for both input and output in the
! 372: same expression. For example, the main function for integer
! 373: multiplication, `mpz_mul', can be used like this: `mpz_mul (x, x, x)'.
! 374: This computes the square of X and puts the result back in X.
! 375:
! 376: Before you can assign to an MP variable, you need to initialize it by
! 377: calling one of the special initialization functions. When you're done
! 378: with a variable, you need to clear it out, using one of the functions
! 379: for that purpose. Which function to use depends on the type of
! 380: variable. See the chapters on integer functions, rational number
! 381: functions, and floating-point functions for details.
! 382:
! 383: A variable should only be initialized once, or at least cleared out
! 384: between each initialization. After a variable has been initialized, it
! 385: may be assigned to any number of times.
! 386:
! 387: For efficiency reasons, avoid to initialize and clear out a variable in
! 388: loops. Instead, initialize it before entering the loop, and clear it
! 389: out after the loop has exited.
! 390:
! 391: You don't need to be concerned about allocating additional space for MP
! 392: variables. All functions in MP automatically allocate additional space
! 393: when a variable does not already have enough space. They do not,
! 394: however, reduce the space when a smaller number is stored in the object.
! 395: Most of the time, this policy is best, since it avoids frequent
! 396: re-allocation.
! 397:
! 398:
! 399:
! 400: Useful Macros and Constants
! 401: ===========================
! 402:
! 403: -- Global Constant: const int mp_bits_per_limb
! 404: The number of bits per limb.
! 405:
! 406: -- Macro: __GNU_MP_VERSION
! 407: -- Macro: __GNU_MP_VERSION_MINOR
! 408: The major and minor MP version, respectively, as integers.
! 409:
! 410:
! 411: Compatibility with Version 1.x
! 412: ==============================
! 413:
! 414: This version of MP is upward compatible with previous versions of MP,
! 415: with a few exceptions.
! 416:
! 417: @item Integer division functions round the result differently. The old
! 418: functions (@code{mpz_div}, @code{mpz_divmod}, @code{mpz_mdiv},
! 419: @code{mpz_mdivmod}, etc) now all use floor rounding (i.e., they round the
! 420: quotient to @minus{}infinity). There are a lot of new functions for integer
! 421: division, giving the user better control over the rounding.@refill
! 422:
! 423: @item The function @code{mpz_mod} now compute the true @strong{mod} function.
! 424:
! 425: @item The functions @code{mpz_powm} and @code{mpz_powm_ui} now use
! 426: @strong{mod} for reduction.
! 427:
! 428: @item The assignment functions for rational numbers do no longer canonicalize
! 429: their results. In the case a non-canonical result could arise from an
! 430: assignment, the user need to insert an explicit call to
! 431: @code{mpq_canonicalize}. This change was made for efficiency.@refill
! 432:
! 433: @item Output generated by @code{mpz_out_raw} in this release cannot be read
! 434: by @code{mpz_inp_raw} in previous releases. This change was made for making
! 435: the file format truly portable between machines with different word sizes.@refill
! 436:
! 437: @item Several @code{mpn} functions have changed. But they were intentionally
! 438: undocumented in previous releases.@refill
! 439:
! 440: @item The functions @code{mpz_cmp_ui}, @code{mpz_cmp_si}, and @code{mpq_cmp_ui}
! 441: are now implementated as macros, and thereby sometimes evaluate their
! 442: arguments multiple times.@refill
! 443:
! 444: @item The functions @code{mpz_pow_ui} and @code{mpz_ui_pow_ui} now yield 1
! 445: for 0^0. (In version 1, they yielded 0.)@refill
! 446:
! 447: @end enumerate
! 448:
! 449:
! 450: @section Getting the Latest Version of MP
! 451:
! 452: The latest version of the MP library is available by anonymous ftp from
! 453: from @samp{prep.ai.mit.edu}. The file name is
! 454: @file{/pub/gnu/gmp-M.N.tar.gz}. Many sites around the world mirror
! 455: @samp{prep}; please use a mirror site near you.@refill
! 456:
! 457: @node Reporting Bugs, Integer Functions, MP Basics, Top
! 458: @comment node-name, next, previous, up
! 459: @chapter Reporting Bugs
! 460: @cindex Reporting bugs
! 461:
! 462: If you think you have found a bug in the MP library, please investigate it and
! 463: report it. We have made this library available to you, and it is not to ask
! 464: too much from you, to ask you to report the bugs that you find.@refill
! 465:
! 466: There are a few things you should think about when you put your bug report
! 467: together.@refill
! 468:
! 469: You have to send us a test case that makes it possible for us to reproduce the
! 470: bug. Include instructions on how to run the test case.@refill
! 471:
! 472: You also have to explain what is wrong; if you get a crash, or if the results
! 473: printed are incorrect and in that case, in what way.@refill
! 474:
! 475: It is not uncommon that an observed problem is actually due to a bug in the
! 476: compiler used when building MP; the MP code tends to explore interesting
! 477: corners in compilers. Therefore, please include compiler version information
! 478: in your bug report. This can be extracted using @samp{what `which cc`}, or,
! 479: if you're using gcc, @samp{gcc -v}. Also, include the output from @samp{uname
! 480: -a}.@refill
! 481:
! 482: If your bug report is good, we will do our best to help you to get a corrected
! 483: version of the library; if the bug report is poor, we won't do anything about
! 484: it (aside of chiding you to send better bug reports).@refill
! 485:
! 486: Send your bug report to: @samp{bug-gmp@@prep.ai.mit.edu}.@refill
! 487:
! 488: If you think something in this manual is unclear, or downright incorrect, or if
! 489: the language needs to be improved, please send a note to the same address.@refill
! 490:
! 491:
! 492: @node Integer Functions, Rational Number Functions, Reporting Bugs, Top
! 493: @comment node-name, next, previous, up
! 494: @chapter Integer Functions
! 495: @cindex Integer functions
! 496:
! 497: This chapter describes the MP functions for performing integer arithmetic.
! 498: These functions start with the prefix @code{mpz_}.@refill
! 499:
! 500: Arbitrary precision integers are stored in objects of type @code{mpz_t}.@refill
! 501:
! 502: @menu
! 503: * Initializing Integers::
! 504: * Assigning Integers::
! 505: * Simultaneous Integer Init & Assign::
! 506: * Converting Integers::
! 507: * Integer Arithmetic::
! 508: * Comparison Functions::
! 509: * Integer Logic and Bit Fiddling::
! 510: * I/O of Integers::
! 511: * Miscellaneous Integer Functions::
! 512: @end menu
! 513:
! 514: @node Initializing Integers, Assigning Integers, , Integer Functions
! 515: @comment node-name, next, previous, up
! 516: @section Initialization and Assignment Functions
! 517:
! 518: The functions for integer arithmetic assume that all integer objects are
! 519: initialized. You do that by calling the function @code{mpz_init}.@refill
! 520:
! 521: @deftypefun void mpz_init (mpz_t @var{integer})
! 522: Initialize @var{integer} with limb space and set the initial numeric value to
! 523: 0. Each variable should normally only be initialized once, or at least cleared
! 524: out (using @code{mpz_clear}) between each initialization.@refill
! 525: @end deftypefun
! 526:
! 527: Here is an example of using @code{mpz_init}:@refill
! 528:
! 529: @example
! 530: @{
! 531: mpz_t integ;
! 532: mpz_init (integ);
! 533: @dots{}
! 534: mpz_add (integ, @dots{});
! 535: @dots{}
! 536: mpz_sub (integ, @dots{});
! 537:
! 538: /* Unless the program is about to exit, do ... */
! 539: mpz_clear (integ);
! 540: @}
! 541: @end example
! 542:
! 543: @noindent
! 544: As you can see, you can store new values any number of times, once an
! 545: object is initialized.@refill
! 546:
! 547: @deftypefun void mpz_clear (mpz_t @var{integer})
! 548: Free the limb space occupied by @var{integer}. Make sure to call this
! 549: function for all @code{mpz_t} variables when you are done with them.@refill
! 550: @end deftypefun
! 551:
! 552: @deftypefun {void *} _mpz_realloc (mpz_t @var{integer}, mp_size_t @var{new_alloc})
! 553: Change the limb space allocation to @var{new_alloc} limbs. This function is
! 554: not normally called from user code, but it can be used to give memory back to
! 555: the heap, or to increase the space of a variable to avoid repeated automatic
! 556: re-allocation.@refill
! 557: @end deftypefun
! 558:
! 559: @deftypefun void mpz_array_init (mpz_t @var{integer_array}[], size_t @var{array_size}, mp_size_t @var{fixed_num_bits})
! 560: Allocate @strong{fixed} limb space for all @var{array_size} integers in
! 561: @var{integer_array}. The fixed allocation for each integer in the array is
! 562: enough to store @var{fixed_num_bits}. If the fixed space will be insufficient
! 563: for storing the result of a subsequent calculation, the result is
! 564: unpredictable.@refill
! 565:
! 566: This function is useful for decreasing the working set for some algorithms
! 567: that use large integer arrays.@refill
! 568:
! 569: There is no way to de-allocate the storage allocated by this function.
! 570: Don't call @code{mpz_clear}!@refill
! 571: @end deftypefun
! 572:
! 573:
! 574: @node Assigning Integers, Simultaneous Integer Init & Assign, Initializing Integers, Integer Functions
! 575: @comment node-name, next, previous, up
! 576: @subsection Assignment Functions
! 577: @cindex Integer assignment functions
! 578:
! 579: These functions assign new values to already initialized integers
! 580: (@pxref{Initializing Integers}).@refill
! 581:
! 582: @deftypefun void mpz_set (mpz_t @var{rop}, mpz_t @var{op})
! 583: @deftypefunx void mpz_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 584: @deftypefunx void mpz_set_si (mpz_t @var{rop}, signed long int @var{op})
! 585: @deftypefunx void mpz_set_d (mpz_t @var{rop}, double @var{op})
! 586: @deftypefunx void mpz_set_q (mpz_t @var{rop}, mpq_t @var{op})
! 587: @deftypefunx void mpz_set_f (mpz_t @var{rop}, mpf_t @var{op})
! 588: Set the value of @var{rop} from @var{op}.@refill
! 589: @end deftypefun
! 590:
! 591: @deftypefun int mpz_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
! 592: Set the value of @var{rop} from @var{str}, a '\0'-terminated C string in base
! 593: @var{base}. White space is allowed in the string, and is simply ignored. The
! 594: base may vary from 2 to 36. If @var{base} is 0, the actual base is determined
! 595: from the leading characters: if the first two characters are `0x' or `0X',
! 596: hexadecimal is assumed, otherwise if the first character is `0', octal is
! 597: assumed, otherwise decimal is assumed.@refill
! 598:
! 599: This function returns 0 if the entire string up to the '\0' is a valid
! 600: number in base @var{base}. Otherwise it returns @minus{}1.@refill
! 601: @end deftypefun
! 602:
! 603:
! 604: @node Simultaneous Integer Init & Assign, Converting Integers, Assigning Integers, Integer Functions
! 605: @comment node-name, next, previous, up
! 606: @subsection Combined Initialization and Assignment Functions
! 607: @cindex Initialization and assignment functions
! 608:
! 609: For convenience, MP provides a parallel series of initialize-and-set functions
! 610: which initialize the output and then store the value there. These functions'
! 611: names have the form @code{mpz_init_set@dots{}}@refill
! 612:
! 613: Here is an example of using one:@refill
! 614:
! 615: @example
! 616: @{
! 617: mpz_t pie;
! 618: mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10);
! 619: @dots{}
! 620: mpz_sub (pie, @dots{});
! 621: @dots{}
! 622: mpz_clear (pie);
! 623: @}
! 624: @end example
! 625:
! 626: @noindent
! 627: Once the integer has been initialized by any of the @code{mpz_init_set@dots{}}
! 628: functions, it can be used as the source or destination operand for the ordinary
! 629: integer functions. Don't use an initialize-and-set function on a variable
! 630: already initialized!@refill
! 631:
! 632: @deftypefun void mpz_init_set (mpz_t @var{rop}, mpz_t @var{op})
! 633: @deftypefunx void mpz_init_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 634: @deftypefunx void mpz_init_set_si (mpz_t @var{rop}, signed long int @var{op})
! 635: @deftypefunx void mpz_init_set_d (mpz_t @var{rop}, double @var{op})
! 636: Initialize @var{rop} with limb space and set the initial numeric value from
! 637: @var{op}.@refill
! 638: @end deftypefun
! 639:
! 640: @deftypefun int mpz_init_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
! 641: Initialize @var{rop} and set its value like @code{mpz_set_str} (see its
! 642: documentation above for details).@refill
! 643:
! 644: If the string is a correct base @var{base} number, the function returns 0;
! 645: if an error occurs it returns @minus{}1. @var{rop} is initialized even if
! 646: an error occurs. (I.e., you have to call @code{mpz_clear} for it.)@refill
! 647: @end deftypefun
! 648:
! 649:
! 650: @node Converting Integers, Integer Arithmetic, Simultaneous Integer Init & Assign, Integer Functions
! 651: @comment node-name, next, previous, up
! 652: @section Conversion Functions
! 653: @cindex Integer conversion functions
! 654: @cindex Conversion functions
! 655:
! 656: This section describes functions for converting arbitrary precision integers
! 657: to standard C types. Functions for converting @emph{to} arbitrary
! 658: precision integers are described in @ref{Assigning Integers} and @ref{I/O of
! 659: Integers}.@refill
! 660:
! 661: @deftypefun {unsigned long int} mpz_get_ui (mpz_t @var{op})
! 662: Return the least significant part from @var{op}. This function combined
! 663: with @* @code{mpz_tdiv_q_2exp(@dots{}, @var{op}, CHAR_BIT*sizeof(unsigned
! 664: long int))} can be used to extract the limbs of an integer.
! 665: @end deftypefun
! 666:
! 667: @deftypefun {signed long int} mpz_get_si (mpz_t @var{op})
! 668: If @var{op} fits into a @code{signed long int} return the value of @var{op}.
! 669: Otherwise return the least significant part of @var{op}, with the same sign
! 670: as @var{op}.@refill
! 671:
! 672: If @var{op} is too large to fit in a @code{signed long int}, the returned
! 673: result is probably not very useful. @c To find out if the value will fit, use@refill
! 674: @c the function @code{mpz_fits_si}.
! 675: @end deftypefun
! 676:
! 677: @deftypefun double mpz_get_d (mpz_t @var{op})
! 678: Convert @var{op} to a double.@refill
! 679: @end deftypefun
! 680:
! 681: @deftypefun {char *} mpz_get_str (char *@var{str}, int @var{base}, mpz_t @var{op})
! 682: Convert @var{op} to a string of digits in base @var{base}. The base may vary
! 683: from 2 to 36.@refill
! 684:
! 685: If @var{str} is NULL, space for the result string is allocated using the
! 686: default allocation function, and a pointer to the string is returned.@refill
! 687:
! 688: If @var{str} is not NULL, it should point to a block of storage enough large
! 689: for the result. To find out the right amount of space to provide for
! 690: @var{str}, use @code{mpz_sizeinbase (@var{op}, @var{base}) + 2}. The two
! 691: extra bytes are for a possible minus sign, and for the terminating null
! 692: character.@refill
! 693: @end deftypefun
! 694:
! 695:
! 696: @node Integer Arithmetic, Comparison Functions, Converting Integers, Integer Functions
! 697: @comment node-name, next, previous, up
! 698: @section Arithmetic Functions
! 699: @cindex Integer arithmetic functions
! 700: @cindex Arithmetic functions
! 701:
! 702: @deftypefun void mpz_add (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 703: @deftypefunx void mpz_add_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 704: @ifinfo
! 705: Set @var{rop} to @var{op1} + @var{op2}.@refill
! 706: @end ifinfo
! 707: @iftex
! 708: @tex
! 709: Set @var{rop} to $@var{op1} + @var{op2}$.
! 710: @end tex
! 711: @end iftex
! 712: @end deftypefun
! 713:
! 714: @deftypefun void mpz_sub (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 715: @deftypefunx void mpz_sub_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 716: Set @var{rop} to @var{op1} @minus{} @var{op2}.@refill
! 717: @end deftypefun
! 718:
! 719: @deftypefun void mpz_mul (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 720: @deftypefunx void mpz_mul_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 721: @ifinfo
! 722: Set @var{rop} to @var{op1} times @var{op2}.@refill
! 723: @end ifinfo
! 724: @iftex
! 725: @tex
! 726: Set @var{rop} to $@var{op1} \times @var{op2}$.
! 727: @end tex
! 728: @end iftex
! 729: @end deftypefun
! 730:
! 731: @deftypefun void mpz_mul_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 732: @ifinfo
! 733: Set @var{rop} to @var{op1} times 2 raised to @var{op2}. This operation can
! 734: also be defined as a left shift, @var{op2} steps.@refill
! 735: @end ifinfo
! 736: @iftex
! 737: @tex
! 738: Set @var{rop} to $@var{op1} \times 2^{op2}$. This operation can also be
! 739: defined as a left shift, @var{op2} steps.
! 740: @end tex
! 741: @end iftex
! 742: @end deftypefun
! 743:
! 744: @deftypefun void mpz_neg (mpz_t @var{rop}, mpz_t @var{op})
! 745: Set @var{rop} to @minus{}@var{op}.@refill
! 746: @end deftypefun
! 747:
! 748: @deftypefun void mpz_abs (mpz_t @var{rop}, mpz_t @var{op})
! 749: Set @var{rop} to the absolute value of @var{op}.@refill
! 750: @end deftypefun
! 751:
! 752: @deftypefun void mpz_fac_ui (mpz_t @var{rop}, unsigned long int @var{op})
! 753: Set @var{rop} to @var{op}!, the factorial of @var{op}.@refill
! 754: @end deftypefun
! 755:
! 756: @subsection Division functions
! 757:
! 758: Division is undefined if the divisor is zero, and passing a zero divisor to
! 759: the divide or modulo functions, as well passing a zero mod argument to the
! 760: @code{mpz_powm} and @code{mpz_powm_ui} functions, will make these functions
! 761: intentionally divide by zero. This gives the user the possibility to handle
! 762: arithmetic exceptions in these functions in the same manner as other
! 763: arithmetic exceptions.@refill
! 764:
! 765: There are three main groups of division functions:@refill
! 766: @itemize @bullet
! 767: @item
! 768: Functions that truncate the quotient towards 0. The names of these
! 769: functions start with @code{mpz_tdiv}. The @samp{t} in the name is short for
! 770: @samp{truncate}.@refill
! 771: @item
! 772: Functions that round the quotient towards @minus{}infinity. The names of
! 773: these routines start with @code{mpz_fdiv}. The @samp{f} in the name is
! 774: short for @samp{floor}.@refill
! 775: @item
! 776: Functions that round the quotient towards +infinity. The names of
! 777: these routines start with @code{mpz_cdiv}. The @samp{c} in the name is
! 778: short for @samp{ceil}.@refill
! 779: @end itemize
! 780:
! 781: For each rounding mode, there are a couple of variants. Here @samp{q} means
! 782: that the quotient is computed, while @samp{r} means that the remainder is
! 783: computed. Functions that compute both the quotient and remainder have
! 784: @samp{qr} in the name.@refill
! 785:
! 786: @deftypefun void mpz_tdiv_q (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 787: @deftypefunx void mpz_tdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 788: Set @var{rop} to [@var{op1}/@var{op2}]. The quotient is truncated towards
! 789: 0.@refill
! 790: @end deftypefun
! 791:
! 792: @deftypefun void mpz_tdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 793: @deftypefunx void mpz_tdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 794: Set @var{rop} to (@var{op1} - [@var{op1}/@var{op2}] * @var{op2}).
! 795: Unless the remainder is zero, it has the same sign as the dividend.@refill
! 796: @end deftypefun
! 797:
! 798: @deftypefun void mpz_tdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 799: @deftypefunx void mpz_tdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
! 800: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 801: remainder in @var{rop2}. The quotient is rounded towards 0. Unless the
! 802: remainder is zero, it has the same sign as the dividend.@refill
! 803:
! 804: If @var{rop1} and @var{rop2} are the same variable, the results are
! 805: undefined.@refill
! 806: @end deftypefun
! 807:
! 808: @deftypefun void mpz_fdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
! 809: @deftypefunx void mpz_fdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 810: @ifinfo
! 811: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
! 812: @minus{}infinity.@refill
! 813: @end ifinfo
! 814: @iftex
! 815: @tex
! 816: Set @var{rop} to $\lfloor@var{op1}/@var{op2}\rfloor$. (I.e., round
! 817: the quotient towards $-\infty$.)
! 818: @end tex
! 819: @end iftex
! 820: @end deftypefun
! 821:
! 822: @deftypefun void mpz_fdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 823: @deftypefunx {unsigned long int} mpz_fdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 824: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
! 825: the remainder is zero, it has the same sign as the divisor.@refill
! 826:
! 827: For @code{mpz_fdiv_r_ui} the remainder is small enough to fit in an
! 828: @code{unsigned long int}, and is therefore returned.@refill
! 829: @end deftypefun
! 830:
! 831: @deftypefun void mpz_fdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 832: @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})
! 833: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 834: remainder in @var{rop2}. The quotient is rounded towards @minus{}infinity.
! 835: Unless the remainder is zero, it has the same sign as the divisor.@refill
! 836:
! 837: For @code{mpz_fdiv_qr_ui} the remainder is small enough to fit in an
! 838: @code{unsigned long int}, and is therefore returned.@refill
! 839:
! 840: If @var{rop1} and @var{rop2} are the same variable, the results are
! 841: undefined.@refill
! 842: @end deftypefun
! 843:
! 844: @deftypefun {unsigned long int} mpz_fdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 845: This function is similar to @code{mpz_fdiv_r_ui}, but the remainder is only
! 846: returned; it is not stored anywhere.@refill
! 847: @end deftypefun
! 848:
! 849: @deftypefun void mpz_cdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
! 850: @deftypefunx void mpz_cdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 851: @ifinfo
! 852: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
! 853: +infinity.@refill
! 854: @end ifinfo
! 855: @iftex
! 856: @tex
! 857: Set @var{rop} to $\lceil@var{op1}/@var{op2}\rceil$. (I.e., round the
! 858: quotient towards $+\infty$.)
! 859: @end tex
! 860: @end iftex
! 861: @end deftypefun
! 862:
! 863: @deftypefun void mpz_cdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 864: @deftypefunx {unsigned long int} mpz_cdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 865: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
! 866: the remainder is zero, it has the opposite sign as the divisor.@refill
! 867:
! 868: For @code{mpz_cdiv_r_ui} the negated remainder is small enough to fit in an
! 869: @code{unsigned long int}, and it is therefore returned.@refill
! 870: @end deftypefun
! 871:
! 872: @deftypefun void mpz_cdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
! 873: @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})
! 874: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
! 875: remainder in @var{rop2}. The quotient is rounded towards +infinity. Unless
! 876: the remainder is zero, it has the opposite sign as the divisor.@refill
! 877:
! 878: For @code{mpz_cdiv_qr_ui} the negated remainder is small enough to fit in an
! 879: @code{unsigned long int}, and it is therefore returned.@refill
! 880:
! 881: If @var{rop1} and @var{rop2} are the same variable, the results are
! 882: undefined.@refill
! 883: @end deftypefun
! 884:
! 885: @deftypefun {unsigned long int} mpz_cdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 886: Return the negated remainder, similar to @code{mpz_cdiv_r_ui}. (The
! 887: difference is that this function doesn't store the remainder anywhere.)@refill
! 888: @end deftypefun
! 889:
! 890: @deftypefun void mpz_mod (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 891: @deftypefunx {unsigned long int} mpz_mod_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 892: Set @var{rop} to @var{op1} @code{mod} @var{op2}. The sign of the divisor is
! 893: ignored, and the result is always non-negative.@refill
! 894:
! 895: For @code{mpz_mod_ui} the remainder is small enough to fit in an
! 896: @code{unsigned long int}, and is therefore returned.@refill
! 897: @end deftypefun
! 898:
! 899: @deftypefun void mpz_divexact (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 900: Set @var{rop} to @var{op1}/@var{op2}. This function produces correct
! 901: results only when it is known in advance that @var{op2} divides
! 902: @var{op1}.@refill
! 903:
! 904: Since mpz_divexact is much faster than any of the other routines that produce
! 905: the quotient (@pxref{References} Jebelean), it is the best choice for
! 906: instances in which exact division is known to occur, such as reducing a
! 907: rational to lowest terms.@refill
! 908: @end deftypefun
! 909:
! 910: @deftypefun void mpz_tdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 911: @ifinfo
! 912: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
! 913: rounded towards 0.@refill
! 914: @end ifinfo
! 915: @iftex
! 916: @tex
! 917: Set @var{rop} to $@var{op1}/2^{op2}$. The quotient is rounded towards 0.
! 918: @end tex
! 919: @end iftex
! 920: @end deftypefun
! 921:
! 922: @deftypefun void mpz_tdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 923: @ifinfo
! 924: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
! 925: @var{rop}. Unless it is zero, @var{rop} will have the same sign as @var{op1}.@refill
! 926: @end ifinfo
! 927: @iftex
! 928: @tex
! 929: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. Unless it is
! 930: zero, @var{rop} will have the same sign as @var{op1}.
! 931: @end tex
! 932: @end iftex
! 933: @end deftypefun
! 934:
! 935: @deftypefun void mpz_fdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 936: @ifinfo
! 937: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
! 938: rounded towards @minus{}infinity.@refill
! 939: @end ifinfo
! 940: @iftex
! 941: @tex
! 942: Set @var{rop} to $\lfloor@var{op1}/2^{op2}\rfloor$. The quotient is rounded
! 943: towards $-\infty$.
! 944: @end tex
! 945: @end iftex
! 946: @end deftypefun
! 947:
! 948: @deftypefun void mpz_fdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 949: @ifinfo
! 950: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
! 951: @var{rop}. The sign of @var{rop} will always be positive.@refill
! 952: @end ifinfo
! 953: @iftex
! 954: @tex
! 955: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. The sign of
! 956: @var{rop} will always be positive.
! 957: @end tex
! 958: @end iftex
! 959:
! 960: This operation can also be defined as masking of the @var{op2} least
! 961: significant bits.@refill
! 962: @end deftypefun
! 963:
! 964: @subsection Exponentialization Functions
! 965:
! 966: @deftypefun void mpz_powm (mpz_t @var{rop}, mpz_t @var{base}, mpz_t @var{exp}, mpz_t @var{mod})
! 967: @deftypefunx void mpz_powm_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp}, mpz_t @var{mod})
! 968: Set @var{rop} to (@var{base} raised to @var{exp}) @code{mod} @var{mod}. If
! 969: @var{exp} is negative, the result is undefined.@refill
! 970: @end deftypefun
! 971:
! 972: @deftypefun void mpz_pow_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp})
! 973: @deftypefunx void mpz_ui_pow_ui (mpz_t @var{rop}, unsigned long int @var{base}, unsigned long int @var{exp})
! 974: Set @var{rop} to @var{base} raised to @var{exp}.@refill
! 975: @ifinfo
! 976: The case of 0^0 yields 1.@refill
! 977: @end ifinfo
! 978: @iftex
! 979: @tex
! 980: The case of $0^0$ yields 1.
! 981: @end tex
! 982: @end iftex
! 983: @end deftypefun
! 984:
! 985: @subsection Square Root Functions
! 986:
! 987: @deftypefun void mpz_sqrt (mpz_t @var{rop}, mpz_t @var{op})
! 988: @ifinfo
! 989: Set @var{rop} to the truncated integer part of the square root of
! 990: @var{op}.@refill
! 991: @end ifinfo
! 992: @iftex
! 993: @tex
! 994: Set @var{rop} to $\lfloor\sqrt{@var{op}}\rfloor$, the truncated integer
! 995: part of the square root of @var{op}.
! 996: @end tex
! 997: @end iftex
! 998: @end deftypefun
! 999:
! 1000: @deftypefun void mpz_sqrtrem (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op})
! 1001: @ifinfo
! 1002: Set @var{rop1} to the truncated integer part of the square root of @var{op},
! 1003: like @code{mpz_sqrt}. Set @var{rop2} to
! 1004: @var{op}@minus{}@var{rop1}*@var{rop1},@refill
! 1005: @end ifinfo
! 1006: @iftex
! 1007: @tex
! 1008: Set @var{rop1} to $\lfloor\sqrt{@var{op}}\rfloor$, like @code{mpz_sqrt}.
! 1009: Set @var{rop2} to $(@var{op} - @var{rop1}^2)$,
! 1010: @end tex
! 1011: @end iftex
! 1012: (i.e., zero if @var{op} is a perfect square).@refill
! 1013:
! 1014: If @var{rop1} and @var{rop2} are the same variable, the results are
! 1015: undefined.@refill
! 1016: @end deftypefun
! 1017:
! 1018: @deftypefun int mpz_perfect_square_p (mpz_t @var{op})
! 1019: Return non-zero if @var{op} is a perfect square, i.e., if the square root of
! 1020: @var{op} is an integer. Return zero otherwise.@refill
! 1021: @end deftypefun
! 1022:
! 1023: @subsection Number Theoretic Functions
! 1024:
! 1025: @deftypefun int mpz_probab_prime_p (mpz_t @var{op}, int @var{reps})
! 1026: @ifinfo
! 1027: If this function returns 0, @var{op} is definitely not prime. If it returns
! 1028: 1, then @var{op} is `probably' prime. The probability of a false positive is
! 1029: (1/4)**@var{reps}.@refill
! 1030: @end ifinfo
! 1031: @iftex
! 1032: @tex
! 1033: If this function returns 0, @var{op} is definitely not prime. If it returns
! 1034: 1, then @var{op} is `probably' prime. The probability of a false positive is
! 1035: $(1/4)^{{reps}}$.
! 1036: @end tex
! 1037: @end iftex
! 1038: A reasonable value of reps is 25.@refill
! 1039:
! 1040: An implementation of the probabilistic primality test found in Seminumerical
! 1041: Algorithms (@pxref{References} Knuth).@refill
! 1042: @end deftypefun
! 1043:
! 1044: @deftypefun void mpz_gcd (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1045: Set @var{rop} to the greatest common divisor of @var{op1} and @var{op2}.@refill
! 1046: @end deftypefun
! 1047:
! 1048: @deftypefun {unsigned long int} mpz_gcd_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
! 1049: Compute the greatest common divisor of @var{op1} and @var{op2}. If
! 1050: @var{rop} is not NULL, store the result there.@refill
! 1051:
! 1052: If the result is small enough to fit in an @code{unsigned long int}, it is
! 1053: returned. If the result does not fit, 0 is returned, and the result is equal
! 1054: to the argument @var{op1}. Note that the result will always fit if @var{op2}
! 1055: is non-zero.@refill
! 1056: @end deftypefun
! 1057:
! 1058: @deftypefun void mpz_gcdext (mpz_t @var{g}, mpz_t @var{s}, mpz_t @var{t}, mpz_t @var{a}, mpz_t @var{b})
! 1059: Compute @var{g}, @var{s}, and @var{t}, such that @var{a}@var{s} +
! 1060: @var{b}@var{t} = @var{g} = @code{gcd} (@var{a}, @var{b}). If @var{t} is
! 1061: NULL, that argument is not computed.@refill
! 1062: @end deftypefun
! 1063:
! 1064: @deftypefun int mpz_invert (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1065: Compute the inverse of @var{op1} modulo @var{op2} and put the result in
! 1066: @var{rop}. Return non-zero if an inverse exist, zero otherwise. When the
! 1067: function returns zero, do not assume anything about the value in @var{rop}.@refill
! 1068: @end deftypefun
! 1069:
! 1070: @deftypefun int mpz_jacobi (mpz_t @var{op1}, mpz_t @var{op2})
! 1071: @deftypefunx int mpz_legendre (mpz_t @var{op1}, mpz_t @var{op2})
! 1072: Compute the Jacobi and Legendre symbols, respectively.@refill
! 1073: @end deftypefun
! 1074:
! 1075: @need 2000
! 1076: @node Comparison Functions, Integer Logic and Bit Fiddling, Integer Arithmetic, Integer Functions
! 1077: @comment node-name, next, previous, up
! 1078: @section Comparison Functions
! 1079:
! 1080: @deftypefun int mpz_cmp (mpz_t @var{op1}, mpz_t @var{op2})
! 1081: @ifinfo
! 1082: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1083: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1084: @var{op2}.@refill
! 1085: @end ifinfo
! 1086: @iftex
! 1087: @tex
! 1088: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1089: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1090: < @var{op2}$.
! 1091: @end tex
! 1092: @end iftex
! 1093: @end deftypefun
! 1094:
! 1095: @deftypefn Macro int mpz_cmp_ui (mpz_t @var{op1}, unsigned long int @var{op2})
! 1096: @deftypefnx Macro int mpz_cmp_si (mpz_t @var{op1}, signed long int @var{op2})
! 1097: @ifinfo
! 1098: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1099: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1100: @var{op2}.@refill
! 1101: @end ifinfo
! 1102: @iftex
! 1103: @tex
! 1104: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1105: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1106: < @var{op2}$.
! 1107: @end tex
! 1108: @end iftex
! 1109:
! 1110: These functions are actually implemented as macros. They evaluate their
! 1111: arguments multiple times.@refill
! 1112: @end deftypefn
! 1113:
! 1114: @deftypefn Macro int mpz_sgn (mpz_t @var{op})
! 1115: @ifinfo
! 1116: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.@refill
! 1117: @end ifinfo
! 1118: @iftex
! 1119: @tex
! 1120: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1121: @end tex
! 1122: @end iftex
! 1123:
! 1124: This function is actually implemented as a macro. It evaluates its
! 1125: arguments multiple times.@refill
! 1126: @end deftypefn
! 1127:
! 1128: @node Integer Logic and Bit Fiddling, I/O of Integers, Comparison Functions, Integer Functions
! 1129: @comment node-name, next, previous, up
! 1130: @section Logical and Bit Manipulation Functions
! 1131: @cindex Logical functions
! 1132: @cindex Bit manipulation functions
! 1133:
! 1134: These functions behave as if two's complement arithmetic were used (although
! 1135: sign-magnitude is used by the actual implementation).@refill
! 1136:
! 1137: @deftypefun void mpz_and (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1138: Set @var{rop} to @var{op1} logical-and @var{op2}.@refill
! 1139: @end deftypefun
! 1140:
! 1141: @deftypefun void mpz_ior (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1142: Set @var{rop} to @var{op1} inclusive-or @var{op2}.@refill
! 1143: @end deftypefun
! 1144:
! 1145: @c @deftypefun void mpz_xor (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
! 1146: @c Set @var{rop} to @var{op1} exclusive-or @var{op2}.
! 1147: @c @end deftypefun
! 1148:
! 1149: @deftypefun void mpz_com (mpz_t @var{rop}, mpz_t @var{op})
! 1150: Set @var{rop} to the one's complement of @var{op}.@refill
! 1151: @end deftypefun
! 1152:
! 1153: @deftypefun {unsigned long int} mpz_popcount (mpz_t @var{op})
! 1154: For non-negative numbers, return the population count of @var{op}. For
! 1155: negative numbers, return the largest possible value (@var{MAX_ULONG}).@refill
! 1156: @end deftypefun
! 1157:
! 1158: @deftypefun {unsigned long int} mpz_hamdist (mpz_t @var{op1}, mpz_t @var{op2})
! 1159: If @var{op1} and @var{op2} are both non-negative, return the hamming distance
! 1160: between the two operands. Otherwise, return the largest possible value
! 1161: (@var{MAX_ULONG}).@refill
! 1162:
! 1163: It is possible to extend this function to return a useful value when the
! 1164: operands are both negative, but the current implementation returns
! 1165: @var{MAX_ULONG} in this case. @strong{Do not depend on this behavior, since
! 1166: it will change in future versions of the library.}@refill
! 1167: @end deftypefun
! 1168:
! 1169: @deftypefun {unsigned long int} mpz_scan0 (mpz_t @var{op}, unsigned long int @var{starting_bit})
! 1170: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
! 1171: bits, until the first clear bit is found. Return the index of the found bit.@refill
! 1172: @end deftypefun
! 1173:
! 1174: @deftypefun {unsigned long int} mpz_scan1 (mpz_t @var{op}, unsigned long int @var{starting_bit})
! 1175: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
! 1176: bits, until the first set bit is found. Return the index of the found bit.@refill
! 1177: @end deftypefun
! 1178:
! 1179: @deftypefun void mpz_setbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
! 1180: Set bit @var{bit_index} in @var{op1}.@refill
! 1181: @end deftypefun
! 1182:
! 1183: @deftypefun void mpz_clrbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
! 1184: Clear bit @var{bit_index} in @var{op1}.@refill
! 1185: @end deftypefun
! 1186:
! 1187: @node I/O of Integers, Miscellaneous Integer Functions, Integer Logic and Bit Fiddling, Integer Functions
! 1188: @comment node-name, next, previous, up
! 1189: @section Input and Output Functions
! 1190: @cindex Integer input and output functions
! 1191: @cindex Input functions
! 1192: @cindex Output functions
! 1193: @cindex I/O functions
! 1194:
! 1195: Functions that perform input from a stdio stream, and functions that output to
! 1196: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
! 1197: these functions will make them read from @code{stdin} and write to
! 1198: @code{stdout}, respectively.@refill
! 1199:
! 1200: When using any of these functions, it is a good idea to include @file{stdio.h}
! 1201: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
! 1202: for these functions.@refill
! 1203:
! 1204: @deftypefun size_t mpz_out_str (FILE *@var{stream}, int @var{base}, mpz_t @var{op})
! 1205: Output @var{op} on stdio stream @var{stream}, as a string of digits in base
! 1206: @var{base}. The base may vary from 2 to 36.@refill
! 1207:
! 1208: Return the number of bytes written, or if an error occurred, return 0.@refill
! 1209: @end deftypefun
! 1210:
! 1211: @deftypefun size_t mpz_inp_str (mpz_t @var{rop}, FILE *@var{stream}, int @var{base})
! 1212: Input a possibly white-space preceded string in base @var{base} from stdio
! 1213: stream @var{stream}, and put the read integer in @var{rop}. The base may vary
! 1214: from 2 to 36. If @var{base} is 0, the actual base is determined from the
! 1215: leading characters: if the first two characters are `0x' or `0X', hexadecimal
! 1216: is assumed, otherwise if the first character is `0', octal is assumed,
! 1217: otherwise decimal is assumed.@refill
! 1218:
! 1219: Return the number of bytes read, or if an error occurred, return 0.@refill
! 1220: @end deftypefun
! 1221:
! 1222: @deftypefun size_t mpz_out_raw (FILE *@var{stream}, mpz_t @var{op})
! 1223: Output @var{op} on stdio stream @var{stream}, in raw binary format. The
! 1224: integer is written in a portable format, with 4 bytes of size information, and
! 1225: that many bytes of limbs. Both the size and the limbs are written in
! 1226: decreasing significance order (i.e., in big-endian).@refill
! 1227:
! 1228: The output can be read with @code{mpz_inp_raw}.@refill
! 1229:
! 1230: Return the number of bytes written, or if an error occurred, return 0.@refill
! 1231:
! 1232: The output of this can not be read by @code{mpz_inp_raw} from GMP 1, because
! 1233: of changes necessary for compatibility between 32-bit and 64-bit machines.@refill
! 1234: @end deftypefun
! 1235:
! 1236: @deftypefun size_t mpz_inp_raw (mpz_t @var{rop}, FILE *@var{stream})
! 1237: Input from stdio stream @var{stream} in the format written by
! 1238: @code{mpz_out_raw}, and put the result in @var{rop}. Return the number of
! 1239: bytes read, or if an error occurred, return 0.@refill
! 1240:
! 1241: This routine can read the output from @code{mpz_out_raw} also from GMP 1, in
! 1242: spite of changes necessary for compatibility between 32-bit and 64-bit
! 1243: machines.@refill
! 1244: @end deftypefun
! 1245:
! 1246:
! 1247: @need 2000
! 1248: @node Miscellaneous Integer Functions,, I/O of Integers, Integer Functions
! 1249: @comment node-name, next, previous, up
! 1250: @section Miscellaneous Functions
! 1251: @cindex Miscellaneous integer functions
! 1252:
! 1253: @deftypefun void mpz_random (mpz_t @var{rop}, mp_size_t @var{max_size})
! 1254: Generate a random integer of at most @var{max_size} limbs. The generated
! 1255: random number doesn't satisfy any particular requirements of randomness.
! 1256: Negative random numbers are generated when @var{max_size} is negative.@refill
! 1257: @end deftypefun
! 1258:
! 1259: @deftypefun void mpz_random2 (mpz_t @var{rop}, mp_size_t @var{max_size})
! 1260: Generate a random integer of at most @var{max_size} limbs, with long strings
! 1261: of zeros and ones in the binary representation. Useful for testing functions
! 1262: and algorithms, since this kind of random numbers have proven to be more
! 1263: likely to trigger corner-case bugs. Negative random numbers are generated
! 1264: when @var{max_size} is negative.@refill
! 1265: @end deftypefun
! 1266:
! 1267: @deftypefun size_t mpz_size (mpz_t @var{op})
! 1268: Return the size of @var{op} measured in number of limbs. If @var{op} is zero,
! 1269: the returned value will be zero.@refill
! 1270: @c (@xref{Nomenclature}, for an explanation of the concept @dfn{limb}.)
! 1271:
! 1272: @strong{This function is obsolete. It will disappear from future MP
! 1273: releases.}@refill
! 1274: @end deftypefun
! 1275:
! 1276: @deftypefun size_t mpz_sizeinbase (mpz_t @var{op}, int @var{base})
! 1277: Return the size of @var{op} measured in number of digits in base @var{base}.
! 1278: The base may vary from 2 to 36. The returned value will be exact or 1 too
! 1279: big. If @var{base} is a power of 2, the returned value will always be exact.@refill
! 1280:
! 1281: This function is useful in order to allocate the right amount of space before
! 1282: converting @var{op} to a string. The right amount of allocation is normally
! 1283: two more than the value returned by @code{mpz_sizeinbase} (one extra for a
! 1284: minus sign and one for the terminating '\0').@refill
! 1285: @end deftypefun
! 1286:
! 1287:
! 1288: @node Rational Number Functions, Floating-point Functions, Integer Functions, Top
! 1289: @comment node-name, next, previous, up
! 1290: @chapter Rational Number Functions
! 1291: @cindex Rational number functions
! 1292:
! 1293: This chapter describes the MP functions for performing arithmetic on rational
! 1294: numbers. These functions start with the prefix @code{mpq_}.@refill
! 1295:
! 1296: Rational numbers are stored in objects of type @code{mpq_t}.@refill
! 1297:
! 1298: All rational arithmetic functions assume operands have a canonical form, and
! 1299: canonicalize their result. The canonical from means that the denominator and
! 1300: the numerator have no common factors, and that the denominator is positive.
! 1301: Zero has the unique representation 0/1.@refill
! 1302:
! 1303: Pure assignment functions do not canonicalize the assigned variable. It is
! 1304: the responsibility of the user to canonicalize the assigned variable before
! 1305: any arithmetic operations are performed on that variable. @strong{Note that
! 1306: this is an incompatible change from version 1 of the library.}@refill
! 1307:
! 1308: @deftypefun void mpq_canonicalize (mpq_t @var{op})
! 1309: Remove any factors that are common to the numerator and denominator of
! 1310: @var{op}, and make the denominator positive.@refill
! 1311: @end deftypefun
! 1312:
! 1313: @menu
! 1314: * Initializing Rationals::
! 1315: * Assigning Rationals::
! 1316: * Simultaneous Integer Init & Assign::
! 1317: * Comparing Rationals::
! 1318: * Applying Integer Functions::
! 1319: * Miscellaneous Rational Functions::
! 1320: @end menu
! 1321:
! 1322: @node Initializing Rationals, Assigning Rationals, Rational Number Functions, Rational Number Functions
! 1323: @comment node-name, next, previous, up
! 1324: @section Initialization and Assignment Functions
! 1325:
! 1326: @deftypefun void mpq_init (mpq_t @var{dest_rational})
! 1327: Initialize @var{dest_rational} and set it to 0/1. Each variable should
! 1328: normally only be initialized once, or at least cleared out (using the function
! 1329: @code{mpq_clear}) between each initialization.@refill
! 1330: @end deftypefun
! 1331:
! 1332: @deftypefun void mpq_clear (mpq_t @var{rational_number})
! 1333: Free the space occupied by @var{rational_number}. Make sure to call this
! 1334: function for all @code{mpq_t} variables when you are done with them.@refill
! 1335: @end deftypefun
! 1336:
! 1337: @deftypefun void mpq_set (mpq_t @var{rop}, mpq_t @var{op})
! 1338: @deftypefunx void mpq_set_z (mpq_t @var{rop}, mpz_t @var{op})
! 1339: Assign @var{rop} from @var{op}.@refill
! 1340: @end deftypefun
! 1341:
! 1342: @deftypefun void mpq_set_ui (mpq_t @var{rop}, unsigned long int @var{op1}, unsigned long int @var{op2})
! 1343: @deftypefunx void mpq_set_si (mpq_t @var{rop}, signed long int @var{op1}, unsigned long int @var{op2})
! 1344: Set the value of @var{rop} to @var{op1}/@var{op2}. Note that if @var{op1} and
! 1345: @var{op2} have common factors, @var{rop} has to be passed to
! 1346: @code{mpq_canonicalize} before any operations are performed on @var{rop}.@refill
! 1347: @end deftypefun
! 1348:
! 1349: @node Assigning Rationals, Comparing Rationals, Initializing Rationals, Rational Number Functions
! 1350: @comment node-name, next, previous, up
! 1351: @section Arithmetic Functions
! 1352:
! 1353: @deftypefun void mpq_add (mpq_t @var{sum}, mpq_t @var{addend1}, mpq_t @var{addend2})
! 1354: Set @var{sum} to @var{addend1} + @var{addend2}.@refill
! 1355: @end deftypefun
! 1356:
! 1357: @deftypefun void mpq_sub (mpq_t @var{difference}, mpq_t @var{minuend}, mpq_t @var{subtrahend})
! 1358: Set @var{difference} to @var{minuend} @minus{} @var{subtrahend}.@refill
! 1359: @end deftypefun
! 1360:
! 1361: @deftypefun void mpq_mul (mpq_t @var{product}, mpq_t @var{multiplier}, mpq_t @var{multiplicand})
! 1362: @ifinfo
! 1363: Set @var{product} to @var{multiplier} times @var{multiplicand}.@refill
! 1364: @end ifinfo
! 1365: @iftex
! 1366: @tex
! 1367: Set @var{product} to $@var{multiplier} \times @var{multiplicand}$.
! 1368: @end tex
! 1369: @end iftex
! 1370: @end deftypefun
! 1371:
! 1372: @deftypefun void mpq_div (mpq_t @var{quotient}, mpq_t @var{dividend}, mpq_t @var{divisor})
! 1373: Set @var{quotient} to @var{dividend}/@var{divisor}.@refill
! 1374: @end deftypefun
! 1375:
! 1376: @deftypefun void mpq_neg (mpq_t @var{negated_operand}, mpq_t @var{operand})
! 1377: Set @var{negated_operand} to @minus{}@var{operand}.@refill
! 1378: @end deftypefun
! 1379:
! 1380: @deftypefun void mpq_inv (mpq_t @var{inverted_number}, mpq_t @var{number})
! 1381: Set @var{inverted_number} to 1/@var{number}. If the new denominator is
! 1382: zero, this routine will divide by zero.@refill
! 1383: @end deftypefun
! 1384:
! 1385: @node Comparing Rationals, Applying Integer Functions, Assigning Rationals, Rational Number Functions
! 1386: @comment node-name, next, previous, up
! 1387: @section Comparison Functions
! 1388:
! 1389: @deftypefun int mpq_cmp (mpq_t @var{op1}, mpq_t @var{op2})
! 1390: @ifinfo
! 1391: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1392: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1393: @var{op2}.@refill
! 1394: @end ifinfo
! 1395: @iftex
! 1396: @tex
! 1397: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1398: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1399: < @var{op2}$.
! 1400: @end tex
! 1401: @end iftex
! 1402:
! 1403: To determine if two rationals are equal, @code{mpq_equal} is faster than
! 1404: @code{mpq_cmp}.@refill
! 1405: @end deftypefun
! 1406:
! 1407: @deftypefn Macro int mpq_cmp_ui (mpq_t @var{op1}, unsigned long int @var{num2}, unsigned long int @var{den2})
! 1408: @ifinfo
! 1409: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
! 1410: @var{op1} > @var{num2}/@var{den2}, zero if @var{op1} = @var{num2}/@var{den2},
! 1411: and a negative value if @var{op1} < @var{num2}/@var{den2}.@refill
! 1412: @end ifinfo
! 1413: @iftex
! 1414: @tex
! 1415: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
! 1416: $@var{op1} > @var{num2}/@var{den2}$, zero if $@var{op1} =
! 1417: @var{num2}/@var{den2}$, and a negative value if $@var{op1} <
! 1418: @var{num2}/@var{den2}$.
! 1419: @end tex
! 1420: @end iftex
! 1421:
! 1422: This routine allows that @var{num2} and @var{den2} have common factors.@refill
! 1423:
! 1424: This function is actually implemented as a macro. It evaluates its
! 1425: arguments multiple times.@refill
! 1426: @end deftypefn
! 1427:
! 1428: @deftypefn Macro int mpq_sgn (mpq_t @var{op})
! 1429: @ifinfo
! 1430: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.@refill
! 1431: @end ifinfo
! 1432: @iftex
! 1433: @tex
! 1434: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1435: @end tex
! 1436: @end iftex
! 1437:
! 1438: This function is actually implemented as a macro. It evaluates its
! 1439: arguments multiple times.@refill
! 1440: @end deftypefn
! 1441:
! 1442: @deftypefun int mpq_equal (mpq_t @var{op1}, mpq_t @var{op2})
! 1443: Return non-zero if @var{op1} and @var{op2} are equal, zero if they are
! 1444: non-equal. Although @code{mpq_cmp} can be used for the same purpose, this
! 1445: function is much faster.@refill
! 1446: @end deftypefun
! 1447:
! 1448: @node Applying Integer Functions, Miscellaneous Rational Functions, Comparing Rationals, Rational Number Functions
! 1449: @comment node-name, next, previous, up
! 1450: @section Applying Integer Functions to Rationals
! 1451:
! 1452: The set of @code{mpq} functions is quite small. In particular, there are no
! 1453: functions for either input or output. But there are two macros that allow us
! 1454: to apply any @code{mpz} function on the numerator or denominator of a rational
! 1455: number. If these macros are used to assign to the rational number,
! 1456: @code{mpq_canonicalize} normally need to be called afterwards.@refill
! 1457:
! 1458: @deftypefn Macro mpz_t mpq_numref (mpq_t @var{op})
! 1459: @deftypefnx Macro mpz_t mpq_denref (mpq_t @var{op})
! 1460: Return a reference to the numerator and denominator of @var{op}, respectively.
! 1461: The @code{mpz} functions can be used on the result of these macros.@refill
! 1462: @end deftypefn
! 1463:
! 1464: @need 2000
! 1465: @node Miscellaneous Rational Functions, , Applying Integer Functions, Rational Number Functions
! 1466: @comment node-name, next, previous, up
! 1467: @section Miscellaneous Functions
! 1468:
! 1469: @deftypefun double mpq_get_d (mpq_t @var{op})
! 1470: Convert @var{op} to a double.@refill
! 1471: @end deftypefun
! 1472:
! 1473: These functions assign between either the numerator or denominator of a
! 1474: rational, and an integer. Instead of using these functions, it is preferable
! 1475: to use the more general mechanisms @code{mpq_numref} and @code{mpq_denref},
! 1476: together with @code{mpz_set}.@refill
! 1477:
! 1478: @deftypefun void mpq_set_num (mpq_t @var{rational}, mpz_t @var{numerator})
! 1479: Copy @var{numerator} to the numerator of @var{rational}. When this risks to
! 1480: make the numerator and denominator of @var{rational} have common factors, you
! 1481: have to pass @var{rational} to @code{mpq_canonicalize} before any operations
! 1482: are performed on @var{rational}.@refill
! 1483:
! 1484: This function is equivalent to
! 1485: @code{mpz_set (mpq_numref (@var{rational}), @var{numerator})}.@refill
! 1486: @end deftypefun
! 1487:
! 1488: @deftypefun void mpq_set_den (mpq_t @var{rational}, mpz_t @var{denominator})
! 1489: Copy @var{denominator} to the denominator of @var{rational}. When this risks
! 1490: to make the numerator and denominator of @var{rational} have common factors,
! 1491: or if the denominator might be negative, you have to pass @var{rational} to
! 1492: @code{mpq_canonicalize} before any operations are performed on @var{rational}.@refill
! 1493:
! 1494: @strong{In version 1 of the library, negative denominators were handled by
! 1495: copying the sign to the numerator. That is no longer done.}@refill
! 1496:
! 1497: This function is equivalent to
! 1498: @code{mpz_set (mpq_denref (@var{rational}), @var{denominators})}.@refill
! 1499: @end deftypefun
! 1500:
! 1501: @deftypefun void mpq_get_num (mpz_t @var{numerator}, mpq_t @var{rational})
! 1502: Copy the numerator of @var{rational} to the integer @var{numerator}, to
! 1503: prepare for integer operations on the numerator.@refill
! 1504:
! 1505: This function is equivalent to
! 1506: @code{mpz_set (@var{numerator}, mpq_numref (@var{rational}))}.@refill
! 1507: @end deftypefun
! 1508:
! 1509: @deftypefun void mpq_get_den (mpz_t @var{denominator}, mpq_t @var{rational})
! 1510: Copy the denominator of @var{rational} to the integer @var{denominator}, to
! 1511: prepare for integer operations on the denominator.@refill
! 1512:
! 1513: This function is equivalent to
! 1514: @code{mpz_set (@var{denominator}, mpq_denref (@var{rational}))}.@refill
! 1515: @end deftypefun
! 1516:
! 1517:
! 1518: @node Floating-point Functions, Low-level Functions, Rational Number Functions, Top
! 1519: @comment node-name, next, previous, up
! 1520: @chapter Floating-point Functions
! 1521: @cindex Floating-point functions
! 1522: @cindex Float functions
! 1523:
! 1524: This is a description of the @emph{preliminary} interface for floating-point
! 1525: arithmetic in GNU MP 2.@refill
! 1526:
! 1527: The floating-point functions expect arguments of type @code{mpf_t}.@refill
! 1528:
! 1529: The MP floating-point functions have an interface that is similar to the MP
! 1530: integer functions. The function prefix for floating-point operations is
! 1531: @code{mpf_}.@refill
! 1532:
! 1533: There is one significant characteristic of floating-point numbers that has
! 1534: motivated a difference between this function class and other MP function
! 1535: classes: the inherent inexactness of floating point arithmetic. The user has
! 1536: to specify the precision of each variable. A computation that assigns a
! 1537: variable will take place with the precision of the assigned variable; the
! 1538: precision of variables used as input is ignored.@refill
! 1539:
! 1540: @cindex User-defined precision
! 1541: The precision of a calculation is defined as follows: Compute the requested
! 1542: operation exactly (with "infinite precision"), and truncate the result to
! 1543: the destination variable precision. Even if the user has asked for a very
! 1544: high precision, MP will not calculate with superfluous digits. For example,
! 1545: if two low-precision numbers of nearly equal magnitude are added, the
! 1546: precision of the result will be limited to what is required to represent the
! 1547: result accurately.@refill
! 1548:
! 1549: The MP floating-point functions are @emph{not} intended as a smooth extension
! 1550: to the IEEE P754 arithmetic. Specifically, the results obtained on one
! 1551: computer often differs from the results obtained on a computer with a
! 1552: different word size.@refill
! 1553:
! 1554: @menu
! 1555: * Initializing Floats::
! 1556: * Assigning Floats::
! 1557: * Simultaneous Float Init & Assign::
! 1558: * Converting Floats::
! 1559: * Float Arithmetic::
! 1560: * Float Comparison::
! 1561: * I/O of Floats::
! 1562: * Miscellaneous Float Functions::
! 1563: @end menu
! 1564:
! 1565: @node Initializing Floats, Assigning Floats, , Floating-point Functions
! 1566: @comment node-name, next, previous, up
! 1567: @section Initialization and Assignment Functions
! 1568:
! 1569: @deftypefun void mpf_set_default_prec (unsigned long int @var{prec})
! 1570: Set the default precision to be @strong{at least} @var{prec} bits. All
! 1571: subsequent calls to @code{mpf_init} will use this precision, but previously
! 1572: initialized variables are unaffected.@refill
! 1573: @end deftypefun
! 1574:
! 1575: An @code{mpf_t} object must be initialized before storing the first value in
! 1576: it. The functions @code{mpf_init} and @code{mpf_init2} are used for that
! 1577: purpose.@refill
! 1578:
! 1579: @deftypefun void mpf_init (mpf_t @var{x})
! 1580: Initialize @var{x} to 0. Normally, a variable should be initialized once only
! 1581: or at least be cleared, using @code{mpf_clear}, between initializations. The
! 1582: precision of @var{x} is undefined unless a default precision has already been
! 1583: established by a call to @code{mpf_set_default_prec}.@refill
! 1584: @end deftypefun
! 1585:
! 1586: @deftypefun void mpf_init2 (mpf_t @var{x}, unsigned long int @var{prec})
! 1587: Initialize @var{x} to 0 and set its precision to be @strong{at least}
! 1588: @var{prec} bits. Normally, a variable should be initialized once only or at
! 1589: least be cleared, using @code{mpf_clear}, between initializations.@refill
! 1590: @end deftypefun
! 1591:
! 1592: @deftypefun void mpf_clear (mpf_t @var{x})
! 1593: Free the space occupied by @var{x}. Make sure to call this function for all
! 1594: @code{mpf_t} variables when you are done with them.@refill
! 1595: @end deftypefun
! 1596:
! 1597: @need 2000
! 1598: Here is an example on how to initialize floating-point variables:@refill
! 1599: @example
! 1600: @{
! 1601: mpf_t x, y;
! 1602: mpf_init (x); /* use default precision */
! 1603: mpf_init2 (y, 256); /* precision @emph{at least} 256 bits */
! 1604: @dots{}
! 1605: /* Unless the program is about to exit, do ... */
! 1606: mpf_clear (x);
! 1607: mpf_clear (y);
! 1608: @}
! 1609: @end example
! 1610:
! 1611: The following three functions are useful for changing the precision during a
! 1612: calculation. A typical use would be for adjusting the precision gradually in
! 1613: iterative algorithms like Newton-Raphson, making the computation precision
! 1614: closely match the actual accurate part of the numbers.@refill
! 1615:
! 1616: @deftypefun void mpf_set_prec (mpf_t @var{rop}, unsigned long int @var{prec})
! 1617: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits.
! 1618: Since changing the precision involves calls to @code{realloc}, this routine
! 1619: should not be called in a tight loop.@refill
! 1620: @end deftypefun
! 1621:
! 1622: @deftypefun {unsigned long int} mpf_get_prec (mpf_t @var{op})
! 1623: Return the precision actually used for assignments of @var{op}.@refill
! 1624: @end deftypefun
! 1625:
! 1626: @deftypefun void mpf_set_prec_raw (mpf_t @var{rop}, unsigned long int @var{prec})
! 1627: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits. This
! 1628: is a low-level function that does not change the allocation. The @var{prec}
! 1629: argument must not be larger that the precision previously returned by
! 1630: @code{mpf_get_prec}. It is crucial that the precision of @var{rop} is
! 1631: ultimately reset to exactly the value returned by @code{mpf_get_prec}.@refill
! 1632: @end deftypefun
! 1633:
! 1634:
! 1635: @node Assigning Floats, Simultaneous Float Init & Assign, Initializing Floats, Floating-point Functions
! 1636: @comment node-name, next, previous, up
! 1637: @subsection Assignment Functions
! 1638: @cindex Float assignment functions
! 1639:
! 1640: These functions assign new values to already initialized floats
! 1641: (@pxref{Initializing Floats}).@refill
! 1642:
! 1643: @deftypefun void mpf_set (mpf_t @var{rop}, mpf_t @var{op})
! 1644: @deftypefunx void mpf_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1645: @deftypefunx void mpf_set_si (mpf_t @var{rop}, signed long int @var{op})
! 1646: @deftypefunx void mpf_set_d (mpf_t @var{rop}, double @var{op})
! 1647: @deftypefunx void mpf_set_z (mpf_t @var{rop}, mpz_t @var{op})
! 1648: @deftypefunx void mpf_set_q (mpf_t @var{rop}, mpq_t @var{op})
! 1649: Set the value of @var{rop} from @var{op}.@refill
! 1650: @end deftypefun
! 1651:
! 1652: @deftypefun int mpf_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
! 1653: Set the value of @var{rop} from the string in @var{str}. The string is of the
! 1654: form @samp{M@@N} or, if the base is 10 or less, alternatively @samp{MeN}.
! 1655: @samp{M} is the mantissa and @samp{N} is the exponent. The mantissa is always
! 1656: in the specified base. The exponent is either in the specified base or, if
! 1657: @var{base} is negative, in decimal.@refill
! 1658:
! 1659: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
! 1660: @minus{}2. Negative values are used to specify that the exponent is in
! 1661: decimal.@refill
! 1662:
! 1663: Unlike the corresponding @code{mpz} function, the base will not be determined
! 1664: from the leading characters of the string if @var{base} is 0. This is so that
! 1665: numbers like @samp{0.23} are not interpreted as octal.@refill
! 1666:
! 1667: White space is allowed in the string, and is simply ignored.@refill
! 1668:
! 1669: This function returns 0 if the entire string up to the '\0' is a valid number
! 1670: in base @var{base}. Otherwise it returns @minus{}1.@refill
! 1671: @end deftypefun
! 1672:
! 1673:
! 1674: @node Simultaneous Float Init & Assign, Converting Floats, Assigning Floats, Floating-point Functions
! 1675: @comment node-name, next, previous, up
! 1676: @subsection Combined Initialization and Assignment Functions
! 1677: @cindex Initialization and assignment functions
! 1678:
! 1679: For convenience, MP provides a parallel series of initialize-and-set functions
! 1680: which initialize the output and then store the value there. These functions'
! 1681: names have the form @code{mpf_init_set@dots{}}@refill
! 1682:
! 1683: Once the float has been initialized by any of the @code{mpf_init_set@dots{}}
! 1684: functions, it can be used as the source or destination operand for the ordinary
! 1685: float functions. Don't use an initialize-and-set function on a variable
! 1686: already initialized!@refill
! 1687:
! 1688: @deftypefun void mpf_init_set (mpf_t @var{rop}, mpf_t @var{op})
! 1689: @deftypefunx void mpf_init_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1690: @deftypefunx void mpf_init_set_si (mpf_t @var{rop}, signed long int @var{op})
! 1691: @deftypefunx void mpf_init_set_d (mpf_t @var{rop}, double @var{op})
! 1692: Initialize @var{rop} and set its value from @var{op}.@refill
! 1693:
! 1694: The precision of @var{rop} will be taken from the active default precision, as
! 1695: set by @code{mpf_set_default_prec}.@refill
! 1696: @end deftypefun
! 1697:
! 1698: @deftypefun int mpf_init_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
! 1699: Initialize @var{rop} and set its value from the string in @var{str}. See
! 1700: @code{mpf_set_str} above for details on the assignment operation.@refill
! 1701:
! 1702: Note that @var{rop} is initialized even if an error occurs. (I.e., you have to
! 1703: call @code{mpf_clear} for it.)@refill
! 1704:
! 1705: The precision of @var{rop} will be taken from the active default precision, as
! 1706: set by @code{mpf_set_default_prec}.@refill
! 1707: @end deftypefun
! 1708:
! 1709:
! 1710: @node Converting Floats, Float Arithmetic, Simultaneous Float Init & Assign, Floating-point Functions
! 1711: @comment node-name, next, previous, up
! 1712: @section Conversion Functions
! 1713: @cindex Conversion functions
! 1714:
! 1715: @deftypefun double mpf_get_d (mpf_t @var{op})
! 1716: Convert @var{op} to a double.@refill
! 1717: @end deftypefun
! 1718:
! 1719: @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})
! 1720: Convert @var{op} to a string of digits in base @var{base}. The base may vary
! 1721: from 2 to 36. Generate at most @var{n_digits} significant digits, or if
! 1722: @var{n_digits} is 0, the maximum number of digits accurately representable by
! 1723: @var{op}.@refill
! 1724:
! 1725: If @var{str} is NULL, space for the mantissa is allocated using the default
! 1726: allocation function, and a pointer to the string is returned.@refill
! 1727:
! 1728: If @var{str} is not NULL, it should point to a block of storage enough large
! 1729: for the mantissa, i.e., @var{n_digits} + 2. The two extra bytes are for a
! 1730: possible minus sign, and for the terminating null character.@refill
! 1731:
! 1732: The exponent is written through the pointer @var{expptr}.@refill
! 1733:
! 1734: If @var{n_digits} is 0, the maximum number of digits meaningfully achievable
! 1735: from the precision of @var{op} will be generated. Note that the space
! 1736: requirements for @var{str} in this case will be impossible for the user to
! 1737: predetermine. Therefore, you need to pass NULL for the string argument
! 1738: whenever @var{n_digits} is 0.@refill
! 1739:
! 1740: The generated string is a fraction, with an implicit radix point immediately
! 1741: to the left of the first digit. For example, the number 3.1416 would be
! 1742: returned as "31416" in the string and 1 written at @var{expptr}.@refill
! 1743: @end deftypefun
! 1744:
! 1745:
! 1746: @node Float Arithmetic, Float Comparison, Converting Floats, Floating-point Functions
! 1747: @comment node-name, next, previous, up
! 1748: @section Arithmetic Functions
! 1749: @cindex Float arithmetic functions
! 1750: @cindex Arithmetic functions
! 1751:
! 1752: @deftypefun void mpf_add (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1753: @deftypefunx void mpf_add_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1754: @ifinfo
! 1755: Set @var{rop} to @var{op1} + @var{op2}.@refill
! 1756: @end ifinfo
! 1757: @iftex
! 1758: @tex
! 1759: Set @var{rop} to $@var{op1} + @var{op2}$.
! 1760: @end tex
! 1761: @end iftex
! 1762: @end deftypefun
! 1763:
! 1764: @deftypefun void mpf_sub (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1765: @deftypefunx void mpf_ui_sub (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
! 1766: @deftypefunx void mpf_sub_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1767: Set @var{rop} to @var{op1} @minus{} @var{op2}.@refill
! 1768: @end deftypefun
! 1769:
! 1770: @deftypefun void mpf_mul (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1771: @deftypefunx void mpf_mul_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1772: @ifinfo
! 1773: Set @var{rop} to @var{op1} times @var{op2}.@refill
! 1774: @end ifinfo
! 1775: @iftex
! 1776: @tex
! 1777: Set @var{rop} to $@var{op1} \times @var{op2}$.
! 1778: @end tex
! 1779: @end iftex
! 1780: @end deftypefun
! 1781:
! 1782: Division is undefined if the divisor is zero, and passing a zero divisor to
! 1783: the divide functions will make these functions intentionally divide by zero.
! 1784: This gives the user the possibility to handle arithmetic exceptions in these
! 1785: functions in the same manner as other arithmetic exceptions.@refill
! 1786:
! 1787: @deftypefun void mpf_div (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1788: @deftypefunx void mpf_ui_div (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
! 1789: @deftypefunx void mpf_div_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1790: Set @var{rop} to @var{op1}/@var{op2}.@refill
! 1791: @end deftypefun
! 1792:
! 1793: @deftypefun void mpf_sqrt (mpf_t @var{rop}, mpf_t @var{op})
! 1794: @deftypefunx void mpf_sqrt_ui (mpf_t @var{rop}, unsigned long int @var{op})
! 1795: @ifinfo
! 1796: Set @var{rop} to the square root of @var{op}.@refill
! 1797: @end ifinfo
! 1798: @iftex
! 1799: @tex
! 1800: Set @var{rop} to $\sqrt{@var{op}}$.
! 1801: @end tex
! 1802: @end iftex
! 1803: @end deftypefun
! 1804:
! 1805: @c @deftypefun void mpf_pow_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1806: @c Set @var{rop} to @var{op1} raised to @var{op2}.
! 1807: @c @end deftypefun
! 1808:
! 1809: @deftypefun void mpf_neg (mpf_t @var{rop}, mpf_t @var{op})
! 1810: Set @var{rop} to @minus{}@var{op}.@refill
! 1811: @end deftypefun
! 1812:
! 1813: @deftypefun void mpf_abs (mpf_t @var{rop}, mpf_t @var{op})
! 1814: Set @var{rop} to the absolute value of @var{op}.@refill
! 1815: @end deftypefun
! 1816:
! 1817: @deftypefun void mpf_mul_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1818: @ifinfo
! 1819: Set @var{rop} to @var{op1} times 2 raised to @var{op2}.@refill
! 1820: @end ifinfo
! 1821: @iftex
! 1822: @tex
! 1823: Set @var{rop} to $@var{op1} \times 2^{op2}$.
! 1824: @end tex
! 1825: @end iftex
! 1826: @end deftypefun
! 1827:
! 1828: @deftypefun void mpf_div_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
! 1829: @ifinfo
! 1830: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.@refill
! 1831: @end ifinfo
! 1832: @iftex
! 1833: @tex
! 1834: Set @var{rop} to $@var{op1}/2^{op2}$.
! 1835: @end tex
! 1836: @end iftex
! 1837: @end deftypefun
! 1838:
! 1839: @node Float Comparison, I/O of Floats, Float Arithmetic, Floating-point Functions
! 1840: @comment node-name, next, previous, up
! 1841: @section Comparison Functions
! 1842: @cindex Float comparisons functions
! 1843: @cindex Comparison functions
! 1844:
! 1845: @deftypefun int mpf_cmp (mpf_t @var{op1}, mpf_t @var{op2})
! 1846: @deftypefunx int mpf_cmp_ui (mpf_t @var{op1}, unsigned long int @var{op2})
! 1847: @deftypefunx int mpf_cmp_si (mpf_t @var{op1}, signed long int @var{op2})
! 1848: @ifinfo
! 1849: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
! 1850: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
! 1851: @var{op2}.@refill
! 1852: @end ifinfo
! 1853: @iftex
! 1854: @tex
! 1855: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
! 1856: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
! 1857: < @var{op2}$.
! 1858: @end tex
! 1859: @end iftex
! 1860: @end deftypefun
! 1861:
! 1862: @deftypefun int mpf_eq (mpf_t @var{op1}, mpf_t @var{op2}, unsigned long int op3)
! 1863: Return non-zero if the first @var{op3} bits of @var{op1} and @var{op2} are
! 1864: equal, zero otherwise. I.e., test of @var{op1} and @var{op2} are
! 1865: approximately equal.@refill
! 1866: @end deftypefun
! 1867:
! 1868: @deftypefun void mpf_reldiff (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
! 1869: Compute the relative difference between @var{op1} and @var{op2} and store the
! 1870: result in @var{rop}.@refill
! 1871: @end deftypefun
! 1872:
! 1873: @deftypefn Macro int mpf_sgn (mpf_t @var{op})
! 1874: @ifinfo
! 1875: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.@refill
! 1876: @end ifinfo
! 1877: @iftex
! 1878: @tex
! 1879: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
! 1880: @end tex
! 1881: @end iftex
! 1882:
! 1883: This function is actually implemented as a macro. It evaluates its
! 1884: arguments multiple times.@refill
! 1885: @end deftypefn
! 1886:
! 1887: @node I/O of Floats, Miscellaneous Float Functions, Float Comparison, Floating-point Functions
! 1888: @comment node-name, next, previous, up
! 1889: @section Input and Output Functions
! 1890: @cindex Float input and output functions
! 1891: @cindex Input functions
! 1892: @cindex Output functions
! 1893: @cindex I/O functions
! 1894:
! 1895: Functions that perform input from a stdio stream, and functions that output to
! 1896: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
! 1897: these functions will make them read from @code{stdin} and write to
! 1898: @code{stdout}, respectively.@refill
! 1899:
! 1900: When using any of these functions, it is a good idea to include @file{stdio.h}
! 1901: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
! 1902: for these functions.@refill
! 1903:
! 1904: @deftypefun size_t mpf_out_str (FILE *@var{stream}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
! 1905: Output @var{op} on stdio stream @var{stream}, as a string of digits in
! 1906: base @var{base}. The base may vary from 2 to 36. Print at most
! 1907: @var{n_digits} significant digits, or if @var{n_digits} is 0, the maximum
! 1908: number of digits accurately representable by @var{op}.@refill
! 1909:
! 1910: In addition to the significant digits, a leading @samp{0.} and a
! 1911: trailing exponent, in the form @samp{eNNN}, are printed. If @var{base}
! 1912: is greater than 10, @samp{@@} will be used instead of @samp{e} as
! 1913: exponent delimiter.@refill
! 1914:
! 1915: Return the number of bytes written, or if an error occurred, return 0.@refill
! 1916: @end deftypefun
! 1917:
! 1918: @deftypefun size_t mpf_inp_str (mpf_t @var{rop}, FILE *@var{stream}, int @var{base})
! 1919: Input a string in base @var{base} from stdio stream @var{stream}, and put the
! 1920: read float in @var{rop}. The string is of the form @samp{M@@N} or, if the
! 1921: base is 10 or less, alternatively @samp{MeN}. @samp{M} is the mantissa and
! 1922: @samp{N} is the exponent. The mantissa is always in the specified base. The
! 1923: exponent is either in the specified base or, if @var{base} is negative, in
! 1924: decimal.@refill
! 1925:
! 1926: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
! 1927: @minus{}2. Negative values are used to specify that the exponent is in
! 1928: decimal.@refill
! 1929:
! 1930: Unlike the corresponding @code{mpz} function, the base will not be determined
! 1931: from the leading characters of the string if @var{base} is 0. This is so that
! 1932: numbers like @samp{0.23} are not interpreted as octal.@refill
! 1933:
! 1934: Return the number of bytes read, or if an error occurred, return 0.@refill
! 1935: @end deftypefun
! 1936:
! 1937: @c @deftypefun void mpf_out_raw (FILE *@var{stream}, mpf_t @var{float})
! 1938: @c Output @var{float} on stdio stream @var{stream}, in raw binary
! 1939: @c format. The float is written in a portable format, with 4 bytes of
! 1940: @c size information, and that many bytes of limbs. Both the size and the
! 1941: @c limbs are written in decreasing significance order.
! 1942: @c @end deftypefun
! 1943:
! 1944: @c @deftypefun void mpf_inp_raw (mpf_t @var{float}, FILE *@var{stream})
! 1945: @c Input from stdio stream @var{stream} in the format written by
! 1946: @c @code{mpf_out_raw}, and put the result in @var{float}.
! 1947: @c @end deftypefun
! 1948:
! 1949:
! 1950: @node Miscellaneous Float Functions, , I/O of Floats, Floating-point Functions
! 1951: @comment node-name, next, previous, up
! 1952: @section Miscellaneous Functions
! 1953: @cindex Miscellaneous float functions
! 1954:
! 1955: @deftypefun void mpf_random2 (mpf_t @var{rop}, mp_size_t @var{max_size}, mp_exp_t @var{max_exp})
! 1956: Generate a random float of at most @var{max_size} limbs, with long strings of
! 1957: zeros and ones in the binary representation. The exponent of the number is in
! 1958: the interval @minus{}@var{exp} to @var{exp}. This function is useful for
! 1959: testing functions and algorithms, since this kind of random numbers have
! 1960: proven to be more likely to trigger corner-case bugs. Negative random numbers
! 1961: are generated when @var{max_size} is negative.@refill
! 1962: @end deftypefun
! 1963:
! 1964: @c @deftypefun size_t mpf_size (mpf_t @var{op})
! 1965: @c Return the size of @var{op} measured in number of limbs. If @var{op} is
! 1966: @c zero, the returned value will be zero. (@xref{Nomenclature}, for an
! 1967: @c explanation of the concept @dfn{limb}.)
! 1968: @c
! 1969: @c @strong{This function is obsolete. It will disappear from future MP
! 1970: @c releases.}
! 1971: @c @end deftypefun
! 1972:
! 1973: @node Low-level Functions, BSD Compatible Functions, Floating-point Functions, Top
! 1974: @comment node-name, next, previous, up
! 1975: @chapter Low-level Functions
! 1976: @cindex Low-level functions
! 1977:
! 1978: This chapter describes low-level MP functions, used to implement the high-level
! 1979: MP functions, but also intended for time-critical user code.@refill
! 1980:
! 1981: These functions start with the prefix @code{mpn_}.@refill
! 1982:
! 1983: @c 1. Some of these function clobber input operands.
! 1984: @c
! 1985:
! 1986: The @code{mpn} functions are designed to be as fast as possible, @strong{not}
! 1987: to provide a coherent calling interface. The different functions have somewhat
! 1988: similar interfaces, but there are variations that make them hard to use. These
! 1989: functions do as little as possible apart from the real multiple precision
! 1990: computation, so that no time is spent on things that not all callers need.@refill
! 1991:
! 1992: A source operand is specified by a pointer to the least significant limb and a
! 1993: limb count. A destination operand is specified by just a pointer. It is the
! 1994: responsibility of the caller to ensure that the destination has enough space
! 1995: for storing the result.@refill
! 1996:
! 1997: With this way of specifying operands, it is possible to perform computations
! 1998: on subranges of an argument, and store the result into a subrange of a
! 1999: destination.@refill
! 2000:
! 2001: A common requirement for all functions is that each source area needs at least
! 2002: one limb. No size argument may be zero.@refill
! 2003:
! 2004: The @code{mpn} functions is the base for the implementation of the @code{mpz_},
! 2005: @code{mpf_}, and @code{mpq_} functions.@refill
! 2006:
! 2007: This example adds the number beginning at @var{src1_ptr} and the number
! 2008: beginning at @var{src2_ptr} and writes the sum at @var{dest_ptr}. All areas
! 2009: have @var{size} limbs.@refill
! 2010:
! 2011: @example
! 2012: cy = mpn_add_n (dest_ptr, src1_ptr, src2_ptr, size)
! 2013: @end example
! 2014:
! 2015: @noindent
! 2016: In the notation used here, a source operand is identified by the pointer to
! 2017: the least significant limb, and the limb count in braces. For example,
! 2018: @{s1_ptr, s1_size@}.@refill
! 2019:
! 2020: @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})
! 2021: Add @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@}, and
! 2022: write the @var{size} least significant limbs of the result to @var{dest_ptr}.
! 2023: Return carry, either 0 or 1.@refill
! 2024:
! 2025: This is the lowest-level function for addition. It is the preferred function
! 2026: for addition, since it is written in assembly for most targets. For addition
! 2027: of a variable to itself (i.e., @var{src1_ptr} equals @var{src2_ptr}, use
! 2028: @code{mpn_lshift} with a count of 1 for optimal speed.@refill
! 2029: @end deftypefun
! 2030:
! 2031: @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})
! 2032: Add @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
! 2033: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
! 2034: carry, either 0 or 1.@refill
! 2035: @end deftypefun
! 2036:
! 2037: @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})
! 2038: Add @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
! 2039: @var{src2_size}@}, and write the @var{src1_size} least significant limbs of
! 2040: the result to @var{dest_ptr}. Return carry, either 0 or 1.@refill
! 2041:
! 2042: This function requires that @var{src1_size} is greater than or equal to
! 2043: @var{src2_size}.@refill
! 2044: @end deftypefun
! 2045:
! 2046: @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})
! 2047: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
! 2048: @var{size}@}, and write the @var{size} least significant limbs of the result
! 2049: to @var{dest_ptr}. Return borrow, either 0 or 1.@refill
! 2050:
! 2051: This is the lowest-level function for subtraction. It is the preferred
! 2052: function for subtraction, since it is written in assembly for most targets.@refill
! 2053: @end deftypefun
! 2054:
! 2055: @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})
! 2056: Subtract @var{src2_limb} from @{@var{src1_ptr}, @var{size}@}, and write the
! 2057: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
! 2058: borrow, either 0 or 1.@refill
! 2059: @end deftypefun
! 2060:
! 2061: @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})
! 2062: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
! 2063: @var{src1_size}@}, and write the @var{src1_size} least significant limbs of
! 2064: the result to @var{dest_ptr}. Return borrow, either 0 or 1.@refill
! 2065:
! 2066: This function requires that @var{src1_size} is greater than or equal to
! 2067: @var{src2_size}.@refill
! 2068: @end deftypefun
! 2069:
! 2070: @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})
! 2071: Multiply @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@},
! 2072: and write the @strong{entire} result to @var{dest_ptr}.@refill
! 2073:
! 2074: The destination has to have space for 2@var{size} limbs, even if the
! 2075: significant result might be one limb smaller.@refill
! 2076: @end deftypefun
! 2077:
! 2078: @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})
! 2079: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
! 2080: @var{size} least significant limbs of the product to @var{dest_ptr}. Return
! 2081: the most significant limb of the product.@refill
! 2082:
! 2083: This is a low-level function that is a building block for general
! 2084: multiplication as well as other operations in MP. It is written in assembly
! 2085: for most targets.@refill
! 2086:
! 2087: Don't call this function if @var{src2_limb} is a power of 2; use
! 2088: @code{mpn_lshift} with a count equal to the logarithm of @var{src2_limb}
! 2089: instead, for optimal speed.@refill
! 2090: @end deftypefun
! 2091:
! 2092: @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})
! 2093: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and add the
! 2094: @var{size} least significant limbs of the product to @{@var{dest_ptr},
! 2095: @var{size}@} and write the result to @var{dest_ptr} @var{dest_ptr}. Return
! 2096: the most significant limb of the product, plus carry-out from the addition.@refill
! 2097:
! 2098: This is a low-level function that is a building block for general
! 2099: multiplication as well as other operations in MP. It is written in assembly
! 2100: for most targets.@refill
! 2101: @end deftypefun
! 2102:
! 2103: @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})
! 2104: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and subtract the
! 2105: @var{size} least significant limbs of the product from @{@var{dest_ptr},
! 2106: @var{size}@} and write the result to @var{dest_ptr}. Return the most
! 2107: significant limb of the product, minus borrow-out from the subtraction.@refill
! 2108:
! 2109: This is a low-level function that is a building block for general
! 2110: multiplication and division as well as other operations in MP. It is written
! 2111: in assembly for most targets.@refill
! 2112: @end deftypefun
! 2113:
! 2114: @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})
! 2115: Multiply @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
! 2116: @var{src2_size}@}, and write the result to @var{dest_ptr}. Return the most
! 2117: significant limb of the result.@refill
! 2118:
! 2119: The destination has to have space for @var{src1_size} + @var{src1_size}
! 2120: limbs, even if the result might be one limb smaller.@refill
! 2121:
! 2122: This function requires that @var{src1_size} is greater than or equal to
! 2123: @var{src2_size}. The destination must be distinct from either input operands.@refill
! 2124: @end deftypefun
! 2125:
! 2126: @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})
! 2127: Divide @{@var{rs2p}, @var{rs2size}@} by @{@var{s3p}, @var{s3size}@}, and
! 2128: write the quotient at @var{r1p}, with the exception of the most significant
! 2129: limb, which is returned. The remainder replaces the dividend at @var{rs2p}.@refill
! 2130:
! 2131: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
! 2132: and stored after the integral limbs. For most usages, @var{xsize} will be
! 2133: zero.@refill
! 2134:
! 2135: It is required that @var{rs2size} is greater than or equal to @var{s3size}.
! 2136: It is required that the most significant bit of the divisor is set.@refill
! 2137:
! 2138: If the quotient is not needed, pass @var{rs2p} + @var{s3size} as @var{r1p}.
! 2139: Aside from that special case, no overlap between arguments is permitted.@refill
! 2140:
! 2141: Return the most significant limb of the quotient, either 0 or 1.@refill
! 2142:
! 2143: The area at @var{r1p} needs to be @var{rs2size} @minus{} @var{s3size} +
! 2144: @var{xsize} limbs large.@refill
! 2145: @end deftypefun
! 2146:
! 2147: @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})
! 2148: Divide @{@var{s2p}, @var{s2size}@} by @var{s3limb}, and write the quotient
! 2149: at @var{r1p}. Return the remainder.@refill
! 2150:
! 2151: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
! 2152: and stored after the integral limbs. For most usages, @var{xsize} will be
! 2153: zero.@refill
! 2154:
! 2155: The areas at @var{r1p} and @var{s2p} have to be identical or completely
! 2156: separate, not partially overlapping.@refill
! 2157: @end deftypefun
! 2158:
! 2159: @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})
! 2160: @strong{This interface is obsolete. It will disappear from future releases.
! 2161: Use @code{mpn_divrem} in its stead.}@refill
! 2162: @end deftypefun
! 2163:
! 2164: @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})
! 2165: @strong{This interface is obsolete. It will disappear from future releases.
! 2166: Use @code{mpn_divrem_1} in its stead.}@refill
! 2167: @end deftypefun
! 2168:
! 2169: @deftypefun mp_limb_t mpn_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb})
! 2170: Divide @{@var{s1p}, @var{s1size}@} by @var{s2limb}, and return the remainder.@refill
! 2171: @end deftypefun
! 2172:
! 2173: @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})
! 2174: @strong{This interface is obsolete. It will disappear from future releases.
! 2175: Use @code{mpn_mod_1} in its stead.}@refill
! 2176: @end deftypefun
! 2177:
! 2178: @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})
! 2179: The function puts the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
! 2180: @var{q} =
! 2181: @{@var{s1p}, @var{s1size}@}/@{@var{s2p}, @var{s2size}@}
! 2182: mod 2^@var{d}
! 2183: at @var{dest_ptr},
! 2184: and returns the high @var{d} mod @var{BITS_PER_MP_LIMB} bits of @var{q}.@refill
! 2185:
! 2186: @{@var{s1p}, @var{s1size}@} - @var{q} * @{@var{s2p}, @var{s2size}@}
! 2187: mod 2^(@var{s1size}*@var{BITS_PER_MP_LIMB})
! 2188: is placed at @var{s1p}.
! 2189: Since the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
! 2190: this difference are zero, it is possible to overwrite the low limbs at
! 2191: @var{s1p} with this difference,
! 2192: provided @var{dest_ptr} <= @var{s1p}.@refill
! 2193:
! 2194: This function requires that @var{s1size} * @var{BITS_PER_MP_LIMB} >= @var{D},
! 2195: and that @{@var{s2p}, @var{s2size}@} is odd.@refill
! 2196:
! 2197: @strong{This interface is preliminary. It might change incompatibly in
! 2198: future revisions.}@refill
! 2199: @end deftypefun
! 2200:
! 2201: @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})
! 2202: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the left, and
! 2203: write the @var{src_size} least significant limbs of the result to
! 2204: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
! 2205: n-bit machine. The bits shifted out to the left are returned.@refill
! 2206:
! 2207: Overlapping of the destination space and the source space is allowed in this
! 2208: function, provided @var{dest_ptr} >= @var{src_ptr}.@refill
! 2209:
! 2210: This function is written in assembly for most targets.@refill
! 2211: @end deftypefun
! 2212:
! 2213: @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})
! 2214: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the right, and
! 2215: write the @var{src_size} most significant limbs of the result to
! 2216: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
! 2217: n-bit machine. The bits shifted out to the right are returned.@refill
! 2218:
! 2219: Overlapping of the destination space and the source space is allowed in this
! 2220: function, provided @var{dest_ptr} <= @var{src_ptr}.@refill
! 2221:
! 2222: This function is written in assembly for most targets.@refill
! 2223: @end deftypefun
! 2224:
! 2225: @deftypefun int mpn_cmp (const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
! 2226: Compare @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@} and
! 2227: return a positive value if src1 > src2, 0 of they are equal, and a negative
! 2228: value if src1 < src2.@refill
! 2229: @end deftypefun
! 2230:
! 2231: @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})
! 2232: Puts at @var{dest_ptr} the greatest common divisor of @{@var{src1_ptr},
! 2233: @var{src1_size}@} and @{@var{src2_ptr}, @var{src2_size}@}; both source
! 2234: operands are destroyed by the operation. The size in limbs of the greatest
! 2235: common divisor is returned.@refill
! 2236:
! 2237: @{@var{src1_ptr}, @var{src1_size}@} must be odd, and @{@var{src2_ptr},
! 2238: @var{src2_size}@} must have at least as many bits as @{@var{src1_ptr},
! 2239: @var{src1_size}@}.@refill
! 2240:
! 2241: @strong{This interface is preliminary. It might change incompatibly in
! 2242: future revisions.}@refill
! 2243: @end deftypefun
! 2244:
! 2245: @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})
! 2246: Return the greatest common divisor of @{@var{src1_ptr}, @var{src1_size}@}
! 2247: and @var{src2_limb}, where @var{src2_limb} (as well as @var{src1_size})
! 2248: must be different from 0.@refill
! 2249: @end deftypefun
! 2250:
! 2251: @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})
! 2252: Puts at @var{r1p} the greatest common divisor of @{@var{s1p}, @var{s1size}@}
! 2253: and @{@var{s2p}, @var{s2size}@}. The first cofactor is written at
! 2254: @var{r2p}. Both source operands are destroyed by the operation. The size
! 2255: in limbs of the greatest common divisor is returned.@refill
! 2256:
! 2257: @strong{This interface is preliminary. It might change incompatibly in
! 2258: future revisions.}@refill
! 2259: @end deftypefun
! 2260:
! 2261: @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})
! 2262: Compute the square root of @{@var{sp}, @var{size}@} and put the result at
! 2263: @var{r1p}. Write the remainder at @var{r2p}, unless @var{r2p} is NULL.@refill
! 2264:
! 2265: Return the size of the remainder, whether @var{r2p} was NULL or non-NULL.
! 2266: Iff the operand was a perfect square, the return value will be 0.@refill
! 2267:
! 2268: The areas at @var{r1p} and @var{sp} have to be distinct. The areas at
! 2269: @var{r2p} and @var{sp} have to be identical or completely separate, not
! 2270: partially overlapping.@refill
! 2271:
! 2272: @ifinfo
! 2273: The area at @var{r1p} needs to have space for ceil(@var{size}/2) limbs.@refill
! 2274: @end ifinfo
! 2275: @iftex
! 2276: @tex
! 2277: The area at @var{r1p} needs to have space for $\lceil@var{size}/2\rceil$ limbs.
! 2278: @end tex
! 2279: @end iftex
! 2280: The area at @var{r2p} needs to be @var{size} limbs large.@refill
! 2281:
! 2282: @strong{This interface is preliminary. It might change incompatibly in
! 2283: future revisions.}@refill
! 2284: @end deftypefun
! 2285:
! 2286: @deftypefun mp_size_t mpn_get_str (unsigned char *@var{str}, int @var{base}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size})
! 2287: Convert @{@var{s1p}, @var{s1size}@} to a raw unsigned char array in base
! 2288: @var{base}. The string is not in ASCII; to convert it to printable format,
! 2289: add the ASCII codes for @samp{0} or @samp{A}, depending on the base and
! 2290: range. There may be leading zeros in the string.@refill
! 2291:
! 2292: The area at @var{s1p} is clobbered.@refill
! 2293:
! 2294: Return the number of characters in @var{str}.@refill
! 2295:
! 2296: The area at @var{str} has to have space for the largest possible number
! 2297: represented by a @var{s1size} long limb array, plus one extra character.@refill
! 2298: @end deftypefun
! 2299:
! 2300: @deftypefun mp_size_t mpn_set_str (mp_limb_t * @var{r1p}, const char *@var{str}, size_t {strsize}, int @var{base})
! 2301: Convert the raw unsigned char array at @var{str} of length @var{strsize} to
! 2302: a limb array @{@var{s1p}, @var{s1size}@}. The base of @var{str} is
! 2303: @var{base}.@refill
! 2304:
! 2305: Return the number of limbs stored in @var{r1p}.@refill
! 2306: @end deftypefun
! 2307:
! 2308: @deftypefun {unsigned long int} mpn_scan0 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
! 2309: Scan @var{s1p} from bit position @var{bit} for the next clear bit.@refill
! 2310:
! 2311: It is required that there be a clear bit within the area at @var{s1p} at or
! 2312: beyond bit position @var{bit}, so that the function has something to return.@refill
! 2313:
! 2314: @strong{This interface is preliminary. It might change incompatibly in
! 2315: future revisions.}@refill
! 2316: @end deftypefun
! 2317:
! 2318: @deftypefun {unsigned long int} mpn_scan1 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
! 2319: Scan @var{s1p} from bit position @var{bit} for the next set bit.@refill
! 2320:
! 2321: It is required that there be a set bit within the area at @var{s1p} at or
! 2322: beyond bit position @var{bit}, so that the function has something to return.@refill
! 2323:
! 2324: @strong{This interface is preliminary. It might change incompatibly in
! 2325: future revisions.}@refill
! 2326: @end deftypefun
! 2327:
! 2328: @deftypefun void mpn_random2 (mp_limb_t * @var{r1p}, mp_size_t @var{r1size})
! 2329: Generate a random number of length @var{r1size} with long strings of zeros
! 2330: and ones in the binary representation, and store it at @var{r1p}.@refill
! 2331:
! 2332: The generated random numbers are intended for testing the correctness of the
! 2333: implementation of the @code{mpn} routines.@refill
! 2334: @end deftypefun
! 2335:
! 2336: @deftypefun {unsigned long int} mpn_popcount (const mp_limb_t * @var{s1p}, unsigned long int @var{size})
! 2337: Count the number of set bits in @{@var{s1p}, @var{size}@}.@refill
! 2338: @end deftypefun
! 2339:
! 2340: @deftypefun {unsigned long int} mpn_hamdist (const mp_limb_t * @var{s1p}, const mp_limb_t * @var{s2p}, unsigned long int @var{size})
! 2341: Compute the hamming distance between @{@var{s1p}, @var{size}@} and
! 2342: @{@var{s2p}, @var{size}@}.@refill
! 2343: @end deftypefun
! 2344:
! 2345: @deftypefun int mpn_perfect_square_p (const mp_limb_t * @var{s1p}, mp_size_t @var{size})
! 2346: Return non-zero iff @{@var{s1p}, @var{size}@} is a perfect square.@refill
! 2347: @end deftypefun
! 2348:
! 2349:
! 2350: @node BSD Compatible Functions, Custom Allocation, Low-level Functions, Top
! 2351: @comment node-name, next, previous, up
! 2352: @chapter Berkeley MP Compatible Functions
! 2353: @cindex BSD MP compatible functions
! 2354:
! 2355: These functions are intended to be fully compatible with the Berkeley MP
! 2356: library which is available on many BSD derived U*ix systems.@refill
! 2357:
! 2358: The original Berkeley MP library has a usage restriction: you cannot use the
! 2359: same variable as both source and destination in a single function call. The
! 2360: compatible functions in GNU MP do not share this restriction--inputs and
! 2361: outputs may overlap.@refill
! 2362:
! 2363: It is not recommended that new programs are written using these functions.
! 2364: Apart from the incomplete set of functions, the interface for initializing
! 2365: @code{MINT} objects is more error prone, and the @code{pow} function collides
! 2366: with @code{pow} in @file{libm.a}.@refill
! 2367:
! 2368: @cindex @file{mp.h}
! 2369: Include the header @file{mp.h} to get the definition of the necessary types
! 2370: and functions. If you are on a BSD derived system, make sure to include GNU
! 2371: @file{mp.h} if you are going to link the GNU @file{libmp.a} to you program.
! 2372: This means that you probably need to give the -I<dir> option to the compiler,
! 2373: where <dir> is the directory where you have GNU @file{mp.h}.@refill
! 2374:
! 2375: @deftypefun {MINT *} itom (signed short int @var{initial_value})
! 2376: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
! 2377: Initialize the integer to @var{initial_value}. Return a pointer to the
! 2378: @code{MINT} object.@refill
! 2379: @end deftypefun
! 2380:
! 2381: @deftypefun {MINT *} xtom (char *@var{initial_value})
! 2382: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
! 2383: Initialize the integer from @var{initial_value}, a hexadecimal, '\0'-terminate
! 2384: C string. Return a pointer to the @code{MINT} object.@refill
! 2385: @end deftypefun
! 2386:
! 2387: @deftypefun void move (MINT *@var{src}, MINT *@var{dest})
! 2388: Set @var{dest} to @var{src} by copying. Both variables must be previously
! 2389: initialized.@refill
! 2390: @end deftypefun
! 2391:
! 2392: @deftypefun void madd (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2393: Add @var{src_1} and @var{src_2} and put the sum in @var{destination}.@refill
! 2394: @end deftypefun
! 2395:
! 2396: @deftypefun void msub (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2397: Subtract @var{src_2} from @var{src_1} and put the difference in
! 2398: @var{destination}.@refill
! 2399: @end deftypefun
! 2400:
! 2401: @deftypefun void mult (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
! 2402: Multiply @var{src_1} and @var{src_2} and put the product in
! 2403: @var{destination}.@refill
! 2404: @end deftypefun
! 2405:
! 2406: @deftypefun void mdiv (MINT *@var{dividend}, MINT *@var{divisor}, MINT *@var{quotient}, MINT *@var{remainder})
! 2407: @deftypefunx void sdiv (MINT *@var{dividend}, signed short int @var{divisor}, MINT *@var{quotient}, signed short int *@var{remainder})
! 2408: Set @var{quotient} to @var{dividend}/@var{divisor}, and @var{remainder} to
! 2409: @var{dividend} mod @var{divisor}. The quotient is rounded towards zero; the
! 2410: remainder has the same sign as the dividend unless it is zero.@refill
! 2411:
! 2412: Some implementations of these functions work differently--or not at all--for
! 2413: negative arguments.@refill
! 2414: @end deftypefun
! 2415:
! 2416: @deftypefun void msqrt (MINT *@var{operand}, MINT *@var{root}, MINT *@var{remainder})
! 2417: @ifinfo
! 2418: Set @var{root} to the truncated integer part of the square root of
! 2419: @var{operand}. Set @var{remainder} to
! 2420: @var{operand}@minus{}@var{root}*@var{root},@refill
! 2421: @end ifinfo
! 2422: @iftex
! 2423: @tex
! 2424: Set @var{root} to $\lfloor\sqrt{@var{operand}}\rfloor$, like
! 2425: @code{mpz_sqrt}. Set @var{remainder} to $(operand - root^2)$,
! 2426: @end tex
! 2427: @end iftex
! 2428: (i.e., zero if @var{operand} is a perfect square).@refill
! 2429:
! 2430: If @var{root} and @var{remainder} are the same variable, the results are
! 2431: undefined.@refill
! 2432: @end deftypefun
! 2433:
! 2434: @deftypefun void pow (MINT *@var{base}, MINT *@var{exp}, MINT *@var{mod}, MINT *@var{dest})
! 2435: Set @var{dest} to (@var{base} raised to @var{exp}) modulo @var{mod}.@refill
! 2436: @end deftypefun
! 2437:
! 2438: @deftypefun void rpow (MINT *@var{base}, signed short int @var{exp}, MINT *@var{dest})
! 2439: Set @var{dest} to @var{base} raised to @var{exp}.@refill
! 2440: @end deftypefun
! 2441:
! 2442: @deftypefun void gcd (MINT *@var{operand1}, MINT *@var{operand2}, MINT *@var{res})
! 2443: Set @var{res} to the greatest common divisor of @var{operand1} and
! 2444: @var{operand2}.@refill
! 2445: @end deftypefun
! 2446:
! 2447: @deftypefun int mcmp (MINT *@var{operand1}, MINT *@var{operand2})
! 2448: Compare @var{operand1} and @var{operand2}. Return a positive value if
! 2449: @var{operand1} > @var{operand2}, zero if @var{operand1} =
! 2450: @var{operand2}, and a negative value if @var{operand1} < @var{operand2}.@refill
! 2451: @end deftypefun
! 2452:
! 2453: @deftypefun void min (MINT *@var{dest})
! 2454: Input a decimal string from @code{stdin}, and put the read integer in
! 2455: @var{dest}. SPC and TAB are allowed in the number string, and are ignored.@refill
! 2456: @end deftypefun
! 2457:
! 2458: @deftypefun void mout (MINT *@var{src})
! 2459: Output @var{src} to @code{stdout}, as a decimal string. Also output a newline.@refill
! 2460: @end deftypefun
! 2461:
! 2462: @deftypefun {char *} mtox (MINT *@var{operand})
! 2463: Convert @var{operand} to a hexadecimal string, and return a pointer to the
! 2464: string. The returned string is allocated using the default memory allocation
! 2465: function, @code{malloc} by default.@refill
! 2466: @end deftypefun
! 2467:
! 2468: @deftypefun void mfree (MINT *@var{operand})
! 2469: De-allocate, the space used by @var{operand}. @strong{This function should
! 2470: only be passed a value returned by @code{itom} or @code{xtom}.}@refill
! 2471: @end deftypefun
! 2472:
! 2473: @node Custom Allocation, Contributors, BSD Compatible Functions, Top
! 2474: @comment node-name, next, previous, up
! 2475: @chapter Custom Allocation
! 2476:
! 2477: By default, the MP functions use @code{malloc}, @code{realloc}, and
! 2478: @code{free} for memory allocation. If @code{malloc} or @code{realloc} fails,
! 2479: the MP library terminates execution after printing a fatal error message to
! 2480: standard error.@refill
! 2481:
! 2482: For some applications, you may wish to allocate memory in other ways, or you
! 2483: may not want to have a fatal error when there is no more memory available. To
! 2484: accomplish this, you can specify alternative memory allocation functions.@refill
! 2485:
! 2486: @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))
! 2487: Replace the current allocation functions from the arguments. If an argument
! 2488: is NULL, the corresponding default function is retained.@refill
! 2489:
! 2490: @strong{Make sure to call this function in such a way that there are no active
! 2491: MP objects that were allocated using the previously active allocation
! 2492: function! Usually, that means that you have to call this function before any
! 2493: other MP function.}@refill
! 2494: @end deftypefun
! 2495:
! 2496: The functions you supply should fit the following declarations:@refill
! 2497:
! 2498: @deftypefun {void *} allocate_function (size_t @var{alloc_size})
! 2499: This function should return a pointer to newly allocated space with at least
! 2500: @var{alloc_size} storage units.@refill
! 2501: @end deftypefun
! 2502:
! 2503: @deftypefun {void *} reallocate_function (void *@var{ptr}, size_t @var{old_size}, size_t @var{new_size})
! 2504: This function should return a pointer to newly allocated space of at least
! 2505: @var{new_size} storage units, after copying at least the first @var{old_size}
! 2506: storage units from @var{ptr}. It should also de-allocate the space at
! 2507: @var{ptr}.@refill
! 2508:
! 2509: You can assume that the space at @var{ptr} was formerly returned from
! 2510: @code{allocate_function} or @code{reallocate_function}, for a request for
! 2511: @var{old_size} storage units.@refill
! 2512: @end deftypefun
! 2513:
! 2514: @deftypefun void deallocate_function (void *@var{ptr}, size_t @var{size})
! 2515: De-allocate the space pointed to by @var{ptr}.@refill
! 2516:
! 2517: You can assume that the space at @var{ptr} was formerly returned from
! 2518: @code{allocate_function} or @code{reallocate_function}, for a request for
! 2519: @var{size} storage units.@refill
! 2520: @end deftypefun
! 2521:
! 2522: (A @dfn{storage unit} is the unit in which the @code{sizeof} operator returns
! 2523: the size of an object, normally an 8 bit byte.)@refill
! 2524:
! 2525:
! 2526: @node Contributors, References, Custom Allocation, Top
! 2527: @comment node-name, next, previous, up
! 2528: @unnumbered Contributors
! 2529:
! 2530: I would like to thank Gunnar Sjoedin and Hans Riesel for their help with
! 2531: mathematical problems, Richard Stallman for his help with design issues and
! 2532: for revising the first version of this manual, Brian Beuning and Doug Lea for
! 2533: their testing of early versions of the library.@refill
! 2534:
! 2535: John Amanatides of York University in Canada contributed the function
! 2536: @code{mpz_probab_prime_p}.@refill
! 2537:
! 2538: Paul Zimmermann of Inria sparked the development of GMP 2, with his
! 2539: comparisons between bignum packages.@refill
! 2540:
! 2541: Ken Weber (Kent State University, Universidade Federal do Rio Grande do Sul)
! 2542: contributed @code{mpz_gcd}, @code{mpz_divexact}, @code{mpn_gcd}, and
! 2543: @code{mpn_bdivmod}, partially supported by CNPq (Brazil) grant 301314194-2.@refill
! 2544:
! 2545: Per Bothner of Cygnus Support helped to set up MP to use Cygnus' configure.
! 2546: He has also made valuable suggestions and tested numerous intermediary
! 2547: releases.@refill
! 2548:
! 2549: Joachim Hollman was involved in the design of the @code{mpf} interface, and in
! 2550: the @code{mpz} design revisions for version 2.@refill
! 2551:
! 2552: Bennet Yee contributed the functions @code{mpz_jacobi} and
! 2553: @code{mpz_legendre}.@refill
! 2554:
! 2555: Andreas Schwab contributed the files @file{mpn/m68k/lshift.S} and
! 2556: @file{mpn/m68k/rshift.S}.@refill
! 2557:
! 2558: The development of floating point functions of GNU MP 2, were supported in
! 2559: part by the ESPRIT-BRA (Basic Research Activities) 6846 project POSSO
! 2560: (POlynomial System SOlving).@refill
! 2561:
! 2562: GNU MP 2 was finished and released by TMG Datakonsult, Sodermannagatan 5, 116
! 2563: 23 STOCKHOLM, SWEDEN, in cooperation with the IDA Center for Computing
! 2564: Sciences, USA.@refill
! 2565:
! 2566:
! 2567: @node References, , Contributors, Top
! 2568: @comment node-name, next, previous, up
! 2569: @unnumbered References
! 2570:
! 2571: @itemize @bullet
! 2572:
! 2573: @item
! 2574: Donald E. Knuth, "The Art of Computer Programming", vol 2,
! 2575: "Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.@refill
! 2576:
! 2577: @item
! 2578: John D. Lipson, "Elements of Algebra and Algebraic Computing",
! 2579: The Benjamin Cummings Publishing Company Inc, 1981.@refill
! 2580:
! 2581: @item
! 2582: Richard M. Stallman, "Using and Porting GCC", Free Software Foundation,
! 2583: 1995.@refill
! 2584:
! 2585: @item
! 2586: Peter L. Montgomery, "Modular Multiplication Without Trial Division", in
! 2587: Mathematics of Computation, volume 44, number 170, April 1985.@refill
! 2588:
! 2589: @item
! 2590: Torbjorn Granlund and Peter L. Montgomery, "Division by Invariant
! 2591: Integers using Multiplication", in Proceedings of the SIGPLAN
! 2592: PLDI'94 Conference, June 1994.@refill
! 2593:
! 2594: @item
! 2595: Tudor Jebelean,
! 2596: "An algorithm for exact division",
! 2597: Journal of Symbolic Computation,
! 2598: v. 15, 1993, pp. 169-180.@refill
! 2599:
! 2600: @item
! 2601: Kenneth Weber, "The accelerated integer GCD algorithm",
! 2602: ACM Transactions on Mathematical Software,
! 2603: v. 21 (March), 1995, pp. 111-122.@refill
! 2604: @end itemize
! 2605:
! 2606: @node Concept Index, , , Top
! 2607: @comment node-name, next, previous, up
! 2608: @unnumbered Concept Index
! 2609: @printindex cp
! 2610:
! 2611: @node Function Index, , , Top
! 2612: @comment node-name, next, previous, up
! 2613: @unnumbered Function and Type Index
! 2614: @printindex fn
! 2615:
! 2616:
! 2617: @contents
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