Annotation of OpenXM_contrib/gmp/gmp.texi, Revision 1.1.1.1
1.1 maekawa 1: \input texinfo @c -*-texinfo-*-
2: @c %**start of header
3: @setfilename gmp.info
4: @settitle GNU MP 2.0.2
5: @synindex tp fn
6: @iftex
7: @afourpaper
8: @end iftex
9: @comment %**end of header
10:
11: @ifinfo
12: @format
13: START-INFO-DIR-ENTRY
14: * gmp: (gmp.info). GNU Multiple Precision Arithmetic Library.
15: END-INFO-DIR-ENTRY
16: @end format
17: @end ifinfo
18:
19: @c smallbook
20:
21: @iftex
22: @finalout
23: @end iftex
24:
25: @c Note: the edition number is listed in *three* places; please update
26: @c all three. Also, update the month and year where appropriate.
27:
28: @c ==> Update edition number for settitle and subtitle, and in the
29: @c ==> following paragraph; update date, too.
30:
31:
32: @ifinfo
33: This file documents GNU MP, a library for arbitrary-precision arithmetic.
34:
35: Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
36:
37: Permission is granted to make and distribute verbatim copies of
38: this manual provided the copyright notice and this permission notice
39: are preserved on all copies.
40:
41: @ignore
42: Permission is granted to process this file through TeX and print the
43: results, provided the printed document carries copying permission
44: notice identical to this one except for the removal of this paragraph
45: (this paragraph not being relevant to the printed manual).
46:
47: @end ignore
48: Permission is granted to copy and distribute modified versions of this
49: manual under the conditions for verbatim copying, provided that the entire
50: resulting derived work is distributed under the terms of a permission
51: notice identical to this one.
52:
53: Permission is granted to copy and distribute translations of this manual
54: into another language, under the above conditions for modified versions,
55: except that this permission notice may be stated in a translation approved
56: by the Foundation.
57: @end ifinfo
58:
59: @setchapternewpage on
60: @titlepage
61: @c use the new format for titles
62:
63: @title GNU MP
64: @subtitle The GNU Multiple Precision Arithmetic Library
65: @subtitle Edition 2.0.2
66: @subtitle June 1996
67:
68: @author by Torbj@"orn Granlund, TMG Datakonsult
69:
70: @c Include the Distribution inside the titlepage so
71: @c that headings are turned off.
72:
73: @tex
74: \global\parindent=0pt
75: \global\parskip=8pt
76: \global\baselineskip=13pt
77: @end tex
78:
79: @page
80: @vskip 0pt plus 1filll
81: Copyright @copyright{} 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
82:
83: @sp 2
84:
85: Published by the Free Software Foundation @*
86: 59 Temple Place - Suite 330 @*
87: Boston, MA 02111-1307, USA @*
88:
89: Permission is granted to make and distribute verbatim copies of
90: this manual provided the copyright notice and this permission notice
91: are preserved on all copies.
92:
93: Permission is granted to copy and distribute modified versions of this
94: manual under the conditions for verbatim copying, provided that the entire
95: resulting derived work is distributed under the terms of a permission
96: notice identical to this one.
97:
98: Permission is granted to copy and distribute translations of this manual
99: into another language, under the above conditions for modified versions,
100: except that this permission notice may be stated in a translation approved
101: by the Foundation.
102: @end titlepage
103: @headings double
104:
105: @ifinfo
106: @node Top, Copying, (dir), (dir)
107:
108: @top GNU MP
109:
110: This manual documents how to install and use the GNU multiple precision
111: arithmetic library, version 2.0.2.
112:
113: @end ifinfo
114:
115: @menu
116: * Copying:: GMP Copying Conditions (LGPL).
117: * Introduction to MP:: Brief introduction to GNU MP.
118: * Installing MP:: How to configure and compile the MP library.
119: * MP Basics:: What every MP user should now.
120: * Reporting Bugs:: How to usefully report bugs.
121: * Integer Functions:: Functions for arithmetic on signed integers.
122: * Rational Number Functions:: Functions for arithmetic on rational numbers.
123: * Floating-point Functions:: Functions for arithmetic on floats.
124: * Low-level Functions:: Fast functions for natural numbers.
125: * BSD Compatible Functions:: All functions found in BSD MP.
126: * Custom Allocation:: How to customize the internal allocation.
127:
128: * Contributors::
129: * References::
130: * Concept Index::
131: * Function Index::
132: @end menu
133:
134: @node Copying, Introduction to MP, Top, Top
135: @comment node-name, next, previous, up
136: @unnumbered GNU MP Copying Conditions
137: @cindex Copying conditions
138: @cindex Conditions for copying GNU MP
139:
140: This library is @dfn{free}; this means that everyone is free to use it and
141: free to redistribute it on a free basis. The library is not in the public
142: domain; it is copyrighted and there are restrictions on its distribution, but
143: these restrictions are designed to permit everything that a good cooperating
144: citizen would want to do. What is not allowed is to try to prevent others
145: from further sharing any version of this library that they might get from
146: you.@refill
147:
148: Specifically, we want to make sure that you have the right to give away copies
149: of the library, that you receive source code or else can get it if you want
150: it, that you can change this library or use pieces of it in new free programs,
151: and that you know you can do these things.@refill
152:
153: To make sure that everyone has such rights, we have to forbid you to deprive
154: anyone else of these rights. For example, if you distribute copies of the GNU
155: MP library, you must give the recipients all the rights that you have. You
156: must make sure that they, too, receive or can get the source code. And you
157: must tell them their rights.@refill
158:
159: Also, for our own protection, we must make certain that everyone finds out
160: that there is no warranty for the GNU MP library. If it is modified by
161: someone else and passed on, we want their recipients to know that what they
162: have is not what we distributed, so that any problems introduced by others
163: will not reflect on our reputation.@refill
164:
165: The precise conditions of the license for the GNU MP library are found in the
166: Library General Public License that accompany the source code.@refill
167:
168: @node Introduction to MP, Installing MP, Copying, Top
169: @comment node-name, next, previous, up
170: @chapter Introduction to GNU MP
171:
172:
173: GNU MP is a portable library written in C for arbitrary precision arithmetic
174: on integers, rational numbers, and floating-point numbers. It aims to provide
175: the fastest possible arithmetic for all applications that need higher
176: precision than is directly supported by the basic C types.
177:
178: Many applications use just a few hundred bits of precision; but some
179: applications may need thousands or even millions of bits. MP is designed to
180: give good performance for both, by choosing algorithms based on the sizes of
181: the operands, and by carefully keeping the overhead at a minimum.
182:
183: The speed of MP is achieved by using fullwords as the basic arithmetic type,
184: by using sophisticated algorithms, by including carefully optimized assembly
185: code for the most common inner loops for many different CPUs, and by a general
186: emphasis on speed (as opposed to simplicity or elegance).
187:
188: There is carefully optimized assembly code for these CPUs: DEC Alpha, Amd
189: 29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, Intel i960, Motorola
190: MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC, National
191: NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, generic SPARCv8,
192: and DEC VAX. Some optimizations also for ARM, Clipper, IBM ROMP (RT), and
193: Pyramid AP/XP.
194:
195: This version of MP is released under a more liberal license than previous
196: versions. It is now permitted to link MP to non-free programs, as long as MP
197: source code is provided when distributing the non-free program.
198:
199:
200: @section How to use this Manual
201:
202: Everyone should read @ref{MP Basics}. If you need to install the library
203: yourself, you need to read @ref{Installing MP}, too.
204:
205: The rest of the manual can be used for later reference, although it is
206: probably a good idea to glance through it.
207:
208:
209: @node Installing MP, MP Basics, Introduction to MP, Top
210: @comment node-name, next, previous, up
211: @chapter Installing MP
212: @cindex Installation
213:
214: To build MP, you first have to configure it for your CPU and operating system.
215: You need a C compiler, preferably GCC, but any reasonable compiler should
216: work. And you need a standard Unix @samp{make} program, plus some other
217: standard Unix utility programs.
218:
219: (If you're on an MS-DOS machine, your can build MP using @file{make.bat}. It
220: requires that djgpp is installed. It does not require configuration, nor is
221: @samp{make} needed; @file{make.bat} both configures and builds the library.)
222:
223: Here are the steps needed to install the library on Unix systems:
224:
225: @enumerate
226: @item
227: In most cases, @samp{./configure --target=cpu-vendor-os}, should work both for
228: native and cross-compilation. If you get error messages, your machine might
229: not be supported.
230:
231: If you want to compile in a separate object directory, cd to that directory,
232: and prefix the configure command with the path to the MP source directory.
233: Not all @samp{make} programs have the necessary features to support this. In
234: particular, SunOS and Slowaris @samp{make} have bugs that makes them unable to
235: build from a separate object directory. Use GNU @samp{make} instead.
236:
237: In addition to the standard cpu-vendor-os tuples, MP recognizes sparc8 and
238: supersparc as valid CPU names. Specifying these CPU names for relevant
239: systems will improve performance significantly.
240:
241: In general, if you want a library that runs as fast as possible, you should
242: make sure you configure MP for the exact CPU type your system uses.
243:
244: If you have @code{gcc} in your @code{PATH}, it will be used by default. To
245: override this, pass @samp{-with-gcc=no} to @file{configure}.
246:
247: @item
248: @samp{make}
249:
250: This will compile MP, and create a library archive file @file{libgmp.a} in the
251: working directory.
252:
253: @item
254: @samp{make check}
255:
256: This will make sure MP was built correctly. If you get error messages, please
257: report this to @samp{bug-gmp@@prep.ai.mit.edu}. (@xref{Reporting Bugs}, for
258: information on what to include in useful bug reports.)
259:
260: @item
261: @samp{make install}
262:
263: This will copy the file @file{gmp.h} and @file{libgmp.a}, as well as the info
264: files, to @file{/usr/local} (or if you passed the @samp{--prefix} option to
265: @file{configure}, to the directory given as argument to @samp{--prefix}).
266: @end enumerate
267:
268: @noindent
269: If you wish to build and install the BSD MP compatible functions, use
270: @samp{make libmp.a} and @samp{make install-bsdmp}.
271:
272: There are some other useful make targets:
273:
274: @itemize @bullet
275: @item
276: @samp{doc}
277:
278: Create a DVI version of the manual, in @file{gmp.dvi} and a set of info files,
279: in @file{gmp.info}, @file{gmp.info-1}, @file{gmp.info-2}, etc.
280:
281: @item
282: @samp{ps}
283:
284: Create a Postscript version of the manual, in @file{gmp.ps}.
285:
286: @item
287: @samp{html}
288:
289: Create a HTML version of the manual, in @file{gmp.html}.
290:
291: @item
292: @samp{clean}
293:
294: Delete all object files and archive files, but not the configuration files.
295:
296: @item
297: @samp{distclean}
298:
299: Delete all files not included in the distribution.
300:
301: @item
302: @samp{uninstall}
303:
304: Delete all files copied by @samp{make install}.
305: @end itemize
306:
307:
308: @section Known Build Problems
309:
310: GCC 2.7.2 (as well as 2.6.3) for the RS/6000 and PowerPC can not be used to
311: compile MP, due to a bug in GCC. If you want to use GCC for these machines,
312: you need to apply the patch below to GCC, or use a later version of the
313: compiler.
314:
315: If you are on a Sequent Symmetry, use the GNU assembler instead of the
316: system's assembler, since the latter has serious bugs.
317:
318: The system compiler on NeXT is a massacred and old gcc, even if the compiler
319: calls itself @file{cc}. This compiler cannot be used to build MP. You need
320: to get a real gcc, and install that before you compile MP. (NeXT might have
321: fixed this in newer releases of their system.)
322:
323: The system C compiler under SunOS 4 has a bug that makes it miscompile
324: mpq/get_d.c. This will make @samp{make check} fail.
325:
326: Please report other problems to @samp{bug-gmp@@prep.ai.mit.edu}.
327: @xref{Reporting Bugs}.
328:
329:
330: Patch to apply to GCC 2.6.3 and 2.7.2:
331:
332: @example
333: *** config/rs6000/rs6000.md Sun Feb 11 08:22:11 1996
334: --- config/rs6000/rs6000.md.new Sun Feb 18 03:33:37 1996
335: ***************
336: *** 920,926 ****
337: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
338: (not:SI (match_dup 1)))]
339: ""
340: ! "nor. %0,%2,%1"
341: [(set_attr "type" "compare")])
342:
343: (define_insn ""
344: --- 920,926 ----
345: (set (match_operand:SI 0 "gpc_reg_operand" "=r")
346: (not:SI (match_dup 1)))]
347: ""
348: ! "nor. %0,%1,%1"
349: [(set_attr "type" "compare")])
350:
351: (define_insn ""
352: @end example
353:
354: @node MP Basics, Reporting Bugs, Installing MP, Top
355: @comment node-name, next, previous, up
356: @chapter MP Basics
357:
358:
359: @cindex @file{gmp.h}
360: All declarations needed to use MP are collected in the include file
361: @file{gmp.h}. It is designed to work with both C and C++ compilers.
362:
363:
364: @section Nomenclature and Types
365:
366: @cindex Integer
367: @tindex @code{mpz_t}
368: @noindent
369: In this manual, @dfn{integer} usually means a multiple precision integer, as
370: defined by the MP library. The C data type for such integers is @code{mpz_t}.
371: Here are some examples of how to declare such integers:
372:
373: @example
374: mpz_t sum;
375:
376: struct foo @{ mpz_t x, y; @};
377:
378: mpz_t vec[20];
379: @end example
380:
381: @cindex Rational number
382: @tindex @code{mpq_t}
383: @noindent
384: @dfn{Rational number} means a multiple precision fraction. The C data type
385: for these fractions is @code{mpq_t}. For example:
386:
387: @example
388: mpq_t quotient;
389: @end example
390:
391: @cindex Floating-point number
392: @tindex @code{mpf_t}
393: @noindent
394: @dfn{Floating point number} or @dfn{Float} for short, is an arbitrary precision
395: mantissa with an limited precision exponent. The C data type for such objects
396: is @code{mpf_t}.
397:
398: @cindex Limb
399: @tindex @code{mp_limb_t}
400: @noindent
401: A @dfn{limb} means the part of a multi-precision number that fits in a single
402: word. (We chose this word because a limb of the human body is analogous to a
403: digit, only larger, and containing several digits.) Normally a limb contains
404: 32 or 64 bits. The C data type for a limb is @code{mp_limb_t}.
405:
406:
407: @section Function Classes
408:
409: There are six classes of functions in the MP library:
410:
411: @enumerate
412: @item
413: Functions for signed integer arithmetic, with names beginning with
414: @code{mpz_}. The associated type is @code{mpz_t}. There are about 100
415: functions in this class.
416:
417: @item
418: Functions for rational number arithmetic, with names beginning with
419: @code{mpq_}. The associated type is @code{mpq_t}. There are about 20
420: functions in this class, but the functions in the previous class can be used
421: for performing arithmetic on the numerator and denominator separately.
422:
423: @item
424: Functions for floating-point arithmetic, with names beginning with
425: @code{mpf_}. The associated type is @code{mpf_t}. There are about 50
426: functions is this class.
427:
428: @item
429: Functions compatible with Berkeley MP, such as @code{itom}, @code{madd}, and
430: @code{mult}. The associated type is @code{MINT}.
431:
432: @item
433: Fast low-level functions that operate on natural numbers. These are used by
434: the functions in the preceding groups, and you can also call them directly
435: from very time-critical user programs. These functions' names begin with
436: @code{mpn_}. There are about 30 (hard-to-use) functions in this class.
437:
438: The associated type is array of @code{mp_limb_t}.
439:
440: @item
441: Miscellaneous functions. Functions for setting up custom allocation.
442: @end enumerate
443:
444:
445: @section MP Variable Conventions
446:
447: As a general rule, all MP functions expect output arguments before input
448: arguments. This notation is based on an analogy with the assignment operator.
449: (The BSD MP compatibility functions disobey this rule, having the output
450: argument(s) last.)
451:
452: MP allows you to use the same variable for both input and output in the same
453: expression. For example, the main function for integer multiplication,
454: @code{mpz_mul}, can be used like this: @code{mpz_mul (x, x, x)}. This
455: computes the square of @var{x} and puts the result back in @var{x}.
456:
457: Before you can assign to an MP variable, you need to initialize it by calling
458: one of the special initialization functions. When you're done with a
459: variable, you need to clear it out, using one of the functions for that
460: purpose. Which function to use depends on the type of variable. See the
461: chapters on integer functions, rational number functions, and floating-point
462: functions for details.
463:
464: A variable should only be initialized once, or at least cleared out between
465: each initialization. After a variable has been initialized, it may be
466: assigned to any number of times.
467:
468: For efficiency reasons, avoid to initialize and clear out a variable in loops.
469: Instead, initialize it before entering the loop, and clear it out after the
470: loop has exited.
471:
472: You don't need to be concerned about allocating additional space for MP
473: variables. All functions in MP automatically allocate additional space when a
474: variable does not already have enough space. They do not, however, reduce the
475: space when a smaller number is stored in the object. Most of the time, this
476: policy is best, since it avoids frequent re-allocation.
477:
478:
479: @section Useful Macros and Constants
480:
481: @deftypevr {Global Constant} {const int} mp_bits_per_limb
482: The number of bits per limb.
483: @end deftypevr
484:
485: @defmac __GNU_MP_VERSION
486: @defmacx __GNU_MP_VERSION_MINOR
487: The major and minor MP version, respectively, as integers.
488: @end defmac
489:
490: @section Compatibility with Version 1.x
491:
492: This version of MP is upward compatible with previous versions of MP, with a
493: few exceptions.
494:
495: @enumerate
496: @item Integer division functions round the result differently. The old
497: functions (@code{mpz_div}, @code{mpz_divmod}, @code{mpz_mdiv},
498: @code{mpz_mdivmod}, etc) now all use floor rounding (i.e., they round the
499: quotient to @minus{}infinity). There are a lot of new functions for integer
500: division, giving the user better control over the rounding.
501:
502: @item The function @code{mpz_mod} now compute the true @strong{mod} function.
503:
504: @item The functions @code{mpz_powm} and @code{mpz_powm_ui} now use
505: @strong{mod} for reduction.
506:
507: @item The assignment functions for rational numbers do no longer canonicalize
508: their results. In the case a non-canonical result could arise from an
509: assignment, the user need to insert an explicit call to
510: @code{mpq_canonicalize}. This change was made for efficiency.
511:
512: @item Output generated by @code{mpz_out_raw} in this release cannot be read
513: by @code{mpz_inp_raw} in previous releases. This change was made for making
514: the file format truly portable between machines with different word sizes.
515:
516: @item Several @code{mpn} functions have changed. But they were intentionally
517: undocumented in previous releases.
518:
519: @item The functions @code{mpz_cmp_ui}, @code{mpz_cmp_si}, and @code{mpq_cmp_ui}
520: are now implementated as macros, and thereby sometimes evaluate their
521: arguments multiple times.
522:
523: @item The functions @code{mpz_pow_ui} and @code{mpz_ui_pow_ui} now yield 1
524: for 0^0. (In version 1, they yielded 0.)
525:
526: @end enumerate
527:
528:
529: @section Getting the Latest Version of MP
530:
531: The latest version of the MP library is available by anonymous ftp from
532: from @samp{prep.ai.mit.edu}. The file name is
533: @file{/pub/gnu/gmp-M.N.tar.gz}. Many sites around the world mirror
534: @samp{prep}; please use a mirror site near you.
535:
536: @node Reporting Bugs, Integer Functions, MP Basics, Top
537: @comment node-name, next, previous, up
538: @chapter Reporting Bugs
539: @cindex Reporting bugs
540:
541: If you think you have found a bug in the MP library, please investigate it and
542: report it. We have made this library available to you, and it is not to ask
543: too much from you, to ask you to report the bugs that you find.
544:
545: There are a few things you should think about when you put your bug report
546: together.
547:
548: You have to send us a test case that makes it possible for us to reproduce the
549: bug. Include instructions on how to run the test case.
550:
551: You also have to explain what is wrong; if you get a crash, or if the results
552: printed are incorrect and in that case, in what way.
553:
554: It is not uncommon that an observed problem is actually due to a bug in the
555: compiler used when building MP; the MP code tends to explore interesting
556: corners in compilers. Therefore, please include compiler version information
557: in your bug report. This can be extracted using @samp{what `which cc`}, or,
558: if you're using gcc, @samp{gcc -v}. Also, include the output from @samp{uname
559: -a}.
560:
561: If your bug report is good, we will do our best to help you to get a corrected
562: version of the library; if the bug report is poor, we won't do anything about
563: it (aside of chiding you to send better bug reports).
564:
565: Send your bug report to: @samp{bug-gmp@@prep.ai.mit.edu}.
566:
567: If you think something in this manual is unclear, or downright incorrect, or if
568: the language needs to be improved, please send a note to the same address.
569:
570:
571: @node Integer Functions, Rational Number Functions, Reporting Bugs, Top
572: @comment node-name, next, previous, up
573: @chapter Integer Functions
574: @cindex Integer functions
575:
576: This chapter describes the MP functions for performing integer arithmetic.
577: These functions start with the prefix @code{mpz_}.
578:
579: Arbitrary precision integers are stored in objects of type @code{mpz_t}.
580:
581: @menu
582: * Initializing Integers::
583: * Assigning Integers::
584: * Simultaneous Integer Init & Assign::
585: * Converting Integers::
586: * Integer Arithmetic::
587: * Comparison Functions::
588: * Integer Logic and Bit Fiddling::
589: * I/O of Integers::
590: * Miscellaneous Integer Functions::
591: @end menu
592:
593: @node Initializing Integers, Assigning Integers, , Integer Functions
594: @comment node-name, next, previous, up
595: @section Initialization and Assignment Functions
596:
597: The functions for integer arithmetic assume that all integer objects are
598: initialized. You do that by calling the function @code{mpz_init}.
599:
600: @deftypefun void mpz_init (mpz_t @var{integer})
601: Initialize @var{integer} with limb space and set the initial numeric value to
602: 0. Each variable should normally only be initialized once, or at least cleared
603: out (using @code{mpz_clear}) between each initialization.
604: @end deftypefun
605:
606: Here is an example of using @code{mpz_init}:
607:
608: @example
609: @{
610: mpz_t integ;
611: mpz_init (integ);
612: @dots{}
613: mpz_add (integ, @dots{});
614: @dots{}
615: mpz_sub (integ, @dots{});
616:
617: /* Unless the program is about to exit, do ... */
618: mpz_clear (integ);
619: @}
620: @end example
621:
622: @noindent
623: As you can see, you can store new values any number of times, once an
624: object is initialized.
625:
626: @deftypefun void mpz_clear (mpz_t @var{integer})
627: Free the limb space occupied by @var{integer}. Make sure to call this
628: function for all @code{mpz_t} variables when you are done with them.
629: @end deftypefun
630:
631: @deftypefun {void *} _mpz_realloc (mpz_t @var{integer}, mp_size_t @var{new_alloc})
632: Change the limb space allocation to @var{new_alloc} limbs. This function is
633: not normally called from user code, but it can be used to give memory back to
634: the heap, or to increase the space of a variable to avoid repeated automatic
635: re-allocation.
636: @end deftypefun
637:
638: @deftypefun void mpz_array_init (mpz_t @var{integer_array}[], size_t @var{array_size}, mp_size_t @var{fixed_num_bits})
639: Allocate @strong{fixed} limb space for all @var{array_size} integers in
640: @var{integer_array}. The fixed allocation for each integer in the array is
641: enough to store @var{fixed_num_bits}. If the fixed space will be insufficient
642: for storing the result of a subsequent calculation, the result is
643: unpredictable.
644:
645: This function is useful for decreasing the working set for some algorithms
646: that use large integer arrays.
647:
648: There is no way to de-allocate the storage allocated by this function.
649: Don't call @code{mpz_clear}!
650: @end deftypefun
651:
652:
653: @node Assigning Integers, Simultaneous Integer Init & Assign, Initializing Integers, Integer Functions
654: @comment node-name, next, previous, up
655: @subsection Assignment Functions
656: @cindex Integer assignment functions
657:
658: These functions assign new values to already initialized integers
659: (@pxref{Initializing Integers}).
660:
661: @deftypefun void mpz_set (mpz_t @var{rop}, mpz_t @var{op})
662: @deftypefunx void mpz_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
663: @deftypefunx void mpz_set_si (mpz_t @var{rop}, signed long int @var{op})
664: @deftypefunx void mpz_set_d (mpz_t @var{rop}, double @var{op})
665: @deftypefunx void mpz_set_q (mpz_t @var{rop}, mpq_t @var{op})
666: @deftypefunx void mpz_set_f (mpz_t @var{rop}, mpf_t @var{op})
667: Set the value of @var{rop} from @var{op}.
668: @end deftypefun
669:
670: @deftypefun int mpz_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
671: Set the value of @var{rop} from @var{str}, a '\0'-terminated C string in base
672: @var{base}. White space is allowed in the string, and is simply ignored. The
673: base may vary from 2 to 36. If @var{base} is 0, the actual base is determined
674: from the leading characters: if the first two characters are `0x' or `0X',
675: hexadecimal is assumed, otherwise if the first character is `0', octal is
676: assumed, otherwise decimal is assumed.
677:
678: This function returns 0 if the entire string up to the '\0' is a valid
679: number in base @var{base}. Otherwise it returns @minus{}1.
680: @end deftypefun
681:
682:
683: @node Simultaneous Integer Init & Assign, Converting Integers, Assigning Integers, Integer Functions
684: @comment node-name, next, previous, up
685: @subsection Combined Initialization and Assignment Functions
686: @cindex Initialization and assignment functions
687:
688: For convenience, MP provides a parallel series of initialize-and-set functions
689: which initialize the output and then store the value there. These functions'
690: names have the form @code{mpz_init_set@dots{}}
691:
692: Here is an example of using one:
693:
694: @example
695: @{
696: mpz_t pie;
697: mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10);
698: @dots{}
699: mpz_sub (pie, @dots{});
700: @dots{}
701: mpz_clear (pie);
702: @}
703: @end example
704:
705: @noindent
706: Once the integer has been initialized by any of the @code{mpz_init_set@dots{}}
707: functions, it can be used as the source or destination operand for the ordinary
708: integer functions. Don't use an initialize-and-set function on a variable
709: already initialized!
710:
711: @deftypefun void mpz_init_set (mpz_t @var{rop}, mpz_t @var{op})
712: @deftypefunx void mpz_init_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
713: @deftypefunx void mpz_init_set_si (mpz_t @var{rop}, signed long int @var{op})
714: @deftypefunx void mpz_init_set_d (mpz_t @var{rop}, double @var{op})
715: Initialize @var{rop} with limb space and set the initial numeric value from
716: @var{op}.
717: @end deftypefun
718:
719: @deftypefun int mpz_init_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
720: Initialize @var{rop} and set its value like @code{mpz_set_str} (see its
721: documentation above for details).
722:
723: If the string is a correct base @var{base} number, the function returns 0;
724: if an error occurs it returns @minus{}1. @var{rop} is initialized even if
725: an error occurs. (I.e., you have to call @code{mpz_clear} for it.)
726: @end deftypefun
727:
728:
729: @node Converting Integers, Integer Arithmetic, Simultaneous Integer Init & Assign, Integer Functions
730: @comment node-name, next, previous, up
731: @section Conversion Functions
732: @cindex Integer conversion functions
733: @cindex Conversion functions
734:
735: This section describes functions for converting arbitrary precision integers
736: to standard C types. Functions for converting @emph{to} arbitrary
737: precision integers are described in @ref{Assigning Integers} and @ref{I/O of
738: Integers}.
739:
740: @deftypefun {unsigned long int} mpz_get_ui (mpz_t @var{op})
741: Return the least significant part from @var{op}. This function combined
742: with @* @code{mpz_tdiv_q_2exp(@dots{}, @var{op}, CHAR_BIT*sizeof(unsigned
743: long int))} can be used to extract the limbs of an integer.
744: @end deftypefun
745:
746: @deftypefun {signed long int} mpz_get_si (mpz_t @var{op})
747: If @var{op} fits into a @code{signed long int} return the value of @var{op}.
748: Otherwise return the least significant part of @var{op}, with the same sign
749: as @var{op}.
750:
751: If @var{op} is too large to fit in a @code{signed long int}, the returned
752: result is probably not very useful. @c To find out if the value will fit, use
753: @c the function @code{mpz_fits_si}.
754: @end deftypefun
755:
756: @deftypefun double mpz_get_d (mpz_t @var{op})
757: Convert @var{op} to a double.
758: @end deftypefun
759:
760: @deftypefun {char *} mpz_get_str (char *@var{str}, int @var{base}, mpz_t @var{op})
761: Convert @var{op} to a string of digits in base @var{base}. The base may vary
762: from 2 to 36.
763:
764: If @var{str} is NULL, space for the result string is allocated using the
765: default allocation function, and a pointer to the string is returned.
766:
767: If @var{str} is not NULL, it should point to a block of storage enough large
768: for the result. To find out the right amount of space to provide for
769: @var{str}, use @code{mpz_sizeinbase (@var{op}, @var{base}) + 2}. The two
770: extra bytes are for a possible minus sign, and for the terminating null
771: character.
772: @end deftypefun
773:
774:
775: @node Integer Arithmetic, Comparison Functions, Converting Integers, Integer Functions
776: @comment node-name, next, previous, up
777: @section Arithmetic Functions
778: @cindex Integer arithmetic functions
779: @cindex Arithmetic functions
780:
781: @deftypefun void mpz_add (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
782: @deftypefunx void mpz_add_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
783: @ifinfo
784: Set @var{rop} to @var{op1} + @var{op2}.
785: @end ifinfo
786: @iftex
787: @tex
788: Set @var{rop} to $@var{op1} + @var{op2}$.
789: @end tex
790: @end iftex
791: @end deftypefun
792:
793: @deftypefun void mpz_sub (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
794: @deftypefunx void mpz_sub_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
795: Set @var{rop} to @var{op1} @minus{} @var{op2}.
796: @end deftypefun
797:
798: @deftypefun void mpz_mul (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
799: @deftypefunx void mpz_mul_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
800: @ifinfo
801: Set @var{rop} to @var{op1} times @var{op2}.
802: @end ifinfo
803: @iftex
804: @tex
805: Set @var{rop} to $@var{op1} \times @var{op2}$.
806: @end tex
807: @end iftex
808: @end deftypefun
809:
810: @deftypefun void mpz_mul_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
811: @ifinfo
812: Set @var{rop} to @var{op1} times 2 raised to @var{op2}. This operation can
813: also be defined as a left shift, @var{op2} steps.
814: @end ifinfo
815: @iftex
816: @tex
817: Set @var{rop} to $@var{op1} \times 2^{op2}$. This operation can also be
818: defined as a left shift, @var{op2} steps.
819: @end tex
820: @end iftex
821: @end deftypefun
822:
823: @deftypefun void mpz_neg (mpz_t @var{rop}, mpz_t @var{op})
824: Set @var{rop} to @minus{}@var{op}.
825: @end deftypefun
826:
827: @deftypefun void mpz_abs (mpz_t @var{rop}, mpz_t @var{op})
828: Set @var{rop} to the absolute value of @var{op}.
829: @end deftypefun
830:
831: @deftypefun void mpz_fac_ui (mpz_t @var{rop}, unsigned long int @var{op})
832: Set @var{rop} to @var{op}!, the factorial of @var{op}.
833: @end deftypefun
834:
835: @subsection Division functions
836:
837: Division is undefined if the divisor is zero, and passing a zero divisor to
838: the divide or modulo functions, as well passing a zero mod argument to the
839: @code{mpz_powm} and @code{mpz_powm_ui} functions, will make these functions
840: intentionally divide by zero. This gives the user the possibility to handle
841: arithmetic exceptions in these functions in the same manner as other
842: arithmetic exceptions.
843:
844: There are three main groups of division functions:
845: @itemize @bullet
846: @item
847: Functions that truncate the quotient towards 0. The names of these
848: functions start with @code{mpz_tdiv}. The @samp{t} in the name is short for
849: @samp{truncate}.
850: @item
851: Functions that round the quotient towards @minus{}infinity. The names of
852: these routines start with @code{mpz_fdiv}. The @samp{f} in the name is
853: short for @samp{floor}.
854: @item
855: Functions that round the quotient towards +infinity. The names of
856: these routines start with @code{mpz_cdiv}. The @samp{c} in the name is
857: short for @samp{ceil}.
858: @end itemize
859:
860: For each rounding mode, there are a couple of variants. Here @samp{q} means
861: that the quotient is computed, while @samp{r} means that the remainder is
862: computed. Functions that compute both the quotient and remainder have
863: @samp{qr} in the name.
864:
865: @deftypefun void mpz_tdiv_q (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
866: @deftypefunx void mpz_tdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
867: Set @var{rop} to [@var{op1}/@var{op2}]. The quotient is truncated towards
868: 0.
869: @end deftypefun
870:
871: @deftypefun void mpz_tdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
872: @deftypefunx void mpz_tdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
873: Set @var{rop} to (@var{op1} - [@var{op1}/@var{op2}] * @var{op2}).
874: Unless the remainder is zero, it has the same sign as the dividend.
875: @end deftypefun
876:
877: @deftypefun void mpz_tdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
878: @deftypefunx void mpz_tdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
879: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
880: remainder in @var{rop2}. The quotient is rounded towards 0. Unless the
881: remainder is zero, it has the same sign as the dividend.
882:
883: If @var{rop1} and @var{rop2} are the same variable, the results are
884: undefined.
885: @end deftypefun
886:
887: @deftypefun void mpz_fdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
888: @deftypefunx void mpz_fdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
889: @ifinfo
890: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
891: @minus{}infinity.
892: @end ifinfo
893: @iftex
894: @tex
895: Set @var{rop} to $\lfloor@var{op1}/@var{op2}\rfloor$. (I.e., round
896: the quotient towards $-\infty$.)
897: @end tex
898: @end iftex
899: @end deftypefun
900:
901: @deftypefun void mpz_fdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
902: @deftypefunx {unsigned long int} mpz_fdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
903: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
904: the remainder is zero, it has the same sign as the divisor.
905:
906: For @code{mpz_fdiv_r_ui} the remainder is small enough to fit in an
907: @code{unsigned long int}, and is therefore returned.
908: @end deftypefun
909:
910: @deftypefun void mpz_fdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
911: @deftypefunx {unsigned long int} mpz_fdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
912: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
913: remainder in @var{rop2}. The quotient is rounded towards @minus{}infinity.
914: Unless the remainder is zero, it has the same sign as the divisor.
915:
916: For @code{mpz_fdiv_qr_ui} the remainder is small enough to fit in an
917: @code{unsigned long int}, and is therefore returned.
918:
919: If @var{rop1} and @var{rop2} are the same variable, the results are
920: undefined.
921: @end deftypefun
922:
923: @deftypefun {unsigned long int} mpz_fdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
924: This function is similar to @code{mpz_fdiv_r_ui}, but the remainder is only
925: returned; it is not stored anywhere.
926: @end deftypefun
927:
928: @deftypefun void mpz_cdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
929: @deftypefunx void mpz_cdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
930: @ifinfo
931: Set @var{rop} to @var{op1}/@var{op2}. The quotient is rounded towards
932: +infinity.
933: @end ifinfo
934: @iftex
935: @tex
936: Set @var{rop} to $\lceil@var{op1}/@var{op2}\rceil$. (I.e., round the
937: quotient towards $+\infty$.)
938: @end tex
939: @end iftex
940: @end deftypefun
941:
942: @deftypefun void mpz_cdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
943: @deftypefunx {unsigned long int} mpz_cdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
944: Divide @var{op1} by @var{op2} and put the remainder in @var{rop}. Unless
945: the remainder is zero, it has the opposite sign as the divisor.
946:
947: For @code{mpz_cdiv_r_ui} the negated remainder is small enough to fit in an
948: @code{unsigned long int}, and it is therefore returned.
949: @end deftypefun
950:
951: @deftypefun void mpz_cdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
952: @deftypefunx {unsigned long int} mpz_cdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
953: Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
954: remainder in @var{rop2}. The quotient is rounded towards +infinity. Unless
955: the remainder is zero, it has the opposite sign as the divisor.
956:
957: For @code{mpz_cdiv_qr_ui} the negated remainder is small enough to fit in an
958: @code{unsigned long int}, and it is therefore returned.
959:
960: If @var{rop1} and @var{rop2} are the same variable, the results are
961: undefined.
962: @end deftypefun
963:
964: @deftypefun {unsigned long int} mpz_cdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
965: Return the negated remainder, similar to @code{mpz_cdiv_r_ui}. (The
966: difference is that this function doesn't store the remainder anywhere.)
967: @end deftypefun
968:
969: @deftypefun void mpz_mod (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
970: @deftypefunx {unsigned long int} mpz_mod_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
971: Set @var{rop} to @var{op1} @code{mod} @var{op2}. The sign of the divisor is
972: ignored, and the result is always non-negative.
973:
974: For @code{mpz_mod_ui} the remainder is small enough to fit in an
975: @code{unsigned long int}, and is therefore returned.
976: @end deftypefun
977:
978: @deftypefun void mpz_divexact (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
979: Set @var{rop} to @var{op1}/@var{op2}. This function produces correct
980: results only when it is known in advance that @var{op2} divides
981: @var{op1}.
982:
983: Since mpz_divexact is much faster than any of the other routines that produce
984: the quotient (@pxref{References} Jebelean), it is the best choice for
985: instances in which exact division is known to occur, such as reducing a
986: rational to lowest terms.
987: @end deftypefun
988:
989: @deftypefun void mpz_tdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
990: @ifinfo
991: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
992: rounded towards 0.
993: @end ifinfo
994: @iftex
995: @tex
996: Set @var{rop} to $@var{op1}/2^{op2}$. The quotient is rounded towards 0.
997: @end tex
998: @end iftex
999: @end deftypefun
1000:
1001: @deftypefun void mpz_tdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
1002: @ifinfo
1003: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
1004: @var{rop}. Unless it is zero, @var{rop} will have the same sign as @var{op1}.
1005: @end ifinfo
1006: @iftex
1007: @tex
1008: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. Unless it is
1009: zero, @var{rop} will have the same sign as @var{op1}.
1010: @end tex
1011: @end iftex
1012: @end deftypefun
1013:
1014: @deftypefun void mpz_fdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
1015: @ifinfo
1016: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}. The quotient is
1017: rounded towards @minus{}infinity.
1018: @end ifinfo
1019: @iftex
1020: @tex
1021: Set @var{rop} to $\lfloor@var{op1}/2^{op2}\rfloor$. The quotient is rounded
1022: towards $-\infty$.
1023: @end tex
1024: @end iftex
1025: @end deftypefun
1026:
1027: @deftypefun void mpz_fdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
1028: @ifinfo
1029: Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
1030: @var{rop}. The sign of @var{rop} will always be positive.
1031: @end ifinfo
1032: @iftex
1033: @tex
1034: Divide @var{op1} by $2^{op2}$ and put the remainder in @var{rop}. The sign of
1035: @var{rop} will always be positive.
1036: @end tex
1037: @end iftex
1038:
1039: This operation can also be defined as masking of the @var{op2} least
1040: significant bits.
1041: @end deftypefun
1042:
1043: @subsection Exponentialization Functions
1044:
1045: @deftypefun void mpz_powm (mpz_t @var{rop}, mpz_t @var{base}, mpz_t @var{exp}, mpz_t @var{mod})
1046: @deftypefunx void mpz_powm_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp}, mpz_t @var{mod})
1047: Set @var{rop} to (@var{base} raised to @var{exp}) @code{mod} @var{mod}. If
1048: @var{exp} is negative, the result is undefined.
1049: @end deftypefun
1050:
1051: @deftypefun void mpz_pow_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp})
1052: @deftypefunx void mpz_ui_pow_ui (mpz_t @var{rop}, unsigned long int @var{base}, unsigned long int @var{exp})
1053: Set @var{rop} to @var{base} raised to @var{exp}.
1054: @ifinfo
1055: The case of 0^0 yields 1.
1056: @end ifinfo
1057: @iftex
1058: @tex
1059: The case of $0^0$ yields 1.
1060: @end tex
1061: @end iftex
1062: @end deftypefun
1063:
1064: @subsection Square Root Functions
1065:
1066: @deftypefun void mpz_sqrt (mpz_t @var{rop}, mpz_t @var{op})
1067: @ifinfo
1068: Set @var{rop} to the truncated integer part of the square root of
1069: @var{op}.
1070: @end ifinfo
1071: @iftex
1072: @tex
1073: Set @var{rop} to $\lfloor\sqrt{@var{op}}\rfloor$, the truncated integer
1074: part of the square root of @var{op}.
1075: @end tex
1076: @end iftex
1077: @end deftypefun
1078:
1079: @deftypefun void mpz_sqrtrem (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op})
1080: @ifinfo
1081: Set @var{rop1} to the truncated integer part of the square root of @var{op},
1082: like @code{mpz_sqrt}. Set @var{rop2} to
1083: @var{op}@minus{}@var{rop1}*@var{rop1},
1084: @end ifinfo
1085: @iftex
1086: @tex
1087: Set @var{rop1} to $\lfloor\sqrt{@var{op}}\rfloor$, like @code{mpz_sqrt}.
1088: Set @var{rop2} to $(@var{op} - @var{rop1}^2)$,
1089: @end tex
1090: @end iftex
1091: (i.e., zero if @var{op} is a perfect square).
1092:
1093: If @var{rop1} and @var{rop2} are the same variable, the results are
1094: undefined.
1095: @end deftypefun
1096:
1097: @deftypefun int mpz_perfect_square_p (mpz_t @var{op})
1098: Return non-zero if @var{op} is a perfect square, i.e., if the square root of
1099: @var{op} is an integer. Return zero otherwise.
1100: @end deftypefun
1101:
1102: @subsection Number Theoretic Functions
1103:
1104: @deftypefun int mpz_probab_prime_p (mpz_t @var{op}, int @var{reps})
1105: @ifinfo
1106: If this function returns 0, @var{op} is definitely not prime. If it returns
1107: 1, then @var{op} is `probably' prime. The probability of a false positive is
1108: (1/4)**@var{reps}.
1109: @end ifinfo
1110: @iftex
1111: @tex
1112: If this function returns 0, @var{op} is definitely not prime. If it returns
1113: 1, then @var{op} is `probably' prime. The probability of a false positive is
1114: $(1/4)^{{reps}}$.
1115: @end tex
1116: @end iftex
1117: A reasonable value of reps is 25.
1118:
1119: An implementation of the probabilistic primality test found in Seminumerical
1120: Algorithms (@pxref{References} Knuth).
1121: @end deftypefun
1122:
1123: @deftypefun void mpz_gcd (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
1124: Set @var{rop} to the greatest common divisor of @var{op1} and @var{op2}.
1125: @end deftypefun
1126:
1127: @deftypefun {unsigned long int} mpz_gcd_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
1128: Compute the greatest common divisor of @var{op1} and @var{op2}. If
1129: @var{rop} is not NULL, store the result there.
1130:
1131: If the result is small enough to fit in an @code{unsigned long int}, it is
1132: returned. If the result does not fit, 0 is returned, and the result is equal
1133: to the argument @var{op1}. Note that the result will always fit if @var{op2}
1134: is non-zero.
1135: @end deftypefun
1136:
1137: @deftypefun void mpz_gcdext (mpz_t @var{g}, mpz_t @var{s}, mpz_t @var{t}, mpz_t @var{a}, mpz_t @var{b})
1138: Compute @var{g}, @var{s}, and @var{t}, such that @var{a}@var{s} +
1139: @var{b}@var{t} = @var{g} = @code{gcd} (@var{a}, @var{b}). If @var{t} is
1140: NULL, that argument is not computed.
1141: @end deftypefun
1142:
1143: @deftypefun int mpz_invert (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
1144: Compute the inverse of @var{op1} modulo @var{op2} and put the result in
1145: @var{rop}. Return non-zero if an inverse exist, zero otherwise. When the
1146: function returns zero, do not assume anything about the value in @var{rop}.
1147: @end deftypefun
1148:
1149: @deftypefun int mpz_jacobi (mpz_t @var{op1}, mpz_t @var{op2})
1150: @deftypefunx int mpz_legendre (mpz_t @var{op1}, mpz_t @var{op2})
1151: Compute the Jacobi and Legendre symbols, respectively.
1152: @end deftypefun
1153:
1154: @need 2000
1155: @node Comparison Functions, Integer Logic and Bit Fiddling, Integer Arithmetic, Integer Functions
1156: @comment node-name, next, previous, up
1157: @section Comparison Functions
1158:
1159: @deftypefun int mpz_cmp (mpz_t @var{op1}, mpz_t @var{op2})
1160: @ifinfo
1161: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
1162: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
1163: @var{op2}.
1164: @end ifinfo
1165: @iftex
1166: @tex
1167: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
1168: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
1169: < @var{op2}$.
1170: @end tex
1171: @end iftex
1172: @end deftypefun
1173:
1174: @deftypefn Macro int mpz_cmp_ui (mpz_t @var{op1}, unsigned long int @var{op2})
1175: @deftypefnx Macro int mpz_cmp_si (mpz_t @var{op1}, signed long int @var{op2})
1176: @ifinfo
1177: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
1178: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
1179: @var{op2}.
1180: @end ifinfo
1181: @iftex
1182: @tex
1183: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
1184: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
1185: < @var{op2}$.
1186: @end tex
1187: @end iftex
1188:
1189: These functions are actually implemented as macros. They evaluate their
1190: arguments multiple times.
1191: @end deftypefn
1192:
1193: @deftypefn Macro int mpz_sgn (mpz_t @var{op})
1194: @ifinfo
1195: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
1196: @end ifinfo
1197: @iftex
1198: @tex
1199: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
1200: @end tex
1201: @end iftex
1202:
1203: This function is actually implemented as a macro. It evaluates its
1204: arguments multiple times.
1205: @end deftypefn
1206:
1207: @node Integer Logic and Bit Fiddling, I/O of Integers, Comparison Functions, Integer Functions
1208: @comment node-name, next, previous, up
1209: @section Logical and Bit Manipulation Functions
1210: @cindex Logical functions
1211: @cindex Bit manipulation functions
1212:
1213: These functions behave as if two's complement arithmetic were used (although
1214: sign-magnitude is used by the actual implementation).
1215:
1216: @deftypefun void mpz_and (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
1217: Set @var{rop} to @var{op1} logical-and @var{op2}.
1218: @end deftypefun
1219:
1220: @deftypefun void mpz_ior (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
1221: Set @var{rop} to @var{op1} inclusive-or @var{op2}.
1222: @end deftypefun
1223:
1224: @c @deftypefun void mpz_xor (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
1225: @c Set @var{rop} to @var{op1} exclusive-or @var{op2}.
1226: @c @end deftypefun
1227:
1228: @deftypefun void mpz_com (mpz_t @var{rop}, mpz_t @var{op})
1229: Set @var{rop} to the one's complement of @var{op}.
1230: @end deftypefun
1231:
1232: @deftypefun {unsigned long int} mpz_popcount (mpz_t @var{op})
1233: For non-negative numbers, return the population count of @var{op}. For
1234: negative numbers, return the largest possible value (@var{MAX_ULONG}).
1235: @end deftypefun
1236:
1237: @deftypefun {unsigned long int} mpz_hamdist (mpz_t @var{op1}, mpz_t @var{op2})
1238: If @var{op1} and @var{op2} are both non-negative, return the hamming distance
1239: between the two operands. Otherwise, return the largest possible value
1240: (@var{MAX_ULONG}).
1241:
1242: It is possible to extend this function to return a useful value when the
1243: operands are both negative, but the current implementation returns
1244: @var{MAX_ULONG} in this case. @strong{Do not depend on this behavior, since
1245: it will change in future versions of the library.}
1246: @end deftypefun
1247:
1248: @deftypefun {unsigned long int} mpz_scan0 (mpz_t @var{op}, unsigned long int @var{starting_bit})
1249: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
1250: bits, until the first clear bit is found. Return the index of the found bit.
1251: @end deftypefun
1252:
1253: @deftypefun {unsigned long int} mpz_scan1 (mpz_t @var{op}, unsigned long int @var{starting_bit})
1254: Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
1255: bits, until the first set bit is found. Return the index of the found bit.
1256: @end deftypefun
1257:
1258: @deftypefun void mpz_setbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
1259: Set bit @var{bit_index} in @var{op1}.
1260: @end deftypefun
1261:
1262: @deftypefun void mpz_clrbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
1263: Clear bit @var{bit_index} in @var{op1}.
1264: @end deftypefun
1265:
1266: @node I/O of Integers, Miscellaneous Integer Functions, Integer Logic and Bit Fiddling, Integer Functions
1267: @comment node-name, next, previous, up
1268: @section Input and Output Functions
1269: @cindex Integer input and output functions
1270: @cindex Input functions
1271: @cindex Output functions
1272: @cindex I/O functions
1273:
1274: Functions that perform input from a stdio stream, and functions that output to
1275: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
1276: these functions will make them read from @code{stdin} and write to
1277: @code{stdout}, respectively.
1278:
1279: When using any of these functions, it is a good idea to include @file{stdio.h}
1280: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
1281: for these functions.
1282:
1283: @deftypefun size_t mpz_out_str (FILE *@var{stream}, int @var{base}, mpz_t @var{op})
1284: Output @var{op} on stdio stream @var{stream}, as a string of digits in base
1285: @var{base}. The base may vary from 2 to 36.
1286:
1287: Return the number of bytes written, or if an error occurred, return 0.
1288: @end deftypefun
1289:
1290: @deftypefun size_t mpz_inp_str (mpz_t @var{rop}, FILE *@var{stream}, int @var{base})
1291: Input a possibly white-space preceded string in base @var{base} from stdio
1292: stream @var{stream}, and put the read integer in @var{rop}. The base may vary
1293: from 2 to 36. If @var{base} is 0, the actual base is determined from the
1294: leading characters: if the first two characters are `0x' or `0X', hexadecimal
1295: is assumed, otherwise if the first character is `0', octal is assumed,
1296: otherwise decimal is assumed.
1297:
1298: Return the number of bytes read, or if an error occurred, return 0.
1299: @end deftypefun
1300:
1301: @deftypefun size_t mpz_out_raw (FILE *@var{stream}, mpz_t @var{op})
1302: Output @var{op} on stdio stream @var{stream}, in raw binary format. The
1303: integer is written in a portable format, with 4 bytes of size information, and
1304: that many bytes of limbs. Both the size and the limbs are written in
1305: decreasing significance order (i.e., in big-endian).
1306:
1307: The output can be read with @code{mpz_inp_raw}.
1308:
1309: Return the number of bytes written, or if an error occurred, return 0.
1310:
1311: The output of this can not be read by @code{mpz_inp_raw} from GMP 1, because
1312: of changes necessary for compatibility between 32-bit and 64-bit machines.
1313: @end deftypefun
1314:
1315: @deftypefun size_t mpz_inp_raw (mpz_t @var{rop}, FILE *@var{stream})
1316: Input from stdio stream @var{stream} in the format written by
1317: @code{mpz_out_raw}, and put the result in @var{rop}. Return the number of
1318: bytes read, or if an error occurred, return 0.
1319:
1320: This routine can read the output from @code{mpz_out_raw} also from GMP 1, in
1321: spite of changes necessary for compatibility between 32-bit and 64-bit
1322: machines.
1323: @end deftypefun
1324:
1325:
1326: @need 2000
1327: @node Miscellaneous Integer Functions,, I/O of Integers, Integer Functions
1328: @comment node-name, next, previous, up
1329: @section Miscellaneous Functions
1330: @cindex Miscellaneous integer functions
1331:
1332: @deftypefun void mpz_random (mpz_t @var{rop}, mp_size_t @var{max_size})
1333: Generate a random integer of at most @var{max_size} limbs. The generated
1334: random number doesn't satisfy any particular requirements of randomness.
1335: Negative random numbers are generated when @var{max_size} is negative.
1336: @end deftypefun
1337:
1338: @deftypefun void mpz_random2 (mpz_t @var{rop}, mp_size_t @var{max_size})
1339: Generate a random integer of at most @var{max_size} limbs, with long strings
1340: of zeros and ones in the binary representation. Useful for testing functions
1341: and algorithms, since this kind of random numbers have proven to be more
1342: likely to trigger corner-case bugs. Negative random numbers are generated
1343: when @var{max_size} is negative.
1344: @end deftypefun
1345:
1346: @deftypefun size_t mpz_size (mpz_t @var{op})
1347: Return the size of @var{op} measured in number of limbs. If @var{op} is zero,
1348: the returned value will be zero.
1349: @c (@xref{Nomenclature}, for an explanation of the concept @dfn{limb}.)
1350:
1351: @strong{This function is obsolete. It will disappear from future MP
1352: releases.}
1353: @end deftypefun
1354:
1355: @deftypefun size_t mpz_sizeinbase (mpz_t @var{op}, int @var{base})
1356: Return the size of @var{op} measured in number of digits in base @var{base}.
1357: The base may vary from 2 to 36. The returned value will be exact or 1 too
1358: big. If @var{base} is a power of 2, the returned value will always be exact.
1359:
1360: This function is useful in order to allocate the right amount of space before
1361: converting @var{op} to a string. The right amount of allocation is normally
1362: two more than the value returned by @code{mpz_sizeinbase} (one extra for a
1363: minus sign and one for the terminating '\0').
1364: @end deftypefun
1365:
1366:
1367: @node Rational Number Functions, Floating-point Functions, Integer Functions, Top
1368: @comment node-name, next, previous, up
1369: @chapter Rational Number Functions
1370: @cindex Rational number functions
1371:
1372: This chapter describes the MP functions for performing arithmetic on rational
1373: numbers. These functions start with the prefix @code{mpq_}.
1374:
1375: Rational numbers are stored in objects of type @code{mpq_t}.
1376:
1377: All rational arithmetic functions assume operands have a canonical form, and
1378: canonicalize their result. The canonical from means that the denominator and
1379: the numerator have no common factors, and that the denominator is positive.
1380: Zero has the unique representation 0/1.
1381:
1382: Pure assignment functions do not canonicalize the assigned variable. It is
1383: the responsibility of the user to canonicalize the assigned variable before
1384: any arithmetic operations are performed on that variable. @strong{Note that
1385: this is an incompatible change from version 1 of the library.}
1386:
1387: @deftypefun void mpq_canonicalize (mpq_t @var{op})
1388: Remove any factors that are common to the numerator and denominator of
1389: @var{op}, and make the denominator positive.
1390: @end deftypefun
1391:
1392: @menu
1393: * Initializing Rationals::
1394: * Assigning Rationals::
1395: * Simultaneous Integer Init & Assign::
1396: * Comparing Rationals::
1397: * Applying Integer Functions::
1398: * Miscellaneous Rational Functions::
1399: @end menu
1400:
1401: @node Initializing Rationals, Assigning Rationals, Rational Number Functions, Rational Number Functions
1402: @comment node-name, next, previous, up
1403: @section Initialization and Assignment Functions
1404:
1405: @deftypefun void mpq_init (mpq_t @var{dest_rational})
1406: Initialize @var{dest_rational} and set it to 0/1. Each variable should
1407: normally only be initialized once, or at least cleared out (using the function
1408: @code{mpq_clear}) between each initialization.
1409: @end deftypefun
1410:
1411: @deftypefun void mpq_clear (mpq_t @var{rational_number})
1412: Free the space occupied by @var{rational_number}. Make sure to call this
1413: function for all @code{mpq_t} variables when you are done with them.
1414: @end deftypefun
1415:
1416: @deftypefun void mpq_set (mpq_t @var{rop}, mpq_t @var{op})
1417: @deftypefunx void mpq_set_z (mpq_t @var{rop}, mpz_t @var{op})
1418: Assign @var{rop} from @var{op}.
1419: @end deftypefun
1420:
1421: @deftypefun void mpq_set_ui (mpq_t @var{rop}, unsigned long int @var{op1}, unsigned long int @var{op2})
1422: @deftypefunx void mpq_set_si (mpq_t @var{rop}, signed long int @var{op1}, unsigned long int @var{op2})
1423: Set the value of @var{rop} to @var{op1}/@var{op2}. Note that if @var{op1} and
1424: @var{op2} have common factors, @var{rop} has to be passed to
1425: @code{mpq_canonicalize} before any operations are performed on @var{rop}.
1426: @end deftypefun
1427:
1428: @node Assigning Rationals, Comparing Rationals, Initializing Rationals, Rational Number Functions
1429: @comment node-name, next, previous, up
1430: @section Arithmetic Functions
1431:
1432: @deftypefun void mpq_add (mpq_t @var{sum}, mpq_t @var{addend1}, mpq_t @var{addend2})
1433: Set @var{sum} to @var{addend1} + @var{addend2}.
1434: @end deftypefun
1435:
1436: @deftypefun void mpq_sub (mpq_t @var{difference}, mpq_t @var{minuend}, mpq_t @var{subtrahend})
1437: Set @var{difference} to @var{minuend} @minus{} @var{subtrahend}.
1438: @end deftypefun
1439:
1440: @deftypefun void mpq_mul (mpq_t @var{product}, mpq_t @var{multiplier}, mpq_t @var{multiplicand})
1441: @ifinfo
1442: Set @var{product} to @var{multiplier} times @var{multiplicand}.
1443: @end ifinfo
1444: @iftex
1445: @tex
1446: Set @var{product} to $@var{multiplier} \times @var{multiplicand}$.
1447: @end tex
1448: @end iftex
1449: @end deftypefun
1450:
1451: @deftypefun void mpq_div (mpq_t @var{quotient}, mpq_t @var{dividend}, mpq_t @var{divisor})
1452: Set @var{quotient} to @var{dividend}/@var{divisor}.
1453: @end deftypefun
1454:
1455: @deftypefun void mpq_neg (mpq_t @var{negated_operand}, mpq_t @var{operand})
1456: Set @var{negated_operand} to @minus{}@var{operand}.
1457: @end deftypefun
1458:
1459: @deftypefun void mpq_inv (mpq_t @var{inverted_number}, mpq_t @var{number})
1460: Set @var{inverted_number} to 1/@var{number}. If the new denominator is
1461: zero, this routine will divide by zero.
1462: @end deftypefun
1463:
1464: @node Comparing Rationals, Applying Integer Functions, Assigning Rationals, Rational Number Functions
1465: @comment node-name, next, previous, up
1466: @section Comparison Functions
1467:
1468: @deftypefun int mpq_cmp (mpq_t @var{op1}, mpq_t @var{op2})
1469: @ifinfo
1470: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
1471: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
1472: @var{op2}.
1473: @end ifinfo
1474: @iftex
1475: @tex
1476: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
1477: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
1478: < @var{op2}$.
1479: @end tex
1480: @end iftex
1481:
1482: To determine if two rationals are equal, @code{mpq_equal} is faster than
1483: @code{mpq_cmp}.
1484: @end deftypefun
1485:
1486: @deftypefn Macro int mpq_cmp_ui (mpq_t @var{op1}, unsigned long int @var{num2}, unsigned long int @var{den2})
1487: @ifinfo
1488: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
1489: @var{op1} > @var{num2}/@var{den2}, zero if @var{op1} = @var{num2}/@var{den2},
1490: and a negative value if @var{op1} < @var{num2}/@var{den2}.
1491: @end ifinfo
1492: @iftex
1493: @tex
1494: Compare @var{op1} and @var{num2}/@var{den2}. Return a positive value if
1495: $@var{op1} > @var{num2}/@var{den2}$, zero if $@var{op1} =
1496: @var{num2}/@var{den2}$, and a negative value if $@var{op1} <
1497: @var{num2}/@var{den2}$.
1498: @end tex
1499: @end iftex
1500:
1501: This routine allows that @var{num2} and @var{den2} have common factors.
1502:
1503: This function is actually implemented as a macro. It evaluates its
1504: arguments multiple times.
1505: @end deftypefn
1506:
1507: @deftypefn Macro int mpq_sgn (mpq_t @var{op})
1508: @ifinfo
1509: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
1510: @end ifinfo
1511: @iftex
1512: @tex
1513: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
1514: @end tex
1515: @end iftex
1516:
1517: This function is actually implemented as a macro. It evaluates its
1518: arguments multiple times.
1519: @end deftypefn
1520:
1521: @deftypefun int mpq_equal (mpq_t @var{op1}, mpq_t @var{op2})
1522: Return non-zero if @var{op1} and @var{op2} are equal, zero if they are
1523: non-equal. Although @code{mpq_cmp} can be used for the same purpose, this
1524: function is much faster.
1525: @end deftypefun
1526:
1527: @node Applying Integer Functions, Miscellaneous Rational Functions, Comparing Rationals, Rational Number Functions
1528: @comment node-name, next, previous, up
1529: @section Applying Integer Functions to Rationals
1530:
1531: The set of @code{mpq} functions is quite small. In particular, there are no
1532: functions for either input or output. But there are two macros that allow us
1533: to apply any @code{mpz} function on the numerator or denominator of a rational
1534: number. If these macros are used to assign to the rational number,
1535: @code{mpq_canonicalize} normally need to be called afterwards.
1536:
1537: @deftypefn Macro mpz_t mpq_numref (mpq_t @var{op})
1538: @deftypefnx Macro mpz_t mpq_denref (mpq_t @var{op})
1539: Return a reference to the numerator and denominator of @var{op}, respectively.
1540: The @code{mpz} functions can be used on the result of these macros.
1541: @end deftypefn
1542:
1543: @need 2000
1544: @node Miscellaneous Rational Functions, , Applying Integer Functions, Rational Number Functions
1545: @comment node-name, next, previous, up
1546: @section Miscellaneous Functions
1547:
1548: @deftypefun double mpq_get_d (mpq_t @var{op})
1549: Convert @var{op} to a double.
1550: @end deftypefun
1551:
1552: These functions assign between either the numerator or denominator of a
1553: rational, and an integer. Instead of using these functions, it is preferable
1554: to use the more general mechanisms @code{mpq_numref} and @code{mpq_denref},
1555: together with @code{mpz_set}.
1556:
1557: @deftypefun void mpq_set_num (mpq_t @var{rational}, mpz_t @var{numerator})
1558: Copy @var{numerator} to the numerator of @var{rational}. When this risks to
1559: make the numerator and denominator of @var{rational} have common factors, you
1560: have to pass @var{rational} to @code{mpq_canonicalize} before any operations
1561: are performed on @var{rational}.
1562:
1563: This function is equivalent to
1564: @code{mpz_set (mpq_numref (@var{rational}), @var{numerator})}.
1565: @end deftypefun
1566:
1567: @deftypefun void mpq_set_den (mpq_t @var{rational}, mpz_t @var{denominator})
1568: Copy @var{denominator} to the denominator of @var{rational}. When this risks
1569: to make the numerator and denominator of @var{rational} have common factors,
1570: or if the denominator might be negative, you have to pass @var{rational} to
1571: @code{mpq_canonicalize} before any operations are performed on @var{rational}.
1572:
1573: @strong{In version 1 of the library, negative denominators were handled by
1574: copying the sign to the numerator. That is no longer done.}
1575:
1576: This function is equivalent to
1577: @code{mpz_set (mpq_denref (@var{rational}), @var{denominators})}.
1578: @end deftypefun
1579:
1580: @deftypefun void mpq_get_num (mpz_t @var{numerator}, mpq_t @var{rational})
1581: Copy the numerator of @var{rational} to the integer @var{numerator}, to
1582: prepare for integer operations on the numerator.
1583:
1584: This function is equivalent to
1585: @code{mpz_set (@var{numerator}, mpq_numref (@var{rational}))}.
1586: @end deftypefun
1587:
1588: @deftypefun void mpq_get_den (mpz_t @var{denominator}, mpq_t @var{rational})
1589: Copy the denominator of @var{rational} to the integer @var{denominator}, to
1590: prepare for integer operations on the denominator.
1591:
1592: This function is equivalent to
1593: @code{mpz_set (@var{denominator}, mpq_denref (@var{rational}))}.
1594: @end deftypefun
1595:
1596:
1597: @node Floating-point Functions, Low-level Functions, Rational Number Functions, Top
1598: @comment node-name, next, previous, up
1599: @chapter Floating-point Functions
1600: @cindex Floating-point functions
1601: @cindex Float functions
1602:
1603: This is a description of the @emph{preliminary} interface for floating-point
1604: arithmetic in GNU MP 2.
1605:
1606: The floating-point functions expect arguments of type @code{mpf_t}.
1607:
1608: The MP floating-point functions have an interface that is similar to the MP
1609: integer functions. The function prefix for floating-point operations is
1610: @code{mpf_}.
1611:
1612: There is one significant characteristic of floating-point numbers that has
1613: motivated a difference between this function class and other MP function
1614: classes: the inherent inexactness of floating point arithmetic. The user has
1615: to specify the precision of each variable. A computation that assigns a
1616: variable will take place with the precision of the assigned variable; the
1617: precision of variables used as input is ignored.
1618:
1619: @cindex User-defined precision
1620: The precision of a calculation is defined as follows: Compute the requested
1621: operation exactly (with ``infinite precision''), and truncate the result to
1622: the destination variable precision. Even if the user has asked for a very
1623: high precision, MP will not calculate with superfluous digits. For example,
1624: if two low-precision numbers of nearly equal magnitude are added, the
1625: precision of the result will be limited to what is required to represent the
1626: result accurately.
1627:
1628: The MP floating-point functions are @emph{not} intended as a smooth extension
1629: to the IEEE P754 arithmetic. Specifically, the results obtained on one
1630: computer often differs from the results obtained on a computer with a
1631: different word size.
1632:
1633: @menu
1634: * Initializing Floats::
1635: * Assigning Floats::
1636: * Simultaneous Float Init & Assign::
1637: * Converting Floats::
1638: * Float Arithmetic::
1639: * Float Comparison::
1640: * I/O of Floats::
1641: * Miscellaneous Float Functions::
1642: @end menu
1643:
1644: @node Initializing Floats, Assigning Floats, , Floating-point Functions
1645: @comment node-name, next, previous, up
1646: @section Initialization and Assignment Functions
1647:
1648: @deftypefun void mpf_set_default_prec (unsigned long int @var{prec})
1649: Set the default precision to be @strong{at least} @var{prec} bits. All
1650: subsequent calls to @code{mpf_init} will use this precision, but previously
1651: initialized variables are unaffected.
1652: @end deftypefun
1653:
1654: An @code{mpf_t} object must be initialized before storing the first value in
1655: it. The functions @code{mpf_init} and @code{mpf_init2} are used for that
1656: purpose.
1657:
1658: @deftypefun void mpf_init (mpf_t @var{x})
1659: Initialize @var{x} to 0. Normally, a variable should be initialized once only
1660: or at least be cleared, using @code{mpf_clear}, between initializations. The
1661: precision of @var{x} is undefined unless a default precision has already been
1662: established by a call to @code{mpf_set_default_prec}.
1663: @end deftypefun
1664:
1665: @deftypefun void mpf_init2 (mpf_t @var{x}, unsigned long int @var{prec})
1666: Initialize @var{x} to 0 and set its precision to be @strong{at least}
1667: @var{prec} bits. Normally, a variable should be initialized once only or at
1668: least be cleared, using @code{mpf_clear}, between initializations.
1669: @end deftypefun
1670:
1671: @deftypefun void mpf_clear (mpf_t @var{x})
1672: Free the space occupied by @var{x}. Make sure to call this function for all
1673: @code{mpf_t} variables when you are done with them.
1674: @end deftypefun
1675:
1676: @need 2000
1677: Here is an example on how to initialize floating-point variables:
1678: @example
1679: @{
1680: mpf_t x, y;
1681: mpf_init (x); /* use default precision */
1682: mpf_init2 (y, 256); /* precision @emph{at least} 256 bits */
1683: @dots{}
1684: /* Unless the program is about to exit, do ... */
1685: mpf_clear (x);
1686: mpf_clear (y);
1687: @}
1688: @end example
1689:
1690: The following three functions are useful for changing the precision during a
1691: calculation. A typical use would be for adjusting the precision gradually in
1692: iterative algorithms like Newton-Raphson, making the computation precision
1693: closely match the actual accurate part of the numbers.
1694:
1695: @deftypefun void mpf_set_prec (mpf_t @var{rop}, unsigned long int @var{prec})
1696: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits.
1697: Since changing the precision involves calls to @code{realloc}, this routine
1698: should not be called in a tight loop.
1699: @end deftypefun
1700:
1701: @deftypefun {unsigned long int} mpf_get_prec (mpf_t @var{op})
1702: Return the precision actually used for assignments of @var{op}.
1703: @end deftypefun
1704:
1705: @deftypefun void mpf_set_prec_raw (mpf_t @var{rop}, unsigned long int @var{prec})
1706: Set the precision of @var{rop} to be @strong{at least} @var{prec} bits. This
1707: is a low-level function that does not change the allocation. The @var{prec}
1708: argument must not be larger that the precision previously returned by
1709: @code{mpf_get_prec}. It is crucial that the precision of @var{rop} is
1710: ultimately reset to exactly the value returned by @code{mpf_get_prec}.
1711: @end deftypefun
1712:
1713:
1714: @node Assigning Floats, Simultaneous Float Init & Assign, Initializing Floats, Floating-point Functions
1715: @comment node-name, next, previous, up
1716: @subsection Assignment Functions
1717: @cindex Float assignment functions
1718:
1719: These functions assign new values to already initialized floats
1720: (@pxref{Initializing Floats}).
1721:
1722: @deftypefun void mpf_set (mpf_t @var{rop}, mpf_t @var{op})
1723: @deftypefunx void mpf_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
1724: @deftypefunx void mpf_set_si (mpf_t @var{rop}, signed long int @var{op})
1725: @deftypefunx void mpf_set_d (mpf_t @var{rop}, double @var{op})
1726: @deftypefunx void mpf_set_z (mpf_t @var{rop}, mpz_t @var{op})
1727: @deftypefunx void mpf_set_q (mpf_t @var{rop}, mpq_t @var{op})
1728: Set the value of @var{rop} from @var{op}.
1729: @end deftypefun
1730:
1731: @deftypefun int mpf_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
1732: Set the value of @var{rop} from the string in @var{str}. The string is of the
1733: form @samp{M@@N} or, if the base is 10 or less, alternatively @samp{MeN}.
1734: @samp{M} is the mantissa and @samp{N} is the exponent. The mantissa is always
1735: in the specified base. The exponent is either in the specified base or, if
1736: @var{base} is negative, in decimal.
1737:
1738: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
1739: @minus{}2. Negative values are used to specify that the exponent is in
1740: decimal.
1741:
1742: Unlike the corresponding @code{mpz} function, the base will not be determined
1743: from the leading characters of the string if @var{base} is 0. This is so that
1744: numbers like @samp{0.23} are not interpreted as octal.
1745:
1746: White space is allowed in the string, and is simply ignored.
1747:
1748: This function returns 0 if the entire string up to the '\0' is a valid number
1749: in base @var{base}. Otherwise it returns @minus{}1.
1750: @end deftypefun
1751:
1752:
1753: @node Simultaneous Float Init & Assign, Converting Floats, Assigning Floats, Floating-point Functions
1754: @comment node-name, next, previous, up
1755: @subsection Combined Initialization and Assignment Functions
1756: @cindex Initialization and assignment functions
1757:
1758: For convenience, MP provides a parallel series of initialize-and-set functions
1759: which initialize the output and then store the value there. These functions'
1760: names have the form @code{mpf_init_set@dots{}}
1761:
1762: Once the float has been initialized by any of the @code{mpf_init_set@dots{}}
1763: functions, it can be used as the source or destination operand for the ordinary
1764: float functions. Don't use an initialize-and-set function on a variable
1765: already initialized!
1766:
1767: @deftypefun void mpf_init_set (mpf_t @var{rop}, mpf_t @var{op})
1768: @deftypefunx void mpf_init_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
1769: @deftypefunx void mpf_init_set_si (mpf_t @var{rop}, signed long int @var{op})
1770: @deftypefunx void mpf_init_set_d (mpf_t @var{rop}, double @var{op})
1771: Initialize @var{rop} and set its value from @var{op}.
1772:
1773: The precision of @var{rop} will be taken from the active default precision, as
1774: set by @code{mpf_set_default_prec}.
1775: @end deftypefun
1776:
1777: @deftypefun int mpf_init_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
1778: Initialize @var{rop} and set its value from the string in @var{str}. See
1779: @code{mpf_set_str} above for details on the assignment operation.
1780:
1781: Note that @var{rop} is initialized even if an error occurs. (I.e., you have to
1782: call @code{mpf_clear} for it.)
1783:
1784: The precision of @var{rop} will be taken from the active default precision, as
1785: set by @code{mpf_set_default_prec}.
1786: @end deftypefun
1787:
1788:
1789: @node Converting Floats, Float Arithmetic, Simultaneous Float Init & Assign, Floating-point Functions
1790: @comment node-name, next, previous, up
1791: @section Conversion Functions
1792: @cindex Conversion functions
1793:
1794: @deftypefun double mpf_get_d (mpf_t @var{op})
1795: Convert @var{op} to a double.
1796: @end deftypefun
1797:
1798: @deftypefun {char *} mpf_get_str (char *@var{str}, mp_exp_t *@var{expptr}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
1799: Convert @var{op} to a string of digits in base @var{base}. The base may vary
1800: from 2 to 36. Generate at most @var{n_digits} significant digits, or if
1801: @var{n_digits} is 0, the maximum number of digits accurately representable by
1802: @var{op}.
1803:
1804: If @var{str} is NULL, space for the mantissa is allocated using the default
1805: allocation function, and a pointer to the string is returned.
1806:
1807: If @var{str} is not NULL, it should point to a block of storage enough large
1808: for the mantissa, i.e., @var{n_digits} + 2. The two extra bytes are for a
1809: possible minus sign, and for the terminating null character.
1810:
1811: The exponent is written through the pointer @var{expptr}.
1812:
1813: If @var{n_digits} is 0, the maximum number of digits meaningfully achievable
1814: from the precision of @var{op} will be generated. Note that the space
1815: requirements for @var{str} in this case will be impossible for the user to
1816: predetermine. Therefore, you need to pass NULL for the string argument
1817: whenever @var{n_digits} is 0.
1818:
1819: The generated string is a fraction, with an implicit radix point immediately
1820: to the left of the first digit. For example, the number 3.1416 would be
1821: returned as "31416" in the string and 1 written at @var{expptr}.
1822: @end deftypefun
1823:
1824:
1825: @node Float Arithmetic, Float Comparison, Converting Floats, Floating-point Functions
1826: @comment node-name, next, previous, up
1827: @section Arithmetic Functions
1828: @cindex Float arithmetic functions
1829: @cindex Arithmetic functions
1830:
1831: @deftypefun void mpf_add (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
1832: @deftypefunx void mpf_add_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1833: @ifinfo
1834: Set @var{rop} to @var{op1} + @var{op2}.
1835: @end ifinfo
1836: @iftex
1837: @tex
1838: Set @var{rop} to $@var{op1} + @var{op2}$.
1839: @end tex
1840: @end iftex
1841: @end deftypefun
1842:
1843: @deftypefun void mpf_sub (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
1844: @deftypefunx void mpf_ui_sub (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
1845: @deftypefunx void mpf_sub_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1846: Set @var{rop} to @var{op1} @minus{} @var{op2}.
1847: @end deftypefun
1848:
1849: @deftypefun void mpf_mul (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
1850: @deftypefunx void mpf_mul_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1851: @ifinfo
1852: Set @var{rop} to @var{op1} times @var{op2}.
1853: @end ifinfo
1854: @iftex
1855: @tex
1856: Set @var{rop} to $@var{op1} \times @var{op2}$.
1857: @end tex
1858: @end iftex
1859: @end deftypefun
1860:
1861: Division is undefined if the divisor is zero, and passing a zero divisor to
1862: the divide functions will make these functions intentionally divide by zero.
1863: This gives the user the possibility to handle arithmetic exceptions in these
1864: functions in the same manner as other arithmetic exceptions.
1865:
1866: @deftypefun void mpf_div (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
1867: @deftypefunx void mpf_ui_div (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
1868: @deftypefunx void mpf_div_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1869: Set @var{rop} to @var{op1}/@var{op2}.
1870: @end deftypefun
1871:
1872: @deftypefun void mpf_sqrt (mpf_t @var{rop}, mpf_t @var{op})
1873: @deftypefunx void mpf_sqrt_ui (mpf_t @var{rop}, unsigned long int @var{op})
1874: @ifinfo
1875: Set @var{rop} to the square root of @var{op}.
1876: @end ifinfo
1877: @iftex
1878: @tex
1879: Set @var{rop} to $\sqrt{@var{op}}$.
1880: @end tex
1881: @end iftex
1882: @end deftypefun
1883:
1884: @c @deftypefun void mpf_pow_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1885: @c Set @var{rop} to @var{op1} raised to @var{op2}.
1886: @c @end deftypefun
1887:
1888: @deftypefun void mpf_neg (mpf_t @var{rop}, mpf_t @var{op})
1889: Set @var{rop} to @minus{}@var{op}.
1890: @end deftypefun
1891:
1892: @deftypefun void mpf_abs (mpf_t @var{rop}, mpf_t @var{op})
1893: Set @var{rop} to the absolute value of @var{op}.
1894: @end deftypefun
1895:
1896: @deftypefun void mpf_mul_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1897: @ifinfo
1898: Set @var{rop} to @var{op1} times 2 raised to @var{op2}.
1899: @end ifinfo
1900: @iftex
1901: @tex
1902: Set @var{rop} to $@var{op1} \times 2^{op2}$.
1903: @end tex
1904: @end iftex
1905: @end deftypefun
1906:
1907: @deftypefun void mpf_div_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
1908: @ifinfo
1909: Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.
1910: @end ifinfo
1911: @iftex
1912: @tex
1913: Set @var{rop} to $@var{op1}/2^{op2}$.
1914: @end tex
1915: @end iftex
1916: @end deftypefun
1917:
1918: @node Float Comparison, I/O of Floats, Float Arithmetic, Floating-point Functions
1919: @comment node-name, next, previous, up
1920: @section Comparison Functions
1921: @cindex Float comparisons functions
1922: @cindex Comparison functions
1923:
1924: @deftypefun int mpf_cmp (mpf_t @var{op1}, mpf_t @var{op2})
1925: @deftypefunx int mpf_cmp_ui (mpf_t @var{op1}, unsigned long int @var{op2})
1926: @deftypefunx int mpf_cmp_si (mpf_t @var{op1}, signed long int @var{op2})
1927: @ifinfo
1928: Compare @var{op1} and @var{op2}. Return a positive value if @var{op1} >
1929: @var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
1930: @var{op2}.
1931: @end ifinfo
1932: @iftex
1933: @tex
1934: Compare @var{op1} and @var{op2}. Return a positive value if $@var{op1} >
1935: @var{op2}$, zero if $@var{op1} = @var{op2}$, and a negative value if $@var{op1}
1936: < @var{op2}$.
1937: @end tex
1938: @end iftex
1939: @end deftypefun
1940:
1941: @deftypefun int mpf_eq (mpf_t @var{op1}, mpf_t @var{op2}, unsigned long int op3)
1942: Return non-zero if the first @var{op3} bits of @var{op1} and @var{op2} are
1943: equal, zero otherwise. I.e., test of @var{op1} and @var{op2} are
1944: approximately equal.
1945: @end deftypefun
1946:
1947: @deftypefun void mpf_reldiff (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
1948: Compute the relative difference between @var{op1} and @var{op2} and store the
1949: result in @var{rop}.
1950: @end deftypefun
1951:
1952: @deftypefn Macro int mpf_sgn (mpf_t @var{op})
1953: @ifinfo
1954: Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
1955: @end ifinfo
1956: @iftex
1957: @tex
1958: Return $+1$ if $@var{op} > 0$, 0 if $@var{op} = 0$, and $-1$ if $@var{op} < 0$.
1959: @end tex
1960: @end iftex
1961:
1962: This function is actually implemented as a macro. It evaluates its
1963: arguments multiple times.
1964: @end deftypefn
1965:
1966: @node I/O of Floats, Miscellaneous Float Functions, Float Comparison, Floating-point Functions
1967: @comment node-name, next, previous, up
1968: @section Input and Output Functions
1969: @cindex Float input and output functions
1970: @cindex Input functions
1971: @cindex Output functions
1972: @cindex I/O functions
1973:
1974: Functions that perform input from a stdio stream, and functions that output to
1975: a stdio stream. Passing a NULL pointer for a @var{stream} argument to any of
1976: these functions will make them read from @code{stdin} and write to
1977: @code{stdout}, respectively.
1978:
1979: When using any of these functions, it is a good idea to include @file{stdio.h}
1980: before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
1981: for these functions.
1982:
1983: @deftypefun size_t mpf_out_str (FILE *@var{stream}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
1984: Output @var{op} on stdio stream @var{stream}, as a string of digits in
1985: base @var{base}. The base may vary from 2 to 36. Print at most
1986: @var{n_digits} significant digits, or if @var{n_digits} is 0, the maximum
1987: number of digits accurately representable by @var{op}.
1988:
1989: In addition to the significant digits, a leading @samp{0.} and a
1990: trailing exponent, in the form @samp{eNNN}, are printed. If @var{base}
1991: is greater than 10, @samp{@@} will be used instead of @samp{e} as
1992: exponent delimiter.
1993:
1994: Return the number of bytes written, or if an error occurred, return 0.
1995: @end deftypefun
1996:
1997: @deftypefun size_t mpf_inp_str (mpf_t @var{rop}, FILE *@var{stream}, int @var{base})
1998: Input a string in base @var{base} from stdio stream @var{stream}, and put the
1999: read float in @var{rop}. The string is of the form @samp{M@@N} or, if the
2000: base is 10 or less, alternatively @samp{MeN}. @samp{M} is the mantissa and
2001: @samp{N} is the exponent. The mantissa is always in the specified base. The
2002: exponent is either in the specified base or, if @var{base} is negative, in
2003: decimal.
2004:
2005: The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
2006: @minus{}2. Negative values are used to specify that the exponent is in
2007: decimal.
2008:
2009: Unlike the corresponding @code{mpz} function, the base will not be determined
2010: from the leading characters of the string if @var{base} is 0. This is so that
2011: numbers like @samp{0.23} are not interpreted as octal.
2012:
2013: Return the number of bytes read, or if an error occurred, return 0.
2014: @end deftypefun
2015:
2016: @c @deftypefun void mpf_out_raw (FILE *@var{stream}, mpf_t @var{float})
2017: @c Output @var{float} on stdio stream @var{stream}, in raw binary
2018: @c format. The float is written in a portable format, with 4 bytes of
2019: @c size information, and that many bytes of limbs. Both the size and the
2020: @c limbs are written in decreasing significance order.
2021: @c @end deftypefun
2022:
2023: @c @deftypefun void mpf_inp_raw (mpf_t @var{float}, FILE *@var{stream})
2024: @c Input from stdio stream @var{stream} in the format written by
2025: @c @code{mpf_out_raw}, and put the result in @var{float}.
2026: @c @end deftypefun
2027:
2028:
2029: @node Miscellaneous Float Functions, , I/O of Floats, Floating-point Functions
2030: @comment node-name, next, previous, up
2031: @section Miscellaneous Functions
2032: @cindex Miscellaneous float functions
2033:
2034: @deftypefun void mpf_random2 (mpf_t @var{rop}, mp_size_t @var{max_size}, mp_exp_t @var{max_exp})
2035: Generate a random float of at most @var{max_size} limbs, with long strings of
2036: zeros and ones in the binary representation. The exponent of the number is in
2037: the interval @minus{}@var{exp} to @var{exp}. This function is useful for
2038: testing functions and algorithms, since this kind of random numbers have
2039: proven to be more likely to trigger corner-case bugs. Negative random numbers
2040: are generated when @var{max_size} is negative.
2041: @end deftypefun
2042:
2043: @c @deftypefun size_t mpf_size (mpf_t @var{op})
2044: @c Return the size of @var{op} measured in number of limbs. If @var{op} is
2045: @c zero, the returned value will be zero. (@xref{Nomenclature}, for an
2046: @c explanation of the concept @dfn{limb}.)
2047: @c
2048: @c @strong{This function is obsolete. It will disappear from future MP
2049: @c releases.}
2050: @c @end deftypefun
2051:
2052: @node Low-level Functions, BSD Compatible Functions, Floating-point Functions, Top
2053: @comment node-name, next, previous, up
2054: @chapter Low-level Functions
2055: @cindex Low-level functions
2056:
2057: This chapter describes low-level MP functions, used to implement the high-level
2058: MP functions, but also intended for time-critical user code.
2059:
2060: These functions start with the prefix @code{mpn_}.
2061:
2062: @c 1. Some of these function clobber input operands.
2063: @c
2064:
2065: The @code{mpn} functions are designed to be as fast as possible, @strong{not}
2066: to provide a coherent calling interface. The different functions have somewhat
2067: similar interfaces, but there are variations that make them hard to use. These
2068: functions do as little as possible apart from the real multiple precision
2069: computation, so that no time is spent on things that not all callers need.
2070:
2071: A source operand is specified by a pointer to the least significant limb and a
2072: limb count. A destination operand is specified by just a pointer. It is the
2073: responsibility of the caller to ensure that the destination has enough space
2074: for storing the result.
2075:
2076: With this way of specifying operands, it is possible to perform computations
2077: on subranges of an argument, and store the result into a subrange of a
2078: destination.
2079:
2080: A common requirement for all functions is that each source area needs at least
2081: one limb. No size argument may be zero.
2082:
2083: The @code{mpn} functions is the base for the implementation of the @code{mpz_},
2084: @code{mpf_}, and @code{mpq_} functions.
2085:
2086: This example adds the number beginning at @var{src1_ptr} and the number
2087: beginning at @var{src2_ptr} and writes the sum at @var{dest_ptr}. All areas
2088: have @var{size} limbs.
2089:
2090: @example
2091: cy = mpn_add_n (dest_ptr, src1_ptr, src2_ptr, size)
2092: @end example
2093:
2094: @noindent
2095: In the notation used here, a source operand is identified by the pointer to
2096: the least significant limb, and the limb count in braces. For example,
2097: @{s1_ptr, s1_size@}.
2098:
2099: @deftypefun mp_limb_t mpn_add_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
2100: Add @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@}, and
2101: write the @var{size} least significant limbs of the result to @var{dest_ptr}.
2102: Return carry, either 0 or 1.
2103:
2104: This is the lowest-level function for addition. It is the preferred function
2105: for addition, since it is written in assembly for most targets. For addition
2106: of a variable to itself (i.e., @var{src1_ptr} equals @var{src2_ptr}, use
2107: @code{mpn_lshift} with a count of 1 for optimal speed.
2108: @end deftypefun
2109:
2110: @deftypefun mp_limb_t mpn_add_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
2111: Add @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
2112: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
2113: carry, either 0 or 1.
2114: @end deftypefun
2115:
2116: @deftypefun mp_limb_t mpn_add (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
2117: Add @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
2118: @var{src2_size}@}, and write the @var{src1_size} least significant limbs of
2119: the result to @var{dest_ptr}. Return carry, either 0 or 1.
2120:
2121: This function requires that @var{src1_size} is greater than or equal to
2122: @var{src2_size}.
2123: @end deftypefun
2124:
2125: @deftypefun mp_limb_t mpn_sub_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
2126: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
2127: @var{size}@}, and write the @var{size} least significant limbs of the result
2128: to @var{dest_ptr}. Return borrow, either 0 or 1.
2129:
2130: This is the lowest-level function for subtraction. It is the preferred
2131: function for subtraction, since it is written in assembly for most targets.
2132: @end deftypefun
2133:
2134: @deftypefun mp_limb_t mpn_sub_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
2135: Subtract @var{src2_limb} from @{@var{src1_ptr}, @var{size}@}, and write the
2136: @var{size} least significant limbs of the result to @var{dest_ptr}. Return
2137: borrow, either 0 or 1.
2138: @end deftypefun
2139:
2140: @deftypefun mp_limb_t mpn_sub (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
2141: Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
2142: @var{src1_size}@}, and write the @var{src1_size} least significant limbs of
2143: the result to @var{dest_ptr}. Return borrow, either 0 or 1.
2144:
2145: This function requires that @var{src1_size} is greater than or equal to
2146: @var{src2_size}.
2147: @end deftypefun
2148:
2149: @deftypefun void mpn_mul_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
2150: Multiply @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@},
2151: and write the @strong{entire} result to @var{dest_ptr}.
2152:
2153: The destination has to have space for 2@var{size} limbs, even if the
2154: significant result might be one limb smaller.
2155: @end deftypefun
2156:
2157: @deftypefun mp_limb_t mpn_mul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
2158: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
2159: @var{size} least significant limbs of the product to @var{dest_ptr}. Return
2160: the most significant limb of the product.
2161:
2162: This is a low-level function that is a building block for general
2163: multiplication as well as other operations in MP. It is written in assembly
2164: for most targets.
2165:
2166: Don't call this function if @var{src2_limb} is a power of 2; use
2167: @code{mpn_lshift} with a count equal to the logarithm of @var{src2_limb}
2168: instead, for optimal speed.
2169: @end deftypefun
2170:
2171: @deftypefun mp_limb_t mpn_addmul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
2172: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and add the
2173: @var{size} least significant limbs of the product to @{@var{dest_ptr},
2174: @var{size}@} and write the result to @var{dest_ptr} @var{dest_ptr}. Return
2175: the most significant limb of the product, plus carry-out from the addition.
2176:
2177: This is a low-level function that is a building block for general
2178: multiplication as well as other operations in MP. It is written in assembly
2179: for most targets.
2180: @end deftypefun
2181:
2182: @deftypefun mp_limb_t mpn_submul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
2183: Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and subtract the
2184: @var{size} least significant limbs of the product from @{@var{dest_ptr},
2185: @var{size}@} and write the result to @var{dest_ptr}. Return the most
2186: significant limb of the product, minus borrow-out from the subtraction.
2187:
2188: This is a low-level function that is a building block for general
2189: multiplication and division as well as other operations in MP. It is written
2190: in assembly for most targets.
2191: @end deftypefun
2192:
2193: @deftypefun mp_limb_t mpn_mul (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
2194: Multiply @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
2195: @var{src2_size}@}, and write the result to @var{dest_ptr}. Return the most
2196: significant limb of the result.
2197:
2198: The destination has to have space for @var{src1_size} + @var{src1_size}
2199: limbs, even if the result might be one limb smaller.
2200:
2201: This function requires that @var{src1_size} is greater than or equal to
2202: @var{src2_size}. The destination must be distinct from either input operands.
2203: @end deftypefun
2204:
2205: @deftypefun mp_size_t mpn_divrem (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
2206: Divide @{@var{rs2p}, @var{rs2size}@} by @{@var{s3p}, @var{s3size}@}, and
2207: write the quotient at @var{r1p}, with the exception of the most significant
2208: limb, which is returned. The remainder replaces the dividend at @var{rs2p}.
2209:
2210: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
2211: and stored after the integral limbs. For most usages, @var{xsize} will be
2212: zero.
2213:
2214: It is required that @var{rs2size} is greater than or equal to @var{s3size}.
2215: It is required that the most significant bit of the divisor is set.
2216:
2217: If the quotient is not needed, pass @var{rs2p} + @var{s3size} as @var{r1p}.
2218: Aside from that special case, no overlap between arguments is permitted.
2219:
2220: Return the most significant limb of the quotient, either 0 or 1.
2221:
2222: The area at @var{r1p} needs to be @var{rs2size} @minus{} @var{s3size} +
2223: @var{xsize} limbs large.
2224: @end deftypefun
2225:
2226: @deftypefun mp_limb_t mpn_divrem_1 (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
2227: Divide @{@var{s2p}, @var{s2size}@} by @var{s3limb}, and write the quotient
2228: at @var{r1p}. Return the remainder.
2229:
2230: In addition to an integer quotient, @var{xsize} fraction limbs are developed,
2231: and stored after the integral limbs. For most usages, @var{xsize} will be
2232: zero.
2233:
2234: The areas at @var{r1p} and @var{s2p} have to be identical or completely
2235: separate, not partially overlapping.
2236: @end deftypefun
2237:
2238: @deftypefun mp_size_t mpn_divmod (mp_limb_t * @var{r1p}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
2239: @strong{This interface is obsolete. It will disappear from future releases.
2240: Use @code{mpn_divrem} in its stead.}
2241: @end deftypefun
2242:
2243: @deftypefun mp_limb_t mpn_divmod_1 (mp_limb_t * @var{r1p}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
2244: @strong{This interface is obsolete. It will disappear from future releases.
2245: Use @code{mpn_divrem_1} in its stead.}
2246: @end deftypefun
2247:
2248: @deftypefun mp_limb_t mpn_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb})
2249: Divide @{@var{s1p}, @var{s1size}@} by @var{s2limb}, and return the remainder.
2250: @end deftypefun
2251:
2252: @deftypefun mp_limb_t mpn_preinv_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb}, mp_limb_t @var{s3limb})
2253: @strong{This interface is obsolete. It will disappear from future releases.
2254: Use @code{mpn_mod_1} in its stead.}
2255: @end deftypefun
2256:
2257: @deftypefun mp_limb_t mpn_bdivmod (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, const mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, unsigned long int @var{d})
2258: The function puts the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
2259: @var{q} =
2260: @{@var{s1p}, @var{s1size}@}/@{@var{s2p}, @var{s2size}@}
2261: mod 2^@var{d}
2262: at @var{dest_ptr},
2263: and returns the high @var{d} mod @var{BITS_PER_MP_LIMB} bits of @var{q}.
2264:
2265: @{@var{s1p}, @var{s1size}@} - @var{q} * @{@var{s2p}, @var{s2size}@}
2266: mod 2^(@var{s1size}*@var{BITS_PER_MP_LIMB})
2267: is placed at @var{s1p}.
2268: Since the low [@var{d}/@var{BITS_PER_MP_LIMB}] limbs of
2269: this difference are zero, it is possible to overwrite the low limbs at
2270: @var{s1p} with this difference,
2271: provided @var{dest_ptr} <= @var{s1p}.
2272:
2273: This function requires that @var{s1size} * @var{BITS_PER_MP_LIMB} >= @var{D},
2274: and that @{@var{s2p}, @var{s2size}@} is odd.
2275:
2276: @strong{This interface is preliminary. It might change incompatibly in
2277: future revisions.}
2278: @end deftypefun
2279:
2280: @deftypefun mp_limb_t mpn_lshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
2281: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the left, and
2282: write the @var{src_size} least significant limbs of the result to
2283: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
2284: n-bit machine. The bits shifted out to the left are returned.
2285:
2286: Overlapping of the destination space and the source space is allowed in this
2287: function, provided @var{dest_ptr} >= @var{src_ptr}.
2288:
2289: This function is written in assembly for most targets.
2290: @end deftypefun
2291:
2292: @deftypefun mp_limp_t mpn_rshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
2293: Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the right, and
2294: write the @var{src_size} most significant limbs of the result to
2295: @var{dest_ptr}. @var{count} might be in the range 1 to n @minus{} 1, on an
2296: n-bit machine. The bits shifted out to the right are returned.
2297:
2298: Overlapping of the destination space and the source space is allowed in this
2299: function, provided @var{dest_ptr} <= @var{src_ptr}.
2300:
2301: This function is written in assembly for most targets.
2302: @end deftypefun
2303:
2304: @deftypefun int mpn_cmp (const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
2305: Compare @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@} and
2306: return a positive value if src1 > src2, 0 of they are equal, and a negative
2307: value if src1 < src2.
2308: @end deftypefun
2309:
2310: @deftypefun mp_size_t mpn_gcd (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
2311: Puts at @var{dest_ptr} the greatest common divisor of @{@var{src1_ptr},
2312: @var{src1_size}@} and @{@var{src2_ptr}, @var{src2_size}@}; both source
2313: operands are destroyed by the operation. The size in limbs of the greatest
2314: common divisor is returned.
2315:
2316: @{@var{src1_ptr}, @var{src1_size}@} must be odd, and @{@var{src2_ptr},
2317: @var{src2_size}@} must have at least as many bits as @{@var{src1_ptr},
2318: @var{src1_size}@}.
2319:
2320: @strong{This interface is preliminary. It might change incompatibly in
2321: future revisions.}
2322: @end deftypefun
2323:
2324: @deftypefun mp_limb_t mpn_gcd_1 (const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t @var{src2_limb})
2325: Return the greatest common divisor of @{@var{src1_ptr}, @var{src1_size}@}
2326: and @var{src2_limb}, where @var{src2_limb} (as well as @var{src1_size})
2327: must be different from 0.
2328: @end deftypefun
2329:
2330: @deftypefun mp_size_t mpn_gcdext (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size})
2331: Puts at @var{r1p} the greatest common divisor of @{@var{s1p}, @var{s1size}@}
2332: and @{@var{s2p}, @var{s2size}@}. The first cofactor is written at
2333: @var{r2p}. Both source operands are destroyed by the operation. The size
2334: in limbs of the greatest common divisor is returned.
2335:
2336: @strong{This interface is preliminary. It might change incompatibly in
2337: future revisions.}
2338: @end deftypefun
2339:
2340: @deftypefun mp_size_t mpn_sqrtrem (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, const mp_limb_t * @var{sp}, mp_size_t @var{size})
2341: Compute the square root of @{@var{sp}, @var{size}@} and put the result at
2342: @var{r1p}. Write the remainder at @var{r2p}, unless @var{r2p} is NULL.
2343:
2344: Return the size of the remainder, whether @var{r2p} was NULL or non-NULL.
2345: Iff the operand was a perfect square, the return value will be 0.
2346:
2347: The areas at @var{r1p} and @var{sp} have to be distinct. The areas at
2348: @var{r2p} and @var{sp} have to be identical or completely separate, not
2349: partially overlapping.
2350:
2351: @ifinfo
2352: The area at @var{r1p} needs to have space for ceil(@var{size}/2) limbs.
2353: @end ifinfo
2354: @iftex
2355: @tex
2356: The area at @var{r1p} needs to have space for $\lceil@var{size}/2\rceil$ limbs.
2357: @end tex
2358: @end iftex
2359: The area at @var{r2p} needs to be @var{size} limbs large.
2360:
2361: @strong{This interface is preliminary. It might change incompatibly in
2362: future revisions.}
2363: @end deftypefun
2364:
2365: @deftypefun mp_size_t mpn_get_str (unsigned char *@var{str}, int @var{base}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size})
2366: Convert @{@var{s1p}, @var{s1size}@} to a raw unsigned char array in base
2367: @var{base}. The string is not in ASCII; to convert it to printable format,
2368: add the ASCII codes for @samp{0} or @samp{A}, depending on the base and
2369: range. There may be leading zeros in the string.
2370:
2371: The area at @var{s1p} is clobbered.
2372:
2373: Return the number of characters in @var{str}.
2374:
2375: The area at @var{str} has to have space for the largest possible number
2376: represented by a @var{s1size} long limb array, plus one extra character.
2377: @end deftypefun
2378:
2379: @deftypefun mp_size_t mpn_set_str (mp_limb_t * @var{r1p}, const char *@var{str}, size_t {strsize}, int @var{base})
2380: Convert the raw unsigned char array at @var{str} of length @var{strsize} to
2381: a limb array @{@var{s1p}, @var{s1size}@}. The base of @var{str} is
2382: @var{base}.
2383:
2384: Return the number of limbs stored in @var{r1p}.
2385: @end deftypefun
2386:
2387: @deftypefun {unsigned long int} mpn_scan0 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
2388: Scan @var{s1p} from bit position @var{bit} for the next clear bit.
2389:
2390: It is required that there be a clear bit within the area at @var{s1p} at or
2391: beyond bit position @var{bit}, so that the function has something to return.
2392:
2393: @strong{This interface is preliminary. It might change incompatibly in
2394: future revisions.}
2395: @end deftypefun
2396:
2397: @deftypefun {unsigned long int} mpn_scan1 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
2398: Scan @var{s1p} from bit position @var{bit} for the next set bit.
2399:
2400: It is required that there be a set bit within the area at @var{s1p} at or
2401: beyond bit position @var{bit}, so that the function has something to return.
2402:
2403: @strong{This interface is preliminary. It might change incompatibly in
2404: future revisions.}
2405: @end deftypefun
2406:
2407: @deftypefun void mpn_random2 (mp_limb_t * @var{r1p}, mp_size_t @var{r1size})
2408: Generate a random number of length @var{r1size} with long strings of zeros
2409: and ones in the binary representation, and store it at @var{r1p}.
2410:
2411: The generated random numbers are intended for testing the correctness of the
2412: implementation of the @code{mpn} routines.
2413: @end deftypefun
2414:
2415: @deftypefun {unsigned long int} mpn_popcount (const mp_limb_t * @var{s1p}, unsigned long int @var{size})
2416: Count the number of set bits in @{@var{s1p}, @var{size}@}.
2417: @end deftypefun
2418:
2419: @deftypefun {unsigned long int} mpn_hamdist (const mp_limb_t * @var{s1p}, const mp_limb_t * @var{s2p}, unsigned long int @var{size})
2420: Compute the hamming distance between @{@var{s1p}, @var{size}@} and
2421: @{@var{s2p}, @var{size}@}.
2422: @end deftypefun
2423:
2424: @deftypefun int mpn_perfect_square_p (const mp_limb_t * @var{s1p}, mp_size_t @var{size})
2425: Return non-zero iff @{@var{s1p}, @var{size}@} is a perfect square.
2426: @end deftypefun
2427:
2428:
2429: @node BSD Compatible Functions, Custom Allocation, Low-level Functions, Top
2430: @comment node-name, next, previous, up
2431: @chapter Berkeley MP Compatible Functions
2432: @cindex BSD MP compatible functions
2433:
2434: These functions are intended to be fully compatible with the Berkeley MP
2435: library which is available on many BSD derived U*ix systems.
2436:
2437: The original Berkeley MP library has a usage restriction: you cannot use the
2438: same variable as both source and destination in a single function call. The
2439: compatible functions in GNU MP do not share this restriction---inputs and
2440: outputs may overlap.
2441:
2442: It is not recommended that new programs are written using these functions.
2443: Apart from the incomplete set of functions, the interface for initializing
2444: @code{MINT} objects is more error prone, and the @code{pow} function collides
2445: with @code{pow} in @file{libm.a}.
2446:
2447: @cindex @file{mp.h}
2448: Include the header @file{mp.h} to get the definition of the necessary types
2449: and functions. If you are on a BSD derived system, make sure to include GNU
2450: @file{mp.h} if you are going to link the GNU @file{libmp.a} to you program.
2451: This means that you probably need to give the -I<dir> option to the compiler,
2452: where <dir> is the directory where you have GNU @file{mp.h}.
2453:
2454: @deftypefun {MINT *} itom (signed short int @var{initial_value})
2455: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
2456: Initialize the integer to @var{initial_value}. Return a pointer to the
2457: @code{MINT} object.
2458: @end deftypefun
2459:
2460: @deftypefun {MINT *} xtom (char *@var{initial_value})
2461: Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
2462: Initialize the integer from @var{initial_value}, a hexadecimal, '\0'-terminate
2463: C string. Return a pointer to the @code{MINT} object.
2464: @end deftypefun
2465:
2466: @deftypefun void move (MINT *@var{src}, MINT *@var{dest})
2467: Set @var{dest} to @var{src} by copying. Both variables must be previously
2468: initialized.
2469: @end deftypefun
2470:
2471: @deftypefun void madd (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
2472: Add @var{src_1} and @var{src_2} and put the sum in @var{destination}.
2473: @end deftypefun
2474:
2475: @deftypefun void msub (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
2476: Subtract @var{src_2} from @var{src_1} and put the difference in
2477: @var{destination}.
2478: @end deftypefun
2479:
2480: @deftypefun void mult (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
2481: Multiply @var{src_1} and @var{src_2} and put the product in
2482: @var{destination}.
2483: @end deftypefun
2484:
2485: @deftypefun void mdiv (MINT *@var{dividend}, MINT *@var{divisor}, MINT *@var{quotient}, MINT *@var{remainder})
2486: @deftypefunx void sdiv (MINT *@var{dividend}, signed short int @var{divisor}, MINT *@var{quotient}, signed short int *@var{remainder})
2487: Set @var{quotient} to @var{dividend}/@var{divisor}, and @var{remainder} to
2488: @var{dividend} mod @var{divisor}. The quotient is rounded towards zero; the
2489: remainder has the same sign as the dividend unless it is zero.
2490:
2491: Some implementations of these functions work differently---or not at all---for
2492: negative arguments.
2493: @end deftypefun
2494:
2495: @deftypefun void msqrt (MINT *@var{operand}, MINT *@var{root}, MINT *@var{remainder})
2496: @ifinfo
2497: Set @var{root} to the truncated integer part of the square root of
2498: @var{operand}. Set @var{remainder} to
2499: @var{operand}@minus{}@var{root}*@var{root},
2500: @end ifinfo
2501: @iftex
2502: @tex
2503: Set @var{root} to $\lfloor\sqrt{@var{operand}}\rfloor$, like
2504: @code{mpz_sqrt}. Set @var{remainder} to $(operand - root^2)$,
2505: @end tex
2506: @end iftex
2507: (i.e., zero if @var{operand} is a perfect square).
2508:
2509: If @var{root} and @var{remainder} are the same variable, the results are
2510: undefined.
2511: @end deftypefun
2512:
2513: @deftypefun void pow (MINT *@var{base}, MINT *@var{exp}, MINT *@var{mod}, MINT *@var{dest})
2514: Set @var{dest} to (@var{base} raised to @var{exp}) modulo @var{mod}.
2515: @end deftypefun
2516:
2517: @deftypefun void rpow (MINT *@var{base}, signed short int @var{exp}, MINT *@var{dest})
2518: Set @var{dest} to @var{base} raised to @var{exp}.
2519: @end deftypefun
2520:
2521: @deftypefun void gcd (MINT *@var{operand1}, MINT *@var{operand2}, MINT *@var{res})
2522: Set @var{res} to the greatest common divisor of @var{operand1} and
2523: @var{operand2}.
2524: @end deftypefun
2525:
2526: @deftypefun int mcmp (MINT *@var{operand1}, MINT *@var{operand2})
2527: Compare @var{operand1} and @var{operand2}. Return a positive value if
2528: @var{operand1} > @var{operand2}, zero if @var{operand1} =
2529: @var{operand2}, and a negative value if @var{operand1} < @var{operand2}.
2530: @end deftypefun
2531:
2532: @deftypefun void min (MINT *@var{dest})
2533: Input a decimal string from @code{stdin}, and put the read integer in
2534: @var{dest}. SPC and TAB are allowed in the number string, and are ignored.
2535: @end deftypefun
2536:
2537: @deftypefun void mout (MINT *@var{src})
2538: Output @var{src} to @code{stdout}, as a decimal string. Also output a newline.
2539: @end deftypefun
2540:
2541: @deftypefun {char *} mtox (MINT *@var{operand})
2542: Convert @var{operand} to a hexadecimal string, and return a pointer to the
2543: string. The returned string is allocated using the default memory allocation
2544: function, @code{malloc} by default.
2545: @end deftypefun
2546:
2547: @deftypefun void mfree (MINT *@var{operand})
2548: De-allocate, the space used by @var{operand}. @strong{This function should
2549: only be passed a value returned by @code{itom} or @code{xtom}.}
2550: @end deftypefun
2551:
2552: @node Custom Allocation, Contributors, BSD Compatible Functions, Top
2553: @comment node-name, next, previous, up
2554: @chapter Custom Allocation
2555:
2556: By default, the MP functions use @code{malloc}, @code{realloc}, and
2557: @code{free} for memory allocation. If @code{malloc} or @code{realloc} fails,
2558: the MP library terminates execution after printing a fatal error message to
2559: standard error.
2560:
2561: For some applications, you may wish to allocate memory in other ways, or you
2562: may not want to have a fatal error when there is no more memory available. To
2563: accomplish this, you can specify alternative memory allocation functions.
2564:
2565: @deftypefun void mp_set_memory_functions (@* void *(*@var{alloc_func_ptr}) (size_t), @* void *(*@var{realloc_func_ptr}) (void *, size_t, size_t), @* void (*@var{free_func_ptr}) (void *, size_t))
2566: Replace the current allocation functions from the arguments. If an argument
2567: is NULL, the corresponding default function is retained.
2568:
2569: @strong{Make sure to call this function in such a way that there are no active
2570: MP objects that were allocated using the previously active allocation
2571: function! Usually, that means that you have to call this function before any
2572: other MP function.}
2573: @end deftypefun
2574:
2575: The functions you supply should fit the following declarations:
2576:
2577: @deftypefun {void *} allocate_function (size_t @var{alloc_size})
2578: This function should return a pointer to newly allocated space with at least
2579: @var{alloc_size} storage units.
2580: @end deftypefun
2581:
2582: @deftypefun {void *} reallocate_function (void *@var{ptr}, size_t @var{old_size}, size_t @var{new_size})
2583: This function should return a pointer to newly allocated space of at least
2584: @var{new_size} storage units, after copying at least the first @var{old_size}
2585: storage units from @var{ptr}. It should also de-allocate the space at
2586: @var{ptr}.
2587:
2588: You can assume that the space at @var{ptr} was formerly returned from
2589: @code{allocate_function} or @code{reallocate_function}, for a request for
2590: @var{old_size} storage units.
2591: @end deftypefun
2592:
2593: @deftypefun void deallocate_function (void *@var{ptr}, size_t @var{size})
2594: De-allocate the space pointed to by @var{ptr}.
2595:
2596: You can assume that the space at @var{ptr} was formerly returned from
2597: @code{allocate_function} or @code{reallocate_function}, for a request for
2598: @var{size} storage units.
2599: @end deftypefun
2600:
2601: (A @dfn{storage unit} is the unit in which the @code{sizeof} operator returns
2602: the size of an object, normally an 8 bit byte.)
2603:
2604:
2605: @node Contributors, References, Custom Allocation, Top
2606: @comment node-name, next, previous, up
2607: @unnumbered Contributors
2608:
2609: I would like to thank Gunnar Sjoedin and Hans Riesel for their help with
2610: mathematical problems, Richard Stallman for his help with design issues and
2611: for revising the first version of this manual, Brian Beuning and Doug Lea for
2612: their testing of early versions of the library.
2613:
2614: John Amanatides of York University in Canada contributed the function
2615: @code{mpz_probab_prime_p}.
2616:
2617: Paul Zimmermann of Inria sparked the development of GMP 2, with his
2618: comparisons between bignum packages.
2619:
2620: Ken Weber (Kent State University, Universidade Federal do Rio Grande do Sul)
2621: contributed @code{mpz_gcd}, @code{mpz_divexact}, @code{mpn_gcd}, and
2622: @code{mpn_bdivmod}, partially supported by CNPq (Brazil) grant 301314194-2.
2623:
2624: Per Bothner of Cygnus Support helped to set up MP to use Cygnus' configure.
2625: He has also made valuable suggestions and tested numerous intermediary
2626: releases.
2627:
2628: Joachim Hollman was involved in the design of the @code{mpf} interface, and in
2629: the @code{mpz} design revisions for version 2.
2630:
2631: Bennet Yee contributed the functions @code{mpz_jacobi} and
2632: @code{mpz_legendre}.
2633:
2634: Andreas Schwab contributed the files @file{mpn/m68k/lshift.S} and
2635: @file{mpn/m68k/rshift.S}.
2636:
2637: The development of floating point functions of GNU MP 2, were supported in
2638: part by the ESPRIT-BRA (Basic Research Activities) 6846 project POSSO
2639: (POlynomial System SOlving).
2640:
2641: GNU MP 2 was finished and released by TMG Datakonsult, Sodermannagatan 5, 116
2642: 23 STOCKHOLM, SWEDEN, in cooperation with the IDA Center for Computing
2643: Sciences, USA.
2644:
2645:
2646: @node References, , Contributors, Top
2647: @comment node-name, next, previous, up
2648: @unnumbered References
2649:
2650: @itemize @bullet
2651:
2652: @item
2653: Donald E. Knuth, "The Art of Computer Programming", vol 2,
2654: "Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
2655:
2656: @item
2657: John D. Lipson, "Elements of Algebra and Algebraic Computing",
2658: The Benjamin Cummings Publishing Company Inc, 1981.
2659:
2660: @item
2661: Richard M. Stallman, "Using and Porting GCC", Free Software Foundation,
2662: 1995.
2663:
2664: @item
2665: Peter L. Montgomery, "Modular Multiplication Without Trial Division", in
2666: Mathematics of Computation, volume 44, number 170, April 1985.
2667:
2668: @item
2669: Torbjorn Granlund and Peter L. Montgomery, "Division by Invariant
2670: Integers using Multiplication", in Proceedings of the SIGPLAN
2671: PLDI'94 Conference, June 1994.
2672:
2673: @item
2674: Tudor Jebelean,
2675: "An algorithm for exact division",
2676: Journal of Symbolic Computation,
2677: v. 15, 1993, pp. 169-180.
2678:
2679: @item
2680: Kenneth Weber, "The accelerated integer GCD algorithm",
2681: ACM Transactions on Mathematical Software,
2682: v. 21 (March), 1995, pp. 111-122.
2683: @end itemize
2684:
2685: @node Concept Index, , , Top
2686: @comment node-name, next, previous, up
2687: @unnumbered Concept Index
2688: @printindex cp
2689:
2690: @node Function Index, , , Top
2691: @comment node-name, next, previous, up
2692: @unnumbered Function and Type Index
2693: @printindex fn
2694:
2695:
2696: @contents
2697: @bye
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