1Math::BigInt::Lib(3) User Contributed Perl Documentation Math::BigInt::Lib(3)
2
6 Math::BigInt::Lib - virtual parent class for Math::BigInt libraries
7
9 # In the backend library for Math::BigInt et al.
10 package Math::BigInt::MyBackend;
12 use Math::BigInt::lib;
14 our @ISA = qw< Math::BigInt::lib >;
15 sub _new { ... }
17 sub _str { ... }
18 sub _add { ... }
19 str _sub { ... }
20 ...
21 # In your main program.
23 use Math::BigInt lib => 'MyBackend';
25
27 This module provides support for big integer calculations. It is not
28 intended to be used directly, but rather as a parent class for backend
29 libraries used by Math::BigInt, Math::BigFloat, Math::BigRat, and
30 related modules.
31 Other backend libraries include Math::BigInt::Calc,
33 Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.
34 In order to allow for multiple big integer libraries, Math::BigInt was
36 rewritten to use a plug-in library for core math routines. Any module
37 which conforms to the API can be used by Math::BigInt by using this in
38 your program:
39 use Math::BigInt lib => 'libname';
41 'libname' is either the long name, like 'Math::BigInt::Pari', or only
43 the short version, like 'Pari'.
44 General Notes
46 A library only needs to deal with unsigned big integers. Testing of
47 input parameter validity is done by the caller, so there is no need to
48 worry about underflow (e.g., in "_sub()" and "_dec()") or about
49 division by zero (e.g., in "_div()" and "_mod()")) or similar cases.
50 Some libraries use methods that don't modify their argument, and some
52 libraries don't even use objects, but rather unblessed references.
53 Because of this, liberary methods are always called as class methods,
54 not instance methods:
55 $x = Class -> method($x, $y); # like this
57 $x = $x -> method($y); # not like this ...
58 $x -> method($y); # ... or like this
59 And with boolean methods
61 $bool = Class -> method($x, $y); # like this
63 $bool = $x -> method($y); # not like this
64 Return values are always objects, strings, Perl scalars, or true/false
66 for comparison routines.
67 API version
69 CLASS->api_version()
71 Return API version as a Perl scalar, 1 for Math::BigInt v1.70, 2
72 for Math::BigInt v1.83.
73 This method is no longer used. Methods that are not implemented by
75 a subclass will be inherited from this class.
76 Constructors
78 The following methods are mandatory: _new(), _str(), _add(), and
80 _sub(). However, computations will be very slow without _mul() and
81 _div().
82 CLASS->_new(STR)
84 Convert a string representing an unsigned decimal number to an
85 object representing the same number. The input is normalized, i.e.,
86 it matches "^(0|[1-9]\d*)$".
87 CLASS->_zero()
89 Return an object representing the number zero.
90 CLASS->_one()
92 Return an object representing the number one.
93 CLASS->_two()
95 Return an object representing the number two.
96 CLASS->_ten()
98 Return an object representing the number ten.
99 CLASS->_from_bin(STR)
101 Return an object given a string representing a binary number. The
102 input has a '0b' prefix and matches the regular expression
103 "^0[bB](0|1[01]*)$".
104 CLASS->_from_oct(STR)
106 Return an object given a string representing an octal number. The
107 input has a '0' prefix and matches the regular expression
108 "^0[1-7]*$".
109 CLASS->_from_hex(STR)
111 Return an object given a string representing a hexadecimal number.
112 The input has a '0x' prefix and matches the regular expression
113 "^0x(0|[1-9a-fA-F][\da-fA-F]*)$".
114 CLASS->_from_bytes(STR)
116 Returns an object given a byte string representing the number. The
117 byte string is in big endian byte order, so the two-byte input
118 string "\x01\x00" should give an output value representing the
119 number 256.
120 Mathematical functions
122 CLASS->_add(OBJ1, OBJ2)
124 Returns the result of adding OBJ2 to OBJ1.
125 CLASS->_mul(OBJ1, OBJ2)
127 Returns the result of multiplying OBJ2 and OBJ1.
128 CLASS->_div(OBJ1, OBJ2)
130 In scalar context, returns the quotient after dividing OBJ1 by OBJ2
131 and truncating the result to an integer. In list context, return
132 the quotient and the remainder.
133 CLASS->_sub(OBJ1, OBJ2, FLAG)
135 CLASS->_sub(OBJ1, OBJ2)
136 Returns the result of subtracting OBJ2 by OBJ1. If "flag" is false
137 or omitted, OBJ1 might be modified. If "flag" is true, OBJ2 might
138 be modified.
139 CLASS->_dec(OBJ)
141 Returns the result after decrementing OBJ by one.
142 CLASS->_inc(OBJ)
144 Returns the result after incrementing OBJ by one.
145 CLASS->_mod(OBJ1, OBJ2)
147 Returns OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1
148 by OBJ2.
149 CLASS->_sqrt(OBJ)
151 Returns the square root of OBJ, truncated to an integer.
152 CLASS->_root(OBJ, N)
154 Returns the Nth root of OBJ, truncated to an integer.
155 CLASS->_fac(OBJ)
157 Returns the factorial of OBJ, i.e., the product of all positive
158 integers up to and including OBJ.
159 CLASS->_dfac(OBJ)
161 Returns the double factorial of OBJ. If OBJ is an even integer,
162 returns the product of all positive, even integers up to and
163 including OBJ, i.e., 2*4*6*...*OBJ. If OBJ is an odd integer,
164 returns the product of all positive, odd integers, i.e.,
165 1*3*5*...*OBJ.
166 CLASS->_pow(OBJ1, OBJ2)
168 Returns OBJ1 raised to the power of OBJ2. By convention, 0**0 = 1.
169 CLASS->_modinv(OBJ1, OBJ2)
171 Returns the modular multiplicative inverse, i.e., return OBJ3 so
172 that
173 (OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2
175 The result is returned as two arguments. If the modular
177 multiplicative inverse does not exist, both arguments are
178 undefined. Otherwise, the arguments are a number (object) and its
179 sign ("+" or "-").
180 The output value, with its sign, must either be a positive value in
182 the range 1,2,...,OBJ2-1 or the same value subtracted OBJ2. For
183 instance, if the input arguments are objects representing the
184 numbers 7 and 5, the method must either return an object
185 representing the number 3 and a "+" sign, since (3*7) % 5 = 1 % 5,
186 or an object representing the number 2 and a "-" sign, since (-2*7)
187 % 5 = 1 % 5.
188 CLASS->_modpow(OBJ1, OBJ2, OBJ3)
190 Returns the modular exponentiation, i.e., (OBJ1 ** OBJ2) % OBJ3.
191 CLASS->_rsft(OBJ, N, B)
193 Returns the result after shifting OBJ N digits to thee right in
194 base B. This is equivalent to performing integer division by B**N
195 and discarding the remainder, except that it might be much faster.
196 For instance, if the object $obj represents the hexadecimal number
198 0xabcde, then "_rsft($obj, 2, 16)" returns an object representing
199 the number 0xabc. The "remainer", 0xde, is discarded and not
200 returned.
201 CLASS->_lsft(OBJ, N, B)
203 Returns the result after shifting OBJ N digits to the left in base
204 B. This is equivalent to multiplying by B**N, except that it might
205 be much faster.
206 CLASS->_log_int(OBJ, B)
208 Returns the logarithm of OBJ to base BASE truncted to an integer.
209 This method has two output arguments, the OBJECT and a STATUS. The
210 STATUS is Perl scalar; it is 1 if OBJ is the exact result, 0 if the
211 result was truncted to give OBJ, and undef if it is unknown whether
212 OBJ is the exact result.
213 CLASS->_gcd(OBJ1, OBJ2)
215 Returns the greatest common divisor of OBJ1 and OBJ2.
216 CLASS->_lcm(OBJ1, OBJ2)
218 Return the least common multiple of OBJ1 and OBJ2.
219 CLASS->_fib(OBJ)
221 In scalar context, returns the nth Fibonacci number: _fib(0)
222 returns 0, _fib(1) returns 1, _fib(2) returns 1, _fib(3) returns 2
223 etc. In list context, returns the Fibonacci numbers from F(0) to
224 F(n): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
225 CLASS->_lucas(OBJ)
227 In scalar context, returns the nth Lucas number: _lucas(0) returns
228 2, _lucas(1) returns 1, _lucas(2) returns 3, etc. In list context,
229 returns the Lucas numbers from L(0) to L(n): 2, 1, 3, 4, 7, 11, 18,
230 29,47, 76, ...
231 Bitwise operators
233 CLASS->_and(OBJ1, OBJ2)
235 Returns bitwise and.
236 CLASS->_or(OBJ1, OBJ2)
238 Return bitwise or.
239 CLASS->_xor(OBJ1, OBJ2)
241 Return bitwise exclusive or.
242 Boolean operators
244 CLASS->_is_zero(OBJ)
246 Returns a true value if OBJ is zero, and false value otherwise.
247 CLASS->_is_one(OBJ)
249 Returns a true value if OBJ is one, and false value otherwise.
250 CLASS->_is_two(OBJ)
252 Returns a true value if OBJ is two, and false value otherwise.
253 CLASS->_is_ten(OBJ)
255 Returns a true value if OBJ is ten, and false value otherwise.
256 CLASS->_is_even(OBJ)
258 Return a true value if OBJ is an even integer, and a false value
259 otherwise.
260 CLASS->_is_odd(OBJ)
262 Return a true value if OBJ is an even integer, and a false value
263 otherwise.
264 CLASS->_acmp(OBJ1, OBJ2)
266 Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is
267 numerically less than, equal to, or larger than OBJ2, respectively.
268 String conversion
270 CLASS->_str(OBJ)
272 Returns a string representing OBJ in decimal notation. The returned
273 string should have no leading zeros, i.e., it should match
274 "^(0|[1-9]\d*)$".
275 CLASS->_to_bin(OBJ)
277 Returns the binary string representation of OBJ.
278 CLASS->_to_oct(OBJ)
280 Returns the octal string representation of the number.
281 CLASS->_to_hex(OBJ)
283 Returns the hexadecimal string representation of the number.
284 CLASS->_to_bytes(OBJ)
286 Returns a byte string representation of OBJ. The byte string is in
287 big endian byte order, so if OBJ represents the number 256, the
288 output should be the two-byte string "\x01\x00".
289 CLASS->_as_bin(OBJ)
291 Like "_to_bin()" but with a '0b' prefix.
292 CLASS->_as_oct(OBJ)
294 Like "_to_oct()" but with a '0' prefix.
295 CLASS->_as_hex(OBJ)
297 Like "_to_hex()" but with a '0x' prefix.
298 CLASS->_as_bytes(OBJ)
300 This is an alias to "_to_bytes()".
301 Numeric conversion
303 CLASS->_num(OBJ)
305 Returns a Perl scalar number representing the number OBJ as close
306 as possible. Since Perl scalars have limited precision, the
307 returned value might not be exactly the same as OBJ.
308 Miscellaneous
310 CLASS->_copy(OBJ)
312 Returns a true copy OBJ.
313 CLASS->_len(OBJ)
315 Returns the number of the decimal digits in OBJ. The output is a
316 Perl scalar.
317 CLASS->_zeros(OBJ)
319 Returns the number of trailing decimal zeros. The output is a Perl
320 scalar. The number zero has no trailing decimal zeros.
321 CLASS->_digit(OBJ, N)
323 Returns the Nth digit in OBJ as a Perl scalar. N is a Perl scalar,
324 where zero refers to the rightmost (least significant) digit, and
325 negative values count from the left (most significant digit). If
326 $obj represents the number 123, then
327 CLASS->_digit($obj, 0) # returns 3
329 CLASS->_digit($obj, 1) # returns 2
330 CLASS->_digit($obj, 2) # returns 1
331 CLASS->_digit($obj, -1) # returns 1
332 CLASS->_check(OBJ)
334 Returns true if the object is invalid and false otherwise.
335 Preferably, the true value is a string describing the problem with
336 the object. This is a check routine to test the internal state of
337 the object for corruption.
338 CLASS->_set(OBJ)
340 xxx
341 API version 2
343 The following methods are required for an API version of 2 or greater.
344 Constructors
346 CLASS->_1ex(N)
348 Return an object representing the number 10**N where N >= 0 is a
349 Perl scalar.
350 Mathematical functions
352 CLASS->_nok(OBJ1, OBJ2)
354 Return the binomial coefficient OBJ1 over OBJ1.
355 Miscellaneous
357 CLASS->_alen(OBJ)
359 Return the approximate number of decimal digits of the object. The
360 output is a Perl scalar.
361 API optional methods
363 The following methods are optional, and can be defined if the
364 underlying lib has a fast way to do them. If undefined, Math::BigInt
365 will use pure Perl (hence slow) fallback routines to emulate these:
366 Signed bitwise operators.
368 CLASS->_signed_or(OBJ1, OBJ2, SIGN1, SIGN2)
370 Return the signed bitwise or.
371 CLASS->_signed_and(OBJ1, OBJ2, SIGN1, SIGN2)
373 Return the signed bitwise and.
374 CLASS->_signed_xor(OBJ1, OBJ2, SIGN1, SIGN2)
376 Return the signed bitwise exclusive or.
377
379 If you want to port your own favourite C library for big numbers to the
380 Math::BigInt interface, you can take any of the already existing
381 modules as a rough guideline. You should really wrap up the latest
382 Math::BigInt and Math::BigFloat testsuites with your module, and
383 replace in them any of the following:
384 use Math::BigInt;
386 by this:
388 use Math::BigInt lib => 'yourlib';
390 This way you ensure that your library really works 100% within
392 Math::BigInt.
393
395 Please report any bugs or feature requests to "bug-math-bigint at
396 rt.cpan.org", or through the web interface at
397 <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (requires
398 login). We will be notified, and then you'll automatically be notified
399 of progress on your bug as I make changes.
400
402 You can find documentation for this module with the perldoc command.
403 perldoc Math::BigInt::Calc
405 You can also look for information at:
407 · RT: CPAN's request tracker
409 <https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt>
411 · AnnoCPAN: Annotated CPAN documentation
413 <http://annocpan.org/dist/Math-BigInt>
415 · CPAN Ratings
417 <http://cpanratings.perl.org/dist/Math-BigInt>
419 · Search CPAN
421 <http://search.cpan.org/dist/Math-BigInt/>
423 · CPAN Testers Matrix
425 <http://matrix.cpantesters.org/?dist=Math-BigInt>
427 · The Bignum mailing list
429 · Post to mailing list
431 "bignum at lists.scsys.co.uk"
433 · View mailing list
435 <http://lists.scsys.co.uk/pipermail/bignum/>
437 · Subscribe/Unsubscribe
439 <http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>
441
443 This program is free software; you may redistribute it and/or modify it
444 under the same terms as Perl itself.
445
447 Peter John Acklam, <pjacklam@online.no>
448 Code and documentation based on the Math::BigInt::Calc module by Tels
450 <nospam-abuse@bloodgate.com>
451
453 Math::BigInt, Math::BigInt::Calc, Math::BigInt::GMP,
454 Math::BigInt::FastCalc and Math::BigInt::Pari.
455perl v5.26.3 2017-03-15 Math::BigInt::Lib(3)