Math::BigInt::Lib
Section: User Contributed Perl Documentation (3)
Updated: 20200728
Page Index
NAME
Math::BigInt::Lib  virtual parent class for Math::BigInt libraries
SYNOPSIS
# In the backend library for Math::BigInt et al.
package Math::BigInt::MyBackend;
use Math::BigInt::lib;
our @ISA = qw< Math::BigInt::lib >;
sub _new { ... }
sub _str { ... }
sub _add { ... }
str _sub { ... }
...
# In your main program.
use Math::BigInt lib => 'MyBackend';
DESCRIPTION
This module provides support for big integer calculations. It is not intended
to be used directly, but rather as a parent class for backend libraries used by
Math::BigInt, Math::BigFloat, Math::BigRat, and related modules.
Other backend libraries include Math::BigInt::Calc, Math::BigInt::FastCalc,
Math::BigInt::GMP, and Math::BigInt::Pari.
In order to allow for multiple big integer libraries, Math::BigInt was
rewritten to use a plugin library for core math routines. Any module which
conforms to the API can be used by Math::BigInt by using this in your program:
use Math::BigInt lib => 'libname';
'libname' is either the long name, like 'Math::BigInt::Pari', or only the short
version, like 'Pari'.
General Notes
A library only needs to deal with unsigned big integers. Testing of input
parameter validity is done by the caller, so there is no need to worry about
underflow (e.g., in
"_sub()" and
"_dec()") or about division by zero (e.g.,
in
"_div()" and
"_mod()")) or similar cases.
Some libraries use methods that don't modify their argument, and some libraries
don't even use objects, but rather unblessed references. Because of this,
liberary methods are always called as class methods, not instance methods:
$x = Class > method($x, $y); # like this
$x = $x > method($y); # not like this ...
$x > method($y); # ... or like this
And with boolean methods
$bool = Class > method($x, $y); # like this
$bool = $x > method($y); # not like this
Return values are always objects, strings, Perl scalars, or true/false for
comparison routines.
API version
 CLASS>api_version()

This method is no longer used and can be omitted. Methods that are not
implemented by a subclass will be inherited from this class.
Constructors
The following methods are mandatory: _new(), _str(), _add(), and _sub().
However, computations will be very slow without _mul() and _div().
 CLASS>_new(STR)

Convert a string representing an unsigned decimal number to an object
representing the same number. The input is normalized, i.e., it matches
"^(0[19]\d*)$".
 CLASS>_zero()

Return an object representing the number zero.
 CLASS>_one()

Return an object representing the number one.
 CLASS>_two()

Return an object representing the number two.
 CLASS>_ten()

Return an object representing the number ten.
 CLASS>_from_bin(STR)

Return an object given a string representing a binary number. The input has a
'0b' prefix and matches the regular expression "^0[bB](01[01]*)$".
 CLASS>_from_oct(STR)

Return an object given a string representing an octal number. The input has a
'0' prefix and matches the regular expression "^0[17]*$".
 CLASS>_from_hex(STR)

Return an object given a string representing a hexadecimal number. The input
has a '0x' prefix and matches the regular expression
"^0x(0[19afAF][\dafAF]*)$".
 CLASS>_from_bytes(STR)

Returns an object given a byte string representing the number. The byte string
is in big endian byte order, so the twobyte input string ``\x01\x00'' should
give an output value representing the number 256.
 CLASS>_from_base(STR, BASE, COLLSEQ)

Returns an object given a string STR, a base BASE, and a collation sequence
COLLSEQ. Each character in STR represents a numerical value identical to the
character's position in COLLSEQ. All characters in STR must be present in
COLLSEQ.
If BASE is less than or equal to 94, and a collation sequence is not specified,
the following default collation sequence is used. It contains of all the 94
printable ASCII characters except space/blank:
0123456789 # ASCII 48 to 57
ABCDEFGHIJKLMNOPQRSTUVWXYZ # ASCII 65 to 90
abcdefghijklmnopqrstuvwxyz # ASCII 97 to 122
!"#$%&'()*+,./ # ASCII 33 to 47
:;<=>?@ # ASCII 58 to 64
[\]^_` # ASCII 91 to 96
{}~ # ASCII 123 to 126
If the default collation sequence is used, and the BASE is less than or equal
to 36, the letter case in STR is ignored.
For instance, with base 3 and collation sequence ``/'', the character ``''
represents 0, ``/'' represents 1, and ``'' represents 2. So if STR is ``/'', the
output is 1 * 3**2 + 2 * 3**1 + 0 * 3**0 = 15.
The following examples show standard binary, octal, decimal, and hexadecimal
conversion. All examples return 250.
$x = $class > _from_base("11111010", 2)
$x = $class > _from_base("372", 8)
$x = $class > _from_base("250", 10)
$x = $class > _from_base("FA", 16)
Some more examples, all returning 250:
$x = $class > _from_base("100021", 3)
$x = $class > _from_base("3322", 4)
$x = $class > _from_base("2000", 5)
$x = $class > _from_base("caaa", 5, "abcde")
$x = $class > _from_base("42", 62)
$x = $class > _from_base("2!", 94)
Mathematical functions
 CLASS>_add(OBJ1, OBJ2)

Returns the result of adding OBJ2 to OBJ1.
 CLASS>_mul(OBJ1, OBJ2)

Returns the result of multiplying OBJ2 and OBJ1.
 CLASS>_div(OBJ1, OBJ2)

In scalar context, returns the quotient after dividing OBJ1 by OBJ2 and
truncating the result to an integer. In list context, return the quotient and
the remainder.
 CLASS>_sub(OBJ1, OBJ2, FLAG)

 CLASS>_sub(OBJ1, OBJ2)

Returns the result of subtracting OBJ2 by OBJ1. If "flag" is false or omitted,
OBJ1 might be modified. If "flag" is true, OBJ2 might be modified.
 CLASS>_dec(OBJ)

Returns the result after decrementing OBJ by one.
 CLASS>_inc(OBJ)

Returns the result after incrementing OBJ by one.
 CLASS>_mod(OBJ1, OBJ2)

Returns OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by OBJ2.
 CLASS>_sqrt(OBJ)

Returns the square root of OBJ, truncated to an integer.
 CLASS>_root(OBJ, N)

Returns the Nth root of OBJ, truncated to an integer.
 CLASS>_fac(OBJ)

Returns the factorial of OBJ, i.e., the product of all positive integers up to
and including OBJ.
 CLASS>_dfac(OBJ)

Returns the double factorial of OBJ. If OBJ is an even integer, returns the
product of all positive, even integers up to and including OBJ, i.e.,
2*4*6*...*OBJ. If OBJ is an odd integer, returns the product of all positive,
odd integers, i.e., 1*3*5*...*OBJ.
 CLASS>_pow(OBJ1, OBJ2)

Returns OBJ1 raised to the power of OBJ2. By convention, 0**0 = 1.
 CLASS>_modinv(OBJ1, OBJ2)

Returns the modular multiplicative inverse, i.e., return OBJ3 so that
(OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2
The result is returned as two arguments. If the modular multiplicative inverse
does not exist, both arguments are undefined. Otherwise, the arguments are a
number (object) and its sign (``+'' or ``'').
The output value, with its sign, must either be a positive value in the range
1,2,...,OBJ21 or the same value subtracted OBJ2. For instance, if the input
arguments are objects representing the numbers 7 and 5, the method must either
return an object representing the number 3 and a ``+'' sign, since (3*7) % 5 = 1
% 5, or an object representing the number 2 and a ``'' sign, since (2*7) % 5 = 1
% 5.
 CLASS>_modpow(OBJ1, OBJ2, OBJ3)

Returns the modular exponentiation, i.e., (OBJ1 ** OBJ2) % OBJ3.
 CLASS>_rsft(OBJ, N, B)

Returns the result after shifting OBJ N digits to thee right in base B. This is
equivalent to performing integer division by B**N and discarding the remainder,
except that it might be much faster.
For instance, if the object $obj represents the hexadecimal number 0xabcde,
then "_rsft($obj, 2, 16)" returns an object representing the number 0xabc. The
``remainer'', 0xde, is discarded and not returned.
 CLASS>_lsft(OBJ, N, B)

Returns the result after shifting OBJ N digits to the left in base B. This is
equivalent to multiplying by B**N, except that it might be much faster.
 CLASS>_log_int(OBJ, B)

Returns the logarithm of OBJ to base BASE truncted to an integer. This method
has two output arguments, the OBJECT and a STATUS. The STATUS is Perl scalar;
it is 1 if OBJ is the exact result, 0 if the result was truncted to give OBJ,
and undef if it is unknown whether OBJ is the exact result.
 CLASS>_gcd(OBJ1, OBJ2)

Returns the greatest common divisor of OBJ1 and OBJ2.
 CLASS>_lcm(OBJ1, OBJ2)

Return the least common multiple of OBJ1 and OBJ2.
 CLASS>_fib(OBJ)

In scalar context, returns the nth Fibonacci number: _fib(0) returns 0, _fib(1)
returns 1, _fib(2) returns 1, _fib(3) returns 2 etc. In list context, returns
the Fibonacci numbers from F(0) to F(n): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
 CLASS>_lucas(OBJ)

In scalar context, returns the nth Lucas number: _lucas(0) returns 2, _lucas(1)
returns 1, _lucas(2) returns 3, etc. In list context, returns the Lucas numbers
from L(0) to L(n): 2, 1, 3, 4, 7, 11, 18, 29,47, 76, ...
Bitwise operators
 CLASS>_and(OBJ1, OBJ2)

Returns bitwise and.
 CLASS>_or(OBJ1, OBJ2)

Returns bitwise or.
 CLASS>_xor(OBJ1, OBJ2)

Returns bitwise exclusive or.
 CLASS>_sand(OBJ1, OBJ2, SIGN1, SIGN2)

Returns bitwise signed and.
 CLASS>_sor(OBJ1, OBJ2, SIGN1, SIGN2)

Returns bitwise signed or.
 CLASS>_sxor(OBJ1, OBJ2, SIGN1, SIGN2)

Returns bitwise signed exclusive or.
Boolean operators
 CLASS>_is_zero(OBJ)

Returns a true value if OBJ is zero, and false value otherwise.
 CLASS>_is_one(OBJ)

Returns a true value if OBJ is one, and false value otherwise.
 CLASS>_is_two(OBJ)

Returns a true value if OBJ is two, and false value otherwise.
 CLASS>_is_ten(OBJ)

Returns a true value if OBJ is ten, and false value otherwise.
 CLASS>_is_even(OBJ)

Return a true value if OBJ is an even integer, and a false value otherwise.
 CLASS>_is_odd(OBJ)

Return a true value if OBJ is an even integer, and a false value otherwise.
 CLASS>_acmp(OBJ1, OBJ2)

Compare OBJ1 and OBJ2 and return 1, 0, or 1, if OBJ1 is numerically less than,
equal to, or larger than OBJ2, respectively.
String conversion
 CLASS>_str(OBJ)

Returns a string representing OBJ in decimal notation. The returned string
should have no leading zeros, i.e., it should match "^(0[19]\d*)$".
 CLASS>_to_bin(OBJ)

Returns the binary string representation of OBJ.
 CLASS>_to_oct(OBJ)

Returns the octal string representation of the number.
 CLASS>_to_hex(OBJ)

Returns the hexadecimal string representation of the number.
 CLASS>_to_bytes(OBJ)

Returns a byte string representation of OBJ. The byte string is in big endian
byte order, so if OBJ represents the number 256, the output should be the
twobyte string ``\x01\x00''.
 CLASS>_to_base(OBJ, BASE, COLLSEQ)

Returns a string representation of OBJ in base BASE with collation sequence
COLLSEQ.
$val = $class > _new("210");
$str = $class > _to_base($val, 10, "xyz") # $str is "zyx"
$val = $class > _new("32");
$str = $class > _to_base($val, 2, "") # $str is ""
See _from_base() for more information.
 CLASS>_as_bin(OBJ)

Like "_to_bin()" but with a '0b' prefix.
 CLASS>_as_oct(OBJ)

Like "_to_oct()" but with a '0' prefix.
 CLASS>_as_hex(OBJ)

Like "_to_hex()" but with a '0x' prefix.
 CLASS>_as_bytes(OBJ)

This is an alias to "_to_bytes()".
Numeric conversion
 CLASS>_num(OBJ)

Returns a Perl scalar number representing the number OBJ as close as
possible. Since Perl scalars have limited precision, the returned value might
not be exactly the same as OBJ.
Miscellaneous
 CLASS>_copy(OBJ)

Returns a true copy OBJ.
 CLASS>_len(OBJ)

Returns the number of the decimal digits in OBJ. The output is a Perl scalar.
 CLASS>_zeros(OBJ)

Returns the number of trailing decimal zeros. The output is a Perl scalar. The
number zero has no trailing decimal zeros.
 CLASS>_digit(OBJ, N)

Returns the Nth digit in OBJ as a Perl scalar. N is a Perl scalar, where zero
refers to the rightmost (least significant) digit, and negative values count
from the left (most significant digit). If $obj represents the number 123, then
CLASS>_digit($obj, 0) # returns 3
CLASS>_digit($obj, 1) # returns 2
CLASS>_digit($obj, 2) # returns 1
CLASS>_digit($obj, 1) # returns 1
 CLASS>_digitsum(OBJ)

Returns the sum of the base 10 digits.
 CLASS>_check(OBJ)

Returns true if the object is invalid and false otherwise. Preferably, the true
value is a string describing the problem with the object. This is a check
routine to test the internal state of the object for corruption.
 CLASS>_set(OBJ)

xxx
API version 2
The following methods are required for an
API version of 2 or greater.
Constructors
 CLASS>_1ex(N)

Return an object representing the number 10**N where N >= 0 is a Perl
scalar.
Mathematical functions
 CLASS>_nok(OBJ1, OBJ2)

Return the binomial coefficient OBJ1 over OBJ1.
Miscellaneous
 CLASS>_alen(OBJ)

Return the approximate number of decimal digits of the object. The output is a
Perl scalar.
WRAP YOUR OWN
If you want to port your own favourite C library for big numbers to the
Math::BigInt interface, you can take any of the already existing modules as a
rough guideline. You should really wrap up the latest Math::BigInt and
Math::BigFloat testsuites with your module, and replace in them any of the
following:
use Math::BigInt;
by this:
use Math::BigInt lib => 'yourlib';
This way you ensure that your library really works 100% within Math::BigInt.
BUGS
Please report any bugs or feature requests to
"bugmathbigint at rt.cpan.org", or through the web interface at
<
https://rt.cpan.org/Ticket/Create.html?Queue=MathBigInt>
(requires login).
We will be notified, and then you'll automatically be notified of progress on
your bug as I make changes.
SUPPORT
You can find documentation for this module with the perldoc command.
perldoc Math::BigInt::Calc
You can also look for information at:
 •

RT: CPAN's request tracker
<https://rt.cpan.org/Public/Dist/Display.html?Name=MathBigInt>
 •

AnnoCPAN: Annotated CPAN documentation
<http://annocpan.org/dist/MathBigInt>
 •

CPAN Ratings
<https://cpanratings.perl.org/dist/MathBigInt>
 •

MetaCPAN
<https://metacpan.org/release/MathBigInt>
 •

CPAN Testers Matrix
<http://matrix.cpantesters.org/?dist=MathBigInt>
 •

The Bignum mailing list

 •

Post to mailing list
"bignum at lists.scsys.co.uk"
 •

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<http://lists.scsys.co.uk/pipermail/bignum/>
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LICENSE
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
AUTHOR
Peter John Acklam, <
pjacklam@online.no>
Code and documentation based on the Math::BigInt::Calc module by Tels
<nospamabuse@bloodgate.com>
SEE ALSO
Math::BigInt, Math::BigInt::Calc, Math::BigInt::GMP,
Math::BigInt::FastCalc and Math::BigInt::Pari.