Math::...nt::Lib(3perl) Perl Programmers Reference GuideMath::...nt::Lib(3perl)
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 plug-in 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|[1-9]\d*)$".
CLASS->_zero()
Return an object representing the number zero.
CLASS->_one()
Return an object representing the number one.
CLASS->_two()
Return an object representing the number two.
CLASS->_ten()
Return an object representing the number ten.
CLASS->_from_bin(STR)
Return an object given a string representing a binary number. The
input has a '0b' prefix and matches the regular expression
"^0[bB](0|1[01]*)$".
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[1-7]*$".
CLASS->_from_hex(STR)
Return an object given a string representing a hexadecimal number.
The input has a '0x' prefix and matches the regular expression
"^0x(0|[1-9a-fA-F][\da-fA-F]*)$".
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 two-byte 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)
CLASS->_from_base_num(ARRAY, BASE)
Returns an object given an array of values and a base. This method
is equivalent to _from_base(), but works on numbers in an array
rather than characters in a string. Unlike _from_base(), all input
values may be arbitrarily large.
$x = $class -> _from_base_num([1, 1, 0, 1], 2) # $x is 13
$x = $class -> _from_base_num([3, 125, 39], 128) # $x is 65191
Mathematical functions
CLASS->_add(OBJ1, OBJ2)
Addition. Returns the result of adding OBJ2 to OBJ1.
CLASS->_mul(OBJ1, OBJ2)
Multiplication. Returns the result of multiplying OBJ2 and OBJ1.
CLASS->_div(OBJ1, OBJ2)
Division. In scalar context, returns the quotient after dividing
OBJ1 by OBJ2 and truncating the result to an integer. In list
context, return the quotient and the remainder.
CLASS->_sub(OBJ1, OBJ2, FLAG)
CLASS->_sub(OBJ1, OBJ2)
Subtraction. Returns the result of subtracting OBJ2 by OBJ1. If
"flag" is false or omitted, OBJ1 might be modified. If "flag" is
true, OBJ2 might be modified.
CLASS->_sadd(OBJ1, SIGN1, OBJ2, SIGN2)
Signed addition. Returns the result of adding OBJ2 with sign SIGN2
to OBJ1 with sign SIGN1.
($obj3, $sign3) = $class -> _sadd($obj1, $sign1, $obj2, $sign2);
CLASS->_ssub(OBJ1, SIGN1, OBJ2, SIGN2)
Signed subtraction. Returns the result of subtracting OBJ2 with sign
SIGN2 to OBJ1 with sign SIGN1.
($obj3, $sign3) = $class -> _sadd($obj1, $sign1, $obj2, $sign2);
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,...,OBJ2-1 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->_ilog2(OBJ)
Returns the base 2 logarithm of OBJ rounded downwards to the nearest
integer, i.e., "int(log2(OBJ))". In list context, this method
returns 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.
This method is equivalent to the more general method _log_int() when
it is used with base 2 argument, but _ilog2() method might be
faster.
CLASS->_ilog10(OBJ)
Returns the base 10 logarithm of OBJ rounded downwards to the
nearest integer, i.e., "int(log2(OBJ))". In list context, this
method returns 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.
This method is equivalent to the more general method _log_int() when
it is used with base 10 argument, but _ilog10() method might be
faster.
Also, the output from _ilog10() is always 1 smaller than the output
from _len().
CLASS->_clog2(OBJ)
Returns the base 2 logarithm of OBJ rounded upwards to the nearest
integer, i.e., "ceil(log2(OBJ))". In list context, this method
returns 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->_clog10(OBJ)
Returns the base 10 logarithm of OBJ rounded upnwards to the nearest
integer, i.e., "ceil(log2(OBJ))". In list context, this method
returns 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|[1-9]\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 two-byte 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->_to_base_num(OBJ, BASE)
Converts the given number to the given base. This method is
equivalent to _to_base(), but returns numbers in an array rather
than characters in a string. In the output, the first element is the
most significant. Unlike _to_base(), all input values may be
arbitrarily large.
$x = $class -> _to_base_num(13, 2) # $x is [1, 1, 0, 1]
$x = $class -> _to_base_num(65191, 128) # $x is [3, 125, 39]
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 "bug-math-bigint at
rt.cpan.org", or through the web interface at
<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (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:
• GitHub Source Repository
<https://github.com/pjacklam/p5-Math-BigInt>
• RT: CPAN's request tracker
<https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt>
• MetaCPAN
<https://metacpan.org/release/Math-BigInt>
• CPAN Testers Matrix
<http://matrix.cpantesters.org/?dist=Math-BigInt>
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@gmail.com>
Code and documentation based on the Math::BigInt::Calc module by Tels
<nospam-abuse@bloodgate.com>
SEE ALSO
Math::BigInt, Math::BigInt::Calc, Math::BigInt::GMP,
Math::BigInt::FastCalc and Math::BigInt::Pari.
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