Math::BigInt::Calc(3pm)Perl Programmers Reference GuideMath::BigInt::Calc(3pm)
NAME
Math::BigInt::Calc - Pure Perl module to support Math::BigInt
SYNOPSIS
This library provides support for big integer calculations. It is not
intended to be used by other modules. Other modules which support the
same API (see below) can also be used to support Math::BigInt, like
Math::BigInt::GMP and Math::BigInt::Pari.
DESCRIPTION
In this library, the numbers are represented in base B = 10**N, where N
is the largest possible value that does not cause overflow in the
intermediate computations. The base B elements are stored in an array,
with the least significant element stored in array element zero. There
are no leading zero elements, except a single zero element when the
number is zero.
For instance, if B = 10000, the number 1234567890 is represented
internally as [3456, 7890, 12].
THE Math::BigInt API
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()") nor about
division by zero (e.g., in "_div()") or similar cases.
For some methods, the first parameter can be modified. That includes
the possibility that you return a reference to a completely different
object instead. Although keeping the reference and just changing its
contents is preferred over creating and returning a different
reference.
Return values are always objects, strings, Perl scalars, or true/false
for comparison routines.
API version 1
The following methods must be defined in order to support the use by
Math::BigInt v1.70 or later.
API version
api_version()
Return API version as a Perl scalar, 1 for Math::BigInt v1.70, 2
for Math::BigInt v1.83.
Constructors
_new(STR)
Convert a string representing an unsigned decimal number to an
object representing the same number. The input is normalize, i.e.,
it matches "^(0|[1-9]\d*)$".
_zero()
Return an object representing the number zero.
_one()
Return an object representing the number one.
_two()
Return an object representing the number two.
_ten()
Return an object representing the number ten.
_from_bin(STR)
Return an object given a string representing a binary number. The
input has a '0b' prefix and matches the regular expression
"^0[bB](0|1[01]*)$".
_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]*$".
_from_hex(STR)
Return an object given a string representing a hexadecimal number.
The input has a '0x' prefix and matches the regular expression
"^0x(0|[1-9a-fA-F][\da-fA-F]*)$".
Mathematical functions
Each of these methods may modify the first input argument, except
_bgcd(), which shall not modify any input argument, and _sub() which
may modify the second input argument.
_add(OBJ1, OBJ2)
Returns the result of adding OBJ2 to OBJ1.
_mul(OBJ1, OBJ2)
Returns the result of multiplying OBJ2 and OBJ1.
_div(OBJ1, OBJ2)
Returns the result of dividing OBJ1 by OBJ2 and truncating the
result to an integer.
_sub(OBJ1, OBJ2, FLAG)
_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.
_dec(OBJ)
Decrement OBJ by one.
_inc(OBJ)
Increment OBJ by one.
_mod(OBJ1, OBJ2)
Return OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by
OBJ2.
_sqrt(OBJ)
Return the square root of the object, truncated to integer.
_root(OBJ, N)
Return Nth root of the object, truncated to int. N is >= 3.
_fac(OBJ)
Return factorial of object (1*2*3*4*...).
_pow(OBJ1, OBJ2)
Return OBJ1 to the power of OBJ2. By convention, 0**0 = 1.
_modinv(OBJ1, OBJ2)
Return 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 "-" sign, since (-2*7) %
5 = 1 % 5.
_modpow(OBJ1, OBJ2, OBJ3)
Return modular exponentiation, (OBJ1 ** OBJ2) % OBJ3.
_rsft(OBJ, N, B)
Shift object N digits right in base B and return the resulting
object. This is equivalent to performing integer division by B**N
and discarding the remainder, except that it might be much faster,
depending on how the number is represented internally.
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.
_lsft(OBJ, N, B)
Shift the object N digits left in base B. This is equivalent to
multiplying by B**N, except that it might be much faster, depending
on how the number is represented internally.
_log_int(OBJ, B)
Return integer log of OBJ to base BASE. 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.
_gcd(OBJ1, OBJ2)
Return the greatest common divisor of OBJ1 and OBJ2.
Bitwise operators
Each of these methods may modify the first input argument.
_and(OBJ1, OBJ2)
Return bitwise and. If necessary, the smallest number is padded
with leading zeros.
_or(OBJ1, OBJ2)
Return bitwise or. If necessary, the smallest number is padded with
leading zeros.
_xor(OBJ1, OBJ2)
Return bitwise exclusive or. If necessary, the smallest number is
padded with leading zeros.
Boolean operators
_is_zero(OBJ)
Returns a true value if OBJ is zero, and false value otherwise.
_is_one(OBJ)
Returns a true value if OBJ is one, and false value otherwise.
_is_two(OBJ)
Returns a true value if OBJ is two, and false value otherwise.
_is_ten(OBJ)
Returns a true value if OBJ is ten, and false value otherwise.
_is_even(OBJ)
Return a true value if OBJ is an even integer, and a false value
otherwise.
_is_odd(OBJ)
Return a true value if OBJ is an even integer, and a false value
otherwise.
_acmp(OBJ1, OBJ2)
Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is less than,
equal to, or larger than OBJ2, respectively.
String conversion
_str(OBJ)
Return a string representing the object. The returned string should
have no leading zeros, i.e., it should match "^(0|[1-9]\d*)$".
_as_bin(OBJ)
Return the binary string representation of the number. The string
must have a '0b' prefix.
_as_oct(OBJ)
Return the octal string representation of the number. The string
must have a '0x' prefix.
Note: This method was required from Math::BigInt version 1.78, but
the required API version number was not incremented, so there are
older libraries that support API version 1, but do not support
"_as_oct()".
_as_hex(OBJ)
Return the hexadecimal string representation of the number. The
string must have a '0x' prefix.
Numeric conversion
_num(OBJ)
Given an object, return a Perl scalar number (int/float)
representing this number.
Miscellaneous
_copy(OBJ)
Return a true copy of the object.
_len(OBJ)
Returns the number of the decimal digits in the number. The output
is a Perl scalar.
_zeros(OBJ)
Return the number of trailing decimal zeros. The output is a Perl
scalar.
_digit(OBJ, N)
Return the Nth digit 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
$obj represents the number 123, then _digit($obj, 0) is 3 and
_digit(123, -1) is 1.
_check(OBJ)
Return a true value if the object is OK, and a false value
otherwise. This is a check routine to test the internal state of
the object for corruption.
API version 2
The following methods are required for an API version of 2 or greater.
Constructors
_1ex(N)
Return an object representing the number 10**N where N >= 0 is a
Perl scalar.
Mathematical functions
_nok(OBJ1, OBJ2)
Return the binomial coefficient OBJ1 over OBJ1.
Miscellaneous
_alen(OBJ)
Return the approximate number of decimal digits of the object. The
output is one Perl scalar. This estimate must be greater than or
equal to what "_len()" returns.
API optional methods
The following methods are optional, and can be defined if the
underlying lib has a fast way to do them. If undefined, Math::BigInt
will use pure Perl (hence slow) fallback routines to emulate these:
Signed bitwise operators.
Each of these methods may modify the first input argument.
_signed_or(OBJ1, OBJ2, SIGN1, SIGN2)
Return the signed bitwise or.
_signed_and(OBJ1, OBJ2, SIGN1, SIGN2)
Return the signed bitwise and.
_signed_xor(OBJ1, OBJ2, SIGN1, SIGN2)
Return the signed bitwise exclusive or.
WRAP YOUR OWN
If you want to port your own favourite c-lib 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
BigInt and 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.
LICENSE
This program is free software; you may redistribute it and/or modify it
under the same terms as Perl itself.
AUTHORS
o Original math code by Mark Biggar, rewritten by Tels
<http://bloodgate.com/>; in late 2000.
o Separated from BigInt and shaped API with the help of John Peacock.
o Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2007.
o API documentation corrected and extended by Peter John Acklam,
<pjacklam AT online.no>
SEE ALSO
Math::BigInt, Math::BigFloat, Math::BigInt::GMP, Math::BigInt::FastCalc
and Math::BigInt::Pari.
perl v5.16.3 2013-03-04 Math::BigInt::Calc(3pm)
Linux-Distributionen
Huschi als Linux-Admin