Math::BigInt::Calc (3)

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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 (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 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.

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 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.

BUGS

Please report any bugs or feature requests to "bug-math-bigint at rt.cpan.org", or through the web interface at <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:

*

RT: CPAN

's request tracker

<rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt>

*

AnnoCPAN: Annotated

CPAN

documentation

<annocpan.org/dist/Math-BigInt>

*

CPAN

Ratings

<cpanratings.perl.org/dist/Math-BigInt>

*

Search

CPAN

<search.cpan.org/dist/Math-BigInt>

*

CPAN

Testers Matrix

<matrix.cpantesters.org/?dist=Math-BigInt>

*

The Bignum mailing list

*

Post to mailing list

"bignum at lists.scsys.co.uk"

*

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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.

AUTHORS

*

Original math code by Mark Biggar, rewritten by Tels <bloodgate.com> in late 2000.

*

Separated from BigInt and shaped

API

with the help of John Peacock.

*

Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2007.

*

API

documentation corrected and extended by Peter John Acklam, <pjacklam@online.no>

SEE ALSO

Math::BigInt, Math::BigFloat, Math::BigInt::GMP, Math::BigInt::FastCalc and Math::BigInt::Pari.