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.\" ========================================================================
.\"
.IX Title "Math::BigInt::Calc 3perl"
.TH Math::BigInt::Calc 3perl "2014-12-27" "perl v5.20.2" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::BigInt::Calc \- Pure Perl module to support Math::BigInt
.SH "SYNOPSIS"
.IX Header "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
\&\s-1API \s0(see below) can also be used to support Math::BigInt, like
Math::BigInt::GMP and Math::BigInt::Pari.
.SH "DESCRIPTION"
.IX Header "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.
.PP
For instance, if B = 10000, the number 1234567890 is represented internally
as [3456, 7890, 12].
.SH "THE Math::BigInt API"
.IX Header "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 \s-1API\s0 can be used by Math::BigInt by using this in your program:
.PP
.Vb 1
\&        use Math::BigInt lib => \*(Aqlibname\*(Aq;
.Ve
.PP
\&'libname' is either the long name, like 'Math::BigInt::Pari', or only the short
version, like 'Pari'.
.SS "General Notes"
.IX Subsection "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 \f(CW\*(C`_sub()\*(C'\fR and \f(CW\*(C`_dec()\*(C'\fR) nor about division by zero (e.g.,
in \f(CW\*(C`_div()\*(C'\fR) or similar cases.
.PP
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.
.PP
Return values are always objects, strings, Perl scalars, or true/false for
comparison routines.
.SS "\s-1API\s0 version 1"
.IX Subsection "API version 1"
The following methods must be defined in order to support the use by
Math::BigInt v1.70 or later.
.PP
\fI\s-1API\s0 version\fR
.IX Subsection "API version"
.IP "\fI\fIapi_version()\fI\fR" 4
.IX Item "api_version()"
Return \s-1API\s0 version as a Perl scalar, 1 for Math::BigInt v1.70, 2 for
Math::BigInt v1.83.
.PP
\fIConstructors\fR
.IX Subsection "Constructors"
.IP "\fI_new(\s-1STR\s0)\fR" 4
.IX Item "_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
\&\f(CW\*(C`^(0|[1\-9]\ed*)$\*(C'\fR.
.IP "\fI\fI_zero()\fI\fR" 4
.IX Item "_zero()"
Return an object representing the number zero.
.IP "\fI\fI_one()\fI\fR" 4
.IX Item "_one()"
Return an object representing the number one.
.IP "\fI\fI_two()\fI\fR" 4
.IX Item "_two()"
Return an object representing the number two.
.IP "\fI\fI_ten()\fI\fR" 4
.IX Item "_ten()"
Return an object representing the number ten.
.IP "\fI_from_bin(\s-1STR\s0)\fR" 4
.IX Item "_from_bin(STR)"
Return an object given a string representing a binary number. The input has a
\&'0b' prefix and matches the regular expression \f(CW\*(C`^0[bB](0|1[01]*)$\*(C'\fR.
.IP "\fI_from_oct(\s-1STR\s0)\fR" 4
.IX Item "_from_oct(STR)"
Return an object given a string representing an octal number. The input has a
\&'0' prefix and matches the regular expression \f(CW\*(C`^0[1\-7]*$\*(C'\fR.
.IP "\fI_from_hex(\s-1STR\s0)\fR" 4
.IX Item "_from_hex(STR)"
Return an object given a string representing a hexadecimal number. The input
has a '0x' prefix and matches the regular expression
\&\f(CW\*(C`^0x(0|[1\-9a\-fA\-F][\eda\-fA\-F]*)$\*(C'\fR.
.PP
\fIMathematical functions\fR
.IX Subsection "Mathematical functions"
.PP
Each of these methods may modify the first input argument, except \fI\fI_bgcd()\fI\fR,
which shall not modify any input argument, and \fI\fI_sub()\fI\fR which may modify the
second input argument.
.IP "\fI_add(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_add(OBJ1, OBJ2)"
Returns the result of adding \s-1OBJ2\s0 to \s-1OBJ1.\s0
.IP "\fI_mul(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_mul(OBJ1, OBJ2)"
Returns the result of multiplying \s-1OBJ2\s0 and \s-1OBJ1.\s0
.IP "\fI_div(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_div(OBJ1, OBJ2)"
Returns the result of dividing \s-1OBJ1\s0 by \s-1OBJ2\s0 and truncating the result to an
integer.
.IP "\fI_sub(\s-1OBJ1, OBJ2, FLAG\s0)\fR" 4
.IX Item "_sub(OBJ1, OBJ2, FLAG)"
.PD 0
.IP "\fI_sub(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_sub(OBJ1, OBJ2)"
.PD
Returns the result of subtracting \s-1OBJ2\s0 by \s-1OBJ1.\s0 If \f(CW\*(C`flag\*(C'\fR is false or omitted,
\&\s-1OBJ1\s0 might be modified. If \f(CW\*(C`flag\*(C'\fR is true, \s-1OBJ2\s0 might be modified.
.IP "\fI_dec(\s-1OBJ\s0)\fR" 4
.IX Item "_dec(OBJ)"
Decrement \s-1OBJ\s0 by one.
.IP "\fI_inc(\s-1OBJ\s0)\fR" 4
.IX Item "_inc(OBJ)"
Increment \s-1OBJ\s0 by one.
.IP "\fI_mod(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_mod(OBJ1, OBJ2)"
Return \s-1OBJ1\s0 modulo \s-1OBJ2,\s0 i.e., the remainder after dividing \s-1OBJ1\s0 by \s-1OBJ2.\s0
.IP "\fI_sqrt(\s-1OBJ\s0)\fR" 4
.IX Item "_sqrt(OBJ)"
Return the square root of the object, truncated to integer.
.IP "\fI_root(\s-1OBJ, N\s0)\fR" 4
.IX Item "_root(OBJ, N)"
Return Nth root of the object, truncated to int. N is >= 3.
.IP "\fI_fac(\s-1OBJ\s0)\fR" 4
.IX Item "_fac(OBJ)"
Return factorial of object (1*2*3*4*...).
.IP "\fI_pow(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_pow(OBJ1, OBJ2)"
Return \s-1OBJ1\s0 to the power of \s-1OBJ2.\s0 By convention, 0**0 = 1.
.IP "\fI_modinv(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_modinv(OBJ1, OBJ2)"
Return modular multiplicative inverse, i.e., return \s-1OBJ3\s0 so that
.Sp
.Vb 1
\&    (OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2
.Ve
.Sp
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 (\*(L"+\*(R" or \*(L"\-\*(R").
.Sp
The output value, with its sign, must either be a positive value in the
range 1,2,...,OBJ2\-1 or the same value subtracted \s-1OBJ2.\s0 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 \*(L"+\*(R" sign, since
(3*7) % 5 = 1 % 5, or an object representing the number 2 and \*(L"\-\*(R" sign,
since (\-2*7) % 5 = 1 % 5.
.IP "\fI_modpow(\s-1OBJ1, OBJ2, OBJ3\s0)\fR" 4
.IX Item "_modpow(OBJ1, OBJ2, OBJ3)"
Return modular exponentiation, (\s-1OBJ1\s0 ** \s-1OBJ2\s0) % \s-1OBJ3.\s0
.IP "\fI_rsft(\s-1OBJ, N, B\s0)\fR" 4
.IX Item "_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.
.Sp
For instance, if the object \f(CW$obj\fR represents the hexadecimal number 0xabcde,
then \f(CW\*(C`_rsft($obj, 2, 16)\*(C'\fR returns an object representing the number 0xabc. The
\&\*(L"remainer\*(R", 0xde, is discarded and not returned.
.IP "\fI_lsft(\s-1OBJ, N, B\s0)\fR" 4
.IX Item "_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.
.IP "\fI_log_int(\s-1OBJ, B\s0)\fR" 4
.IX Item "_log_int(OBJ, B)"
Return integer log of \s-1OBJ\s0 to base \s-1BASE.\s0 This method has two output arguments,
the \s-1OBJECT\s0 and a \s-1STATUS.\s0 The \s-1STATUS\s0 is Perl scalar; it is 1 if \s-1OBJ\s0 is the exact
result, 0 if the result was truncted to give \s-1OBJ,\s0 and undef if it is unknown
whether \s-1OBJ\s0 is the exact result.
.IP "\fI_gcd(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_gcd(OBJ1, OBJ2)"
Return the greatest common divisor of \s-1OBJ1\s0 and \s-1OBJ2.\s0
.PP
\fIBitwise operators\fR
.IX Subsection "Bitwise operators"
.PP
Each of these methods may modify the first input argument.
.IP "\fI_and(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_and(OBJ1, OBJ2)"
Return bitwise and. If necessary, the smallest number is padded with leading
zeros.
.IP "\fI_or(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_or(OBJ1, OBJ2)"
Return bitwise or. If necessary, the smallest number is padded with leading
zeros.
.IP "\fI_xor(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_xor(OBJ1, OBJ2)"
Return bitwise exclusive or. If necessary, the smallest number is padded
with leading zeros.
.PP
\fIBoolean operators\fR
.IX Subsection "Boolean operators"
.IP "\fI_is_zero(\s-1OBJ\s0)\fR" 4
.IX Item "_is_zero(OBJ)"
Returns a true value if \s-1OBJ\s0 is zero, and false value otherwise.
.IP "\fI_is_one(\s-1OBJ\s0)\fR" 4
.IX Item "_is_one(OBJ)"
Returns a true value if \s-1OBJ\s0 is one, and false value otherwise.
.IP "\fI_is_two(\s-1OBJ\s0)\fR" 4
.IX Item "_is_two(OBJ)"
Returns a true value if \s-1OBJ\s0 is two, and false value otherwise.
.IP "\fI_is_ten(\s-1OBJ\s0)\fR" 4
.IX Item "_is_ten(OBJ)"
Returns a true value if \s-1OBJ\s0 is ten, and false value otherwise.
.IP "\fI_is_even(\s-1OBJ\s0)\fR" 4
.IX Item "_is_even(OBJ)"
Return a true value if \s-1OBJ\s0 is an even integer, and a false value otherwise.
.IP "\fI_is_odd(\s-1OBJ\s0)\fR" 4
.IX Item "_is_odd(OBJ)"
Return a true value if \s-1OBJ\s0 is an even integer, and a false value otherwise.
.IP "\fI_acmp(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_acmp(OBJ1, OBJ2)"
Compare \s-1OBJ1\s0 and \s-1OBJ2\s0 and return \-1, 0, or 1, if \s-1OBJ1\s0 is less than, equal
to, or larger than \s-1OBJ2,\s0 respectively.
.PP
\fIString conversion\fR
.IX Subsection "String conversion"
.IP "\fI_str(\s-1OBJ\s0)\fR" 4
.IX Item "_str(OBJ)"
Return a string representing the object. The returned string should have no
leading zeros, i.e., it should match \f(CW\*(C`^(0|[1\-9]\ed*)$\*(C'\fR.
.IP "\fI_as_bin(\s-1OBJ\s0)\fR" 4
.IX Item "_as_bin(OBJ)"
Return the binary string representation of the number. The string must have a
\&'0b' prefix.
.IP "\fI_as_oct(\s-1OBJ\s0)\fR" 4
.IX Item "_as_oct(OBJ)"
Return the octal string representation of the number. The string must have
a '0x' prefix.
.Sp
Note: This method was required from Math::BigInt version 1.78, but the required
\&\s-1API\s0 version number was not incremented, so there are older libraries that
support \s-1API\s0 version 1, but do not support \f(CW\*(C`_as_oct()\*(C'\fR.
.IP "\fI_as_hex(\s-1OBJ\s0)\fR" 4
.IX Item "_as_hex(OBJ)"
Return the hexadecimal string representation of the number. The string must
have a '0x' prefix.
.PP
\fINumeric conversion\fR
.IX Subsection "Numeric conversion"
.IP "\fI_num(\s-1OBJ\s0)\fR" 4
.IX Item "_num(OBJ)"
Given an object, return a Perl scalar number (int/float) representing this
number.
.PP
\fIMiscellaneous\fR
.IX Subsection "Miscellaneous"
.IP "\fI_copy(\s-1OBJ\s0)\fR" 4
.IX Item "_copy(OBJ)"
Return a true copy of the object.
.IP "\fI_len(\s-1OBJ\s0)\fR" 4
.IX Item "_len(OBJ)"
Returns the number of the decimal digits in the number. The output is a
Perl scalar.
.IP "\fI_zeros(\s-1OBJ\s0)\fR" 4
.IX Item "_zeros(OBJ)"
Return the number of trailing decimal zeros. The output is a Perl scalar.
.IP "\fI_digit(\s-1OBJ, N\s0)\fR" 4
.IX Item "_digit(OBJ, N)"
Return the Nth digit as a Perl scalar. N is a Perl scalar, where zero refers to
the rightmost (least significant) digit, and negative values count from the
left (most significant digit). If \f(CW$obj\fR represents the number 123, then
\&\fI_digit($obj, 0)\fR is 3 and \fI_digit(123, \-1)\fR is 1.
.IP "\fI_check(\s-1OBJ\s0)\fR" 4
.IX Item "_check(OBJ)"
Return a true value if the object is \s-1OK,\s0 and a false value otherwise. This is a
check routine to test the internal state of the object for corruption.
.SS "\s-1API\s0 version 2"
.IX Subsection "API version 2"
The following methods are required for an \s-1API\s0 version of 2 or greater.
.PP
\fIConstructors\fR
.IX Subsection "Constructors"
.IP "\fI_1ex(N)\fR" 4
.IX Item "_1ex(N)"
Return an object representing the number 10**N where N >= 0 is a Perl
scalar.
.PP
\fIMathematical functions\fR
.IX Subsection "Mathematical functions"
.IP "\fI_nok(\s-1OBJ1, OBJ2\s0)\fR" 4
.IX Item "_nok(OBJ1, OBJ2)"
Return the binomial coefficient \s-1OBJ1\s0 over \s-1OBJ1.\s0
.PP
\fIMiscellaneous\fR
.IX Subsection "Miscellaneous"
.IP "\fI_alen(\s-1OBJ\s0)\fR" 4
.IX Item "_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 \f(CW\*(C`_len()\*(C'\fR returns.
.SS "\s-1API\s0 optional methods"
.IX Subsection "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:
.PP
\fISigned bitwise operators.\fR
.IX Subsection "Signed bitwise operators."
.PP
Each of these methods may modify the first input argument.
.IP "\fI_signed_or(\s-1OBJ1, OBJ2, SIGN1, SIGN2\s0)\fR" 4
.IX Item "_signed_or(OBJ1, OBJ2, SIGN1, SIGN2)"
Return the signed bitwise or.
.IP "\fI_signed_and(\s-1OBJ1, OBJ2, SIGN1, SIGN2\s0)\fR" 4
.IX Item "_signed_and(OBJ1, OBJ2, SIGN1, SIGN2)"
Return the signed bitwise and.
.IP "\fI_signed_xor(\s-1OBJ1, OBJ2, SIGN1, SIGN2\s0)\fR" 4
.IX Item "_signed_xor(OBJ1, OBJ2, SIGN1, SIGN2)"
Return the signed bitwise exclusive or.
.SH "WRAP YOUR OWN"
.IX Header "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:
.PP
.Vb 1
\&        use Math::BigInt;
.Ve
.PP
by this:
.PP
.Vb 1
\&        use Math::BigInt lib => \*(Aqyourlib\*(Aq;
.Ve
.PP
This way you ensure that your library really works 100% within Math::BigInt.
.SH "LICENSE"
.IX Header "LICENSE"
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
.SH "AUTHORS"
.IX Header "AUTHORS"
.IP "\(bu" 4
Original math code by Mark Biggar, rewritten by Tels <http://bloodgate.com/>
in late 2000.
.IP "\(bu" 4
Separated from BigInt and shaped \s-1API\s0 with the help of John Peacock.
.IP "\(bu" 4
Fixed, speed-up, streamlined and enhanced by Tels 2001 \- 2007.
.IP "\(bu" 4
\&\s-1API\s0 documentation corrected and extended by Peter John Acklam,
<pjacklam@online.no>
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::BigInt, Math::BigFloat,
Math::BigInt::GMP, Math::BigInt::FastCalc and Math::BigInt::Pari.