Math::BigInt::Lib(3p) Perl Programmers Reference Guide Math::BigInt::Lib(3p) #
Math::BigInt::Lib(3p) Perl Programmers Reference Guide Math::BigInt::Lib(3p)
NNAAMMEE #
Math::BigInt::Lib - virtual parent class for Math::BigInt libraries
SSYYNNOOPPSSIISS #
# 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';
DDEESSCCRRIIPPTTIIOONN #
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'.
GGeenneerraall NNootteess 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.
_A_P_I _v_e_r_s_i_o_n
CLASS->aappii__vveerrssiioonn(())
This method is no longer used and can be omitted. Methods that are
not implemented by a subclass will be inherited from this class.
_C_o_n_s_t_r_u_c_t_o_r_s
The following methods are mandatory: __nneeww(()), __ssttrr(()), __aadddd(()), and __ssuubb(()).
However, computations will be very slow without __mmuull(()) and __ddiivv(()).
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*)$".
CLASS->__zzeerroo(())
Return an object representing the number zero.
CLASS->__oonnee(())
Return an object representing the number one.
CLASS->__ttwwoo(())
Return an object representing the number two.
CLASS->__tteenn(())
Return an object representing the number ten.
CLASS->_from_bin(STR)
Return an object given a string representing a binary number. The
input has a '0b' prefix and matches the regular expression
"^0[bB](0|1[01]*)$".
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) # $x is 65191
_M_a_t_h_e_m_a_t_i_c_a_l _f_u_n_c_t_i_o_n_s
CLASS->_add(OBJ1, OBJ2)
Addition. Returns the result of adding OBJ2 to OBJ1.
CLASS->_mul(OBJ1, OBJ2)
Multiplication. Returns the result of multiplying OBJ2 and OBJ1.
CLASS->_div(OBJ1, OBJ2)
Division. In scalar context, returns the quotient after dividing OBJ1
by OBJ2 and truncating the result to an integer. In list context,
return the quotient and the remainder.
CLASS->_sub(OBJ1, OBJ2, FLAG)
CLASS->_sub(OBJ1, OBJ2)
Subtraction. Returns the result of subtracting OBJ2 by OBJ1. If
"flag" is false or omitted, OBJ1 might be modified. If "flag" is
true, OBJ2 might be modified.
CLASS->_sadd(OBJ1, SIGN1, OBJ2, SIGN2)
Signed addition. Returns the result of adding OBJ2 with sign SIGN2 to
OBJ1 with sign SIGN1.
($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->_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: __ffiibb(0) returns
0, __ffiibb(1) returns 1, __ffiibb(2) returns 1, __ffiibb(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: __lluuccaass(0) returns 2,
__lluuccaass(1) returns 1, __lluuccaass(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, ...
_B_i_t_w_i_s_e _o_p_e_r_a_t_o_r_s
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.
_B_o_o_l_e_a_n _o_p_e_r_a_t_o_r_s
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.
_S_t_r_i_n_g _c_o_n_v_e_r_s_i_o_n
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 __ffrroomm__bbaassee(()) 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()".
_N_u_m_e_r_i_c _c_o_n_v_e_r_s_i_o_n
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.
_M_i_s_c_e_l_l_a_n_e_o_u_s
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
AAPPII vveerrssiioonn 22 The following methods are required for an API version of 2 or greater.
_C_o_n_s_t_r_u_c_t_o_r_s
CLASS->_1ex(N)
Return an object representing the number 10**N where N >= 0 is a Perl
scalar.
_M_a_t_h_e_m_a_t_i_c_a_l _f_u_n_c_t_i_o_n_s
CLASS->_nok(OBJ1, OBJ2)
Return the binomial coefficient OBJ1 over OBJ1.
_M_i_s_c_e_l_l_a_n_e_o_u_s
CLASS->_alen(OBJ)
Return the approximate number of decimal digits of the object. The
output is a Perl scalar.
WWRRAAPP YYOOUURR OOWWNN #
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.
BBUUGGSS #
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.
SSUUPPPPOORRTT #
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=Math-BigInt>
• AnnoCPAN: Annotated CPAN documentation
<http://annocpan.org/dist/Math-BigInt>
• CPAN Ratings
<https://cpanratings.perl.org/dist/Math-BigInt>
• MetaCPAN
<https://metacpan.org/release/Math-BigInt>
• CPAN Testers Matrix
<http://matrix.cpantesters.org/?dist=Math-BigInt>
• The Bignum mailing list
• Post to mailing list
"bignum at lists.scsys.co.uk"
• View mailing list
<http://lists.scsys.co.uk/pipermail/bignum/>
• Subscribe/Unsubscribe
<http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>
LLIICCEENNSSEE #
This program is free software; you may redistribute it and/or modify it
under the same terms as Perl itself.
AAUUTTHHOORR #
Peter John Acklam, <pjacklam@gmail.com>
Code and documentation based on the Math::BigInt::Calc module by Tels
<nospam-abuse@bloodgate.com>
SSEEEE AALLSSOO #
Math::BigInt, Math::BigInt::Calc, Math::BigInt::GMP,
Math::BigInt::FastCalc and Math::BigInt::Pari.
perl v5.36.3 2023-02-15 Math::BigInt::Lib(3p)