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man : Math::BigRat(3p)
Math::BigRat(3p) Perl Programmers Reference GuideMath::BigRat(3p)
NAME
Math::BigRat - Arbitrary big rational numbers
SYNOPSIS
use Math::BigRat;
my $x = Math::BigRat->new('3/7'); $x += '5/9';
print $x->bstr(),"\n";
print $x ** 2,"\n";
my $y = Math::BigRat->new('inf');
print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n";
my $z = Math::BigRat->new(144); $z->bsqrt();
DESCRIPTION
Math::BigRat complements Math::BigInt and Math::BigFloat
by providing support for arbitrary big rational numbers.
MATH LIBRARY
You can change the underlying module that does the low-
level math operations by using:
use Math::BigRat try => 'GMP';
Note: This needs Math::BigInt::GMP installed.
The following would first try to find Math::BigInt::Foo,
then Math::BigInt::Bar, and when this also fails, revert
to Math::BigInt::Calc:
use Math::BigRat try => 'Foo,Math::BigInt::Bar';
If you want to get warned when the fallback occurs,
replace "try" with "lib":
use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
If you want the code to die instead, replace "try" with
"only":
use Math::BigRat only => 'Foo,Math::BigInt::Bar';
METHODS
Any methods not listed here are derived from
Math::BigFloat (or Math::BigInt), so make sure you check
these two modules for further information.
new()
$x = Math::BigRat->new('1/3');
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Create a new Math::BigRat object. Input can come in
various forms:
$x = Math::BigRat->new(123); # scalars
$x = Math::BigRat->new('inf'); # infinity
$x = Math::BigRat->new('123.3'); # float
$x = Math::BigRat->new('1/3'); # simple string
$x = Math::BigRat->new('1 / 3'); # spaced
$x = Math::BigRat->new('1 / 0.1'); # w/ floats
$x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt
$x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat
$x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite
# You can also give D and N as different objects:
$x = Math::BigRat->new(
Math::BigInt->new(-123),
Math::BigInt->new(7),
); # => -123/7
numerator()
$n = $x->numerator();
Returns a copy of the numerator (the part above the line)
as signed BigInt.
denominator()
$d = $x->denominator();
Returns a copy of the denominator (the part under the
line) as positive BigInt.
parts()
($n,$d) = $x->parts();
Return a list consisting of (signed) numerator and
(unsigned) denominator as BigInts.
numify()
my $y = $x->numify();
Returns the object as a scalar. This will lose some data
if the object cannot be represented by a normal Perl
scalar (integer or float), so use as_int() instead.
This routine is automatically used whenever a scalar is
required:
my $x = Math::BigRat->new('3/1');
@array = (1,2,3);
$y = $array[$x]; # set $y to 3
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as_int()/as_number()
$x = Math::BigRat->new('13/7');
print $x->as_int(),"\n"; # '1'
Returns a copy of the object as BigInt, truncated to an
integer.
"as_number()" is an alias for "as_int()".
as_hex()
$x = Math::BigRat->new('13');
print $x->as_hex(),"\n"; # '0xd'
Returns the BigRat as hexadecimal string. Works only for
integers.
as_bin()
$x = Math::BigRat->new('13');
print $x->as_bin(),"\n"; # '0x1101'
Returns the BigRat as binary string. Works only for
integers.
as_oct()
$x = Math::BigRat->new('13');
print $x->as_oct(),"\n"; # '015'
Returns the BigRat as octal string. Works only for
integers.
from_hex()/from_bin()/from_oct()
my $h = Math::BigRat->from_hex('0x10');
my $b = Math::BigRat->from_bin('0b10000000');
my $o = Math::BigRat->from_oct('020');
Create a BigRat from an hexadecimal, binary or octal
number in string form.
length()
$len = $x->length();
Return the length of $x in digitis for integer values.
digit()
print Math::BigRat->new('123/1')->digit(1); # 1
print Math::BigRat->new('123/1')->digit(-1); # 3
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Return the N'ths digit from X when X is an integer value.
bnorm()
$x->bnorm();
Reduce the number to the shortest form. This routine is
called automatically whenever it is needed.
bfac()
$x->bfac();
Calculates the factorial of $x. For instance:
print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3
print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5
Works currently only for integers.
bround()/round()/bfround()
Are not yet implemented.
bmod()
use Math::BigRat;
my $x = Math::BigRat->new('7/4');
my $y = Math::BigRat->new('4/3');
print $x->bmod($y);
Set $x to the remainder of the division of $x by $y.
bneg()
$x->bneg();
Used to negate the object in-place.
is_one()
print "$x is 1\n" if $x->is_one();
Return true if $x is exactly one, otherwise false.
is_zero()
print "$x is 0\n" if $x->is_zero();
Return true if $x is exactly zero, otherwise false.
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is_pos()/is_positive()
print "$x is >= 0\n" if $x->is_positive();
Return true if $x is positive (greater than or equal to
zero), otherwise false. Please note that '+inf' is also
positive, while 'NaN' and '-inf' aren't.
"is_positive()" is an alias for "is_pos()".
is_neg()/is_negative()
print "$x is < 0\n" if $x->is_negative();
Return true if $x is negative (smaller than zero),
otherwise false. Please note that '-inf' is also negative,
while 'NaN' and '+inf' aren't.
"is_negative()" is an alias for "is_neg()".
is_int()
print "$x is an integer\n" if $x->is_int();
Return true if $x has a denominator of 1 (e.g. no fraction
parts), otherwise false. Please note that '-inf', 'inf'
and 'NaN' aren't integer.
is_odd()
print "$x is odd\n" if $x->is_odd();
Return true if $x is odd, otherwise false.
is_even()
print "$x is even\n" if $x->is_even();
Return true if $x is even, otherwise false.
bceil()
$x->bceil();
Set $x to the next bigger integer value (e.g. truncate the
number to integer and then increment it by one).
bfloor()
$x->bfloor();
Truncate $x to an integer value.
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bsqrt()
$x->bsqrt();
Calculate the square root of $x.
broot()
$x->broot($n);
Calculate the N'th root of $x.
badd()/bmul()/bsub()/bdiv()/bdec()/binc()
Please see the documentation in Math::BigInt.
copy()
my $z = $x->copy();
Makes a deep copy of the object.
Please see the documentation in Math::BigInt for further
details.
bstr()/bsstr()
my $x = Math::BigInt->new('8/4');
print $x->bstr(),"\n"; # prints 1/2
print $x->bsstr(),"\n"; # prints 1/2
Return a string representating this object.
bacmp()/bcmp()
Used to compare numbers.
Please see the documentation in Math::BigInt for further
details.
blsft()/brsft()
Used to shift numbers left/right.
Please see the documentation in Math::BigInt for further
details.
bpow()
$x->bpow($y);
Compute $x ** $y.
Please see the documentation in Math::BigInt for further
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details.
bexp()
$x->bexp($accuracy); # calculate e ** X
Calculates two integers A and B so that A/B is equal to "e
** $x", where "e" is Euler's number.
This method was added in v0.20 of Math::BigRat (May 2007).
See also blog().
bnok()
$x->bnok($y); # x over y (binomial coefficient n over k)
Calculates the binomial coefficient n over k, also called
the "choose" function. The result is equivalent to:
( n ) n!
| - | = -------
( k ) k!(n-k)!
This method was added in v0.20 of Math::BigRat (May 2007).
config()
use Data::Dumper;
print Dumper ( Math::BigRat->config() );
print Math::BigRat->config()->{lib},"\n";
Returns a hash containing the configuration, e.g. the
version number, lib loaded etc. The following hash keys
are currently filled in with the appropriate information.
key RO/RW Description
Example
============================================================
lib RO Name of the Math library
Math::BigInt::Calc
lib_version RO Version of 'lib'
0.30
class RO The class of config you just called
Math::BigRat
version RO version number of the class you used
0.10
upgrade RW To which class numbers are upgraded
undef
downgrade RW To which class numbers are downgraded
undef
precision RW Global precision
undef
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accuracy RW Global accuracy
undef
round_mode RW Global round mode
even
div_scale RW Fallback accuracy for div
40
trap_nan RW Trap creation of NaN (undef = no)
undef
trap_inf RW Trap creation of +inf/-inf (undef = no)
undef
By passing a reference to a hash you may set the
configuration values. This works only for values that a
marked with a "RW" above, anything else is read-only.
BUGS
Some things are not yet implemented, or only implemented
half-way:
inf handling (partial)
NaN handling (partial)
rounding (not implemented except for bceil/bfloor)
$x ** $y where $y is not an integer
bmod(), blog(), bmodinv() and bmodpow() (partial)
LICENSE
This program is free software; you may redistribute it
and/or modify it under the same terms as Perl itself.
SEE ALSO
Math::BigFloat and Math::Big as well as
Math::BigInt::BitVect, Math::BigInt::Pari and
Math::BigInt::GMP.
See <http://search.cpan.org/search?dist=bignum>; for a way
to use Math::BigRat.
The package at
<http://search.cpan.org/search?dist=Math%3A%3ABigRat> may
contain more documentation and examples as well as
testcases.
AUTHORS
(C) by Tels <http://bloodgate.com/>; 2001 - 2007.
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