Provided by: perl-doc_5.36.0-7_all 
NAME
Math::BigRat - arbitrary size rational number math package
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');
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.
dparts()
Returns the integer part and the fraction part.
fparts()
Returns the smallest possible numerator and denominator so that the numerator divided
by the denominator gives back the original value. For finite numbers, both values are
integers. Mnemonic: fraction.
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()" or
"as_float()" instead.
This routine is automatically used whenever a scalar is required:
my $x = Math::BigRat->new('3/1');
@array = (0, 1, 2, 3);
$y = $array[$x]; # set $y to 3
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_float()
$x = Math::BigRat->new('13/7');
print $x->as_float(), "\n"; # '1'
$x = Math::BigRat->new('2/3');
print $x->as_float(5), "\n"; # '0.66667'
Returns a copy of the object as BigFloat, preserving the accuracy as wanted, or the
default of 40 digits.
This method was added in v0.22 of Math::BigRat (April 2008).
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()
my $h = Math::BigRat->from_hex('0x10');
Create a BigRat from a hexadecimal number in string form.
from_oct()
my $o = Math::BigRat->from_oct('020');
Create a BigRat from an octal number in string form.
from_bin()
my $b = Math::BigRat->from_bin('0b10000000');
Create a BigRat from an binary number in string form.
bnan()
$x = Math::BigRat->bnan();
Creates a new BigRat object representing NaN (Not A Number). If used on an object, it
will set it to NaN:
$x->bnan();
bzero()
$x = Math::BigRat->bzero();
Creates a new BigRat object representing zero. If used on an object, it will set it
to zero:
$x->bzero();
binf()
$x = Math::BigRat->binf($sign);
Creates a new BigRat object representing infinity. The optional argument is either '-'
or '+', indicating whether you want infinity or minus infinity. If used on an object,
it will set it to infinity:
$x->binf();
$x->binf('-');
bone()
$x = Math::BigRat->bone($sign);
Creates a new BigRat object representing one. The optional argument is either '-' or
'+', indicating whether you want one or minus one. If used on an object, it will set
it to one:
$x->bone(); # +1
$x->bone('-'); # -1
length()
$len = $x->length();
Return the length of $x in digits for integer values.
digit()
print Math::BigRat->new('123/1')->digit(1); # 1
print Math::BigRat->new('123/1')->digit(-1); # 3
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()
$x->bmod($y);
Returns $x modulo $y. When $x is finite, and $y is finite and non-zero, the result is
identical to the remainder after floored division (F-division). If, in addition, both
$x and $y are integers, the result is identical to the result from Perl's % operator.
bmodinv()
$x->bmodinv($mod); # modular multiplicative inverse
Returns the multiplicative inverse of $x modulo $mod. If
$y = $x -> copy() -> bmodinv($mod)
then $y is the number closest to zero, and with the same sign as $mod, satisfying
($x * $y) % $mod = 1 % $mod
If $x and $y are non-zero, they must be relative primes, i.e., "bgcd($y, $mod)==1".
'"NaN"' is returned when no modular multiplicative inverse exists.
bmodpow()
$num->bmodpow($exp,$mod); # modular exponentiation
# ($num**$exp % $mod)
Returns the value of $num taken to the power $exp in the modulus $mod using binary
exponentiation. "bmodpow" is far superior to writing
$num ** $exp % $mod
because it is much faster - it reduces internal variables into the modulus whenever
possible, so it operates on smaller numbers.
"bmodpow" also supports negative exponents.
bmodpow($num, -1, $mod)
is exactly equivalent to
bmodinv($num, $mod)
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 $x is exactly zero, otherwise false.
is_pos()/is_positive()
print "$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.
bint()
$x->bint();
Round $x towards zero.
bsqrt()
$x->bsqrt();
Calculate the square root of $x.
broot()
$x->broot($n);
Calculate the N'th root of $x.
badd()
$x->badd($y);
Adds $y to $x and returns the result.
bmul()
$x->bmul($y);
Multiplies $y to $x and returns the result.
bsub()
$x->bsub($y);
Subtracts $y from $x and returns the result.
bdiv()
$q = $x->bdiv($y);
($q, $r) = $x->bdiv($y);
In scalar context, divides $x by $y and returns the result. In list context, does
floored division (F-division), returning an integer $q and a remainder $r so that $x =
$q * $y + $r. The remainer (modulo) is equal to what is returned by "$x->bmod($y)".
binv()
$x->binv();
Inverse of $x.
bdec()
$x->bdec();
Decrements $x by 1 and returns the result.
binc()
$x->binc();
Increments $x by 1 and returns the result.
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::BigRat->new('8/4');
print $x->bstr(), "\n"; # prints 1/2
print $x->bsstr(), "\n"; # prints 1/2
Return a string representing this object.
bcmp()
$x->bcmp($y);
Compares $x with $y and takes the sign into account. Returns -1, 0, 1 or undef.
bacmp()
$x->bacmp($y);
Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or undef.
beq()
$x -> beq($y);
Returns true if and only if $x is equal to $y, and false otherwise.
bne()
$x -> bne($y);
Returns true if and only if $x is not equal to $y, and false otherwise.
blt()
$x -> blt($y);
Returns true if and only if $x is equal to $y, and false otherwise.
ble()
$x -> ble($y);
Returns true if and only if $x is less than or equal to $y, and false otherwise.
bgt()
$x -> bgt($y);
Returns true if and only if $x is greater than $y, and false otherwise.
bge()
$x -> bge($y);
Returns true if and only if $x is greater than or equal to $y, and false otherwise.
blsft()/brsft()
Used to shift numbers left/right.
Please see the documentation in Math::BigInt for further details.
band()
$x->band($y); # bitwise and
bior()
$x->bior($y); # bitwise inclusive or
bxor()
$x->bxor($y); # bitwise exclusive or
bnot()
$x->bnot(); # bitwise not (two's complement)
bpow()
$x->bpow($y);
Compute $x ** $y.
Please see the documentation in Math::BigInt for further details.
blog()
$x->blog($base, $accuracy); # logarithm of x to the base $base
If $base is not defined, Euler's number (e) is used:
print $x->blog(undef, 100); # log(x) to 100 digits
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()
Math::BigRat->config("trap_nan" => 1); # set
$accu = Math::BigRat->config("accuracy"); # get
Set or get configuration parameter values. Read-only parameters are marked as RO.
Read-write parameters are marked as RW. The following parameters are supported.
Parameter RO/RW Description
Example
============================================================
lib RO Name of the math backend library
Math::BigInt::Calc
lib_version RO Version of the math backend library
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
accuracy RW Global accuracy
undef
round_mode RW Global round mode
even
div_scale RW Fallback accuracy for div, sqrt etc.
40
trap_nan RW Trap NaNs
undef
trap_inf RW Trap +inf/-inf
undef
NUMERIC LITERALS
After "use Math::BigRat ':constant'" all numeric literals in the given scope are converted
to "Math::BigRat" objects. This conversion happens at compile time. Every non-integer is
convert to a NaN.
For example,
perl -MMath::BigRat=:constant -le 'print 2**150'
prints the exact value of "2**150". Note that without conversion of constants to objects
the expression "2**150" is calculated using Perl scalars, which leads to an inaccurate
result.
Please note that strings are not affected, so that
use Math::BigRat qw/:constant/;
$x = "1234567890123456789012345678901234567890"
+ "123456789123456789";
does give you what you expect. You need an explicit Math::BigRat->new() around at least
one of the operands. You should also quote large constants to prevent loss of precision:
use Math::BigRat;
$x = Math::BigRat->new("1234567889123456789123456789123456789");
Without the quotes Perl first converts the large number to a floating point constant at
compile time, and then converts the result to a Math::BigRat object at run time, which
results in an inaccurate result.
Hexadecimal, octal, and binary floating point literals
Perl (and this module) accepts hexadecimal, octal, and binary floating point literals, but
use them with care with Perl versions before v5.32.0, because some versions of Perl
silently give the wrong result. Below are some examples of different ways to write the
number decimal 314.
Hexadecimal floating point literals:
0x1.3ap+8 0X1.3AP+8
0x1.3ap8 0X1.3AP8
0x13a0p-4 0X13A0P-4
Octal floating point literals (with "0" prefix):
01.164p+8 01.164P+8
01.164p8 01.164P8
011640p-4 011640P-4
Octal floating point literals (with "0o" prefix) (requires v5.34.0):
0o1.164p+8 0O1.164P+8
0o1.164p8 0O1.164P8
0o11640p-4 0O11640P-4
Binary floating point literals:
0b1.0011101p+8 0B1.0011101P+8
0b1.0011101p8 0B1.0011101P8
0b10011101000p-2 0B10011101000P-2
BUGS
Please report any bugs or feature requests to "bug-math-bigrat at rt.cpan.org", or through
the web interface at <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigRat> (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::BigRat
You can also look for information at:
• GitHub
<https://github.com/pjacklam/p5-Math-BigRat>
• RT: CPAN's request tracker
<https://rt.cpan.org/Dist/Display.html?Name=Math-BigRat>
• MetaCPAN
<https://metacpan.org/release/Math-BigRat>
• CPAN Testers Matrix
<http://matrix.cpantesters.org/?dist=Math-BigRat>
• CPAN Ratings
<https://cpanratings.perl.org/dist/Math-BigRat>
LICENSE
This program is free software; you may redistribute it and/or modify it under the same
terms as Perl itself.
SEE ALSO
bigrat, Math::BigFloat and Math::BigInt as well as the backends Math::BigInt::FastCalc,
Math::BigInt::GMP, and Math::BigInt::Pari.
AUTHORS
• Tels <http://bloodgate.com/> 2001-2009.
• Maintained by Peter John Acklam <pjacklam@gmail.com> 2011-