# phpman > perldoc > Math::BigRat ## NAME [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) - Arbitrary big rational numbers ## SYNOPSIS use [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown); my $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('3/7'); $x += '5/9'; print $x->bstr(), "\n"; print $x ** 2, "\n"; my $y = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('inf'); print "$y ", ($y->is_inf ? 'is' : 'is not'), " infinity\n"; my $z = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->[new(144)](https://www.chedong.com/phpMan.php/man/new/144/markdown); $z->bsqrt(); ## DESCRIPTION [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) complements [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) and [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) try => 'GMP'; Note: This needs [Math::BigInt::GMP](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AGMP/markdown) installed. The following would first try to find [Math::BigInt::Foo](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AFoo/markdown), then [Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown), and when this also fails, revert to [Math::BigInt::Calc](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ACalc/markdown): use [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) try => 'Foo,[Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown)'; If you want to get warned when the fallback occurs, replace "try" with "lib": use [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) lib => 'Foo,[Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown)'; If you want the code to die instead, replace "try" with "only": use [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) only => 'Foo,[Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown)'; ## METHODS Any methods not listed here are derived from [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) (or [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)), so make sure you check these two modules for further information. ### new $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('1/3'); Create a new [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) object. Input can come in various forms: $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->[new(123)](https://www.chedong.com/phpMan.php/man/new/123/markdown); # scalars $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('inf'); # infinity $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('123.3'); # float $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('1/3'); # simple string $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('1 / 3'); # spaced $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('1 / 0.1'); # w/ floats $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new([Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)->[new(3)](https://www.chedong.com/phpMan.php/man/new/3/markdown)); # BigInt $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new([Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new('3.1')); # BigFloat $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new([Math::BigInt::Lite](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ALite/markdown)->new('2')); # BigLite # You can also give D and N as different objects: $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new( [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)->new(-123), [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)->[new(7)](https://www.chedong.com/phpMan.php/man/new/7/markdown), ); # => -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()" or "as_float()" instead. This routine is automatically used whenever a scalar is required: my $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('3/1'); @array = (0, 1, 2, 3); $y = $array[$x]; # set $y to 3 ### as_int ### as_number $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('13/7'); print $x->as_float(), "\n"; # '1' $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('2/3'); print $x->[as_float(5)](https://www.chedong.com/phpMan.php/man/asfloat/5/markdown), "\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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) (April 2008). ### as_hex $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('13'); print $x->as_hex(), "\n"; # '0xd' Returns the BigRat as hexadecimal string. Works only for integers. ### as_bin $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('13'); print $x->as_bin(), "\n"; # '0x1101' Returns the BigRat as binary string. Works only for integers. ### as_oct $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('13'); print $x->as_oct(), "\n"; # '015' Returns the BigRat as octal string. Works only for integers. ### from_hex my $h = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->from_hex('0x10'); Create a BigRat from a hexadecimal number in string form. ### from_oct my $o = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->from_oct('020'); Create a BigRat from an octal number in string form. ### from_bin my $b = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->from_bin('0b10000000'); Create a BigRat from an binary number in string form. ### bnan $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->bzero(); Creates a new BigRat object representing zero. If used on an object, it will set it to zero: $x->bzero(); ### binf $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->binf($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 $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->bone($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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('123/1')->[digit(1)](https://www.chedong.com/phpMan.php/man/digit/1/markdown); # 1 print [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('3/1')->bfac(), "\n"; # 1*2*3 print [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->new('5/1')->bfac(), "\n"; # 1*2*3*4*5 Works currently only for integers. ### bround 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 $x is exactly zero, otherwise false. ### is_pos print "$x is >= 0\n" if $x->is_positive(); Return true if $x is positive (greater than or equal to zero), otherwise false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't. "is_positive()" is an alias for "is_pos()". ### is_neg print "$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)>. ### 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) for further details. ### bstr my $x = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->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 Used to shift numbers left/right. Please see the documentation in [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) (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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) (May 2007). ### config [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->config("trap_nan" => 1); # set $accu = [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ACalc/markdown) lib_version RO Version of the math backend library 0.30 class RO The class of config you just called [Math::BigRat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) 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 ## BUGS Please report any bugs or feature requests to "bug-math-bigrat at rt.cpan.org", or through the web interface at <> (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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigRat/markdown) You can also look for information at: * RT: CPAN's request tracker <> * AnnoCPAN: Annotated CPAN documentation <> * CPAN Ratings <> * Search CPAN <> * CPAN Testers Matrix <> * The Bignum mailing list * Post to mailing list "bignum at lists.scsys.co.uk" * View mailing list <> * Subscribe/Unsubscribe <> ## 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) and [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) as well as the backends [Math::BigInt::FastCalc](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AFastCalc/markdown), [Math::BigInt::GMP](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AGMP/markdown), and [Math::BigInt::Pari](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3APari/markdown). ## AUTHORS * Tels <> 2001-2009. * Maintained by Peter John Acklam <> 2011-