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# Math::BigFloat

Section: User Contributed Perl Documentation (3)

Updated: 2018-11-08

Index ## NAME

Math::BigFloat - Arbitrary size floating point math package

## SYNOPSIS

use Math::BigFloat; # Configuration methods (may be used as class methods and instance methods) Math::BigFloat->accuracy(); # get class accuracy Math::BigFloat->accuracy($n); # set class accuracy Math::BigFloat->precision(); # get class precision Math::BigFloat->precision($n); # set class precision Math::BigFloat->round_mode(); # get class rounding mode Math::BigFloat->round_mode($m); # set global round mode, must be one of # 'even', 'odd', '+inf', '-inf', 'zero', # 'trunc', or 'common' Math::BigFloat->config("lib"); # name of backend math library # Constructor methods (when the class methods below are used as instance # methods, the value is assigned the invocand) $x = Math::BigFloat->new($str); # defaults to 0 $x = Math::BigFloat->new('0x123'); # from hexadecimal $x = Math::BigFloat->new('0b101'); # from binary $x = Math::BigFloat->from_hex('0xc.afep+3'); # from hex $x = Math::BigFloat->from_hex('cafe'); # ditto $x = Math::BigFloat->from_oct('1.3267p-4'); # from octal $x = Math::BigFloat->from_oct('0377'); # ditto $x = Math::BigFloat->from_bin('0b1.1001p-4'); # from binary $x = Math::BigFloat->from_bin('0101'); # ditto $x = Math::BigFloat->bzero(); # create a +0 $x = Math::BigFloat->bone(); # create a +1 $x = Math::BigFloat->bone('-'); # create a -1 $x = Math::BigFloat->binf(); # create a +inf $x = Math::BigFloat->binf('-'); # create a -inf $x = Math::BigFloat->bnan(); # create a Not-A-Number $x = Math::BigFloat->bpi(); # returns pi $y = $x->copy(); # make a copy (unlike $y = $x) $y = $x->as_int(); # return as BigInt # Boolean methods (these don't modify the invocand) $x->is_zero(); # if $x is 0 $x->is_one(); # if $x is +1 $x->is_one("+"); # ditto $x->is_one("-"); # if $x is -1 $x->is_inf(); # if $x is +inf or -inf $x->is_inf("+"); # if $x is +inf $x->is_inf("-"); # if $x is -inf $x->is_nan(); # if $x is NaN $x->is_positive(); # if $x > 0 $x->is_pos(); # ditto $x->is_negative(); # if $x < 0 $x->is_neg(); # ditto $x->is_odd(); # if $x is odd $x->is_even(); # if $x is even $x->is_int(); # if $x is an integer # Comparison methods $x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0) $x->bacmp($y); # compare absolutely (undef, < 0, == 0, > 0) $x->beq($y); # true if and only if $x == $y $x->bne($y); # true if and only if $x != $y $x->blt($y); # true if and only if $x < $y $x->ble($y); # true if and only if $x <= $y $x->bgt($y); # true if and only if $x > $y $x->bge($y); # true if and only if $x >= $y # Arithmetic methods $x->bneg(); # negation $x->babs(); # absolute value $x->bsgn(); # sign function (-1, 0, 1, or NaN) $x->bnorm(); # normalize (no-op) $x->binc(); # increment $x by 1 $x->bdec(); # decrement $x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bmuladd($y,$z); # $x = $x * $y + $z $x->bdiv($y); # division (floored), set $x to quotient # return (quo,rem) or quo if scalar $x->btdiv($y); # division (truncated), set $x to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus (x % y) $x->btmod($y); # modulus (truncated) $x->bmodinv($mod); # modular multiplicative inverse $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod) $x->bpow($y); # power of arguments (x ** y) $x->blog(); # logarithm of $x to base e (Euler's number) $x->blog($base); # logarithm of $x to base $base (e.g., base 2) $x->bexp(); # calculate e ** $x where e is Euler's number $x->bnok($y); # x over y (binomial coefficient n over k) $x->bsin(); # sine $x->bcos(); # cosine $x->batan(); # inverse tangent $x->batan2($y); # two-argument inverse tangent $x->bsqrt(); # calculate square root $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) $x->bfac(); # factorial of $x (1*2*3*4*..$x) $x->blsft($n); # left shift $n places in base 2 $x->blsft($n,$b); # left shift $n places in base $b # returns (quo,rem) or quo (scalar context) $x->brsft($n); # right shift $n places in base 2 $x->brsft($n,$b); # right shift $n places in base $b # returns (quo,rem) or quo (scalar context) # Bitwise methods $x->band($y); # bitwise and $x->bior($y); # bitwise inclusive or $x->bxor($y); # bitwise exclusive or $x->bnot(); # bitwise not (two's complement) # Rounding methods $x->round($A,$P,$mode); # round to accuracy or precision using # rounding mode $mode $x->bround($n); # accuracy: preserve $n digits $x->bfround($n); # $n > 0: round to $nth digit left of dec. point # $n < 0: round to $nth digit right of dec. point $x->bfloor(); # round towards minus infinity $x->bceil(); # round towards plus infinity $x->bint(); # round towards zero # Other mathematical methods $x->bgcd($y); # greatest common divisor $x->blcm($y); # least common multiple # Object property methods (do not modify the invocand) $x->sign(); # the sign, either +, - or NaN $x->digit($n); # the nth digit, counting from the right $x->digit(-$n); # the nth digit, counting from the left $x->length(); # return number of digits in number ($xl,$f) = $x->length(); # length of number and length of fraction # part, latter is always 0 digits long # for Math::BigInt objects $x->mantissa(); # return (signed) mantissa as BigInt $x->exponent(); # return exponent as BigInt $x->parts(); # return (mantissa,exponent) as BigInt $x->sparts(); # mantissa and exponent (as integers) $x->nparts(); # mantissa and exponent (normalised) $x->eparts(); # mantissa and exponent (engineering notation) $x->dparts(); # integer and fraction part # Conversion methods (do not modify the invocand) $x->bstr(); # decimal notation, possibly zero padded $x->bsstr(); # string in scientific notation with integers $x->bnstr(); # string in normalized notation $x->bestr(); # string in engineering notation $x->bdstr(); # string in decimal notation $x->as_hex(); # as signed hexadecimal string with prefixed 0x $x->as_bin(); # as signed binary string with prefixed 0b $x->as_oct(); # as signed octal string with prefixed 0 # Other conversion methods $x->numify(); # return as scalar (might overflow or underflow)

## DESCRIPTION

Math::BigFloat provides support for arbitrary precision floating point.Overloading is also provided for Perl operators.

All operators (including basic math operations) are overloaded if youdeclare your big floating point numbers as

$x = Math::BigFloat -> new('12_3.456_789_123_456_789E-2');

Operations with overloaded operators preserve the arguments, which isexactly what you expect.

### Input

Input values to these routines may be any scalar number or string that lookslike a number and represents a floating point number.

- *
- Leading and trailing whitespace is ignored.
- *
- Leading and trailing zeros are ignored.
- *
- If the string has a ``0x'' prefix, it is interpreted as a hexadecimal number.
- *
- If the string has a ``0b'' prefix, it is interpreted as a binary number.
- *
- For hexadecimal and binary numbers, the exponent must be separated from thesignificand (mantissa) by the letter ``p'' or ``P'', not ``e'' or ``E'' as with decimalnumbers.
- *
- One underline is allowed between any two digits, including hexadecimal andbinary digits.
- *
- If the string can not be interpreted, NaN is returned.

Octal numbers are typically prefixed by ``0'', but since leading zeros arestripped, these methods can not automatically recognize octal numbers, so usethe constructor *from_oct()* to interpret octal strings.

Some examples of valid string input

Input string Resulting value 123 123 1.23e2 123 12300e-2 123 0xcafe 51966 0b1101 13 67_538_754 67538754 -4_5_6.7_8_9e+0_1_0 -4567890000000 0x1.921fb5p+1 3.14159262180328369140625e+0 0b1.1001p-4 9.765625e-2

### Output

Output values are usually Math::BigFloat objects.

Boolean operators `"is_zero()"`, `"is_one()"`, `"is_inf()"`, etc. return true orfalse.

Comparison operators `"bcmp()"` and `"bacmp()"`) return -1, 0, 1, orundef.

## METHODS

Math::BigFloat supports all methods that Math::BigInt supports, except itcalculates non-integer results when possible. Please see Math::BigInt for afull description of each method. Below are just the most important differences:

### Configuration methods

*accuracy()* $x->accuracy(5); # local for $x CLASS->accuracy(5); # global for all members of CLASS # Note: This also applies to new()! $A = $x->accuracy(); # read out accuracy that affects $x $A = CLASS->accuracy(); # read out global accuracy

Set or get the global or local accuracy, aka how many significant digits theresults have. If you set a global accuracy, then this also applies to *new()*!

Warning! The accuracy *sticks*, e.g. once you created a number under theinfluence of `"CLASS->accuracy($A)"`, all results from math operations withthat number will also be rounded.

In most cases, you should probably round the results explicitly using one of``*round()*'' in Math::BigInt, ``*bround()*'' in Math::BigInt or ``*bfround()*'' in Math::BigIntor by passing the desired accuracy to the math operation as additionalparameter:

my $x = Math::BigInt->new(30000); my $y = Math::BigInt->new(7); print scalar $x->copy()->bdiv($y, 2); # print 4300 print scalar $x->copy()->bdiv($y)->bround(2); # print 4300

*precision()* $x->precision(-2); # local for $x, round at the second # digit right of the dot $x->precision(2); # ditto, round at the second digit # left of the dot CLASS->precision(5); # Global for all members of CLASS # This also applies to new()! CLASS->precision(-5); # ditto $P = CLASS->precision(); # read out global precision $P = $x->precision(); # read out precision that affects $x

Note: You probably want to use ``*accuracy()*'' instead. With ``*accuracy()*'' youset the number of digits each result should have, with ``*precision()*'' youset the place where to round!

### Constructor methods

*from_hex()* $x -> from_hex("0x1.921fb54442d18p+1"); $x = Math::BigFloat -> from_hex("0x1.921fb54442d18p+1");

Interpret input as a hexadecimal string.A prefix (``0x'', ``x'', ignoring case) isoptional. A single underscore character (``_'') may be placed between any twodigits. If the input is invalid, a NaN is returned. The exponent is in base 2using decimal digits.

If called as an instance method, the value is assigned to the invocand.

*from_oct()* $x -> from_oct("1.3267p-4"); $x = Math::BigFloat -> from_oct("1.3267p-4");

Interpret input as an octal string. A single underscore character (``_'') may beplaced between any two digits. If the input is invalid, a NaN is returned. Theexponent is in base 2 using decimal digits.

If called as an instance method, the value is assigned to the invocand.

*from_bin()* $x -> from_bin("0b1.1001p-4"); $x = Math::BigFloat -> from_bin("0b1.1001p-4");

Interpret input as a hexadecimal string. A prefix (``0b'' or ``b'', ignoring case)is optional. A single underscore character (``_'') may be placed between any twodigits. If the input is invalid, a NaN is returned. The exponent is in base 2using decimal digits.

If called as an instance method, the value is assigned to the invocand.

*bpi()* print Math::BigFloat->bpi(100), "\n";

Calculate PI to N digits (including the 3 before the dot). The result isrounded according to the current rounding mode, which defaults to ``even''.

This method was added in v1.87 of Math::BigInt (June 2007).

### Arithmetic methods

*bmuladd()* $x->bmuladd($y,$z);

Multiply `$x` by `$y`, and then add `$z` to the result.

This method was added in v1.87 of Math::BigInt (June 2007).

*bdiv()* $q = $x->bdiv($y); ($q, $r) = $x->bdiv($y);

In scalar context, divides `$x` by `$y` and returns the result to the given ordefault accuracy/precision. 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)"`.

*bmod()* $x->bmod($y);

Returns `$x` modulo `$y`. When `$x` is finite, and `$y` is finite and non-zero, theresult 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 resultfrom Perl's % operator.

*bexp()* $x->bexp($accuracy); # calculate e ** X

Calculates the expression `"e ** $x"` where `"e"` is Euler's number.

This method was added in v1.82 of Math::BigInt (April 2007).

*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 v1.84 of Math::BigInt (April 2007).

*bsin()* my $x = Math::BigFloat->new(1); print $x->bsin(100), "\n";

Calculate the sinus of `$x`, modifying `$x` in place.

This method was added in v1.87 of Math::BigInt (June 2007).

*bcos()* my $x = Math::BigFloat->new(1); print $x->bcos(100), "\n";

Calculate the cosinus of `$x`, modifying `$x` in place.

This method was added in v1.87 of Math::BigInt (June 2007).

*batan()* my $x = Math::BigFloat->new(1); print $x->batan(100), "\n";

Calculate the arcus tanges of `$x`, modifying `$x` in place. See also ``*batan2()*''.

This method was added in v1.87 of Math::BigInt (June 2007).

*batan2()* my $y = Math::BigFloat->new(2); my $x = Math::BigFloat->new(3); print $y->batan2($x), "\n";

Calculate the arcus tanges of `$y` divided by `$x`, modifying `$y` in place.See also ``*batan()*''.

This method was added in v1.87 of Math::BigInt (June 2007).

*as_float()*- This method is called when Math::BigFloat encounters an object it doesn't knowhow to handle. For instance, assume
`$x` is a Math::BigFloat, or subclassthereof, and `$y` is defined, but not a Math::BigFloat, or subclass thereof. Ifyou do $x -> badd($y);

`$y` needs to be converted into an object that `$x` can deal with. This is done byfirst checking if `$y` is something that `$x` might be upgraded to. If that is thecase, no further attempts are made. The next is to see if `$y` supports themethod `"as_float()"`. The method `"as_float()"` is expected to return either anobject that has the same class as `$x`, a subclass thereof, or a string that`"ref($x)->new()"` can parse to create an object.

In Math::BigFloat, `"as_float()"` has the same effect as `"copy()"`.

### ACCURACY AND PRECISION

See also: Rounding.

Math::BigFloat supports both precision (rounding to a certain place before orafter the dot) and accuracy (rounding to a certain number of digits). For afull documentation, examples and tips on these topics please see the largesection about rounding in Math::BigInt.

Since things like `sqrt(2)` or `"1 / 3"` must presented with a limitedaccuracy lest a operation consumes all resources, each operation producesno more than the requested number of digits.

If there is no global precision or accuracy set, **and** the operation inquestion was not called with a requested precision or accuracy, **and** theinput `$x` has no accuracy or precision set, then a fallback parameter willbe used. For historical reasons, it is called `"div_scale"` and can be accessedvia:

$d = Math::BigFloat->div_scale(); # query Math::BigFloat->div_scale($n); # set to $n digits

The default value for `"div_scale"` is 40.

In case the result of one operation has more digits than specified,it is rounded. The rounding mode taken is either the default mode, or the onesupplied to the operation after the *scale*:

$x = Math::BigFloat->new(2); Math::BigFloat->accuracy(5); # 5 digits max $y = $x->copy()->bdiv(3); # gives 0.66667 $y = $x->copy()->bdiv(3,6); # gives 0.666667 $y = $x->copy()->bdiv(3,6,undef,'odd'); # gives 0.666667 Math::BigFloat->round_mode('zero'); $y = $x->copy()->bdiv(3,6); # will also give 0.666667

Note that `"Math::BigFloat->accuracy()"` and `"Math::BigFloat->precision()"`set the global variables, and thus **any** newly created number will be subjectto the global rounding **immediately**. This means that in the examples above, the`3` as argument to `"bdiv()"` will also get an accuracy of **5**.

It is less confusing to either calculate the result fully, and afterwardsround it explicitly, or use the additional parameters to the mathfunctions like so:

use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3); print $y->bround(5),"\n"; # gives 0.66667 or use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3,5); # gives 0.66667 print "$y\n";

### Rounding

- bfround ( +$scale )
- Rounds to the
`$scale`'th place left from the '.', counting from the dot.The first digit is numbered 1. - bfround ( -$scale )
- Rounds to the
`$scale`'th place right from the '.', counting from the dot. - bfround ( 0 )
- Rounds to an integer.
- bround ( +$scale )
- Preserves accuracy to
`$scale` digits from the left (aka significant digits) andpads the rest with zeros. If the number is between 1 and -1, the significantdigits count from the first non-zero after the '.' - bround ( -$scale ) and bround ( 0 )
- These are effectively no-ops.

All rounding functions take as a second parameter a rounding mode from one ofthe following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'.

The default rounding mode is 'even'. By using`"Math::BigFloat->round_mode($round_mode);"` you can get and set the defaultmode for subsequent rounding. The usage of `"$Math::BigFloat::$round_mode"` isno longer supported.The second parameter to the round functions then overrides the defaulttemporarily.

The `"as_number()"` function returns a BigInt from a Math::BigFloat. It uses'trunc' as rounding mode to make it equivalent to:

$x = 2.5; $y = int($x) + 2;

You can override this by passing the desired rounding mode as parameter to`"as_number()"`:

$x = Math::BigFloat->new(2.5); $y = $x->as_number('odd'); # $y = 3

## Autocreating constants

After

`"use Math::BigFloat ':constant'"` all the floating point constantsin the given scope are converted to

`"Math::BigFloat"`. This conversionhappens at compile time.

In particular

perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"'

prints the value of `"2E-100"`. Note that without conversion ofconstants the expression 2E-100 will be calculated as normal floating pointnumber.

Please note that ':constant' does not affect integer constants, nor binarynor hexadecimal constants. Use bignum or Math::BigInt to get this towork.

### Math library

Math with the numbers is done (by default) by a module calledMath::BigInt::Calc. This is equivalent to saying:

use Math::BigFloat lib => 'Calc';

You can change this by using:

use Math::BigFloat lib => 'GMP';

**Note**: General purpose packages should not be explicit about the libraryto use; let the script author decide which is best.

Note: The keyword 'lib' will warn when the requested library could not beloaded. To suppress the warning use 'try' instead:

use Math::BigFloat try => 'GMP';

If your script works with huge numbers and Calc is too slow for them,you can also for the loading of one of these libraries and if noneof them can be used, the code will die:

use Math::BigFloat only => 'GMP,Pari';

The following would first try to find Math::BigInt::Foo, thenMath::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:

use Math::BigFloat lib => 'Foo,Math::BigInt::Bar';

See the respective low-level library documentation for further details.

Please note that Math::BigFloat does **not** use the denoted library itself,but it merely passes the lib argument to Math::BigInt. So, instead of the needto do:

use Math::BigInt lib => 'GMP'; use Math::BigFloat;

you can roll it all into one line:

use Math::BigFloat lib => 'GMP';

It is also possible to just require Math::BigFloat:

require Math::BigFloat;

This will load the necessary things (like BigInt) when they are needed, andautomatically.

See Math::BigInt for more details than you ever wanted to know about usinga different low-level library.

### Using Math::BigInt::Lite

For backwards compatibility reasons it is still possible torequest a different storage class for use with Math::BigFloat:

use Math::BigFloat with => 'Math::BigInt::Lite';

However, this request is ignored, as the current code now uses the low-levelmath library for directly storing the number parts.

## EXPORTS

`"Math::BigFloat"` exports nothing by default, but can export the

`"bpi()"` method:

use Math::BigFloat qw/bpi/; print bpi(10), "\n";

## CAVEATS

Do not try to be clever to insert some operations in between switchinglibraries:

require Math::BigFloat; my $matter = Math::BigFloat->bone() + 4; # load BigInt and Calc Math::BigFloat->import( lib => 'Pari' ); # load Pari, too my $anti_matter = Math::BigFloat->bone()+4; # now use Pari

This will create objects with numbers stored in two different backend libraries,and **VERY BAD THINGS** will happen when you use these together:

my $flash_and_bang = $matter + $anti_matter; # Don't do this!

- stringify,
*bstr()* - Both stringify and
*bstr()* now drop the leading '+'. The old code would return'+1.23', the new returns '1.23'. See the documentation in Math::BigInt forreasoning and details. *brsft()*- The following will probably not print what you expect:
my $c = Math::BigFloat->new('3.14159'); print $c->brsft(3,10),"\n"; # prints 0.00314153.1415

It prints both quotient and remainder, since print calls `"brsft()"` in listcontext. Also, `"$c->brsft()"` will modify `$c`, so be careful.You probably want to use

print scalar $c->copy()->brsft(3,10),"\n"; # or if you really want to modify $c print scalar $c->brsft(3,10),"\n";

instead.

- Modifying and =
- Beware of:
$x = Math::BigFloat->new(5); $y = $x;

It will not do what you think, e.g. making a copy of `$x`. Instead it just makesa second reference to the **same** object and stores it in `$y`. Thus anythingthat modifies `$x` will modify `$y` (except overloaded math operators), and viceversa. See Math::BigInt for details and how to avoid that.

*precision()* vs. *accuracy()*- A common pitfall is to use ``
*precision()*'' when you want to round a result toa certain number of digits: use Math::BigFloat; Math::BigFloat->precision(4); # does not do what you # think it does my $x = Math::BigFloat->new(12345); # rounds $x to "12000"! print "$x\n"; # print "12000" my $y = Math::BigFloat->new(3); # rounds $y to "0"! print "$y\n"; # print "0" $z = $x / $y; # 12000 / 0 => NaN! print "$z\n"; print $z->precision(),"\n"; # 4

Replacing ``*precision()*'' with ``*accuracy()*'' is probably not what you want, either:

use Math::BigFloat; Math::BigFloat->accuracy(4); # enables global rounding: my $x = Math::BigFloat->new(123456); # rounded immediately # to "12350" print "$x\n"; # print "123500" my $y = Math::BigFloat->new(3); # rounded to "3 print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y),"\n"; # 41170 print $z->accuracy(),"\n"; # 4

What you want to use instead is:

use Math::BigFloat; my $x = Math::BigFloat->new(123456); # no rounding print "$x\n"; # print "123456" my $y = Math::BigFloat->new(3); # no rounding print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y,4),"\n"; # 41150 print $z->accuracy(),"\n"; # undef

In addition to computing what you expected, the last example also does **not**``taint'' the result with an accuracy or precision setting, which wouldinfluence any further operation.

## BUGS

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 onyour bug as I make changes.

## SUPPORT

You can find documentation for this module with the perldoc command.

perldoc Math::BigFloat

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
<http://cpanratings.perl.org/dist/Math-BigInt>

- *
- Search CPAN
<http://search.cpan.org/dist/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>

## LICENSE

This program is free software; you may redistribute it and/or modify it underthe same terms as Perl itself.

## SEE ALSO

Math::BigFloat and Math::BigInt as well as the backendsMath::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.

The pragmas bignum, bigint and bigrat also might be of interestbecause they solve the autoupgrading/downgrading issue, at least partly.

## AUTHORS

- *
- Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.
- *
- Completely rewritten by Tels <http://bloodgate.com> in 2001-2008.
- *
- Florian Ragwitz <floraAATTcpan.org>, 2010.
- *
- Peter John Acklam <pjacklamAATTonline.no>, 2011-.

## Index

- NAME
- SYNOPSIS
- DESCRIPTION
- Input
- Output

- METHODS
- Configuration methods
- Constructor methods
- Arithmetic methods
- ACCURACY AND PRECISION
- Rounding

- Autocreating constants
- Math library
- Using Math::BigInt::Lite

- EXPORTS
- CAVEATS
- BUGS
- SUPPORT
- LICENSE
- SEE ALSO
- AUTHORS

This document was created byman2html,using the manual pages.