Provided by: libmath-bigint-perl_1.999715-1_all 
NAME
Math::BigFloat - Arbitrary size floating point math package
SYNOPSIS
use Math::BigFloat;
# Number creation
my $x = Math::BigFloat->new($str); # defaults to 0
my $y = $x->copy(); # make a true copy
my $nan = Math::BigFloat->bnan(); # create a NotANumber
my $zero = Math::BigFloat->bzero(); # create a +0
my $inf = Math::BigFloat->binf(); # create a +inf
my $inf = Math::BigFloat->binf('-'); # create a -inf
my $one = Math::BigFloat->bone(); # create a +1
my $mone = Math::BigFloat->bone('-'); # create a -1
my $x = Math::BigFloat->bone('-'); #
my $x = Math::BigFloat->from_hex('0xc.afep+3'); # from hexadecimal
my $x = Math::BigFloat->from_bin('0b1.1001p-4'); # from binary
my $x = Math::BigFloat->from_oct('1.3267p-4'); # from octal
my $pi = Math::BigFloat->bpi(100); # PI to 100 digits
# the following examples compute their result to 100 digits accuracy:
my $cos = Math::BigFloat->new(1)->bcos(100); # cosinus(1)
my $sin = Math::BigFloat->new(1)->bsin(100); # sinus(1)
my $atan = Math::BigFloat->new(1)->batan(100); # arcus tangens(1)
my $atan2 = Math::BigFloat->new( 1 )->batan2( 1 ,100); # batan(1)
my $atan2 = Math::BigFloat->new( 1 )->batan2( 8 ,100); # batan(1/8)
my $atan2 = Math::BigFloat->new( -2 )->batan2( 1 ,100); # batan(-2)
# Testing
$x->is_zero(); # true if arg is +0
$x->is_nan(); # true if arg is NaN
$x->is_one(); # true if arg is +1
$x->is_one('-'); # true if arg is -1
$x->is_odd(); # true if odd, false for even
$x->is_even(); # true if even, false for odd
$x->is_pos(); # true if >= 0
$x->is_neg(); # true if < 0
$x->is_inf(sign); # true if +inf, or -inf (default is '+')
$x->bcmp($y); # compare numbers (undef,<0,=0,>0)
$x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
$x->sign(); # return the sign, either +,- or NaN
$x->digit($n); # return the nth digit, counting from right
$x->digit(-$n); # return the nth digit, counting from left
# The following all modify their first argument. If you want to pre-
# serve $x, use $z = $x->copy()->bXXX($y); See under L</CAVEATS> for
# necessary when mixing $a = $b assignments with non-overloaded math.
# set
$x->bzero(); # set $i to 0
$x->bnan(); # set $i to NaN
$x->bone(); # set $x to +1
$x->bone('-'); # set $x to -1
$x->binf(); # set $x to inf
$x->binf('-'); # set $x to -inf
$x->bneg(); # negation
$x->babs(); # absolute value
$x->bnorm(); # normalize (no-op)
$x->bnot(); # two's complement (bit wise not)
$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)
$x->bdiv($y); # divide, set $x to quotient
# return (quo,rem) or quo if scalar
$x->bmod($y); # modulus ($x % $y)
$x->bpow($y); # power of arguments ($x ** $y)
$x->bmodpow($exp,$mod); # modular exponentiation (($num**$exp) % $mod))
$x->blsft($y, $n); # left shift by $y places in base $n
$x->brsft($y, $n); # right shift by $y places in base $n
# returns (quo,rem) or quo if in scalar context
$x->blog(); # logarithm of $x to base e (Euler's number)
$x->blog($base); # logarithm of $x to base $base (f.i. 2)
$x->bexp(); # calculate e ** $x where e is Euler's number
$x->band($y); # bit-wise and
$x->bior($y); # bit-wise inclusive or
$x->bxor($y); # bit-wise exclusive or
$x->bnot(); # bit-wise not (two's complement)
$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)
$x->bround($N); # accuracy: preserve $N digits
$x->bfround($N); # precision: round to the $Nth digit
$x->bfloor(); # return integer less or equal than $x
$x->bceil(); # return integer greater or equal than $x
$x->bint(); # round towards zero
# The following do not modify their arguments:
bgcd(@values); # greatest common divisor
blcm(@values); # lowest common multiplicator
$x->bstr(); # return string
$x->bsstr(); # return string in scientific notation
$x->as_int(); # return $x as BigInt
$x->exponent(); # return exponent as BigInt
$x->mantissa(); # return mantissa as BigInt
$x->parts(); # return (mantissa,exponent) as BigInt
$x->length(); # number of digits (w/o sign and '.')
($l,$f) = $x->length(); # number of digits, and length of fraction
$x->precision(); # return P of $x (or global, if P of $x undef)
$x->precision($n); # set P of $x to $n
$x->accuracy(); # return A of $x (or global, if A of $x undef)
$x->accuracy($n); # set A $x to $n
# these get/set the appropriate global value for all BigFloat objects
Math::BigFloat->precision(); # Precision
Math::BigFloat->accuracy(); # Accuracy
Math::BigFloat->round_mode(); # rounding mode
DESCRIPTION
All operators (including basic math operations) are overloaded if you declare your big floating point
numbers as
$i = Math::BigFloat -> new('12_3.456_789_123_456_789E-2');
Operations with overloaded operators preserve the arguments, which is exactly what you expect.
Input
Input to these routines are either BigFloat objects, or strings of the following four forms:
• "/^[+-]\d+$/"
• "/^[+-]\d+\.\d*$/"
• "/^[+-]\d+E[+-]?\d+$/"
• "/^[+-]\d*\.\d+E[+-]?\d+$/"
all with optional leading and trailing zeros and/or spaces. Additionally, numbers are allowed to have an
underscore between any two digits.
Empty strings as well as other illegal numbers results in 'NaN'.
bnorm() on a BigFloat object is now effectively a no-op, since the numbers are always stored in
normalized form. On a string, it creates a BigFloat object.
Output
Output values are BigFloat objects (normalized), except for bstr() and bsstr().
The string output will always have leading and trailing zeros stripped and drop a plus sign. "bstr()"
will give you always the form with a decimal point, while "bsstr()" (s for scientific) gives you the
scientific notation.
Input bstr() bsstr()
'-0' '0' '0E1'
' -123 123 123' '-123123123' '-123123123E0'
'00.0123' '0.0123' '123E-4'
'123.45E-2' '1.2345' '12345E-4'
'10E+3' '10000' '1E4'
Some routines ("is_odd()", "is_even()", "is_zero()", "is_one()", "is_nan()") return true or false, while
others ("bcmp()", "bacmp()") return either undef, <0, 0 or >0 and are suited for sort.
Actual math is done by using the class defined with "with => Class;" (which defaults to BigInts) to
represent the mantissa and exponent.
The sign "/^[+-]$/" is stored separately. The string 'NaN' is used to represent the result when input
arguments are not numbers, and 'inf' and '-inf' are used to represent positive and negative infinity,
respectively.
mantissa(), exponent() and parts()
mantissa() and exponent() return the said parts of the BigFloat as BigInts such that:
$m = $x->mantissa();
$e = $x->exponent();
$y = $m * ( 10 ** $e );
print "ok\n" if $x == $y;
"($m,$e) = $x->parts();" is just a shortcut giving you both of them.
Currently the mantissa is reduced as much as possible, favouring higher exponents over lower ones (e.g.
returning 1e7 instead of 10e6 or 10000000e0). This might change in the future, so do not depend on it.
Accuracy vs. Precision
See also: Rounding.
Math::BigFloat supports both precision (rounding to a certain place before or after the dot) and accuracy
(rounding to a certain number of digits). For a full documentation, examples and tips on these topics
please see the large section about rounding in Math::BigInt.
Since things like sqrt(2) or "1 / 3" must presented with a limited accuracy lest a operation consumes all
resources, each operation produces no more than the requested number of digits.
If there is no global precision or accuracy set, and the operation in question was not called with a
requested precision or accuracy, and the input $x has no accuracy or precision set, then a fallback
parameter will be used. For historical reasons, it is called "div_scale" and can be accessed via:
$d = Math::BigFloat->div_scale(); # query
Math::BigFloat->div_scale($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 one supplied to the operation after the scale:
$x = Math::BigFloat->new(2);
Math::BigFloat->accuracy(5); # 5 digits max
$y = $x->copy()->bdiv(3); # will give 0.66667
$y = $x->copy()->bdiv(3,6); # will give 0.666667
$y = $x->copy()->bdiv(3,6,undef,'odd'); # will give 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 subject to 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 afterwards round it explicitly, or use the
additional parameters to the math functions like so:
use Math::BigFloat;
$x = Math::BigFloat->new(2);
$y = $x->copy()->bdiv(3);
print $y->bround(5),"\n"; # will give 0.66667
or
use Math::BigFloat;
$x = Math::BigFloat->new(2);
$y = $x->copy()->bdiv(3,5); # will give 0.66667
print "$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 $scale digits from the left (aka significant digits) and pads the rest with
zeros. If the number is between 1 and -1, the significant digits count from the first non-zero after
the '.'
bround ( -$scale ) and bround ( 0 )
These are effectively no-ops.
All rounding functions take as a second parameter a rounding mode from one of the following: 'even',
'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'.
The default rounding mode is 'even'. By using "Math::BigFloat->round_mode($round_mode);" you can get and
set the default mode for subsequent rounding. The usage of "$Math::BigFloat::$round_mode" is no longer
supported. The second parameter to the round functions then overrides the default temporarily.
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
METHODS
Math::BigFloat supports all methods that Math::BigInt supports, except it calculates non-integer results
when possible. Please see Math::BigInt for a full description of each method. Below are just the most
important differences:
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
$A = CLASS->accuracy(); # read out global accuracy
Set or get the global or local accuracy, aka how many significant digits the results have. If you set
a global accuracy, then this also applies to new()!
Warning! The accuracy sticks, e.g. once you created a number under the influence of
"CLASS->accuracy($A)", all results from math operations with that 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::BigInt or by passing the desired
accuracy to the math operation as additional parameter:
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()" you set the number of digits
each result should have, with "precision()" you set the place where to round!
bdiv()
$q = $x->bdiv($y);
($q, $r) = $x->bdiv($y);
In scalar context, divides $x by $y and returns the result to the given or default
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, 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.
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).
bpi()
print Math::BigFloat->bpi(100), "\n";
Calculate PI to N digits (including the 3 before the dot). The result is rounded according to the
current rounding mode, which defaults to "even".
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).
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).
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).
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).
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).
as_float()
This method is called when Math::BigFloat encounters an object it doesn't know how to handle. For
instance, assume $x is a Math::BigFloat, or subclass thereof, and $y is defined, but not a
Math::BigFloat, or subclass thereof. If you do
$x -> badd($y);
$y needs to be converted into an object that $x can deal with. This is done by first checking if $y
is something that $x might be upgraded to. If that is the case, no further attempts are made. The
next is to see if $y supports the method "as_float()". The method "as_float()" is expected to return
either an object 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()".
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) is optional. A single
underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is
returned. The exponent 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 two digits. If the input is invalid, a NaN is
returned. The exponent is in base 2 using 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 be placed between any two
digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits.
If called as an instance method, the value is assigned to the invocand.
Autocreating constants
After "use Math::BigFloat ':constant'" all the floating point constants in the given scope are converted
to "Math::BigFloat". This conversion happens at compile time.
In particular
perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"'
prints the value of "2E-100". Note that without conversion of constants the expression 2E-100 will be
calculated as normal floating point number.
Please note that ':constant' does not affect integer constants, nor binary nor hexadecimal constants. Use
bignum or Math::BigInt to get this to work.
Math library
Math with the numbers is done (by default) by a module called Math::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 library to use; let the script author
decide which is best.
Note: The keyword 'lib' will warn when the requested library could not be loaded. 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 none of them can be used, the code will die:
use Math::BigFloat only => 'GMP,Pari';
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::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 need to 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, and automatically.
See Math::BigInt for more details than you ever wanted to know about using a different low-level library.
Using Math::BigInt::Lite
For backwards compatibility reasons it is still possible to request 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-level math 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 switching libraries:
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 for reasoning and details.
bdiv()
The following will probably not print what you expect:
print $c->bdiv(123.456),"\n";
It prints both quotient and remainder since print works in list context. Also, bdiv() will modify $c,
so be careful. You probably want to use
print $c / 123.456,"\n";
# or if you want to modify $c:
print scalar $c->bdiv(123.456),"\n";
instead.
brsft()
The following will probably not print what you expect:
my $c = Math::BigFloat->new('3.14159');
print $c->brsft(3,10),"\n"; # prints 0.00314153.1415
It prints both quotient and remainder, since print calls "brsft()" in list context. Also,
"$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 makes a second reference to
the same object and stores it in $y. Thus anything that modifies $x will modify $y (except overloaded
math operators), and vice versa. See Math::BigInt for details and how to avoid that.
bpow()
"bpow()" now modifies the first argument, unlike the old code which left it alone and only returned
the result. This is to be consistent with "badd()" etc. The first will modify $x, the second one
won't:
print bpow($x,$i),"\n"; # modify $x
print $x->bpow($i),"\n"; # ditto
print $x ** $i,"\n"; # leave $x alone
precision() vs. accuracy()
A common pitfall is to use "precision()" when you want to round a result to a 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 would influence 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 on your 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 under the same terms as Perl
itself.
SEE ALSO
Math::BigFloat and Math::BigInt as well as the backends Math::BigInt::FastCalc, Math::BigInt::GMP, and
Math::BigInt::Pari.
The pragmas bignum, bigint and bigrat also might be of interest because 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 flora@cpan.org, 2010.
• Peter John Acklam, pjacklam@online.no, 2011-.
perl v5.22.1 2016-01-08 Math::BigFloat(3pm)