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.\" ========================================================================
.IX Title "Math::BigFloat 3"
.TH Math::BigFloat 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide"
Math::BigFloat \- Arbitrary size floating point math package
\& $x = Math::BigFloat->new($str); # defaults to 0
\& $nan = Math::BigFloat->bnan(); # create a NotANumber
\& $zero = Math::BigFloat->bzero(); # create a +0
\& $inf = Math::BigFloat->binf(); # create a +inf
\& $inf = Math::BigFloat->binf('-'); # create a -inf
\& $one = Math::BigFloat->bone(); # create a +1
\& $one = Math::BigFloat->bone('-'); # create a -1
\& $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 preserve
\& # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
\& # neccessary when mixing $a = $b assigments with non-overloaded math.
\& $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)
\& $x->blsft($y); # left shift
\& $x->brsft($y); # right shift
\& # return (quo,rem) or quo if scalar
\& $x->blog(); # logarithm of $x to base e (Euler's number)
\& $x->blog($base); # logarithm of $x to base $base (f.i. 2)
\& $x->band($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
\& # 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
All operators (inlcuding basic math operations) are overloaded if you
declare your big floating point numbers as
\& $i = new Math::BigFloat '12_3.456_789_123_456_789E-2';
Operations with overloaded operators preserve the arguments, which is
.IX Subsection "Canonical notation"
Input to these routines are either BigFloat objects, or strings of the
\&\f(CW\*(C`/^[+\-]\ed+$/\*(C'\fR
\&\f(CW\*(C`/^[+\-]\ed+\e.\ed*$/\*(C'\fR
\&\f(CW\*(C`/^[+\-]\ed+E[+\-]?\ed+$/\*(C'\fR
\&\f(CW\*(C`/^[+\-]\ed*\e.\ed+E[+\-]?\ed+$/\*(C'\fR
all with optional leading and trailing zeros and/or spaces. Additonally,
numbers are allowed to have an underscore between any two digits.
Empty strings as well as other illegal numbers results in 'NaN'.
\&\fIbnorm()\fR on a BigFloat object is now effectively a no\-op, since the numbers
are always stored in normalized form. On a string, it creates a BigFloat
Output values are BigFloat objects (normalized), except for \fIbstr()\fR and \fIbsstr()\fR.
The string output will always have leading and trailing zeros stripped and drop
a plus sign. \f(CW\*(C`bstr()\*(C'\fR will give you always the form with a decimal point,
while \f(CW\*(C`bsstr()\*(C'\fR (s for scientific) gives you the scientific notation.
\& ' -123 123 123' '-123123123' '-123123123E0'
\& '00.0123' '0.0123' '123E-4'
\& '123.45E-2' '1.2345' '12345E-4'
Some routines (\f(CW\*(C`is_odd()\*(C'\fR, \f(CW\*(C`is_even()\*(C'\fR, \f(CW\*(C`is_zero()\*(C'\fR, \f(CW\*(C`is_one()\*(C'\fR,
\&\f(CW\*(C`is_nan()\*(C'\fR) return true or false, while others (\f(CW\*(C`bcmp()\*(C'\fR, \f(CW\*(C`bacmp()\*(C'\fR)
return either undef, <0, 0 or >0 and are suited for sort.
Actual math is done by using the class defined with \f(CW\*(C`with =\*(C'\fR Class;> (which
defaults to BigInts) to represent the mantissa and exponent.
The sign \f(CW\*(C`/^[+\-]$/\*(C'\fR is stored separately. The string 'NaN' is used to
represent the result when input arguments are not numbers, as well as
the result of dividing by zero.
.ie n .Sh """mantissa()""\fP, \f(CW""exponent()""\fP and \f(CW""parts()"""
.el .Sh "\f(CWmantissa()\fP, \f(CWexponent()\fP and \f(CWparts()\fP"
.IX Subsection "mantissa(), exponent() and parts()"
\&\f(CW\*(C`mantissa()\*(C'\fR and \f(CW\*(C`exponent()\*(C'\fR return the said parts of the BigFloat
\& $y = $m * ( 10 ** $e );
\& print "ok\en" if $x == $y;
\&\f(CW\*(C`($m,$e) = $x\->parts();\*(C'\fR is just a shortcut giving you both of them.
A zero is represented and returned as \f(CW0E1\fR, \fBnot\fR \f(CW0E0\fR (after Knuth).
Currently the mantissa is reduced as much as possible, favouring higher
exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0).
This might change in the future, so do not depend on it.
.Sh "Accuracy vs. Precision"
.IX Subsection "Accuracy vs. Precision"
Math::BigFloat supports both precision (rounding to a certain place before or
after the dot) and accuracy (rounding to a certain number of digits). For a
full documentation, examples and tips on these topics please see the large
section about rounding in Math::BigInt.
Since things like \f(CWsqrt(2)\fR or \f(CW\*(C`1 / 3\*(C'\fR must presented with a limited
accuracy lest a operation consumes all resources, each operation produces
no more than the requested number of digits.
If there is no gloabl precision or accuracy set, \fBand\fR the operation in
question was not called with a requested precision or accuracy, \fBand\fR the
input \f(CW$x\fR has no accuracy or precision set, then a fallback parameter will
be used. For historical reasons, it is called \f(CW\*(C`div_scale\*(C'\fR and can be accessed
\& $d = Math::BigFloat->div_scale(); # query
\& Math::BigFloat->div_scale($n); # set to $n digits
The default value for \f(CW\*(C`div_scale\*(C'\fR 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 \fIscale\fR:
\& $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 \f(CW\*(C`Math::BigFloat\->accuracy()\*(C'\fR and \f(CW\*(C`Math::BigFloat\->precision()\*(C'\fR
set the global variables, and thus \fBany\fR newly created number will be subject
to the global rounding \fBimmidiately\fR. This means that in the examples above, the
\&\f(CW3\fR as argument to \f(CW\*(C`bdiv()\*(C'\fR will also get an accuracy of \fB5\fR.
It is less confusing to either calculate the result fully, and afterwards
round it explicitely, or use the additional parameters to the math
\& $x = Math::BigFloat->new(2);
\& $y = $x->copy()->bdiv(3);
\& print $y->bround(5),"\en"; # will give 0.66667
\& $x = Math::BigFloat->new(2);
\& $y = $x->copy()->bdiv(3,5); # will give 0.66667
.IX Subsection "Rounding"
.IP "ffround ( +$scale )" 2
.IX Item "ffround ( +$scale )"
Rounds to the \f(CW$scale\fR'th place left from the '.', counting from the dot.
The first digit is numbered 1.
.IP "ffround ( \-$scale )" 2
.IX Item "ffround ( -$scale )"
Rounds to the \f(CW$scale\fR'th place right from the '.', counting from the dot.
.IP "fround ( +$scale )" 2
.IX Item "fround ( +$scale )"
Preserves accuracy to \f(CW$scale\fR 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 '.'
.IP "fround ( \-$scale ) and fround ( 0 )" 2
.IX Item "fround ( -$scale ) and fround ( 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' or 'trunc'.
The default rounding mode is 'even'. By using
\&\f(CW\*(C`Math::BigFloat\->round_mode($round_mode);\*(C'\fR you can get and set the default
mode for subsequent rounding. The usage of \f(CW\*(C`$Math::BigFloat::$round_mode\*(C'\fR is
The second parameter to the round functions then overrides the default
The \f(CW\*(C`as_number()\*(C'\fR function returns a BigInt from a Math::BigFloat. It uses
\&'trunc' as rounding mode to make it equivalent to:
You can override this by passing the desired rounding mode as parameter to
\&\f(CW\*(C`as_number()\*(C'\fR:
\& $x = Math::BigFloat->new(2.5);
\& $y = $x->as_number('odd'); # $y = 3
.IX Subsection "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
\& $A = CLASS->accuracy(); # read out global accuracy
Set or get the global or local accuracy, aka how many significant digits the
results have. If you set a global accuracy, then this also applies to \fInew()\fR!
Warning! The accuracy \fIsticks\fR, e.g. once you created a number under the
influence of \f(CW\*(C`CLASS\->accuracy($A)\*(C'\fR, all results from math operations with
that number will also be rounded.
In most cases, you should probably round the results explicitely using one of
\&\fIround()\fR, \fIbround()\fR or \fIbfround()\fR 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
.IX Subsection "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 \fIaccuracy()\fR instead. With accuracy you
set the number of digits each result should have, with precision you
set the place where to round!
.SH "Autocreating constants"
.IX Header "Autocreating constants"
After \f(CW\*(C`use Math::BigFloat ':constant'\*(C'\fR all the floating point constants
in the given scope are converted to \f(CW\*(C`Math::BigFloat\*(C'\fR. This conversion
\& perl -MMath::BigFloat=:constant -e 'print 2E-100,"\en"'
prints the value of \f(CW\*(C`2E\-100\*(C'\fR. Note that without conversion of
constants the expression 2E\-100 will be calculated as normal floating point
Please note that ':constant' does not affect integer constants, nor binary
nor hexadecimal constants. Use bignum or Math::BigInt to get this to
.IX Subsection "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 => 'BitVect';
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';
Calc.pm uses as internal format an array of elements of some decimal base
(usually 1e7, but this might be differen for some systems) with the least
significant digit first, while BitVect.pm uses a bit vector of base 2, most
significant bit first. Other modules might use even different means of
representing the numbers. See the respective module documentation for further
Please note that Math::BigFloat does \fBnot\fR use the denoted library itself,
but it merely passes the lib argument to Math::BigInt. So, instead of the need
\& use Math::BigInt lib => 'GMP';
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 neccessary things (like BigInt) when they are needed, and
Use the lib, Luke! And see \*(L"Using Math::BigInt::Lite\*(R" for more details than
you ever wanted to know about loading a different library.
.Sh "Using Math::BigInt::Lite"
.IX Subsection "Using Math::BigInt::Lite"
It is possible to use Math::BigInt::Lite with Math::BigFloat:
\& use Math::BigFloat with => 'Math::BigInt::Lite';
There is no need to \*(L"use Math::BigInt\*(R" or \*(L"use Math::BigInt::Lite\*(R", but you
can combine these if you want. For instance, you may want to use
Math::BigInt objects in your main script, too.
\& use Math::BigFloat with => 'Math::BigInt::Lite';
Of course, you can combine this with the \f(CW\*(C`lib\*(C'\fR parameter.
\& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
There is no need for a \*(L"use Math::BigInt;\*(R" statement, even if you want to
use Math::BigInt's, since Math::BigFloat will needs Math::BigInt and thus
always loads it. But if you add it, add it \fBbefore\fR:
\& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
Notice that the module with the last \f(CW\*(C`lib\*(C'\fR will \*(L"win\*(R" and thus
it's lib will be used if the lib is available:
\& use Math::BigInt lib => 'Bar,Baz';
\& use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo';
That would try to load Foo, Bar, Baz and Calc (in that order). Or in other
words, Math::BigFloat will try to retain previously loaded libs when you
don't specify it onem but if you specify one, it will try to load them.
Actually, the lib loading order would be \*(L"Bar,Baz,Calc\*(R", and then
\&\*(L"Foo,Bar,Baz,Calc\*(R", but independend of which lib exists, the result is the
same as trying the latter load alone, except for the fact that one of Bar or
Baz might be loaded needlessly in an intermidiate step (and thus hang around
and waste memory). If neither Bar nor Baz exist (or don't work/compile), they
will still be tried to be loaded, but this is not as time/memory consuming as
actually loading one of them. Still, this type of usage is not recommended due
The old way (loading the lib only in BigInt) still works though:
\& use Math::BigInt lib => 'Bar,Baz';
You can even load Math::BigInt afterwards:
\& use Math::BigInt lib => 'Bar,Baz';
But this has the same problems like #5, it will first load Calc
(Math::BigFloat needs Math::BigInt and thus loads it) and then later Bar or
Baz, depending on which of them works and is usable/loadable. Since this
loads Calc unnecc., it is not recommended.
Since it also possible to just require Math::BigFloat, this poses the question
about what libary this will use:
\& require Math::BigFloat;
\& my $x = Math::BigFloat->new(123); $x += 123;
It will use Calc. Please note that the call to \fIimport()\fR is still done, but
only when you use for the first time some Math::BigFloat math (it is triggered
via any constructor, so the first time you create a Math::BigFloat, the load
will happen in the background). This means:
\& require Math::BigFloat;
\& Math::BigFloat->import ( lib => 'Foo,Bar' );
\& use Math::BigFloat lib => 'Foo, Bar';
But don't try to be clever to insert some operations in between:
\& require Math::BigFloat;
\& my $x = Math::BigFloat->bone() + 4; # load BigInt and Calc
\& Math::BigFloat->import( lib => 'Pari' ); # load Pari, too
\& $x = Math::BigFloat->bone()+4; # now use Pari
While this works, it loads Calc needlessly. But maybe you just wanted that?
\&\fBExamples #3 is highly recommended\fR for daily usage.
Please see the file \s-1BUGS\s0 in the \s-1CPAN\s0 distribution Math::BigInt for known bugs.
.IP "stringify, \fIbstr()\fR" 1
.IX Item "stringify, bstr()"
Both stringify and \fIbstr()\fR now drop the leading '+'. The old code would return
\&'+1.23', the new returns '1.23'. See the documentation in Math::BigInt for
The following will probably not do what you expect:
\& print $c->bdiv(123.456),"\en";
It prints both quotient and reminder since print works in list context. Also,
\&\fIbdiv()\fR will modify \f(CW$c\fR, so be carefull. You probably want to use
\& print $c / 123.456,"\en";
\& print scalar $c->bdiv(123.456),"\en"; # or if you want to modify $c
.IX Item "Modifying and ="
\& $x = Math::BigFloat->new(5);
It will not do what you think, e.g. making a copy of \f(CW$x\fR. Instead it just makes
a second reference to the \fBsame\fR object and stores it in \f(CW$y\fR. Thus anything
that modifies \f(CW$x\fR will modify \f(CW$y\fR (except overloaded math operators), and vice
versa. See Math::BigInt for details and how to avoid that.
\&\f(CW\*(C`bpow()\*(C'\fR now modifies the first argument, unlike the old code which left
it alone and only returned the result. This is to be consistent with
\&\f(CW\*(C`badd()\*(C'\fR etc. The first will modify \f(CW$x\fR, the second one won't:
\& print bpow($x,$i),"\en"; # modify $x
\& print $x->bpow($i),"\en"; # ditto
\& print $x ** $i,"\en"; # leave $x alone
.IP "\fIprecision()\fR vs. \fIaccuracy()\fR" 1
.IX Item "precision() vs. accuracy()"
A common pitfall is to use \fIprecision()\fR when you want to round a result to
a certain number of digits:
\& Math::BigFloat->precision(4); # does not do what you think it does
\& my $x = Math::BigFloat->new(12345); # rounds $x to "12000"!
\& print "$x\en"; # print "12000"
\& my $y = Math::BigFloat->new(3); # rounds $y to "0"!
\& print "$y\en"; # print "0"
\& $z = $x / $y; # 12000 / 0 => NaN!
\& print $z->precision(),"\en"; # 4
Replacing precision with accuracy is probably not what you want, either:
\& Math::BigFloat->accuracy(4); # enables global rounding:
\& my $x = Math::BigFloat->new(123456); # rounded immidiately to "12350"
\& print "$x\en"; # print "123500"
\& my $y = Math::BigFloat->new(3); # rounded to "3
\& print "$y\en"; # print "3"
\& print $z = $x->copy()->bdiv($y),"\en"; # 41170
\& print $z->accuracy(),"\en"; # 4
What you want to use instead is:
\& my $x = Math::BigFloat->new(123456); # no rounding
\& print "$x\en"; # print "123456"
\& my $y = Math::BigFloat->new(3); # no rounding
\& print "$y\en"; # print "3"
\& print $z = $x->copy()->bdiv($y,4),"\en"; # 41150
\& print $z->accuracy(),"\en"; # undef
In addition to computing what you expected, the last example also does \fBnot\fR
\&\*(L"taint\*(R" the result with an accuracy or precision setting, which would
influence any further operation.
Math::BigInt, Math::BigRat and Math::Big as well as
Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP.
The pragmas bignum, bigint and bigrat might also be of interest
because they solve the autoupgrading/downgrading issue, at least partly.
<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
more documentation including a full version history, testcases, empty
subclass files and benchmarks.
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
Mark Biggar, overloaded interface by Ilya Zakharevich.
Completely rewritten by Tels <http://bloodgate.com> in 2001 \- 2004, and still
projects / OpenSPARC-T2-SAM / blob