Math::BigFloat(3pm) Perl Programmers Reference Guide Math::BigFloat(3pm)
NAME
Math::BigFloat - Arbitrary size floating point math package
SYNOPSIS
use Math::BigFloat;
# Number creation
$x = Math::BigFloat->new($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
# 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 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.
# 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)
$x->blsft($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
DESCRIPTION
All operators (inlcuding basic math operations) are overloaded if you declare your big floating point
numbers as
$i = new Math::BigFloat '12_3.456_789_123_456_789E-2';
Operations with overloaded operators preserve the arguments, which is exactly what you expect.
Canonical notation
Input to these routines are either BigFloat objects, or strings of the following four forms:
"/^[+-]\d+$/"
"/^[+-]\d+\.\d*$/"
"/^[+-]\d+E[+-]?\d+$/"
"/^[+-]\d*\.\d+E[+-]?\d+$/"
all with optional leading and trailing zeros and/or spaces. Additonally, numbers are allowed to have
an underscore between any two digits.
Empty strings as well as other illegal numbers results in 'NaN'.
bnorm() on a BigFloat object is now effectively a no-op, since the numbers are always stored in nor-malized normalized
malized form. On a string, it creates a BigFloat object.
Output
Output values are BigFloat objects (normalized), except for bstr() and bsstr().
The string output will always have leading and trailing zeros stripped and drop a plus sign. "bstr()"
will give you always the form with a decimal point, while "bsstr()" (s for scientific) gives you the
scientific notation.
Input bstr() bsstr()
'-0' '0' '0E1'
' -123 123 123' '-123123123' '-123123123E0'
'00.0123' '0.0123' '123E-4'
'123.45E-2' '1.2345' '12345E-4'
'10E+3' '10000' '1E4'
Some routines ("is_odd()", "is_even()", "is_zero()", "is_one()", "is_nan()") return true or false,
while others ("bcmp()", "bacmp()") return either undef, <0, 0 or >0 and are suited for sort.
Actual math is done by using the class defined with "with =" Class;> (which defaults to BigInts) to
represent the mantissa and exponent.
The sign "/^[+-]$/" is stored separately. The string 'NaN' is used to represent the result when input
arguments are not numbers, as well as the result of dividing by zero.
"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.
A zero is represented and returned as 0E1, not 0E0 (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.
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 gloabl 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 immidiately. 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 explicitely, 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
ffround ( +$scale )
Rounds to the $scale'th place left from the '.', counting from the dot. The first digit is num-bered numbered
bered 1.
ffround ( -$scale )
Rounds to the $scale'th place right from the '.', counting from the dot.
ffround ( 0 )
Rounds to an integer.
fround ( +$scale )
Preserves accuracy to $scale digits from the left (aka significant digits) and pads the rest with
zeros. If the number is between 1 and -1, the significant digits count from the first non-zero
after the '.'
fround ( -$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 "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 temporar-ily. temporarily.
ily.
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
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
$A = CLASS->accuracy(); # read out global accuracy
Set or get the global or local accuracy, aka how many significant digits the results have. If you set
a global accuracy, then this also applies to new()!
Warning! The accuracy sticks, e.g. once you created a number under the influence of "CLASS->accu-racy($A)", "CLASS->accuracy($A)",
racy($A)", 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 round(), bround() or
bfround() 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!
Autocreating constants
After "use Math::BigFloat ':constant'" all the floating point constants in the given scope are con-verted converted
verted 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 => '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 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 neccessary things (like BigInt) when they are needed, and automatically.
Use the lib, Luke! And see "Using Math::BigInt::Lite" for more details than you ever wanted to know
about loading a different library.
Using Math::BigInt::Lite
It is possible to use Math::BigInt::Lite with Math::BigFloat:
# 1
use Math::BigFloat with => 'Math::BigInt::Lite';
There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you can combine these if you
want. For instance, you may want to use Math::BigInt objects in your main script, too.
# 2
use Math::BigInt;
use Math::BigFloat with => 'Math::BigInt::Lite';
Of course, you can combine this with the "lib" parameter.
# 3
use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
There is no need for a "use Math::BigInt;" 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 before:
# 4
use Math::BigInt;
use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
Notice that the module with the last "lib" will "win" and thus it's lib will be used if the lib is
available:
# 5
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 "Bar,Baz,Calc", and then "Foo,Bar,Baz,Calc", 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 to these issues.
The old way (loading the lib only in BigInt) still works though:
# 6
use Math::BigInt lib => 'Bar,Baz';
use Math::BigFloat;
You can even load Math::BigInt afterwards:
# 7
use Math::BigFloat;
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/load-able. usable/loadable.
able. 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 import() 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 cre-ate create
ate a Math::BigFloat, the load will happen in the background). This means:
require Math::BigFloat;
Math::BigFloat->import ( lib => 'Foo,Bar' );
would be the same as:
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?
Examples #3 is highly recommended for daily usage.
BUGS
Please see the file BUGS in the CPAN distribution Math::BigInt for known bugs.
CAVEATS
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 do what you expect:
print $c->bdiv(123.456),"\n";
It prints both quotient and reminder since print works in list context. Also, bdiv() will modify $c,
so be carefull. You probably want to use
print $c / 123.456,"\n";
print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c
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 over-loaded overloaded
loaded 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 dig-its: digits:
its:
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 $x = Math::BigFloat->new(123456); # rounded immidiately to "12350"
print "$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.
SEE ALSO
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 autoupgrad-ing/downgrading autoupgrading/downgrading
ing/downgrading issue, at least partly.
The package at <http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt contains more docu-mentation documentation
mentation including a full version history, testcases, empty subclass files and benchmarks.
LICENSE
This program is free software; you may redistribute it and/or modify it under the same terms as Perl
itself.
AUTHORS
Mark Biggar, overloaded interface by Ilya Zakharevich. Completely rewritten by Tels <http://blood-
gate.com in 2001 - 2004, and still at it in 2005.
perl v5.8.8 2001-09-21 Math::BigFloat(3pm)
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