# MirOS Manual: Math::BigFloat(3p)

```
Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)
```

## 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
# necessary 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

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\$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

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# 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 over-

\$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 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.

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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

Math::BigFloat supports both precision (rounding to a cer-
tain 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 sec-

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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 preci-
sion or accuracy, and the input \$x has no accuracy or preci-
sion set, then a fallback parameter will be used. For his-
torical 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";

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Rounding

ffround ( +\$scale )
Rounds to the \$scale'th place left from the '.', counting
from the dot. The first digit is numbered 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 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

```     accuracy

\$x->accuracy(5);                # local for \$x
CLASS->accuracy(5);             # global for all members of CLASS
# Note: This also applies to new()!

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\$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 signi-
ficant digits the results have. If you set a global accu-
racy, 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 expli-
citely using one of round(), bround() or bfround() or by
passing the desired accuracy to the math operation as addi-
tional 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 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 con-
stants, nor binary nor hexadecimal constants. Use bignum or

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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 documen-
tation 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.

Use the lib, Luke! And see "Using Math::BigInt::Lite" for
different library.

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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

# 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

# 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.

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,
one of them. Still, this type of usage is not recommended

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due to these issues.

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
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 create 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?

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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

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:

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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 exam-
ple also does not "taint" the result with an accuracy or
precision setting, which would influence any further opera-
tion.
```

```     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
issue, at least partly.

The package at
<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt>
contains more documentation including a full version

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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.
```

## AUTHORS

```     Mark Biggar, overloaded interface by Ilya Zakharevich. Com-
pletely rewritten by Tels <http://bloodgate.com> in 2001 -
2004, and still at it in 2005.

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```

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