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
       # 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

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       $x->badd($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

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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-
     loaded 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 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

     See also: Rounding.

     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-
     tion about rounding in Math::BigInt.

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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 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.

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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
     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

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     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/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 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

      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:

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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.

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 autoupgrading/downgrading
     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.

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. Com-
     pletely rewritten by Tels <http://bloodgate.com> in 2001 -
     2004, and still at it in 2005.

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