/ 
Math-1.23
/ Math::BigFloat

NAME

Math::BigFloat - Arbitrary size floating point math package

SYNOPSIS

  use Math::BigFloat;

  # Number creation	
  $x = Math::BigInt->new($str);	# defaults to 0
  $nan  = Math::BigInt->bnan(); # create a NotANumber
  $zero = Math::BigInt->bzero();# create a "+0"

  # Testing
  $x->is_zero();		# return whether arg is zero or not
  $x->is_one();			# return true if arg is +1
  $x->is_one('-');		# return true if arg is -1
  $x->is_odd();			# return true if odd, false for even
  $x->is_even();		# return true if even, false for odd
  $x->bcmp($y);			# compare numbers (undef,<0,=0,>0)
  $x->bacmp($y);		# compare absolutely (undef,<0,=0,>0)
  $x->sign();			# return the sign, either +,- or NaN

  # The following all modify their first argument:

  # set 
  $x->bzero();			# set $i to 0
  $x->bnan();			# set $i to NaN

  $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 $i to quotient
				# return (quo,rem) or quo if scalar

  $x->bmod($y);			# modulus
  $x->bpow($y);			# power of arguments (a**b)
  $x->blsft($y);		# left shift
  $x->brsft($y);		# right shift 
				# return (quo,rem) or quo if scalar
  
  $x->band($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)
  
  # 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->exponent();		# return exponent as BigInt
  $x->mantissa();		# return mantissa as BigInt
  $x->parts();			# return (mantissa,exponent) as BigInt

DESCRIPTION

All operators (inlcuding basic math operations) are overloaded if you declare your big floating point numbers as

$i = new Math::BigFloat '123.456789123456789E-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. Empty stings 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() (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 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.

EXAMPLES

use Math::BigFloat qw(bstr bint);
# not ready yet
$x = bstr("1234")                    # string "1234"
$x = "$x";                           # same as bstr()
$x = bneg("1234")                    # BigFloat "-1234"
$x = Math::BigFloat->bneg("1234");   # BigFloat "1234"
$x = Math::BigFloat->babs("-12345"); # BigFloat "12345"
$x = Math::BigFloat->bnorm("-0 00"); # BigFloat "0"
$x = bint(1) + bint(2);              # BigFloat "3"
$x = bint(1) + "2";                  # ditto (auto-BigFloatify of "2")
$x = bint(1);                        # BigFloat "1"
$x = $x + 5 / 2;                     # BigFloat "3"
$x = $x ** 3;                        # BigFloat "27"
$x *= 2;                             # BigFloat "54"
$x = new Math::BigFloat;             # BigFloat "0"
$x--;                                # BigFloat "-1"

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.

PERFORMANCE

Greatly enhanced ;o) SectionNotReadyYet.

BUGS

None known yet.

CAVEAT

stringify, bstr()

Not ready yet.

Both stringify and bstr() now drop the leading '+'. The old code would return '+1.23', the new returns '1.23'. This is to be consistent with Perl and to make cmp (especially with overloading) to work as you espect. It also solves problems with Test.pm, it's ok() uses 'eq' internally.

Mark said, when asked about to drop the '+' altogether, or make only cmp work:

I agree (with the first alternative), don't add the '+' on positive
numbers.  It's not as important anymore with the new internal 
form for numbers.  It made doing things like abs and neg easier,
but those have to be done differently now anyway.

So, the following examples now work all:

	use Test;
        BEGIN { plan tests => 1 }
	use Math::BigFloat;

	my $x = new Math::BigFloat 3.12;
	my $y = new Math::BigFloat 3.12;

	ok ($x,3.12);
	print "$x eq 3.12" if $x eq $y;
	print "$x eq 3.12" if $x eq '3.12';
	print "$x eq 3.12" if $x eq 3.12;

Additionally, the following still works:

print "$x == 3.12" if $x == $y;
print "$x == 3.12" if $x == 3.12;
print "$x == 3.12" if $x == 3.12;
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.

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

AUTHORS

Mark Biggar, overloaded interface by Ilya Zakharevich. Completely rewritten by Tels http://bloodgate.com in 2001.