math::bigfloat.3

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.\" ========================================================================
.\"
.IX Title "Math::BigFloat 3"
.TH Math::BigFloat 3 "2007-12-18" "perl v5.10.0" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::BigFloat \- Arbitrary size floating point math package
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&  use Math::BigFloat;
\&
\&  # Number creation
\&  my $x = Math::BigFloat\->new($str);    # defaults to 0
\&  my $y = $x\->copy();                   # make a true copy
\&  my $nan  = Math::BigFloat\->bnan();    # create a NotANumber
\&  my $zero = Math::BigFloat\->bzero();   # create a +0
\&  my $inf = Math::BigFloat\->binf();     # create a +inf
\&  my $inf = Math::BigFloat\->binf(\*(Aq\-\*(Aq);  # create a \-inf
\&  my $one = Math::BigFloat\->bone();     # create a +1
\&  my $mone = Math::BigFloat\->bone(\*(Aq\-\*(Aq); # create a \-1
\&
\&  my $pi = Math::BigFloat\->bpi(100);    # PI to 100 digits
\&
\&  # the following examples compute their result to 100 digits accuracy:
\&  my $cos  = Math::BigFloat\->new(1)\->bcos(100);         # cosinus(1)
\&  my $sin  = Math::BigFloat\->new(1)\->bsin(100);         # sinus(1)
\&  my $atan = Math::BigFloat\->new(1)\->batan(100);        # arcus tangens(1)
\&
\&  my $atan2 = Math::BigFloat\->new(  1 )\->batan2( 1 ,100); # batan(1)
\&  my $atan2 = Math::BigFloat\->new(  1 )\->batan2( 8 ,100); # batan(1/8)
\&  my $atan2 = Math::BigFloat\->new( \-2 )\->batan2( 1 ,100); # batan(\-2)
\&
\&  # 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(\*(Aq\-\*(Aq);              # 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 \*(Aq+\*(Aq)
\&
\&  $x\->bcmp($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 assignments 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(\*(Aq\-\*(Aq);                # set $x to \-1
\&  $x\->binf();                   # set $x to inf
\&  $x\->binf(\*(Aq\-\*(Aq);                # set $x to \-inf
\&
\&  $x\->bneg();                   # negation
\&  $x\->babs();                   # absolute value
\&  $x\->bnorm();                  # normalize (no\-op)
\&  $x\->bnot();                   # two\*(Aqs 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)
\&  $x\->bmodpow($exp,$mod);       # modular exponentation (($num**$exp) % $mod))
\&  $x\->blsft($y, $n);            # left shift by $y places in base $n
\&  $x\->brsft($y, $n);            # right shift by $y places in base $n
\&                                # returns (quo,rem) or quo if in scalar context
\&  
\&  $x\->blog();                   # logarithm of $x to base e (Euler\*(Aqs number)
\&  $x\->blog($base);              # logarithm of $x to base $base (f.i. 2)
\&  $x\->bexp();                   # calculate e ** $x where e is Euler\*(Aqs number
\&  
\&  $x\->band($y);                 # bit\-wise and
\&  $x\->bior($y);                 # bit\-wise inclusive or
\&  $x\->bxor($y);                 # bit\-wise exclusive or
\&  $x\->bnot();                   # bit\-wise not (two\*(Aqs complement)
\& 
\&  $x\->bsqrt();                  # calculate square\-root
\&  $x\->broot($y);                # $y\*(Aqth 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
\&
\&  $x\->length();                 # number of digits (w/o sign and \*(Aq.\*(Aq)
\&  ($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
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
All operators (including basic math operations) are overloaded if you
declare your big floating point numbers as
.PP
.Vb 1
\&  $i = new Math::BigFloat \*(Aq12_3.456_789_123_456_789E\-2\*(Aq;
.Ve
.PP
Operations with overloaded operators preserve the arguments, which is
exactly what you expect.
.Sh "Canonical notation"
.IX Subsection "Canonical notation"
Input to these routines are either BigFloat objects, or strings of the
following four forms:
.IP "\(bu" 2
\&\f(CW\*(C`/^[+\-]\ed+$/\*(C'\fR
.IP "\(bu" 2
\&\f(CW\*(C`/^[+\-]\ed+\e.\ed*$/\*(C'\fR
.IP "\(bu" 2