math::bigint.3

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.\" ========================================================================
.\"
.IX Title "Math::BigInt 3"
.TH Math::BigInt 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::BigInt \- Arbitrary size integer/float math package
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&  use Math::BigInt;
\&
\&  # or make it faster: install (optional) Math::BigInt::GMP
\&  # and always use (it will fall back to pure Perl if the
\&  # GMP library is not installed):
\&
\&  # will warn if Math::BigInt::GMP cannot be found
\&  use Math::BigInt lib => \*(AqGMP\*(Aq;
\&
\&  # to supress the warning use this:
\&  # use Math::BigInt try => \*(AqGMP\*(Aq;
\&
\&  my $str = \*(Aq1234567890\*(Aq;
\&  my @values = (64,74,18);
\&  my $n = 1; my $sign = \*(Aq\-\*(Aq;
\&
\&  # Number creation     
\&  my $x = Math::BigInt\->new($str);      # defaults to 0
\&  my $y = $x\->copy();                   # make a true copy
\&  my $nan  = Math::BigInt\->bnan();      # create a NotANumber
\&  my $zero = Math::BigInt\->bzero();     # create a +0
\&  my $inf = Math::BigInt\->binf();       # create a +inf
\&  my $inf = Math::BigInt\->binf(\*(Aq\-\*(Aq);    # create a \-inf
\&  my $one = Math::BigInt\->bone();       # create a +1
\&  my $mone = Math::BigInt\->bone(\*(Aq\-\*(Aq);   # create a \-1
\&
\&  my $pi = Math::BigInt\->bpi();         # returns \*(Aq3\*(Aq
\&                                        # see Math::BigFloat::bpi()
\&
\&  $h = Math::BigInt\->new(\*(Aq0x123\*(Aq);      # from hexadecimal
\&  $b = Math::BigInt\->new(\*(Aq0b101\*(Aq);      # from binary
\&  $o = Math::BigInt\->from_oct(\*(Aq0101\*(Aq);  # from octal
\&
\&  # Testing (don\*(Aqt modify their arguments)
\&  # (return true if the condition is met, otherwise false)
\&
\&  $x\->is_zero();        # if $x is +0
\&  $x\->is_nan();         # if $x is NaN
\&  $x\->is_one();         # if $x is +1
\&  $x\->is_one(\*(Aq\-\*(Aq);      # if $x is \-1
\&  $x\->is_odd();         # if $x is odd
\&  $x\->is_even();        # if $x is even
\&  $x\->is_pos();         # if $x >= 0
\&  $x\->is_neg();         # if $x <  0
\&  $x\->is_inf($sign);    # if $x is +inf, or \-inf (sign is default \*(Aq+\*(Aq)
\&  $x\->is_int();         # if $x is an integer (not a float)
\&
\&  # comparing and digit/sign extraction
\&  $x\->bcmp($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.
\&
\&  $x\->bzero();          # set $x to 0
\&  $x\->bnan();           # set $x 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 in BigInt)
\&  $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
\&
\&  $x\->bmuladd($y,$z);   # $x = $x * $y + $z
\&
\&  $x\->bmod($y);            # modulus (x % y)
\&  $x\->bmodpow($exp,$mod);  # modular exponentation (($num**$exp) % $mod))
\&  $x\->bmodinv($mod);       # the inverse of $x in the given modulus $mod
\&
\&  $x\->bpow($y);            # power of arguments (x ** y)
\&  $x\->blsft($y);           # left shift in base 2
\&  $x\->brsft($y);           # right shift in base 2
\&                           # returns (quo,rem) or quo if in scalar context
\&  $x\->blsft($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
\&  
\&  $x\->band($y);            # bitwise and
\&  $x\->bior($y);            # bitwise inclusive or
\&  $x\->bxor($y);            # bitwise exclusive or
\&  $x\->bnot();              # bitwise 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)
\&
\&  $x\->bnok($y);            # x over y (binomial coefficient n over k)
\&
\&  $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
\&  
\&  $x\->round($A,$P,$mode);  # round to accuracy or precision using mode $mode
\&  $x\->bround($n);          # accuracy: preserve $n digits
\&  $x\->bfround($n);         # $n > 0: round $nth digits,
\&                           # $n < 0: round to the $nth digit after the
\&                           # dot, no\-op for BigInts
\&
\&  # The following do not modify their arguments in BigInt (are no\-ops),
\&  # but do so in BigFloat:
\&
\&  $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:
\&
\&  # greatest common divisor (no OO style)
\&  my $gcd = Math::BigInt::bgcd(@values);
\&  # lowest common multiplicator (no OO style)
\&  my $lcm = Math::BigInt::blcm(@values);        
\& 
\&  $x\->length();            # return number of digits in number
\&  ($xl,$f) = $x\->length(); # length of number and length of fraction part,
\&                           # latter is always 0 digits long for BigInts
\&
\&  $x\->exponent();          # return exponent as BigInt
\&  $x\->mantissa();          # return (signed) mantissa as BigInt
\&  $x\->parts();             # return (mantissa,exponent) as BigInt
\&  $x\->copy();              # make a true copy of $x (unlike $y = $x;)
\&  $x\->as_int();            # return as BigInt (in BigInt: same as copy())
\&  $x\->numify();            # return as scalar (might overflow!)
\&  
\&  # conversation to string (do not modify their argument)
\&  $x\->bstr();              # normalized string (e.g. \*(Aq3\*(Aq)
\&  $x\->bsstr();             # norm. string in scientific notation (e.g. \*(Aq3E0\*(Aq)
\&  $x\->as_hex();            # as signed hexadecimal string with prefixed 0x
\&  $x\->as_bin();            # as signed binary string with prefixed 0b
\&  $x\->as_oct();            # as signed octal string with prefixed 0
\&
\&
\&  # precision and accuracy (see section about rounding for more)
\&  $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
\&
\&  # Global methods
\&  Math::BigInt\->precision();    # get/set global P for all BigInt objects
\&  Math::BigInt\->accuracy();     # get/set global A for all BigInt objects
\&  Math::BigInt\->round_mode();   # get/set global round mode, one of
\&                                # \*(Aqeven\*(Aq, \*(Aqodd\*(Aq, \*(Aq+inf\*(Aq, \*(Aq\-inf\*(Aq, \*(Aqzero\*(Aq, \*(Aqtrunc\*(Aq or \*(Aqcommon\*(Aq
\&  Math::BigInt\->config();       # return hash containing configuration
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
All operators (including basic math operations) are overloaded if you
declare your big integers as
.PP
.Vb 1
\&  $i = new Math::BigInt \*(Aq123_456_789_123_456_789\*(Aq;
.Ve
.PP
Operations with overloaded operators preserve the arguments which is
exactly what you expect.
.IP "Input" 2
.IX Item "Input"
Input values to these routines may be any string, that looks like a number
and results in an integer, including hexadecimal and binary numbers.
.Sp
Scalars holding numbers may also be passed, but note that non-integer numbers
may already have lost precision due to the conversation to float. Quote
your input if you want BigInt to see all the digits:
.Sp
.Vb 2
\&        $x = Math::BigInt\->new(12345678890123456789);   # bad
\&        $x = Math::BigInt\->new(\*(Aq12345678901234567890\*(Aq); # good
.Ve
.Sp
You can include one underscore between any two digits.
.Sp
This means integer values like 1.01E2 or even 1000E\-2 are also accepted.
Non-integer values result in NaN.
.Sp
Hexadecimal (prefixed with \*(L"0x\*(R") and binary numbers (prefixed with \*(L"0b\*(R")
are accepted, too. Please note that octal numbers are not recognized
by \fInew()\fR, so the following will print \*(L"123\*(R":
.Sp
.Vb 1
\&        perl \-MMath::BigInt \-le \*(Aqprint Math::BigInt\->new("0123")\*(Aq
.Ve
.Sp
To convert an octal number, use \fIfrom_oct()\fR;
.Sp
.Vb 1
\&        perl \-MMath::BigInt \-le \*(Aqprint Math::BigInt\->from_oct("0123")\*(Aq
.Ve
.Sp
Currently, \fIMath::BigInt::new()\fR defaults to 0, while Math::BigInt::new('')
results in 'NaN'. This might change in the future, so use always the following
explicit forms to get a zero or NaN:
.Sp
.Vb 2