config()¶

        use Data::Dumper;
        print Dumper ( Math::BigInt->config() );
        print Math::BigInt->config()->{lib},"\n";

Returns a hash containing the configuration, e.g. the version number, lib loaded etc. The following hash keys are currently filled in with the appropriate information.

        key             Description
                        Example
        ============================================================
        lib             Name of the low-level math library
                        Math::BigInt::Calc
        lib_version     Version of low-level math library (see 'lib')
                        0.30
        class           The class name of config() you just called
                        Math::BigInt
        upgrade         To which class math operations might be upgraded
                        Math::BigFloat
        downgrade       To which class math operations might be downgraded
                        undef
        precision       Global precision
                        undef
        accuracy        Global accuracy
                        undef
        round_mode      Global round mode
                        even
        version         version number of the class you used
                        1.61
        div_scale       Fallback accuracy for div
                        40
        trap_nan        If true, traps creation of NaN via croak()
                        1
        trap_inf        If true, traps creation of +inf/-inf via croak()
                        1

The following values can be set by passing "config()" a reference to a hash:

        trap_inf trap_nan
        upgrade downgrade precision accuracy round_mode div_scale

Example:

        $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );

accuracy()¶

        $x->accuracy(5);                # local for $x
        CLASS->accuracy(5);             # global for all members of CLASS
                                        # Note: This also applies to new()!
        $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 significant digits the results have. If you set a global accuracy, 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 explicitly using one of round(), bround() or bfround() or by passing the desired accuracy to the math operation as additional 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

Please see the section about "ACCURACY AND PRECISION" for further details.

Value must be greater than zero. Pass an undef value to disable it:

        $x->accuracy(undef);
        Math::BigInt->accuracy(undef);

Returns the current accuracy. For "$x-"accuracy()> it will return either the local accuracy, or if not defined, the global. This means the return value represents the accuracy that will be in effect for $x:

        $y = Math::BigInt->new(1234567);        # unrounded
        print Math::BigInt->accuracy(4),"\n";   # set 4, print 4
        $x = Math::BigInt->new(123456);         # $x will be automatically rounded!
        print "$x $y\n";                        # '123500 1234567'
        print $x->accuracy(),"\n";              # will be 4
        print $y->accuracy(),"\n";              # also 4, since global is 4
        print Math::BigInt->accuracy(5),"\n";   # set to 5, print 5
        print $x->accuracy(),"\n";              # still 4
        print $y->accuracy(),"\n";              # 5, since global is 5

Note: Works also for subclasses like Math::BigFloat. Each class has it's own globals separated from Math::BigInt, but it is possible to subclass Math::BigInt and make the globals of the subclass aliases to the ones from Math::BigInt.

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!

"precision()" sets or gets the global or local precision, aka at which digit before or after the dot to round all results. A set global precision also applies to all newly created numbers!

In Math::BigInt, passing a negative number precision has no effect since no numbers have digits after the dot. In Math::BigFloat, it will round all results to P digits after the dot.

Please see the section about "ACCURACY AND PRECISION" for further details.

Pass an undef value to disable it:

        $x->precision(undef);
        Math::BigInt->precision(undef);

Returns the current precision. For "$x-"precision()> it will return either the local precision of $x, or if not defined, the global. This means the return value represents the prevision that will be in effect for $x:

        $y = Math::BigInt->new(1234567);        # unrounded
        print Math::BigInt->precision(4),"\n";  # set 4, print 4
        $x = Math::BigInt->new(123456);         # will be automatically rounded
        print $x;                               # print "120000"!

Note: Works also for subclasses like Math::BigFloat. Each class has its own globals separated from Math::BigInt, but it is possible to subclass Math::BigInt and make the globals of the subclass aliases to the ones from Math::BigInt.

brsft()¶

        $x->brsft($y,$n);

Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and 2, but others work, too.

Right shifting usually amounts to dividing $x by $n ** $y and truncating the result:

        $x = Math::BigInt->new(10);
        $x->brsft(1);                   # same as $x >> 1: 5
        $x = Math::BigInt->new(1234);
        $x->brsft(2,10);                # result 12

There is one exception, and that is base 2 with negative $x:

        $x = Math::BigInt->new(-5);
        print $x->brsft(1);

This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the result).

new()¶

        $x = Math::BigInt->new($str,$A,$P,$R);

Creates a new BigInt object from a scalar or another BigInt object. The input is accepted as decimal, hex (with leading '0x') or binary (with leading '0b').

See Input for more info on accepted input formats.

from_oct()¶

        $x = Math::BigInt->from_oct("0775");    # input is octal

from_hex()¶

        $x = Math::BigInt->from_hex("0xcafe");  # input is hexadecimal

from_bin()¶

        $x = Math::BigInt->from_oct("0x10011"); # input is binary

bnan()¶

        $x = Math::BigInt->bnan();

Creates a new BigInt object representing NaN (Not A Number). If used on an object, it will set it to NaN:

        $x->bnan();

bzero()¶

        $x = Math::BigInt->bzero();

Creates a new BigInt object representing zero. If used on an object, it will set it to zero:

        $x->bzero();

binf()¶

        $x = Math::BigInt->binf($sign);

Creates a new BigInt object representing infinity. The optional argument is either '-' or '+', indicating whether you want infinity or minus infinity. If used on an object, it will set it to infinity:

        $x->binf();
        $x->binf('-');

bone()¶

        $x = Math::BigInt->binf($sign);

Creates a new BigInt object representing one. The optional argument is either '-' or '+', indicating whether you want one or minus one. If used on an object, it will set it to one:

        $x->bone();             # +1
        $x->bone('-');          # -1

is_one()/is_zero()/is_nan()/is_inf()¶

        $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_inf();                   # true if +inf
        $x->is_inf('-');                # true if -inf (sign is default '+')

These methods all test the BigInt for being one specific value and return true or false depending on the input. These are faster than doing something like:

        if ($x == 0)

is_pos()/is_neg()/is_positive()/is_negative()¶

        $x->is_pos();                   # true if > 0
        $x->is_neg();                   # true if < 0

The methods return true if the argument is positive or negative, respectively. "NaN" is neither positive nor negative, while "+inf" counts as positive, and "-inf" is negative. A "zero" is neither positive nor negative.

These methods are only testing the sign, and not the value.

"is_positive()" and "is_negative()" are aliases to "is_pos()" and "is_neg()", respectively. "is_positive()" and "is_negative()" were introduced in v1.36, while "is_pos()" and "is_neg()" were only introduced in v1.68.

is_odd()/is_even()/is_int()¶

        $x->is_odd();                   # true if odd, false for even
        $x->is_even();                  # true if even, false for odd
        $x->is_int();                   # true if $x is an integer

The return true when the argument satisfies the condition. "NaN", "+inf", "-inf" are not integers and are neither odd nor even.

In BigInt, all numbers except "NaN", "+inf" and "-inf" are integers.

bcmp()¶

        $x->bcmp($y);

Compares $x with $y and takes the sign into account. Returns -1, 0, 1 or undef.

bacmp()¶

        $x->bacmp($y);

Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.

sign()¶

        $x->sign();

Return the sign, of $x, meaning either "+", "-", "-inf", "+inf" or NaN.

If you want $x to have a certain sign, use one of the following methods:

        $x->babs();             # '+'
        $x->babs()->bneg();     # '-'
        $x->bnan();             # 'NaN'
        $x->binf();             # '+inf'
        $x->binf('-');          # '-inf'

digit()¶

        $x->digit($n);          # return the nth digit, counting from right

If $n is negative, returns the digit counting from left.

bneg()¶

        $x->bneg();

Negate the number, e.g. change the sign between '+' and '-', or between '+inf' and '-inf', respectively. Does nothing for NaN or zero.

babs()¶

        $x->babs();

Set the number to its absolute value, e.g. change the sign from '-' to '+' and from '-inf' to '+inf', respectively. Does nothing for NaN or positive numbers.

bnorm()¶

        $x->bnorm();                    # normalize (no-op)

bnot()¶

        $x->bnot();

Two's complement (bitwise not). This is equivalent to

        $x->binc()->bneg();

but faster.

binc()¶

        $x->binc();                     # increment x by 1

bdec()¶

        $x->bdec();                     # decrement x by 1

badd()¶

        $x->badd($y);                   # addition (add $y to $x)

bsub()¶

        $x->bsub($y);                   # subtraction (subtract $y from $x)

bmul()¶

        $x->bmul($y);                   # multiplication (multiply $x by $y)

bmuladd()¶

        $x->bmuladd($y,$z);

Multiply $x by $y, and then add $z to the result,

This method was added in v1.87 of Math::BigInt (June 2007).

bdiv()¶

        $x->bdiv($y);                   # divide, set $x to quotient
                                        # return (quo,rem) or quo if scalar

bmod()¶

        $x->bmod($y);                   # modulus (x % y)

bmodinv()¶

        num->bmodinv($mod);             # modular inverse

Returns the inverse of $num in the given modulus $mod. '"NaN"' is returned unless $num is relatively prime to $mod, i.e. unless "bgcd($num, $mod)==1".

bmodpow()¶

        $num->bmodpow($exp,$mod);       # modular exponentation
                                        # ($num**$exp % $mod)

Returns the value of $num taken to the power $exp in the modulus $mod using binary exponentation. "bmodpow" is far superior to writing

        $num ** $exp % $mod

because it is much faster - it reduces internal variables into the modulus whenever possible, so it operates on smaller numbers.

"bmodpow" also supports negative exponents.

        bmodpow($num, -1, $mod)

is exactly equivalent to

        bmodinv($num, $mod)

bpow()¶

        $x->bpow($y);                   # power of arguments (x ** y)

blog()¶

        $x->blog($base, $accuracy);     # logarithm of x to the base $base

If $base is not defined, Euler's number (e) is used:

        print $x->blog(undef, 100);     # log(x) to 100 digits

bexp()¶

        $x->bexp($accuracy);            # calculate e ** X

Calculates the expression "e ** $x" where "e" is Euler's number.

This method was added in v1.82 of Math::BigInt (April 2007).

See also blog().

bnok()¶

        $x->bnok($y);              # x over y (binomial coefficient n over k)

Calculates the binomial coefficient n over k, also called the "choose" function. The result is equivalent to:

        ( n )      n!
        | - |  = -------
        ( k )    k!(n-k)!

This method was added in v1.84 of Math::BigInt (April 2007).

bpi()¶

        print Math::BigInt->bpi(100), "\n";             # 3

Returns PI truncated to an integer, with the argument being ignored. This means under BigInt this always returns 3.

If upgrading is in effect, returns PI, rounded to N digits with the current rounding mode:

        use Math::BigFloat;
        use Math::BigInt upgrade => Math::BigFloat;
        print Math::BigInt->bpi(3), "\n";               # 3.14
        print Math::BigInt->bpi(100), "\n";             # 3.1415....

This method was added in v1.87 of Math::BigInt (June 2007).

bcos()¶

        my $x = Math::BigInt->new(1);
        print $x->bcos(100), "\n";

Calculate the cosinus of $x, modifying $x in place.

In BigInt, unless upgrading is in effect, the result is truncated to an integer.

This method was added in v1.87 of Math::BigInt (June 2007).

bsin()¶

        my $x = Math::BigInt->new(1);
        print $x->bsin(100), "\n";

Calculate the sinus of $x, modifying $x in place.

In BigInt, unless upgrading is in effect, the result is truncated to an integer.

This method was added in v1.87 of Math::BigInt (June 2007).

batan2()¶

        my $x = Math::BigInt->new(1);
        my $y = Math::BigInt->new(1);
        print $y->batan2($x), "\n";

Calculate the arcus tangens of $y divided by $x, modifying $y in place.

In BigInt, unless upgrading is in effect, the result is truncated to an integer.

This method was added in v1.87 of Math::BigInt (June 2007).

batan()¶

        my $x = Math::BigFloat->new(0.5);
        print $x->batan(100), "\n";

Calculate the arcus tangens of $x, modifying $x in place.

In BigInt, unless upgrading is in effect, the result is truncated to an integer.

This method was added in v1.87 of Math::BigInt (June 2007).

blsft()¶

        $x->blsft($y);          # left shift in base 2
        $x->blsft($y,$n);       # left shift, in base $n (like 10)

brsft()¶

        $x->brsft($y);          # right shift in base 2
        $x->brsft($y,$n);       # right shift, in base $n (like 10)

band()¶

        $x->band($y);                   # bitwise and

bior()¶

        $x->bior($y);                   # bitwise inclusive or

bxor()¶

        $x->bxor($y);                   # bitwise exclusive or

bnot()¶

        $x->bnot();                     # bitwise not (two's complement)

bsqrt()¶

        $x->bsqrt();                    # calculate square-root

broot()¶

        $x->broot($N);

Calculates the N'th root of $x.

bfac()¶

        $x->bfac();                     # factorial of $x (1*2*3*4*..$x)

round()¶

        $x->round($A,$P,$round_mode);

Round $x to accuracy $A or precision $P using the round mode $round_mode.

bround()¶

        $x->bround($N);               # accuracy: preserve $N digits

bfround()¶

        $x->bfround($N);

If N is > 0, rounds to the Nth digit from the left. If N < 0, rounds to the Nth digit after the dot. Since BigInts are integers, the case N < 0 is a no-op for them.

Examples:

        Input           N               Result
        ===================================================
        123456.123456   3               123500
        123456.123456   2               123450
        123456.123456   -2              123456.12
        123456.123456   -3              123456.123

bfloor()¶

        $x->bfloor();

Set $x to the integer less or equal than $x. This is a no-op in BigInt, but does change $x in BigFloat.

bceil()¶

        $x->bceil();

Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but does change $x in BigFloat.

bgcd()¶

        bgcd(@values);          # greatest common divisor (no OO style)

blcm()¶

        blcm(@values);          # lowest common multiplicator (no OO style)

head2 length()

        $x->length();
        ($xl,$fl) = $x->length();

Returns the number of digits in the decimal representation of the number. In list context, returns the length of the integer and fraction part. For BigInt's, the length of the fraction part will always be 0.

exponent()¶

        $x->exponent();

Return the exponent of $x as BigInt.

mantissa()¶

        $x->mantissa();

Return the signed mantissa of $x as BigInt.

parts()¶

        $x->parts();            # return (mantissa,exponent) as BigInt

copy()¶

        $x->copy();             # make a true copy of $x (unlike $y = $x;)

as_int()/as_number()¶

        $x->as_int();

Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as "copy()".

"as_number()" is an alias to this method. "as_number" was introduced in v1.22, while "as_int()" was only introduced in v1.68.

bstr()¶

        $x->bstr();

Returns a normalized string representation of $x.

bsstr()¶

        $x->bsstr();            # normalized string in scientific notation

as_hex()¶

        $x->as_hex();           # as signed hexadecimal string with prefixed 0x

as_bin()¶

        $x->as_bin();           # as signed binary string with prefixed 0b

as_oct()¶

        $x->as_oct();           # as signed octal string with prefixed 0

numify()¶

        print $x->numify();

This returns a normal Perl scalar from $x. It is used automatically whenever a scalar is needed, for instance in array index operations.

This loses precision, to avoid this use as_int() instead.

modify()¶

        $x->modify('bpowd');

This method returns 0 if the object can be modified with the given peration, or 1 if not.

This is used for instance by Math::BigInt::Constant.

upgrade()/downgrade()¶

Set/get the class for downgrade/upgrade operations. Thuis is used for instance by bignum. The defaults are '', thus the following operation will create a BigInt, not a BigFloat:

        my $i = Math::BigInt->new(123);
        my $f = Math::BigFloat->new('123.1');
        print $i + $f,"\n";                     # print 246

div_scale()¶

Set/get the number of digits for the default precision in divide operations.

round_mode()¶

Set/get the current round mode.

Precision P¶

A fixed number of digits before (positive) or after (negative) the decimal point. For example, 123.45 has a precision of -2. 0 means an integer like 123 (or 120). A precision of 2 means two digits to the left of the decimal point are zero, so 123 with P = 1 becomes 120. Note that numbers with zeros before the decimal point may have different precisions, because 1200 can have p = 0, 1 or 2 (depending on what the inital value was). It could also have p < 0, when the digits after the decimal point are zero.

The string output (of floating point numbers) will be padded with zeros:

        Initial value   P       A       Result          String
        ------------------------------------------------------------
        1234.01         -3              1000            1000
        1234            -2              1200            1200
        1234.5          -1              1230            1230
        1234.001        1               1234            1234.0
        1234.01         0               1234            1234
        1234.01         2               1234.01         1234.01
        1234.01         5               1234.01         1234.01000

For BigInts, no padding occurs.

Accuracy A¶

Number of significant digits. Leading zeros are not counted. A number may have an accuracy greater than the non-zero digits when there are zeros in it or trailing zeros. For example, 123.456 has A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.

The string output (of floating point numbers) will be padded with zeros:

        Initial value   P       A       Result          String
        ------------------------------------------------------------
        1234.01                 3       1230            1230
        1234.01                 6       1234.01         1234.01
        1234.1                  8       1234.1          1234.1000

For BigInts, no padding occurs.

Fallback F¶

When both A and P are undefined, this is used as a fallback accuracy when dividing numbers.

Rounding mode R¶

When rounding a number, different 'styles' or 'kinds' of rounding are possible. (Note that random rounding, as in Math::Round, is not implemented.)

'trunc'

truncation invariably removes all digits following the rounding place, replacing them with zeros. Thus, 987.65 rounded to tens (P=1) becomes 980, and rounded to the fourth sigdig becomes 987.6 (A=4). 123.456 rounded to the second place after the decimal point (P=-2) becomes 123.46.

All other implemented styles of rounding attempt to round to the "nearest digit." If the digit D immediately to the right of the rounding place (skipping the decimal point) is greater than 5, the number is incremented at the rounding place (possibly causing a cascade of incrementation): e.g. when rounding to units, 0.9 rounds to 1, and -19.9 rounds to -20. If D < 5, the number is similarly truncated at the rounding place: e.g. when rounding to units, 0.4 rounds to 0, and -19.4 rounds to -19.

However the results of other styles of rounding differ if the digit immediately to the right of the rounding place (skipping the decimal point) is 5 and if there are no digits, or no digits other than 0, after that 5. In such cases:

'even'

rounds the digit at the rounding place to 0, 2, 4, 6, or 8 if it is not already. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.

'odd'

rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if it is not already. E.g., when rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.

'+inf'

round to plus infinity, i.e. always round up. E.g., when rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, and 0.4501 also becomes 0.5.

'-inf'

round to minus infinity, i.e. always round down. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.

'zero'

round to zero, i.e. positive numbers down, negative ones up. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.5, but 0.4501 becomes 0.5.

'common'

round up if the digit immediately to the right of the rounding place is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and 0.149 becomes 0.1.

The handling of A & P in MBI/MBF (the old core code shipped with Perl versions <= 5.7.2) is like this:

Precision

  * ffround($p) is able to round to $p number of digits after the decimal
    point
  * otherwise P is unused
    

Accuracy (significant digits)

  * fround($a) rounds to $a significant digits
  * only fdiv() and fsqrt() take A as (optional) paramater
    + other operations simply create the same number (fneg etc), or more (fmul)
      of digits
    + rounding/truncating is only done when explicitly calling one of fround
      or ffround, and never for BigInt (not implemented)
  * fsqrt() simply hands its accuracy argument over to fdiv.
  * the documentation and the comment in the code indicate two different ways
    on how fdiv() determines the maximum number of digits it should calculate,
    and the actual code does yet another thing
    POD:
      max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
    Comment:
      result has at most max(scale, length(dividend), length(divisor)) digits
    Actual code:
      scale = max(scale, length(dividend)-1,length(divisor)-1);
      scale += length(divisor) - length(dividend);
    So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3).
    Actually, the 'difference' added to the scale is calculated from the
    number of "significant digits" in dividend and divisor, which is derived
    by looking at the length of the mantissa. Which is wrong, since it includes
    the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops
    again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
    assumption that 124 has 3 significant digits, while 120/7 will get you
    '17', not '17.1' since 120 is thought to have 2 significant digits.
    The rounding after the division then uses the remainder and $y to determine
    wether it must round up or down.
 ?  I have no idea which is the right way. That's why I used a slightly more
 ?  simple scheme and tweaked the few failing testcases to match it.
    

This is how it works now:

Setting/Accessing

  * You can set the A global via C<< Math::BigInt->accuracy() >> or
    C<< Math::BigFloat->accuracy() >> or whatever class you are using.
  * You can also set P globally by using C<< Math::SomeClass->precision() >>
    likewise.
  * Globals are classwide, and not inherited by subclasses.
  * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >>
  * to undefine P, use C<< Math::SomeClass->precision(undef); >>
  * Setting C<< Math::SomeClass->accuracy() >> clears automatically
    C<< Math::SomeClass->precision() >>, and vice versa.
  * To be valid, A must be > 0, P can have any value.
  * If P is negative, this means round to the P'th place to the right of the
    decimal point; positive values mean to the left of the decimal point.
    P of 0 means round to integer.
  * to find out the current global A, use C<< Math::SomeClass->accuracy() >>
  * to find out the current global P, use C<< Math::SomeClass->precision() >>
  * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local
    setting of C<< $x >>.
  * Please note that C<< $x->accuracy() >> respective C<< $x->precision() >>
    return eventually defined global A or P, when C<< $x >>'s A or P is not
    set.
    

Creating numbers

  * When you create a number, you can give the desired A or P via:
    $x = Math::BigInt->new($number,$A,$P);
  * Only one of A or P can be defined, otherwise the result is NaN
  * If no A or P is give ($x = Math::BigInt->new($number) form), then the
    globals (if set) will be used. Thus changing the global defaults later on
    will not change the A or P of previously created numbers (i.e., A and P of
    $x will be what was in effect when $x was created)
  * If given undef for A and P, B<no> rounding will occur, and the globals will
    B<not> be used. This is used by subclasses to create numbers without
    suffering rounding in the parent. Thus a subclass is able to have its own
    globals enforced upon creation of a number by using
    C<< $x = Math::BigInt->new($number,undef,undef) >>:
        use Math::BigInt::SomeSubclass;
        use Math::BigInt;
        Math::BigInt->accuracy(2);
        Math::BigInt::SomeSubClass->accuracy(3);
        $x = Math::BigInt::SomeSubClass->new(1234);     
    $x is now 1230, and not 1200. A subclass might choose to implement
    this otherwise, e.g. falling back to the parent's A and P.
    

Usage

  * If A or P are enabled/defined, they are used to round the result of each
    operation according to the rules below
  * Negative P is ignored in Math::BigInt, since BigInts never have digits
    after the decimal point
  * Math::BigFloat uses Math::BigInt internally, but setting A or P inside
    Math::BigInt as globals does not tamper with the parts of a BigFloat.
    A flag is used to mark all Math::BigFloat numbers as 'never round'.
    

Precedence

  * It only makes sense that a number has only one of A or P at a time.
    If you set either A or P on one object, or globally, the other one will
    be automatically cleared.
  * If two objects are involved in an operation, and one of them has A in
    effect, and the other P, this results in an error (NaN).
  * A takes precedence over P (Hint: A comes before P).
    If neither of them is defined, nothing is used, i.e. the result will have
    as many digits as it can (with an exception for fdiv/fsqrt) and will not
    be rounded.
  * There is another setting for fdiv() (and thus for fsqrt()). If neither of
    A or P is defined, fdiv() will use a fallback (F) of $div_scale digits.
    If either the dividend's or the divisor's mantissa has more digits than
    the value of F, the higher value will be used instead of F.
    This is to limit the digits (A) of the result (just consider what would
    happen with unlimited A and P in the case of 1/3 :-)
  * fdiv will calculate (at least) 4 more digits than required (determined by
    A, P or F), and, if F is not used, round the result
    (this will still fail in the case of a result like 0.12345000000001 with A
    or P of 5, but this can not be helped - or can it?)
  * Thus you can have the math done by on Math::Big* class in two modi:
    + never round (this is the default):
      This is done by setting A and P to undef. No math operation
      will round the result, with fdiv() and fsqrt() as exceptions to guard
      against overflows. You must explicitly call bround(), bfround() or
      round() (the latter with parameters).
      Note: Once you have rounded a number, the settings will 'stick' on it
      and 'infect' all other numbers engaged in math operations with it, since
      local settings have the highest precedence. So, to get SaferRound[tm],
      use a copy() before rounding like this:
        $x = Math::BigFloat->new(12.34);
        $y = Math::BigFloat->new(98.76);
        $z = $x * $y;                           # 1218.6984
        print $x->copy()->fround(3);            # 12.3 (but A is now 3!)
        $z = $x * $y;                           # still 1218.6984, without
                                                # copy would have been 1210!
    + round after each op:
      After each single operation (except for testing like is_zero()), the
      method round() is called and the result is rounded appropriately. By
      setting proper values for A and P, you can have all-the-same-A or
      all-the-same-P modes. For example, Math::Currency might set A to undef,
      and P to -2, globally.
 ?Maybe an extra option that forbids local A & P settings would be in order,
 ?so that intermediate rounding does not 'poison' further math?
    

Overriding globals

  * you will be able to give A, P and R as an argument to all the calculation
    routines; the second parameter is A, the third one is P, and the fourth is
    R (shift right by one for binary operations like badd). P is used only if
    the first parameter (A) is undefined. These three parameters override the
    globals in the order detailed as follows, i.e. the first defined value
    wins:
    (local: per object, global: global default, parameter: argument to sub)
      + parameter A
      + parameter P
      + local A (if defined on both of the operands: smaller one is taken)
      + local P (if defined on both of the operands: bigger one is taken)
      + global A
      + global P
      + global F
  * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two
    arguments (A and P) instead of one
    

Local settings

  * You can set A or P locally by using C<< $x->accuracy() >> or
    C<< $x->precision() >>
    and thus force different A and P for different objects/numbers.
  * Setting A or P this way immediately rounds $x to the new value.
  * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa.
    

Rounding

  * the rounding routines will use the respective global or local settings.
    fround()/bround() is for accuracy rounding, while ffround()/bfround()
    is for precision
  * the two rounding functions take as the second parameter one of the
    following rounding modes (R):
    'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common'
  * you can set/get the global R by using C<< Math::SomeClass->round_mode() >>
    or by setting C<< $Math::SomeClass::round_mode >>
  * after each operation, C<< $result->round() >> is called, and the result may
    eventually be rounded (that is, if A or P were set either locally,
    globally or as parameter to the operation)
  * to manually round a number, call C<< $x->round($A,$P,$round_mode); >>
    this will round the number by using the appropriate rounding function
    and then normalize it.
  * rounding modifies the local settings of the number:
        $x = Math::BigFloat->new(123.456);
        $x->accuracy(5);
        $x->bround(4);
    Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()
    will be 4 from now on.
    

Default values

  * R: 'even'
  * F: 40
  * A: undef
  * P: undef
    

Remarks

  * The defaults are set up so that the new code gives the same results as
    the old code (except in a few cases on fdiv):
    + Both A and P are undefined and thus will not be used for rounding
      after each operation.
    + round() is thus a no-op, unless given extra parameters A and P
    

MATH LIBRARY¶

Math with the numbers is done (by default) by a module called "Math::BigInt::Calc". This is equivalent to saying:

        use Math::BigInt try => 'Calc';

You can change this backend library by using:

        use Math::BigInt try => 'GMP';

Note: General purpose packages should not be explicit about the library to use; let the script author decide which is best.

If your script works with huge numbers and Calc is too slow for them, you can also for the loading of one of these libraries and if none of them can be used, the code will die:

        use Math::BigInt only => 'GMP,Pari';

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::BigInt try => 'Foo,Math::BigInt::Bar';

The library that is loaded last will be used. Note that this can be overwritten at any time by loading a different library, and numbers constructed with different libraries cannot be used in math operations together.

What library to use?

Note: General purpose packages should not be explicit about the library to use; let the script author decide which is best.

Math::BigInt::GMP and Math::BigInt::Pari are in cases involving big numbers much faster than Calc, however it is slower when dealing with very small numbers (less than about 20 digits) and when converting very large numbers to decimal (for instance for printing, rounding, calculating their length in decimal etc).

So please select carefully what libary you want to use.

Different low-level libraries use different formats to store the numbers. However, you should NOT depend on the number having a specific format internally.

See the respective math library module documentation for further details.

SIGN¶

The sign is either '+', '-', 'NaN', '+inf' or '-inf'.

A sign of 'NaN' is used to represent the result when input arguments are not numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively minus infinity. You will get '+inf' when dividing a positive number by 0, and '-inf' when dividing any negative number by 0.

mantissa(), exponent() and parts()¶

"mantissa()" and "exponent()" return the said parts of the BigInt 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 that gives you both of them in one go. Both the returned mantissa and exponent have a sign.

Currently, for BigInts $e is always 0, except +inf and -inf, where it is "+inf"; and for NaN, where it is "NaN"; and for "$x == 0", where it is 1 (to be compatible with Math::BigFloat's internal representation of a zero as 0E1).

$m is currently just a copy of the original number. The relation between $e and $m will stay always the same, though their real values might change.

Alternative math libraries¶

You can use an alternative library to drive Math::BigInt. See the section "MATH LIBRARY" for more information.

For more benchmark results see <http://bloodgate.com/perl/benchmarks.html>.

SUBCLASSING¶

Auto-upgrade¶

The following methods upgrade themselves unconditionally; that is if upgrade is in effect, they will always hand up their work:

bsqrt()

div()

blog()

bexp()

Beware: This list is not complete.

All other methods upgrade themselves only when one (or all) of their arguments are of the class mentioned in $upgrade (This might change in later versions to a more sophisticated scheme):