NAME

Math::BigRat - arbitrary size rational number math package

SYNOPSIS

  use Math::BigRat;
  # Generic constructor method (always returns a new object)
  $x = Math::BigRat->new($str);             # defaults to 0
  $x = Math::BigRat->new('256');            # from decimal
  $x = Math::BigRat->new('0256');           # from decimal
  $x = Math::BigRat->new('0xcafe');         # from hexadecimal
  $x = Math::BigRat->new('0x1.fap+7');      # from hexadecimal
  $x = Math::BigRat->new('0o377');          # from octal
  $x = Math::BigRat->new('0o1.35p+6');      # from octal
  $x = Math::BigRat->new('0b101');          # from binary
  $x = Math::BigRat->new('0b1.101p+3');     # from binary
  # Specific constructor methods (no prefix needed; when used as
  # instance method, the value is assigned to the invocand)
  $x = Math::BigRat->from_dec('234');       # from decimal
  $x = Math::BigRat->from_hex('cafe');      # from hexadecimal
  $x = Math::BigRat->from_hex('1.fap+7');   # from hexadecimal
  $x = Math::BigRat->from_oct('377');       # from octal
  $x = Math::BigRat->from_oct('1.35p+6');   # from octal
  $x = Math::BigRat->from_bin('1101');      # from binary
  $x = Math::BigRat->from_bin('1.101p+3');  # from binary
  $x = Math::BigRat->from_bytes($bytes);    # from byte string
  $x = Math::BigRat->from_base('why', 36);  # from any base
  $x = Math::BigRat->from_base_num([1, 0], 2);  # from any base
  $x = Math::BigRat->from_ieee754($b, $fmt);    # from IEEE-754 bytes
  $x = Math::BigRat->from_fp80($b);         # from x86 80-bit
  $x = Math::BigRat->bzero();               # create a +0
  $x = Math::BigRat->bone();                # create a +1
  $x = Math::BigRat->bone('-');             # create a -1
  $x = Math::BigRat->binf();                # create a +inf
  $x = Math::BigRat->binf('-');             # create a -inf
  $x = Math::BigRat->bnan();                # create a Not-A-Number
  $x = Math::BigRat->bpi();                 # returns pi
  $y = $x->copy();        # make a copy (unlike $y = $x)
  $y = $x->as_int();      # return as a Math::BigInt
  $y = $x->as_float();    # return as a Math::BigFloat
  $y = $x->as_rat();      # return as a Math::BigRat
  # Boolean methods (these don't modify the invocand)
  $x->is_zero();          # true if $x is 0
  $x->is_one();           # true if $x is +1
  $x->is_one("+");        # true if $x is +1
  $x->is_one("-");        # true if $x is -1
  $x->is_inf();           # true if $x is +inf or -inf
  $x->is_inf("+");        # true if $x is +inf
  $x->is_inf("-");        # true if $x is -inf
  $x->is_nan();           # true if $x is NaN
  $x->is_finite();        # true if -inf < $x < inf
  $x->is_positive();      # true if $x > 0
  $x->is_pos();           # true if $x > 0
  $x->is_negative();      # true if $x < 0
  $x->is_neg();           # true if $x < 0
  $x->is_non_positive()   # true if $x <= 0
  $x->is_non_negative()   # true if $x >= 0
  $x->is_odd();           # true if $x is odd
  $x->is_even();          # true if $x is even
  $x->is_int();           # true if $x is an integer
  # Comparison methods (these don't modify the invocand)
  $x->bcmp($y);           # compare numbers (undef, < 0, == 0, > 0)
  $x->bacmp($y);          # compare abs values (undef, < 0, == 0, > 0)
  $x->beq($y);            # true if $x == $y
  $x->bne($y);            # true if $x != $y
  $x->blt($y);            # true if $x < $y
  $x->ble($y);            # true if $x <= $y
  $x->bgt($y);            # true if $x > $y
  $x->bge($y);            # true if $x >= $y
  # Arithmetic methods (these modify the invocand)
  $x->bneg();             # negation
  $x->babs();             # absolute value
  $x->bsgn();             # sign function (-1, 0, 1, or NaN)
  $x->bdigitsum();        # sum of decimal digits
  $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)
  $x->bmuladd($y, $z);    # $x = $x * $y + $z
  $x->bdiv($y);           # division (floored)
  $x->bmod($y);           # modulus (x % y)
  $x->bmodinv($mod);      # modular multiplicative inverse
  $x->bmodpow($y, $mod);  # modular exponentiation (($x ** $y) % $mod)
  $x->btdiv($y);          # division (truncated), set $x to quotient
  $x->btmod($y);          # modulus (truncated)
  $x->binv()              # inverse (1/$x)
  $x->bpow($y);           # power of arguments (x ** y)
  $x->blog();             # logarithm of $x to base e (Euler's number)
  $x->blog($base);        # logarithm of $x to base $base (e.g., base 2)
  $x->bexp();             # calculate e ** $x where e is Euler's number
  $x->bilog2();           # log2($x) rounded down to nearest int
  $x->bilog10();          # log10($x) rounded down to nearest int
  $x->bclog2();           # log2($x) rounded up to nearest int
  $x->bclog10();          # log10($x) rounded up to nearest int
  $x->bnok($y);           # combinations (binomial coefficient n over k)
  $x->bperm($y);          # permutations
  $x->buparrow($n, $y);   # Knuth's up-arrow notation
  $x->bhyperop($n, $y);   # n'th hyperoprator
  $x->backermann($y);     # the Ackermann function
  $x->bsin();             # sine
  $x->bcos();             # cosine
  $x->batan();            # inverse tangent
  $x->batan2($y);         # two-argument inverse tangent
  $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->bdfac();            # double factorial of $x ($x*($x-2)*($x-4)*...)
  $x->btfac();            # triple factorial of $x ($x*($x-3)*($x-6)*...)
  $x->bmfac($k);          # $k'th multi-factorial of $x ($x*($x-$k)*...)
  $x->bfib($k);           # $k'th Fibonacci number
  $x->blucas($k);         # $k'th Lucas number
  $x->blsft($n);          # left shift $n places in base 2
  $x->blsft($n, $b);      # left shift $n places in base $b
  $x->brsft($n);          # right shift $n places in base 2
  $x->brsft($n, $b);      # right shift $n places in base $b
  # Bitwise methods (these modify the invocand)
  $x->bblsft($y);         # bitwise left shift
  $x->bbrsft($y);         # bitwise right shift
  $x->band($y);           # bitwise and
  $x->bior($y);           # bitwise inclusive or
  $x->bxor($y);           # bitwise exclusive or
  $x->bnot();             # bitwise not (two's complement)
  # Rounding methods (these modify the invocand)
  $x->round($A, $P, $R);  # round to accuracy or precision using
                          #   rounding mode $R
  $x->bround($n);         # accuracy: preserve $n digits
  $x->bfround($n);        # $n > 0: round to $nth digit left of dec. point
                          # $n < 0: round to $nth digit right of dec. point
  $x->bfloor();           # round towards minus infinity
  $x->bceil();            # round towards plus infinity
  $x->bint();             # round towards zero
  # Other mathematical methods (these don't modify the invocand)
  $x->bgcd($y);           # greatest common divisor
  $x->blcm($y);           # least common multiple
  # Object property methods (these don't modify the invocand)
  $x->sign();             # the sign, either +, - or NaN
  $x->digit($n);          # the nth digit, counting from the right
  $x->digit(-$n);         # the nth digit, counting from the left
  $x->digitsum();         # sum of decimal digits
  $x->length();           # return number of digits in number
  $x->mantissa();         # return (signed) mantissa as a Math::BigInt
  $x->exponent();         # return exponent as a Math::BigInt
  $x->parts();            # return (mantissa,exponent) as a Math::BigInt
  $x->sparts();           # mantissa and exponent (as integers)
  $x->nparts();           # mantissa and exponent (normalised)
  $x->eparts();           # mantissa and exponent (engineering notation)
  $x->dparts();           # integer and fraction part
  $x->fparts();           # numerator and denominator
  $x->numerator();        # numerator
  $x->denominator();      # denominator
  # Conversion methods (these don't modify the invocand)
  $x->bstr();             # decimal notation (possibly zero padded)
  $x->bnstr();            # string in normalized notation
  $x->bestr();            # string in engineering notation
  $x->bdstr();            # string in decimal notation (no padding)
  $x->bfstr();            # string in fractional notation
  $x->to_hex();           # as signed hexadecimal string
  $x->to_bin();           # as signed binary string
  $x->to_oct();           # as signed octal string
  $x->to_bytes();         # as byte string
  $x->to_base($b);        # as string in any base
  $x->to_base_num($b);    # as array of integers in any base
  $x->to_ieee754($fmt);   # to bytes encoded according to IEEE 754-2008
  $x->to_fp80();          # encode value in x86 80-bit format
  $x->as_hex();           # as signed hexadecimal string with "0x" prefix
  $x->as_bin();           # as signed binary string with "0b" prefix
  $x->as_oct();           # as signed octal string with "0" prefix
  # Other conversion methods (these don't modify the invocand)
  $x->numify();           # return as scalar (might overflow or underflow)

DESCRIPTION

Math::BigRat complements Math::BigInt and Math::BigFloat by providing support for arbitrary big rational numbers.

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

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

    use Math::BigRat lib => 'Foo,Math::BigInt::Bar';

    use Math::BigRat only => 'Foo,Math::BigInt::Bar';

METHODS

Any methods not listed here are derived from Math::BigFloat (or Math::BigInt), so make sure you check these two modules for further information.

new()

    $x = Math::BigRat->new('1/3');
    

Create a new Math::BigRat object. Input can come in various forms:

    $x = Math::BigRat->new(123);                            # scalars
    $x = Math::BigRat->new('inf');                          # infinity
    $x = Math::BigRat->new('123.3');                        # float
    $x = Math::BigRat->new('1/3');                          # simple string
    $x = Math::BigRat->new('1 / 3');                        # spaced
    $x = Math::BigRat->new('1 / 0.1');                      # w/ floats
    $x = Math::BigRat->new(Math::BigInt->new(3));           # BigInt
    $x = Math::BigRat->new(Math::BigFloat->new('3.1'));     # BigFloat
    $x = Math::BigRat->new(Math::BigInt::Lite->new('2'));   # BigLite
    # You can also give D and N as different objects:
    $x = Math::BigRat->new(
            Math::BigInt->new(-123),
            Math::BigInt->new(7),
         );                      # => -123/7
    

from_dec()

    my $h = Math::BigRat->from_dec("1.2");
    

Create a BigRat from a decimal number in string form. It is equivalent to "new()", but does not accept anything but strings representing finite, decimal numbers.

from_hex()

    my $h = Math::BigRat->from_hex("0x10");
    

Create a BigRat from a hexadecimal number in string form.

from_oct()

    my $o = Math::BigRat->from_oct("020");
    

Create a BigRat from an octal number in string form.

from_bin()

    my $b = Math::BigRat->from_bin("0b10000000");
    

Create a BigRat from an binary number in string form.

from_bytes()

    $x = Math::BigRat->from_bytes("\xf3\x6b");  # $x = 62315
    

Interpret the input as a byte string, assuming big endian byte order. The output is always a non-negative, finite integer.

See "from_bytes()" in Math::BigInt.

from_ieee754()

    # set $x to 13176795/4194304, the closest value to pi that can be
    # represented in the binary32 (single) format
    $x = Math::BigRat -> from_ieee754("40490fdb", "binary32");
    

Interpret the input as a value encoded as described in IEEE754-2008.

See "from_ieee754()" in Math::BigFloat.

from_fp80()

    # set $x to 14488038916154245685/4611686018427387904, the closest value
    # to pi that can be represented in the x86 80-bit format
    $x = Math::BigRat -> from_fp80("4000c90fdaa22168c235");
    

Interpret the input as a value encoded in the x86 extended-precision 80-bit format.

See "from_fp80()" in Math::BigFloat.

from_base()

See "from_base()" in Math::BigInt.

bzero()

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

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

    $x->bzero();
    

bone()

    $x = Math::BigRat->bone($sign);
    

Creates a new BigRat 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
    

binf()

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

Creates a new BigRat 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('-');
    

bnan()

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

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

    $x->bnan();
    

bpi()

    $x = Math::BigRat -> bpi();         # default accuracy
    $x = Math::BigRat -> bpi(7);        # specified accuracy
    

Returns a rational approximation of PI accurate to the specified accuracy or the default accuracy if no accuracy is specified. If called as an instance method, the value is assigned to the invocand.

    $x = Math::BigRat -> bpi(1);        # returns "3"
    $x = Math::BigRat -> bpi(3);        # returns "22/7"
    $x = Math::BigRat -> bpi(7);        # returns "355/113"
    

copy()

    my $z = $x->copy();
    

Makes a deep copy of the object.

Please see the documentation in Math::BigInt for further details.

as_int()

    $y = $x -> as_int();        # $y is a Math::BigInt
    

Returns $x as a Math::BigInt object regardless of upgrading and downgrading. If $x is finite, but not an integer, $x is truncated.

as_rat()

    $y = $x -> as_rat();        # $y is a Math::BigRat
    

Returns $x a Math::BigRat object regardless of upgrading and downgrading. The invocand is not modified.

as_float()

    $x = Math::BigRat->new('13/7');
    print $x->as_float(), "\n";             # '1'
    $x = Math::BigRat->new('2/3');
    print $x->as_float(5), "\n";            # '0.66667'
    

Returns a copy of the object as Math::BigFloat object regardless of upgrading and downgrading, preserving the accuracy as wanted, or the default of 40 digits.

bround()/round()/bfround()

Are not yet implemented.

is_zero()

    print "$x is 0\n" if $x->is_zero();
    

Return true if $x is exactly zero, otherwise false.

is_one()

    print "$x is 1\n" if $x->is_one();
    

Return true if $x is exactly one, otherwise false.

is_finite()

    $x->is_finite();    # true if $x is not +inf, -inf or NaN
    

Returns true if the invocand is a finite number, i.e., it is neither +inf, -inf, nor NaN.

is_positive()

is_pos()

    print "$x is >= 0\n" if $x->is_positive();
    

Return true if $x is positive (greater than or equal to zero), otherwise false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't.

"is_positive()" is an alias for "is_pos()".

is_negative()

is_neg()

    print "$x is < 0\n" if $x->is_negative();
    

Return true if $x is negative (smaller than zero), otherwise false. Please note that '-inf' is also negative, while 'NaN' and '+inf' aren't.

"is_negative()" is an alias for "is_neg()".

is_odd()

    print "$x is odd\n" if $x->is_odd();
    

Return true if $x is odd, otherwise false.

is_even()

    print "$x is even\n" if $x->is_even();
    

Return true if $x is even, otherwise false.

is_int()

    print "$x is an integer\n" if $x->is_int();
    

Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise false. Please note that '-inf', 'inf' and 'NaN' aren't integer.

NUMERIC LITERALS

After "use Math::BigRat ':constant'" all numeric literals in the given scope are converted to "Math::BigRat" objects. This conversion happens at compile time. Every non-integer is convert to a NaN.

For example,

    perl -MMath::BigRat=:constant -le 'print 2**150'

prints the exact value of "2**150". Note that without conversion of constants to objects the expression "2**150" is calculated using Perl scalars, which leads to an inaccurate result.

Please note that strings are not affected, so that

    use Math::BigRat qw/:constant/;
    $x = "1234567890123456789012345678901234567890"
            + "123456789123456789";

does give you what you expect. You need an explicit Math::BigRat->new() around at least one of the operands. You should also quote large constants to prevent loss of precision:

    use Math::BigRat;
    $x = Math::BigRat->new("1234567889123456789123456789123456789");

Without the quotes Perl first converts the large number to a floating point constant at compile time, and then converts the result to a Math::BigRat object at run time, which results in an inaccurate result.

    0x1.3ap+8         0X1.3AP+8
    0x1.3ap8          0X1.3AP8
    0x13a0p-4         0X13A0P-4

    01.164p+8         01.164P+8
    01.164p8          01.164P8
    011640p-4         011640P-4

    0o1.164p+8        0O1.164P+8
    0o1.164p8         0O1.164P8
    0o11640p-4        0O11640P-4

    0b1.0011101p+8    0B1.0011101P+8
    0b1.0011101p8     0B1.0011101P8
    0b10011101000p-2  0B10011101000P-2

BUGS

Please report any bugs or feature requests to "bug-math-bigint at rt.cpan.org", or through the web interface at <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

SUPPORT

You can find documentation for this module with the perldoc command.

    perldoc Math::BigInt

You can also look for information at:

• GitHub

  <https://github.com/pjacklam/p5-Math-BigInt>

• RT: CPAN's request tracker

  <https://rt.cpan.org/Dist/Display.html?Name=Math-BigInt>

• MetaCPAN

  <https://metacpan.org/release/Math-BigInt>

• CPAN Testers Matrix

  <http://matrix.cpantesters.org/?dist=Math-BigInt>

LICENSE

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.

SEE ALSO

Math::BigInt and Math::BigFloat as well as the backend libraries Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari, Math::BigInt::GMPz, and Math::BigInt::BitVect.

The pragmas bigint, bigfloat, and bigrat might also be of interest. In addition there is the bignum pragma which does upgrading and downgrading.

AUTHORS

• Tels <http://bloodgate.com/> 2001-2009.
• Maintained by Peter John Acklam <pjacklam@gmail.com> 2011-