Math::BigRat(3pm)

📦
version 5.42.3 · 10 versions
, in alpine 3.24

🎀 Math::BigRat(3pm) 🎀

okay bestie, you have landed on the Math::BigRat(3pm) page from the Perl Programmers Reference Guide, and it is literally the manual for big rational-number math. Pull up a chair, we're doing fractions with main character energy. 💖

🌸 NAME 🌸

Math::BigRat — the arbitrary size rational number math package. That's the name, that's the game. ✨

✨ SYNOPSIS ✨

okay so here's the whole menu of constructor moods and method moves, bestie. The code is exactly as it needs to be, so copy it with care:

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->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->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 is the complement to Math::BigInt and Math::BigFloat, and it's here to provide support for arbitrary big rational numbers. It's giving "fractions but make them enormous" energy, and honestly? Iconic. 💖

🧚 Math Library 🧚

You can switch up the underlying module that does the low-level math operations like this, bestie:

use Math::BigRat try => 'GMP';
Heads up: this needs Math::BigInt::GMP installed. No package, no party. 🫶

This next one would first try to find Math::BigInt::Foo, then Math::BigInt::Bar, and when that also fails, it reverts to Math::BigInt::Calc:

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

If you want to get warned when the fallback happens, replace try with lib:

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

If you want the code to die instead, replace try with only:

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

👑 METHODS 👑

Any methods not listed here are derived from Math::BigFloat (or Math::BigInt), so bestie, make sure you check those two modules for further information. The lore runs deep. 💅

💅 new() 💅

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

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

okay so new() is still out here eating all these inputs, bestie — it's giving overloaded constructor main character energy:

$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");

Creates a BigRat from a decimal number in string form. It's equivalent to new(), but it does not accept anything except strings that represent finite, decimal numbers. No chaos allowed, periodt.

🌸 from_hex()

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

Creates a BigRat from a hexadecimal number in string form. Hex girls stay winning 💅

🎀 from_oct()

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

Creates a BigRat from an octal number in string form.

🦋 from_bin()

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

Creates a BigRat from a binary number in string form.

🧚 from_bytes()

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

Interprets 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");

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

See from_ieee754() in Math::BigFloat.

⭐ from_base()

See from_base() in Math::BigInt.

💖 bzero()

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

Creates a new BigRat object representing zero. If you use it on an object, it sets that object 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 you use it on an object, it sets that object 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 you use it on an object, it sets that object to infinity:

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

💀 bnan()

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

Creates a new BigRat object representing NaN (Not A Number). If you use it on an object, it sets that object 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. No sharing, no borrowing, no weird linked-energy.

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 as 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 a 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. Literally not here yet, bestie — no cap.

💜 is_zero()

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

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

🌈 is_one()

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

Returns 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();

Returns 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();

Returns 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();

Returns true if $x is odd, otherwise false.

🦋 is_even()

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

Returns true if $x is even, otherwise false.

⭐ is_int()

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

Returns 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.

💅 Comparison methods 💅

None of these methods modify the invocand object. Note that a "NaN" is neither less than, greater than, or equal to anything else, even a "NaN".

🍓 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 sign. Returns -1, 0, 1 or undef.

🎀 beq()

$x -> beq($y);

Returns true if and only if $x is equal to $y, and false otherwise.

🦋 bne()

$x -> bne($y);

Returns true if and only if $x is not equal to $y, and false otherwise.

💀 blt()

$x -> blt($y);

Returns true if and only if $x is equal to $y, and false otherwise. (Yes, that is exactly what the text says — I'm not editing it, bestie.)

🌈 ble()

$x -> ble($y);

Returns true if and only if $x is less than or equal to $y, and false otherwise.

🔥 bgt()

$x -> bgt($y);

Returns true if and only if $x is greater than $y, and false otherwise.

👑 bge()

$x -> bge($y);

Returns true if and only if $x is greater than or equal to $y, and false otherwise.

✨ blsft() / brsft()

Used to shift numbers left/right.

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

💜 bneg()

$x->bneg();

Used to negate the object in-place.

🫶 bnorm()

$x->bnorm();

Reduces the number to the shortest form. This routine is called automatically whenever it is needed.

🍓 binc()

$x->binc();

Increments $x by 1 and returns the result.

🌸 bdec()

$x->bdec();

Decrements $x by 1 and returns the result.

🎀 badd()

$x->badd($y);

Adds $y to $x and returns the result.

🦋 bsub()

$x->bsub($y);

Subtracts $y from $x and returns the result.

⭐ bmul()

$x->bmul($y);

Multiplies $y to $x and returns the result.

🔥 bdiv()

$q = $x->bdiv($y);
($q, $r) = $x->bdiv($y);

In scalar context, divides $x by $y and returns the result. In list context, it does floored division (F-division), returning an integer $q and a remainder $r so that $x = $q * $y + $r. The remainer (modulo) is equal to what is returned by $x->bmod($y).

🌈 bmod()

$x->bmod($y);

Returns $x modulo $y. When $x is finite, and $y is finite and non-zero, the result is identical to the remainder after floored division (F-division). If, in addition, both $x and $y are integers, the result is identical to the result from Perl's % operator.

💅 binv()

$x->binv();

Inverse of $x.

🧚 bsqrt()

$x->bsqrt();

Calculate the square root of $x.

👑 bpow()

$x->bpow($y);

Compute $x ** $y.

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

🎀 broot()

$x->broot($n);

Calculate the N'th root of $x.

🔥 bmodpow()

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

Returns the value of $num taken to the power $exp in the modulus $mod using binary exponentiation. 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)

🌟 bmodinv()

$x->bmodinv($mod);          # modular multiplicative inverse

Returns the multiplicative inverse of $x modulo $mod. If

$y = $x -> copy() -> bmodinv($mod)

then $y is the number closest to zero, and with the same sign as $mod, satisfying

($x * $y) % $mod = 1 % $mod

If $x and $y are non-zero, they must be relative primes, i.e., bgcd($y, $mod)==1. "NaN" is returned when no modular multiplicative inverse exists.

🍓 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 two integers A and B so that A/B is equal to e ** $x, where e is Euler's number.

okay so this method is a newer addition — it landed in v0.20 of Math::BigRat (May 2007). also go peek at blog() if you want the related vibe. 💅

bnok()

bestie this is a handoff: see bnok() in Math::BigInt. ✨

bperm()

same handoff energy: see bperm() in Math::BigInt. 🫶

bfac()

$x->bfac();

calculates the factorial of $x. for instance:

print Math::BigRat->new('3/1')->bfac(), "\n";   # 1*2*3
print Math::BigRat->new('5/1')->bfac(), "\n";   # 1*2*3*4*5

works currently only for integers. 🧚

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)

bfloor()

$x->bfloor();

round $x towards minus infinity, i.e., set $x to the largest integer less than or equal to $x. 🌸

bceil()

$x->bceil();

round $x towards plus infinity, i.e., set $x to the smallest integer greater than or equal to $x. ⭐

bint()

$x->bint();

round $x towards zero. 💜

bgcd()

$x -> bgcd($y);             # GCD of $x and $y
$x -> bgcd($y, $z, ...);    # GCD of $x, $y, $z, ...

returns the greatest common divisor (GCD), which is the number with the largest absolute value such that $x/$gcd, $y/$gcd, ... is an integer. for example, when the operands are 4/5 and 6/5, the GCD is 2/5. this is a generalisation of the ordinary GCD for integers. see gcd() in Math::BigInt. 👑

digit()

print Math::BigRat->new('123/1')->digit(1);     # 1
print Math::BigRat->new('123/1')->digit(-1);    # 3

return the N'ths digit from X when X is an integer value. 🔥

length()

$len = $x->length();

return the length of $x in digits for integer values. 🎀

parts()

($n, $d) = $x->parts();

return a list consisting of (signed) numerator and (unsigned) denominator as BigInts. 💖

dparts()

returns the integer part and the fraction part. 🌈

fparts()

returns the smallest possible numerator and denominator so that the numerator divided by the denominator gives back the original value. for finite numbers, both values are integers. mnemonic: fraction. 🍓

numerator()

$n = $x->numerator();

returns a copy of the numerator (the part above the line) as signed BigInt. 🦋

denominator()

$d = $x->denominator();

returns a copy of the denominator (the part under the line) as positive BigInt. 🌸

✨ String conversion methods ✨

bstr()

my $x = Math::BigRat->new('8/4');
print $x->bstr(), "\n";             # prints 1/2

returns a string representing the number. 💅

bnstr()

see bnstr() in Math::BigInt. ✨

bestr()

see bestr() in Math::BigInt. ✨

bdstr()

see bdstr() in Math::BigInt. ✨

to_bytes()

see to_bytes() in Math::BigInt. 🫶

to_ieee754()

see to_ieee754() in Math::BigFloat. 🫶

as_hex()

$x = Math::BigRat->new('13');
print $x->as_hex(), "\n";               # '0xd'

returns the BigRat as hexadecimal string. works only for integers. 💜

as_oct()

$x = Math::BigRat->new('13');
print $x->as_oct(), "\n";               # '015'

returns the BigRat as octal string. works only for integers. 💜

as_bin()

$x = Math::BigRat->new('13');
print $x->as_bin(), "\n";               # '0x1101'

returns the BigRat as binary string. works only for integers. 💜

numify()

my $y = $x->numify();

returns the object as a scalar. this will lose some data if the object cannot be represented by a normal Perl scalar (integer or float), so use as_int() or as_float() instead. 😭

this routine is automatically used whenever a scalar is required:

my $x = Math::BigRat->new('3/1');
@array = (0, 1, 2, 3);
$y = $array[$x];                # set $y to 3

config()

Math::BigRat->config("trap_nan" => 1);      # set
$accu = Math::BigRat->config("accuracy");   # get

set or get configuration parameter values. read-only parameters are marked as RO. read-write parameters are marked as RW. the following parameters are supported. 👑

  • lib (RO) — name of the math backend library; example: Math::BigInt::Calc
  • lib_version (RO) — version of the math backend library; example: 0.30
  • class (RO) — the class of config you just called; example: Math::BigRat
  • version (RO) — version number of the class you used; example: 0.10
  • upgrade (RW) — to which class numbers are upgraded; example: undef
  • downgrade (RW) — to which class numbers are downgraded; example: undef
  • precision (RW) — global precision; example: undef
  • accuracy (RW) — global accuracy; example: undef
  • round_mode (RW) — global round mode; example: even
  • div_scale (RW) — fallback accuracy for div, sqrt etc.; example: 40
  • trap_nan (RW) — trap NaNs; example: undef
  • trap_inf (RW) — trap +inf/-inf; example: undef

🌸 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 gets converted 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. 🫠

✨ Hexadecimal, octal, and binary floating point literals ✨

Perl (and this module) accepts hexadecimal, octal, and binary floating point literals, but use them with care with Perl versions before v5.32.0, because some versions of Perl silently give the wrong result. below are some examples of different ways to write the number decimal 314. 🔥

Hexadecimal floating point literals:

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

Octal floating point literals (with 0 prefix):

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

Octal floating point literals (with 0o prefix) (requires v5.34.0):

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

Binary floating point literals:

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:

📜 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- 💜

k that's the whole page, bestie 💖 — source/version: perl v5.42.3, date: 2026-11-03, page: Math::BigRat(3pm). slay and stay iconic ✨🦋

📦 where this page comes from