Math::BigRat(3perl)

📦

version 5.44.0 · 14 versions

💖 NAME 💖

Math::BigRat — arbitrary size rational number math package 🌸

(that's the whole name bestie, short and iconic, no cap)

✨ SYNOPSIS ✨

okay so here's the whole vibe upfront, no gatekeeping:

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)

like… look at her 💅 every single method is right there. we'll go through all of them, don't stress.

🦋 DESCRIPTION 🦋

So Math::BigRat is the third member of the girl group 🌈 — she complements Math::BigInt and Math::BigFloat by providing support for arbitrary big rational numbers. Big. Rat. Bestie. Rational. She's the moment.

🌸 Math Library 🌸

okay so the low-level math operations? not locked in, you can swap the whole engine underneath bestie. here's how:

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

💀 Note: this needs Math::BigInt::GMP installed. no module, no vibes. install it first fr fr.

and if you're the indecisive type, this next one first tries to find Math::BigInt::Foo, then Math::BigInt::Bar, and when that also fails, it reverts to Math::BigInt::Calc (the trusty default who never lets you down):

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

want a heads-up when the fallback happens, like a little "hey girl just so you know"? swap try for lib:

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

and if you're the dramatic type who would rather ✨ spontaneously combust ✨ than silently fall back — swap try for only so the code just dies:

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

pick your fighter. try = chill, lib = chill but tells you, only = main character energy, no plan B. 😭

🎀 METHODS 🎀

Real talk: any methods not listed here are derived from Math::BigFloat (or Math::BigInt), so make sure you check these two modules for further information. they're the older sisters, they've got lore. 🫶

💜 new() 💜

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

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

okay continuing where we left off — more ways to feed new() its little snack 💫

$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");

Makes a BigRat out of a decimal number that's chillin' in string form. It's basically new() coded, except it's got ✨standards✨ — it will not accept anything that isn't a string representing a finite, decimal number. That's it, that's the whole vibe check.

🍓 `from_hex()` 🍓

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

Builds a BigRat from a hexadecimal string. hex girlies rise 🔥

`from_oct()`

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

Makes a BigRat from an octal string. base 8 representation, no cap.

`from_bin()`

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

Creates a BigRat from a binary string. two's company 🫶

💜 `from_bytes()` 💜

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

Reads the input as a byte string, assuming big endian byte order. The output is always a non-negative, finite integer — always, bestie, no surprises.

See "from_bytes()" in Math::BigInt for the full tea.

🌸 `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");

Takes your input as a value encoded the way IEEE754-2008 describes it. very technically iconic.

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

🧚 `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");

Interprets the input as a value encoded in the x86 extended-precision 80-bit format. yes it goes hard.

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

⭐ `from_base()` ⭐

See "from_base()" in Math::BigInt. (yes king, go read it there 💅)

`bzero()`

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

Spawns a brand new BigRat object that is zero. And if you call it on an object that already exists? It sets it to zero. glow-down, but make it math:

$x->bzero();

`bone()`

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

Makes a fresh BigRat object that is one. The optional argument is either '-' or '+' — so, do you want one, or do you want minus one? your call babe 🎀 And 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 '+' — infinity, or minus infinity, pick your fighter. If you call it on an object, it sets it to infinity:

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

`bnan()`

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

Creates a new BigRat object representing NaN (Not A Number). 💀 And if you call 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

Hands you a rational approximation of PI, accurate to whatever accuracy you asked for — or the default accuracy if you didn't ask for anything. And if you call it as an instance method, the value gets assigned to the invocand. yes ma'am, pi said slay:

$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. not a shallow little situationship — a deep one.

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

`as_int()`

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

Gives you $x back as a Math::BigInt object, no matter what upgrading and downgrading are up to. And if $x is finite but not an integer? It gets truncated. sorry babe, the fraction is not coming with us 🙈

`as_rat()`

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

Gives you $x as a Math::BigRat object, regardless of upgrading and downgrading. The invocand itself is not modified — untouched, unbothered, unshaken ✨

`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, keeping the accuracy as you wanted it — or the default of 40 digits.

`bround()`/`round()`/`bfround()`

Are not yet implemented. that's it, that's the whole thing, they simply are not here yet 😭

`is_zero()`

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

Returns true if $x is exactly zero, otherwise false. zero detected, nothing to see here.

`is_one()`

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

Returns true if $x is exactly one, otherwise false. the one and only (literally).

`is_finite()`

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

Returns true if the invocand is a finite number — meaning it is neither +inf, -inf, nor NaN. all grounded, no chaos energy.

`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. heads up bestie: '+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. and again: '-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. odd one out fr fr.

`is_even()`

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

Returns true if $x is even, otherwise false. even stevens 💅

`is_int()`

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

Returns true if $x has a denominator of 1 (like, no fraction parts at all), otherwise false. and note, bestie: '-inf', 'inf' and 'NaN' are not integers. not even close.

🔥 Comparison methods 🔥

None of these methods modify the invocand object — they look, they don't touch. 🫶

Also super important: a NaN is neither less than, greater than, or equal to anything else. even another NaN. NaN is in its own little world and we respect it.

`bcmp()`

$x->bcmp($y);

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

`bacmp()`

$x->bacmp($y);

Compares $x with $y while completely 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);

okay so the docs literally say this one returns true if and only if $x is equal to $y, and false otherwise. that's what's written, bestie, I'm just the messenger 💀

`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. shifting is a lifestyle 💫

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

`bneg()`

$x->bneg();

Used to negate the object in-place. no copy, no notes, just flipped.

`bnorm()`

$x->bnorm();

Reduces the number to the shortest form it can be. This routine gets called automatically whenever it's needed — it's the responsible friend of the group who cleans up before anybody notices 🧹✨

`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, it 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. And the remainder (modulo) is equal to whatever $x->bmod($y) gives you back.

`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). And if, on top of all that, both $x and $y are integers, the result is identical to what Perl's % operator gives you. consistent queen 👑

`binv()`

$x->binv();

Inverse of $x.

`bsqrt()`

$x->bsqrt();

Calculate the square root of $x.

`bpow()`

$x->bpow($y);

Computes $x ** $y. power move, literally.

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

`broot()`

$x->broot($n);

Calculates 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. And bmodpow is far, far superior to just writing

$num ** $exp % $mod

because it is so much faster — it reduces internal variables into the modulus whenever it possibly can, so it ends up operating on smaller numbers. smaller numbers, bigger slay 💅

bmodpow also supports negative exponents. so:

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. So if

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

then $y is the number closest to zero, with the same sign as $mod, that satisfies

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

And if $x and $y are non-zero, they must be relative primes, i.e., bgcd($y, $mod)==1. When no modular multiplicative inverse exists, "NaN" is returned. sometimes there's just no inverse and that's a valid outcome 🫶

✨ `blog()` ✨

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

If you don’t define $base, it defaults to Euler’s number (e), periodt:

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

🌸 `bexp()` 🌸

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

It crunches out two integers, A and B, such that A/B is equal to e ** $x, where e is Euler’s number.

Fun fact: this method joined the party in v0.20 of Math::BigRat (May 2007).

Also check out blog(), iykyk.

🦋 `bnok()` 🦋

Just peek at bnok() in Math::BigInt, bestie.

🦋 `bperm()` 🦋

Just peek at bperm() in Math::BigInt.

🍓 `bfac()` 🍓

$x->bfac();

It calculates the factorial of $x. Like, for real:

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

Heads up: right now it only works for integers. 🫶

💅 `band()` 💅

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

Bitwise and, slay.

💅 `bior()` 💅

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

Bitwise inclusive or, no cap.

💅 `bxor()` 💅

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

Bitwise exclusive or, periodt.

💅 `bnot()` 💅

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

Bitwise not (two’s complement), iconic.

🌈 `bfloor()` 🌈

$x->bfloor();

Rounds $x toward minus infinity — so $x becomes the biggest integer that’s still less than or equal to $x. 💅

🌈 `bceil()` 🌈

$x->bceil();

Rounds $x toward plus infinity — so $x becomes the smallest integer that’s greater than or equal to $x. ✨

🌈 `bint()` 🌈

$x->bint();

Rounds $x toward zero. Simple as that.

🔥 `bgcd()` 🔥

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

Returns the greatest common divisor (GCD) — the number with the largest absolute value that makes $x/$gcd, $y/$gcd, ... an integer. Example: with 4/5 and 6/5, the GCD is 2/5. It’s basically a glow-up of the regular integer GCD. See gcd() in Math::BigInt.

⭐ `digit()` ⭐

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

Gives you the N'ths digit from X when X is an integer value. 🔢

⭐ `length()` ⭐

$len = $x->length();

Returns how many digits $x has, but only for integer values.

🎀 `parts()` 🎀

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

Returns a list of the (signed) numerator and (unsigned) denominator, both as BigInts.

🎀 `dparts()` 🎀

Hands back the integer part and the fraction part. Cute.

🎀 `fparts()` 🎀

Returns the smallest possible numerator and denominator so that numerator divided by denominator gives you back the original value. For finite numbers, both are integers. Mnemonic: fraction.

🎀 `numerator()` 🎀

$n = $x->numerator();

Returns a copy of the numerator (the bit above the line) as a signed BigInt.

🎀 `denominator()` 🎀

$d = $x->denominator();

Returns a copy of the denominator (the bit under the line) as a positive BigInt.

✨ String conversion methods ✨

💖 `bstr()` 💖

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

Returns a string version of the number. 💖

💖 `bnstr()` 💖

Peep bnstr() in Math::BigInt.

💖 `bestr()` 💖

Peep bestr() in Math::BigInt.

💖 `bdstr()` 💖

Peep bdstr() in Math::BigInt.

💖 `to_bytes()` 💖

Peep to_bytes() in Math::BigInt.

💖 `to_ieee754()` 💖

Peep to_ieee754() in Math::BigFloat.

💖 `to_fp80()` 💖

Peep to_fp80() in Math::BigFloat.

🌟 `as_hex()` 🌟

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

Returns the BigRat as a hexadecimal string.

Heads up: only works for integers. 😭

🌟 `as_oct()` 🌟

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

Returns the BigRat as an octal string.

Heads up: only works for integers. 😭

🌟 `as_bin()` 🌟

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

Returns the BigRat as a binary string.

Heads up: only works for integers. 😭

🌈 `numify()` 🌈

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

Returns the object as a scalar. Be careful: this can lose data if the object can’t be represented by a normal Perl scalar (integer or float), so use as_int() or as_float() instead. 😭

It’s automatically used whenever a scalar is needed, like:

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

Sets or gets config parameter values. Read-only ones are marked RO. Read-write ones are marked RW. The table has columns: Parameter, RO/RW, Description, Example. Here’s the full roster:

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 🌈

Once you do use Math::BigRat ':constant', every numeric literal in that scope gets converted into a Math::BigRat object. This happens at compile time. Any non-integer? Straight up turned into a NaN.

Like, for example,

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

prints the exact value of 2**150. Without that constant-to-object conversion, 2**150 gets calculated with Perl scalars, which gives you an inaccurate result. Not slay.

Also, strings are not affected, so this:

use Math::BigRat qw/:constant/;

$x = "1234567890123456789012345678901234567890"
        + "123456789123456789";

does actually give you what you expect. But you need an explicit Math::BigRat->new() around at least one operand. Also, quote large constants to avoid losing precision:

use Math::BigRat;

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

Without the quotes, Perl first turns the big number into a floating point constant at compile time, then converts it to a Math::BigRat object at run time — and boom, inaccurate result.

🦋 Hexadecimal, octal, and binary floating point literals 🦋

Perl (and this module) accepts hexadecimal, octal, and binary floating point literals, but be careful with Perl versions before v5.32.0, because some versions of Perl will silently give you the wrong result. Here are some ways to write the decimal number 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 🫶

If you find bugs or want to request a feature, please report them to bug-math-bigint at rt.cpan.org, or use the web interface at https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt (you’ll need to log in). We’ll get notified, and then you’ll automatically get updates on your bug as I make changes. 🫶

💖 SUPPORT 💖

You can find docs for this module with the perldoc command:

perldoc Math::BigInt

Or you can snoop around here:

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 can redistribute it and/or modify it under the same terms as Perl itself. 💖

🌈 SEE ALSO 🌈

Go check out Math::BigInt and Math::BigFloat, plus 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 your vibe. And there’s the bignum pragma for upgrading and downgrading.

💜 AUTHORS 💜

Shoutout to the authors:

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

kisses bestie, this page is from perl v5.44.0 and it’s dated 2026-10-17 — and yes, it’s Math::BigRat(3perl) 💅✨

📦 where this page comes from

arch rolling: perl 5.44.0-1 · Artistic-1.0-Perl AND GPL-1.0-or-later
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-11-03: a language model's rewrite of the original, under its terms

Math::BigRat(3perl)

💖 NAME 💖

✨ SYNOPSIS ✨

🦋 DESCRIPTION 🦋

🌸 Math Library 🌸

🎀 METHODS 🎀

💜 new() 💜

✨ from_dec() ✨

🍓 from_hex() 🍓

from_oct()

from_bin()

💜 from_bytes() 💜

🌸 from_ieee754() 🌸

🧚 from_fp80() 🧚

⭐ from_base() ⭐

bzero()

bone()

binf()

bnan()

🥧 bpi() 🥧

copy()

as_int()

as_rat()

as_float()

bround()/round()/bfround()

is_zero()

is_one()

is_finite()

is_positive() / is_pos()

is_negative() / is_neg()

is_odd()

is_even()

is_int()

🔥 Comparison methods 🔥

bcmp()

bacmp()

beq()

bne()

blt()

ble()

bgt()

bge()

blsft()/brsft()

bneg()

bnorm()

binc()

bdec()

badd()

bsub()

bmul()

bdiv()

bmod()

binv()

bsqrt()

bpow()

broot()

🌈 bmodpow() 🌈

💖 bmodinv() 💖

✨ blog() ✨

🌸 bexp() 🌸

🦋 bnok() 🦋

🦋 bperm() 🦋

🍓 bfac() 🍓

💅 band() 💅

💅 bior() 💅

💅 bxor() 💅

💅 bnot() 💅

🌈 bfloor() 🌈

🌈 bceil() 🌈

🌈 bint() 🌈

🔥 bgcd() 🔥

⭐ digit() ⭐

⭐ length() ⭐

🎀 parts() 🎀

🎀 dparts() 🎀

🎀 fparts() 🎀

🎀 numerator() 🎀

🎀 denominator() 🎀

✨ String conversion methods ✨

💖 bstr() 💖

✨ `from_dec()` ✨

🍓 `from_hex()` 🍓

`from_oct()`

`from_bin()`

💜 `from_bytes()` 💜

🌸 `from_ieee754()` 🌸

🧚 `from_fp80()` 🧚

⭐ `from_base()` ⭐

`bzero()`

`bone()`

`binf()`

`bnan()`

🥧 `bpi()` 🥧

`copy()`

`as_int()`

`as_rat()`

`as_float()`

`bround()`/`round()`/`bfround()`

`is_zero()`

`is_one()`

`is_finite()`

`is_positive()` / `is_pos()`

`is_negative()` / `is_neg()`

`is_odd()`

`is_even()`

`is_int()`

`bcmp()`

`bacmp()`

`beq()`

`bne()`

`blt()`

`ble()`

`bgt()`

`bge()`

`blsft()`/`brsft()`

`bneg()`

`bnorm()`

`binc()`

`bdec()`

`badd()`

`bsub()`

`bmul()`

`bdiv()`

`bmod()`

`binv()`

`bsqrt()`

`bpow()`

`broot()`

🌈 `bmodpow()` 🌈

💖 `bmodinv()` 💖

✨ `blog()` ✨

🌸 `bexp()` 🌸

🦋 `bnok()` 🦋

🦋 `bperm()` 🦋

🍓 `bfac()` 🍓

💅 `band()` 💅

💅 `bior()` 💅

💅 `bxor()` 💅

💅 `bnot()` 💅

🌈 `bfloor()` 🌈

🌈 `bceil()` 🌈

🌈 `bint()` 🌈

🔥 `bgcd()` 🔥

⭐ `digit()` ⭐

⭐ `length()` ⭐

🎀 `parts()` 🎀

🎀 `dparts()` 🎀

🎀 `fparts()` 🎀

🎀 `numerator()` 🎀

🎀 `denominator()` 🎀

💖 `bstr()` 💖

💖 `bnstr()` 💖

💖 `bestr()` 💖

💖 `bdstr()` 💖

💖 `to_bytes()` 💖

💖 `to_ieee754()` 💖

💖 `to_fp80()` 💖

🌟 `as_hex()` 🌟

🌟 `as_oct()` 🌟

🌟 `as_bin()` 🌟