Math::BigInt(3perl)
💖 Math::BigInt(3perl) — the arbitrary size integer math package 💖
okay so bestie, you wanna do math with integers that are SO big they don't fit in your regular variables? This is the package for you. It's giving big number energy. No cap. Let's get into it. 💅
🌸 NAME 🌸
Math::BigInt - arbitrary size integer math package
It's literally the package for doing math with integers of arbitrary size. That's the whole name. Iconic.
✨ SYNOPSIS ✨
okay so here's the vibe check on how you actually use this thing. The code below is literally the whole synopsis, so I'm just gonna drop it here. Don't skip it, bestie, it's important. 💕
use Math::BigInt;
# or make it faster with huge numbers: install (optional)
# Math::BigInt::GMP and always use (it falls back to
# pure Perl if the GMP library is not installed):
# (See also the L</Math Library> section!)
# to warn if Math::BigInt::GMP cannot be found, use
use Math::BigInt lib => 'GMP';
# to suppress the warning if Math::BigInt::GMP cannot be found, use
# use Math::BigInt try => 'GMP';
# to die if Math::BigInt::GMP cannot be found, use
# use Math::BigInt only => 'GMP';
# Configuration methods (may be used as class methods and instance methods)
Math::BigInt->accuracy($n); # set accuracy
Math::BigInt->accuracy(); # get accuracy
Math::BigInt->precision($n); # set precision
Math::BigInt->precision(); # get precision
Math::BigInt->round_mode($m); # set rounding mode, must be
# 'even', 'odd', '+inf', '-inf',
# 'zero', 'trunc', or 'common'
Math::BigInt->round_mode(); # get class rounding mode
Math::BigInt->div_scale($n); # set fallback accuracy
Math::BigInt->div_scale(); # get fallback accuracy
Math::BigInt->trap_inf($b); # trap infinities or not
Math::BigInt->trap_inf(); # get trap infinities status
Math::BigInt->trap_nan($b); # trap NaNs or not
Math::BigInt->trap_nan(); # get trap NaNs status
Math::BigInt->config($par, $val); # set configuration parameter
Math::BigInt->config($par); # get configuration parameter
Math::BigInt->config(); # get hash with configuration
Math::BigFloat->config("lib"); # get name of backend library
# Generic constructor method (always returns a new object)
$x = Math::BigInt->new($str); # defaults to 0
$x = Math::BigInt->new('256'); # from decimal
$x = Math::BigInt->new('0256'); # from decimal
$x = Math::BigInt->new('0xcafe'); # from hexadecimal
$x = Math::BigInt->new('0x1.fap+7'); # from hexadecimal
$x = Math::BigInt->new('0o377'); # from octal
$x = Math::BigInt->new('0o1.35p+6'); # from octal
$x = Math::BigInt->new('0b101'); # from binary
$x = Math::BigInt->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::BigInt->from_dec('234'); # from decimal
$x = Math::BigInt->from_hex('cafe'); # from hexadecimal
$x = Math::BigInt->from_hex('1.fap+7'); # from hexadecimal
$x = Math::BigInt->from_oct('377'); # from octal
$x = Math::BigInt->from_oct('1.35p+6'); # from octal
$x = Math::BigInt->from_bin('1101'); # from binary
$x = Math::BigInt->from_bin('1.101p+3'); # from binary
$x = Math::BigInt->from_bytes($bytes); # from byte string
$x = Math::BigInt->from_base('why', 36); # from any base
$x = Math::BigInt->from_base_num([1, 0], 2); # from any base
$x = Math::BigInt->from_ieee754($b, $fmt); # from IEEE-754 bytes
$x = Math::BigInt->from_fp80($b); # from x86 80-bit
$x = Math::BigInt->bzero(); # create a +0
$x = Math::BigInt->bone(); # create a +1
$x = Math::BigInt->bone('-'); # create a -1
$x = Math::BigInt->binf(); # create a +inf
$x = Math::BigInt->binf('-'); # create a -inf
$x = Math::BigInt->bnan(); # create a Not-A-Number
$x = Math::BigInt->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->bsstr(); # string in scientific notation with integers
$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 notationwhew, that's a LOT of methods, bestie, but you'll get the hang of it. 💪 the synopsis is just the appetizer, the real tea comes next. stay tuned. 💅
$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 🦋
okay bestie, here's the whole vibe 💖 Math::BigInt is the module that gives you arbitrary precision integers — numbers so big they have zero chill and no upper limit, no cap. As a lil bonus 🎀 overloading is also provided for Perl operators, so you get to use your normal operators and the module quietly handles the big-number heavy lifting. Queen behaviour, honestly.
📥 Input 📥
So when you feed values into these routines, they can be any scalar number or any string that looks like a number and represents an integer. Basically: anything Perl itself would accept as a literal numeric constant is fair game here 🌈 — with one exception, and it's a big one: finite non-integers return NaN.
Here's the full rundown of the rules, bestie, don't skip:
- Leading and trailing whitespace? Ignored. We don't see it. It's not there. 💅
- Leading zeros get ignored too — except for floating point numbers with a binary exponent, where the number is interpreted as an octal floating point number instead 👀. Like,
"01.4p+0"gives 1.5,"00.4p+0"gives 0.5, but"0.4p+0"gives aNaN. And while"0377"gives 255,"0377p0"gives 255. yes you read that right, stay with me 🫶 - If the string rocks a
"0x"or"0X"prefix, it's read as a hexadecimal number. 🧚 - If the string has a
"0o"or"0O"prefix, it's read as an octal number. A floating point literal with a"0"prefix is also interpreted as an octal number. 💜 - If the string has a
"0b"or"0B"prefix, it's read as a binary number. ⭐ - Underline characters are allowed, in the same way they're allowed in literal numerical constants. Slay. 🎀
- If the string can't be interpreted, or doesn't represent a finite integer, you get
NaNback. sad but true 😭 - For hexadecimal, octal, and binary floating point numbers, the exponent must be separated from the significand (mantissa) by the letter
"p"or"P"— NOT"e"or"E"like it is with decimal numbers. This is the one that trips everybody up, ok, write it down ✍️
Some examples of valid string input 💖
Input string Resulting value
123 123
1.23e2 123
12300e-2 123
67_538_754 67538754
-4_5_6.7_8_9e+0_1_0 -4567890000000
0x13a 314
0x13ap0 314
0x1.3ap+8 314
0x0.00013ap+24 314
0x13a000p-12 314
0o472 314
0o1.164p+8 314
0o0.0001164p+20 314
0o1164000p-10 314
0472 472 Note!
01.164p+8 314
00.0001164p+20 314
01164000p-10 314
0b100111010 314
0b1.0011101p+8 314
0b0.00010011101p+12 314
0b100111010000p-3 314⚠️ heads up on that0472row — see theNote!? That one's a whole situation, bestie. Don't assume it behaves like the octal ones above it. Read carefully or the number will humble you 🙈
And here's a thing nobody tells you until it bites: input given as scalar numbers might lose precision 😭. Quote your input to make sure no digits go missing:
$x = Math::BigInt->new( 56789012345678901234 ); # bad
$x = Math::BigInt->new('56789012345678901234'); # goodCurrently, Math::BigInt->new() (with no input argument) and Math::BigInt->new("") both return 0. This might change in the future 👀, so always use the following explicit form to get yourself a zero:
$zero = Math::BigInt->bzero();no cap, just do it the explicit way and you'll never get jumpscared by a future version 💅
📤 Output 📤
Output values are usually Math::BigInt objects ✨.
Boolean operators like is_zero(), is_one(), is_inf(), etc. do the obvious thing and return true or false. 🌸
Comparison operators bcmp() and bacmp() return -1, 0, 1, or undef. That's the whole menu, bestie 🫶
👑 METHODS 👑
⚙️ Configuration methods ⚙️
ok so every single method below accepts three additional parameters — every one except config(), accuracy() and precision(), those three are the exceptions, don't come for me 💅. Those three extra args are $A, $P and $R, which are accuracy, precision and round_mode. If you want the full lore, go read the ACCURACY AND PRECISION section, iykyk. 📚
Also important: setting a class variable effects all object instance that are created afterwards ⏳✨. So the timing matters, and the past is the past.
✨ accuracy() ✨
Math::BigInt->accuracy(5); # set class accuracy
$x->accuracy(5); # set instance accuracy
$A = Math::BigInt->accuracy(); # get class accuracy
$A = $x->accuracy(); # get instance accuracySet or get the accuracy, i.e. the number of significant digits. The accuracy must be an integer, periodt. And if you set the accuracy to undef, no rounding is done — we just let it be free 🌈.
Alternatively? You can round the results explicitly with one of round(), bround() or bfround(), or by passing the accuracy you want straight into the method as an additional parameter. Both roads lead to the same cute destination:
my $x = Math::BigInt->new(30000);
my $y = Math::BigInt->new(7);
print scalar $x->copy()->bdiv($y, 2); # prints 4300
print scalar $x->copy()->bdiv($y)->bround(2); # prints 4300Please go read the ACCURACY AND PRECISION section for the further details, bestie, it's all there 💖
$y = Math::BigInt->new(1234567); # $y is not rounded
Math::BigInt->accuracy(4); # set class accuracy to 4
$x = Math::BigInt->new(1234567); # $x is rounded automatically
print "$x $y"; # prints "1235000 1234567"
print $x->accuracy(); # prints "4"
print $y->accuracy(); # also prints "4", since
# class accuracy is 4
Math::BigInt->accuracy(5); # set class accuracy to 5
print $x->accuracy(); # prints "4", since instance
# accuracy is 4
print $y->accuracy(); # prints "5", since no instance
# accuracy, and class accuracy is 5Note 📌: each class has it's own globals separated fromMath::BigInt, but it is possible to subclassMath::BigIntand make the globals of the subclass aliases to the ones fromMath::BigInt. cute little inheritance trick, you're welcome 🎀
✨ precision() ✨
Math::BigInt->precision(-2); # set class precision
$x->precision(-2); # set instance precision
$P = Math::BigInt->precision(); # get class precision
$P = $x->precision(); # get instance precisionSet or get the precision — that's the place to round relative to the decimal point 📍. The precision must be an integer. Setting the precision to $P means each number gets rounded up or down (depending on the rounding mode) to the nearest multiple of 10**$P. If the precision is set to undef, no rounding is done. free spirit energy 🦋
Lowkey you might wanna use accuracy() instead 👀 — with accuracy() you set the number of digits each result should have, and with precision() you set the place where to round. Two different flavours, pick your fighter 💅
Full details live in the ACCURACY AND PRECISION section, go get 'em ⭐
$y = Math::BigInt->new(1234567); # $y is not rounded
Math::BigInt->precision(4); # set class precision to 4
$x = Math::BigInt->new(1234567); # $x is rounded automatically
print $x; # prints "1230000"Note 📌: each class has its own globals separated fromMath::BigInt, but it is possible to subclassMath::BigIntand make the globals of the subclass aliases to the ones fromMath::BigInt. yes it's the same note again, it's important ok 🫶
✨ round_mode() ✨
Set/get the rounding mode. 🎯 that's the whole thing, bestie, it sets and gets. iconic, honestly.
✨ div_scale() ✨
Set/get the fallback accuracy. This is the accuracy that gets used when neither accuracy nor precision is set explicitly. It comes in clutch when a computation might otherwise try to return an infinite number of digits 😭 — so yeah, this is the safety net, and it slays at its job.
✨ trap_inf() ✨
Set/get the value determining whether infinities should cause a fatal error or not 💀. Your call, your chaos.
✨ trap_nan() ✨
Set/get the value determining whether NaNs should cause a fatal error or not 💀. same energy, different letter.
✨ upgrade() ✨
Set/get the class for upgrading ⬆️. When a computation might result in a non-integer, the operands are upgraded to this class. This is used for instance by bignum. The default is undef, i.e. no upgrading — everyone stays exactly where they are. 💅
# with no upgrading
$x = Math::BigInt->new(12);
$y = Math::BigInt->new(5);
print $x / $y, "\n"; # 2 as a Math::BigInt
# with upgrading to Math::BigFloat
Math::BigInt -> upgrade("Math::BigFloat");
print $x / $y, "\n"; # 2.4 as a Math::BigFloat
# with upgrading to Math::BigRat (after loading Math::BigRat)
Math::BigInt -> upgrade("Math::BigRat");
print $x / $y, "\n"; # 12/5 as a Math::BigRat✨ downgrade() ✨
Set/get the class for downgrading ⬇️. The default is undef, i.e. no downgrading. And listen: downgrading is not done by Math::BigInt. It just doesn't. So don't come looking here for it, bestie 🙈
✨ modify() ✨
$x->modify('bpowd');This method returns 0 if the object can be modified with the given operation, or 1 if not. That's it, that's the whole method 🫶
This is used for instance by Math::BigInt::Constant. 💜
✨ config() ✨
Math::BigInt->config("trap_nan" => 1); # set
$accu = Math::BigInt->config("accuracy"); # getSet or get class variables ⚙️. Read-only parameters are marked as RO, read-write parameters are marked as RW. And the following parameters are supported: 👇
ok so we’re mid-table, bestie — here’s the rest of the config parameters, same columns, same vibes, no skips 💅
lib— RO — name of the math backend library, e.g.Math::BigInt::Calc🌸lib_version— RO — version of the math backend library, e.g.0.30class— RO — the class of config you just called, e.g.Math::BigRatversion— RO — version number of the class you used, e.g.0.10upgrade— RW — to which class numbers are upgraded, e.g.undefdowngrade— RW — to which class numbers are downgraded, e.g.undefprecision— RW — global precision, e.g.undefaccuracy— RW — global accuracy, e.g.undefround_mode— RW — global round mode, e.g.evendiv_scale— RW — fallback accuracy for division etc., e.g.40trap_nan— RW — trap NaNs, e.g.undeftrap_inf— RW — trap +inf/-inf, e.g.undef
✨ Constructor methods ✨
new()
$x = Math::BigInt->new($str,$A,$P,$R);Creates a new Math::BigInt object from a scalar or another Math::BigInt object. The input is accepted as decimal, hexadecimal (with leading '0x'), octal (with leading ('0o') or binary (with leading '0b').
See "Input" for more info on accepted input formats.
from_dec()
$x = Math::BigInt->from_dec("314159"); # input is decimalInterpret input as a decimal. It is equivalent to new(), but does not accept anything but strings representing finite, decimal numbers.
from_hex()
$x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimalInterpret input as a hexadecimal string. A 0x or x prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned.
from_oct()
$x = Math::BigInt->from_oct("0775"); # input is octalInterpret the input as an octal string and return the corresponding value. A 0 (zero) prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned.
from_bin()
$x = Math::BigInt->from_bin("0b10011"); # input is binaryInterpret the input as a binary string. A 0b or b prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned.
from_bytes()
$x = Math::BigInt->from_bytes("\xf3\x6b"); # $x = 62315Interpret the input as a byte string, assuming big endian byte order. The output is always a non-negative, finite integer.
In some special cases, from_bytes() matches the conversion done by unpack():
$b = "\x4e"; # one char byte string
$x = Math::BigInt->from_bytes($b); # = 78
$y = unpack "C", $b; # ditto, but scalar
$b = "\xf3\x6b"; # two char byte string
$x = Math::BigInt->from_bytes($b); # = 62315
$y = unpack "S>", $b; # ditto, but scalar
$b = "\x2d\xe0\x49\xad"; # four char byte string
$x = Math::BigInt->from_bytes($b); # = 769673645
$y = unpack "L>", $b; # ditto, but scalar
$b = "\x2d\xe0\x49\xad\x2d\xe0\x49\xad"; # eight char byte string
$x = Math::BigInt->from_bytes($b); # = 3305723134637787565
$y = unpack "Q>", $b; # ditto, but scalarfrom_ieee754()
# set $x to 314159
$x = Math::BigInt -> from_ieee754("40490fdb", "binary32");Interpret the input as a value encoded as described in IEEE754-2008. NaN is returned if the value is neither +/-infinity nor an integer.
See "from_ieee754()" in Math::BigFloat.
from_fp80()
# set $x to 314159
$x = Math::BigInt -> from_fp80("40119965e00000000000");Interpret the input as a value encoded in the x86 extended-precision 80-bit format.
See "from_fp80()" in Math::BigFloat.
from_base()
Given a string, a base, and an optional collation sequence, interpret the string as a number in the given base. The collation sequence describes the value of each character in the string.
If a collation sequence is not given, a default collation sequence is used. If the base is less than or equal to 36, the collation sequence is the string consisting of the 36 characters "0" to "9" and "A" to "Z". In this case, the letter case in the input is ignored. If the base is greater than 36, and smaller than or equal to 62, the collation sequence is the string consisting of the 62 characters "0" to "9", "A" to "Z", and "a" to "z". A base larger than 62 requires the collation sequence to be specified explicitly.
These examples show standard binary, octal, and hexadecimal conversion. All cases return 250.
$x = Math::BigInt->from_base("11111010", 2);
$x = Math::BigInt->from_base("372", 8);
$x = Math::BigInt->from_base("fa", 16);When the base is less than or equal to 36, and no collation sequence is given, the letter case is ignored, so both of these also return 250:
$x = Math::BigInt->from_base("6Y", 16);
$x = Math::BigInt->from_base("6y", 16);When the base is greater than 36, and no collation sequence is given, the default collation sequence contains both uppercase and lowercase letters, so the letter case in the input is not ignored:
$x = Math::BigInt->from_base("6S", 37); # $x is 250
$x = Math::BigInt->from_base("6s", 37); # $x is 276
$x = Math::BigInt->from_base("121", 3); # $x is 16
$x = Math::BigInt->from_base("XYZ", 36); # $x is 44027
$x = Math::BigInt->from_base("Why", 42); # $x is 58314The collation sequence can be any set of unique characters. These two cases are equivalent
$x = Math::BigInt->from_base("100", 2, "01"); # $x is 4
$x = Math::BigInt->from_base("|--", 2, "-|"); # $x is 4from_base_num()
Returns a new Math::BigInt object given an array of values and a base. This method is equivalent to from_base(), but works on numbers in an array rather than characters in a string. Unlike from_base(), all input values may be arbitrarily large.
$x = Math::BigInt->from_base_num([1, 1, 0, 1], 2) # $x is 13
$x = Math::BigInt->from_base_num([3, 125, 39], 128) # $x is 65191bzero()
$x = Math::BigInt->bzero();
$x->bzero();Returns a new Math::BigInt object representing zero. If used as an instance method, assigns the value to the invocand.
bone()
$x = Math::BigInt->bone(); # +1
$x = Math::BigInt->bone("+"); # +1
$x = Math::BigInt->bone("-"); # -1
$x->bone(); # +1
$x->bone("+"); # +1
$x->bone('-'); # -1Creates a new Math::BigInt object representing one. The optional argument is either '-' or '+', indicating whether you want plus one or minus one. If used as an instance method, assigns the value to the invocand.
binf()
$x = Math::BigInt->binf($sign);Creates a new Math::BigInt object representing infinity. The optional argument is either '-' or '+', indicating whether you want infinity or minus infinity. If used as an instance method, assigns the value to the invocand.
$x->binf();
$x->binf('-');bnan()
$x = Math::BigInt->bnan();Creates a new Math::BigInt object representing NaN (Not A Number). If used as an instance method, assigns the value to the invocand.
$x->bnan();bpi()
$x = Math::BigInt->bpi(100); # 3
$x->bpi(100); # 3Creates a new Math::BigInt object representing PI. If used as an instance method, assigns the value to the invocand. With Math::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....copy()
$x->copy(); # make a true copy of $x (unlike $y = $x)as_int()
$y = $x -> as_int(); # $y is a Math::BigIntReturns $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::BigRatReturns $x as a Math::BigRat object regardless of upgrading and downgrading. The invocand is not modified.
as_float()
$y = $x -> as_float(); # $y is a Math::BigFloatReturns $x as a Math::BigFloat object regardless of upgrading and downgrading. The invocand is not modified.
✨ Boolean methods ✨
None of these methods modify the invocand object.
is_zero()
$x->is_zero(); # true if $x is 0Returns true if the invocand is zero and false otherwise.
is_one()
$x->is_one(); # true if $x is +1
$x->is_one("+"); # ditto
$x->is_one("-"); # true if $x is -1Returns true if the invocand is one and false otherwise.
is_finite()
$x->is_finite(); # true if $x is not +inf, -inf or NaNReturns true if the invocand is a finite number, i.e., it is neither +inf, -inf, nor NaN.
is_inf()
$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 -infReturns true if the invocand is infinite and false otherwise.
is_nan()
$x->is_nan(); # true if $x is NaNis_positive() / is_pos()
$x->is_positive(); # true if > 0
$x->is_pos(); # dittoBestie, this one's simple: true if the invocand is > 0, false otherwise. And a "NaN"? Nope, not positive and not negative. It's giving undefined-adjacent 💀
is_negative() / is_neg()
$x->is_negative(); # true if < 0
$x->is_neg(); # dittoReturns true if the invocand is negative, false otherwise. Same deal as its twin: a "NaN" is neither positive nor negative. ✨
is_non_positive()
$x->is_non_positive(); # true if <= 0True if your invocand is negative or zero. That's it, that's the whole vibe. 🎀
is_non_negative()
$x->is_non_negative(); # true if >= 0True if the invocand is positive or zero. 👑
is_odd()
$x->is_odd(); # true if odd, false for evenReturns true if the invocand is odd, false otherwise. But heads up 🫶 — "NaN", "+inf", and "-inf" are neither odd nor even. They simply do not participate. 🙈
is_even()
$x->is_even(); # true if $x is evenTrue if the invocand is even, false otherwise. And fr fr — "NaN", "+inf", "-inf" are not integers and they are neither odd nor even. 💀
is_int()
$x->is_int(); # true if $x is an integerTrue if the invocand is an integer, false otherwise. And "NaN", "+inf", "-inf"? Not integers. Periodt. 🚫
💅 Comparison methods
Okay so important: none of these methods modify the invocand object. They just look 👀 and report back.
And here's the tea bestie: a"NaN"is neither less than, greater than, or equal to anything else — not even another"NaN". It's the ultimate main character that refuses every comparison. 🌈
bcmp()
$x->bcmp($y);Returns -1, 0, or 1 depending on whether $x is less than, equal to, or greater than $y. And if any operand is a NaN? Returns undef. 🙈
bacmp()
$x->bacmp($y);Same energy but with absolute values 💫 — returns -1, 0, or 1 depending on whether the absolute value of $x is less than, equal to, or greater than the absolute value of $y. Returns undef if any operand is a NaN.
beq()
$x -> beq($y);True if and only if $x is equal to $y. False otherwise. No cap. ✨
bne()
$x -> bne($y);True if and only if $x is not equal to $y, false otherwise.
blt()
$x -> blt($y);Returns true if and only if $x is equal to $y, and false otherwise.
Yes bestie, that's what the original says, I'm not fixing it, I'm just relaying it. 🙈
ble()
$x -> ble($y);True if and only if $x is less than or equal to $y, false otherwise. 🍓
bgt()
$x -> bgt($y);True if and only if $x is greater than $y, false otherwise.
bge()
$x -> bge($y);True if and only if $x is greater than or equal to $y, false otherwise. Slay. 🔥
🧮 Arithmetic methods
⚠️ Read this twice bestie: these methods modify the invocand object and return it. They're not out here making copies, they're changing $x in place. No take-backs. 💅
bneg()
$x->bneg();Negates the number — flips the sign between '+' and '-', or between '+inf' and '-inf', respectively. Does nothing at all for NaN or zero. 🤷
babs()
$x->babs();Sets the number to its absolute value — flips the sign from '-' to '+', and from '-inf' to '+inf', respectively. Does nothing for NaN or for positive numbers (they're already living their best life ✨).
bsgn()
$x->bsgn();Signum function, iconic behavior. Sets the number to -1, 0, or 1, depending on whether the number is negative, zero, or positive, respectively. Does not modify NaNs. 👑
bnorm()
$x->bnorm(); # normalize (no-op)Normalizes the number. It is a no-op and is provided only for backwards compatibility. It's giving legacy 💀
binc()
$x->binc(); # increment x by 1bdec()
$x->bdec(); # decrement x by 1badd()
$x->badd($y); # addition (add $y to $x)bsub()
$x->bsub($y); # subtraction (subtract $y from $x)bmul()
$x->bmul($y); # multiplication (multiply $x by $y)bdiv()
$x->bdiv($y); # set $x to quotient
($q, $r) = $x->bdiv($y); # also return remainderOkay so the behavior of "bdiv()" and "bmod()" is based on Perl's "%" operator, which is the remainder after performing floored division. 🧚
Because of this, "bdiv()" and "bmod()" are aliases for "bfdiv()" and "bfmod()", respectively. iykyk 💜
bmod()
$x->bmod($y); # modulus (x % y)This is an alias for "bfmod()". That's the whole thing.
bfdiv()
$x->bfdiv($y); # return quotient
($q, $r) = $x->bfdiv($y); # return quotient and remainderDivides $x by $y by doing floored division (F-division), where the quotient is the floored (rounded towards negative infinity) quotient of the two operands. In list context, it returns the quotient and the remainder. In scalar context, only the quotient comes back. 🎀
$q = floor($x / $y) # quotient
$r = $x - $q * $y # remainderWith F-division, the remainder is either zero or has the same sign as the divisor. Watch the signs bestie, they're doing choreography: 🩰
7 / 4 => ( 1, 3)
-7 / 4 => (-2, 1)
-7 / -4 => ( 1, -3)
7 / -4 => (-2, -1)The behavior of the overloaded operator % agrees with the behavior of Perl's built-in % operator (as documented in the perlop manpage), and this equation
$x == ($x / $y) * $y + ($x % $y)holds true for any finite $x and finite, non-zero $y. ✅
Heads up 🫶: Perl's"use integer"might change the behaviour of%and/for scalars. This is because under'use integer'Perl does what the underlying C library thinks is right, and that varies. However,"use integer"does not change the way things are done with Math::BigInt objects. So your BigInts stay unbothered and consistent. 💅
bfmod()
$x->bfmod($y); # floored modulus (x % y)Returns $x modulo $y, i.e., the remainder after floored division (F-division). This method is like Perl's % operator. See "bfdiv()". 🌸
btdiv()
$x->btdiv($y); # divide, set $x to quotientDivides $x by $y by doing truncated division (T-division), where the quotient is the truncated (rounded towards zero) quotient of the two operands. In list context, it returns the quotient and the remainder. The remainder is either zero or has the same sign as the first operand. In scalar context, only the quotient is returned. 👑
btmod()
$x->btmod($y); # modulusReturns the remainder after truncated division (T-division). See "btdiv()". ✨
binv()
$x->binv();Inverts the value of $x, i.e., computes 1/$x.
bsqrt()
$x->bsqrt(); # calculate square rootReturns the square root truncated to an integer. 🍓
If you want a better approximation of the square root, then use:
$x = Math::BigFloat->new(12);
Math::BigFloat->precision(0);
Math::BigFloat->round_mode("even");
print $x->copy->bsqrt(),"\n"; # 4
Math::BigFloat->precision(2);
print $x->bsqrt(),"\n"; # 3.46
print $x->bsqrt(3),"\n"; # 3.464Look at that precision glow-up, we love to see it. 🌈
bpow()
$x->bpow($y); # power of arguments (x ** y)Returns $x raised to the power of $y. The first two modify $x, the last one doesn't:
print $x->bpow($i),"\n"; # modifies $x
print $x **= $i,"\n"; # ditto
print $x ** $i,"\n"; # leaves $x aloneThe form "$x **= $y" is faster than "$x = $x ** $y;", though. Speed queen. 🏃♀️💨
broot()
$x->broot($N);Calculates the $N'th root of $x.
bmuladd()
$x->bmuladd($y,$z);Multiply $x by $y, and then add $z to the result. Two-for-one, no extra charge. 🎀
This method was added in v1.88 of Math::BigInt.
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 bestie, "bmodpow" is far superior to writing
$num ** $exp % $modbecause it is much faster — it reduces internal variables into the modulus whenever possible, so it operates on smaller numbers. It's giving efficiency icon 💅
"bmodpow" also supports negative exponents. 😳
bmodpow($num, -1, $mod)is exactly equivalent to
bmodinv($num, $mod)bmodinv()
$x->bmodinv($mod); # modular multiplicative inverseReturns 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 % $modIf $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. Sorry bestie, it's a NaN situation. 😭
blog()
$x->blog($base, $accuracy); # logarithm of x to the base $baseIf $base is not defined, Euler's number (e) is used:
print $x->blog(undef, 100); # log(x) to 100 digits100 digits of log, we're fancy like that. ✨
bexp()
$x->bexp($accuracy); # calculate e ** XCalculates 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()". 🦋
bilog2()
Base 2 logarithm rounded down towards the nearest integer.
$x->bilog2(); # int(log2(x)) = int(log(x)/log(2))In list context a second argument is returned. This is 1 if the result is exact, i.e., the input is an exact power of 2, and 0 otherwise. 🌟
bilog10()
Base 10 logarithm rounded down towards the nearest integer.
$x->bilog10(); # int(log10(x)) = int(log(x)/log(10))In list context a second argument is returned. This is 1 if the result is exact, i.e., the input is an exact power of 10, and 0 otherwise. 💜
bclog2()
Base 2 logarithm rounded up towards the nearest integer.
$x->bclog2(); # ceil(log2(x)) = ceil(log(x)/log(2))In list context a second argument is returned. This is 1 if the result is exact, i.e., the input is an exact power of 2, and 0 otherwise. 🌸
bclog10()
Base 10 logarithm rounded up towards the nearest integer.
$x->bclog10(); # ceil(log10(x)) = ceil(log(x)/log(10))In list context a second argument is returned. This is 1 if the result is exact, i.e., the input is an exact power of 10, and 0 otherwise. 🎀
bnok()
Combinations. Combinatorics era. 👑
$n->bnok($k); # binomial coefficient n over kOkay so this one is literally the "choose" function, bestie — it calculates the binomial coefficient n over k, which is the number of ways to choose a sample of k elements from a set of n distinct objects where order does not matter and replacements are not allowed. The result is equivalent to:
/ n \ n!
C(n, k) = | | = -------- where 0 <= k <= n
\ k / k!(n-k)!...when n and k are non-negative. 💖 This method implements the full Kronenburg extension (Kronenburg, M.J. "The Binomial Coefficient for Negative Arguments." 18 May 2011. http://arxiv.org/abs/1105.3689/) which the following pseudo-code illustrates:
if n >= 0 and k >= 0:
return binomial(n, k)
if k >= 0:
return (-1)^k*binomial(-n+k-1, k)
if k <= n:
return (-1)^(n-k)*binomial(-k-1, n-k)
else
return 0And the behaviour is identical to what Maple and Mathematica do for negative integers n, k. Slay, consistency. ✨
bperm()
Permutations, bestie.
$n->bperm($k);Calculates the number of ways to choose a sample of k elements from a set of n distinct objects where order does matter and replacements are not allowed.
n!
P(n, k) = ------ where 0 <= k <= n
(n-k)!bhyperop()
hyperop()
$a -> bhyperop($n, $b); # modifies $a
$x = $a -> hyperop($n, $b); # does not modify $aH_n(a, b) = a[n]b is the nth hyperoperator:
n = 0 : succession (b + 1)
n = 1 : addition (a + b)
n = 2 : multiplication (a * b)
n = 3 : exponentiation (a ** b)
n = 4 : tetration (a ** a ** ... ** a) (b occurrences of a)
... / b+1 if n = 0
| a if n = 1 and b = 0
H_n(a, b) = a[n]b = | 0 if n = 2 and b = 0
| 1 if n >= 3 and b = 0
\ H_(n-1)(a, H_n(a, b-1)) otherwiseHeads up bestie — the result can be a very large number, even for tiny little operands. Also, the backend libraryMath::BigInt::GMPsilently returns the incorrect result when the numbers are larger than it can handle. It is better to useMath::BigInt::GMPzorMath::BigInt::Pari— those ones throw an error if they can't handle the number. No silent lies, periodt. 💅
See also buparrow(), <https://en.wikipedia.org/wiki/Hyperoperation>.
buparrow()
uparrow()
$a -> buparrow($n, $b); # modifies $a
$x = $a -> uparrow($n, $b); # does not modify $aThis method implements Knuth's up-arrow notation, where $n is a non-negative integer representing the number of up-arrows. $n = 0 gives multiplication, $n = 1 gives exponentiation, $n = 2 gives tetration, $n = 3 gives hexation etc. The following illustrates the relation between the first values of $n.
The buparrow() method is equivalent to the bhyperop() method with an offset of two. The following two give the same result:
$x -> buparrow($n, $b);
$x -> bhyperop($n + 2, $b);See also bhyperop(), <https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation>.
backermann()
ackermann()
$m -> backermann($n); # modifies $a
$x = $m -> ackermann($n); # does not modify $aThis method implements the Ackermann function:
/ n + 1 if m = 0
A(m, n) = | A(m-1, 1) if m > 0 and n = 0
\ A(m-1, A(m, n-1)) if m > 0 and n > 0Its value grows rapidly, even for small inputs. For example, A(4, 2) is an integer of 19729 decimal digits. 😭
See <https://en.wikipedia.org/wiki/Ackermann_function>
bsin()
my $x = Math::BigInt->new(1);
print $x->bsin(100), "\n";Calculate the sine of $x, modifying $x in place.
In Math::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). 🎀
bcos()
my $x = Math::BigInt->new(1);
print $x->bcos(100), "\n";Calculate the cosine of $x, modifying $x in place.
In Math::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 Math::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 Math::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). 🎀
bfac()
$x->bfac(); # factorial of $xReturns the factorial of $x, i.e., $x*($x-1)*($x-2)*...*2*1, the product of all positive integers up to and including $x. $x must be > -1. The factorial of N is commonly written as N!, or N!1, when using the multifactorial notation.
bdfac()
$x->bdfac(); # double factorial of $xReturns the double factorial of $x, i.e., $x*($x-2)*($x-4)*... $x must be > -2. The double factorial of N is commonly written as N!!, or N!2, when using the multifactorial notation.
btfac()
$x->btfac(); # triple factorial of $xReturns the triple factorial of $x, i.e., $x*($x-3)*($x-6)*... $x must be > -3. The triple factorial of N is commonly written as N!!!, or N!3, when using the multifactorial notation.
bmfac()
$x->bmfac($k); # $k'th multifactorial of $xReturns the multi-factorial of $x, i.e., $x*($x-$k)*($x-2*$k)*... $x must be > -$k. The multi-factorial of N is commonly written as N!K.
bfib()
$F = $n->bfib(); # a single Fibonacci number
@F = $n->bfib(); # a list of Fibonacci numbersIn scalar context, returns a single Fibonacci number. In list context, returns a list of Fibonacci numbers. The invocand is the last element in the output.
The Fibonacci sequence is defined by
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2)In list context, F(0) and F(n) is the first and last number in the output, respectively. For example, if $n is 12, then "@F = $n->bfib()" returns the following values, F(0) to F(12):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144The sequence can also be extended to negative index n using the re-arranged recurrence relation
F(n-2) = F(n) - F(n-1)giving the bidirectional sequence
n -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
F(n) 13 -8 5 -3 2 -1 1 0 1 1 2 3 5 8 13If $n is -12, the following values, F(0) to F(12), are returned:
0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144blucas()
$F = $n->blucas(); # a single Lucas number
@F = $n->blucas(); # a list of Lucas numbersIn scalar context, returns a single Lucas number. In list context, returns a list of Lucas numbers. The invocand is the last element in the output.
The Lucas sequence is defined by
L(0) = 2
L(1) = 1
L(n) = L(n-1) + L(n-2)In list context, L(0) and L(n) is the first and last number in the output, respectively. For example, if $n is 12, then "@L = $n->blucas()" returns the following values, L(0) to L(12):
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322The sequence can also be extended to negative index n using the re-arranged recurrence relation
L(n-2) = L(n) - L(n-1)giving the bidirectional sequence
n -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
L(n) 29 -18 11 -7 4 -3 1 2 1 3 4 7 11 18 29If $n is -12, the following values, L(0) to L(-12), are returned:
2, 1, -3, 4, -7, 11, -18, 29, -47, 76, -123, 199, -322blsft()
Left shift, bb. ⬅️
$x->blsft($n); # left shift $n places in base 2
$x->blsft($n, $b); # left shift $n places in base $bThe latter is equivalent to
$x -> bmul($b -> copy() -> bpow($n));brsft()
Right shift, mmkay. ➡️
$x->brsft($n); # right shift $n places in base 2
$x->brsft($n, $b); # right shift $n places in base $bThe latter is equivalent to
$x -> bdiv($b -> copy() -> bpow($n));✨ Bitwise methods ✨
Okay so for all bitwise methods, the operands are truncated to integers, i.e., rounded towards zero, if necessary, before the method is applied. The bitwise methods never upgrade, and they always return an integer. 💅
bblsft()
Bitwise left shift. This is equivalent to Perl's << operator.
$x -> bblsft($n); # left shift $n places in base 2If $n is negative, the shifting is done in the opposite direction, so these two are equivalent for all $x and $n
$y = $x -> bblsft($n);
$y = $x -> bbrsft(-$n);and also equivalent to
$y = $x -> bmul(ref($x) -> new(2) -> bpow($n)); # if $n > 0
$y = $x -> bdiv(ref($x) -> new(2) -> bpow($n)); # if $n < 0bbrsft()
Bitwise right shift. This is equivalent to Perl's >> operator.
$x -> bbrsft($n); # right shift $n places in base 2If $n is negative, the shifting is done in the opposite direction, so these two are equivalent for all $x and $n
$y = $x -> bbrsft($n);
$y = $x -> bblsft(-$n);and also equivalent to
$y = $x -> bdiv(ref($x) -> new(2) -> bpow($n)); # if $n > 0
$y = $x -> bmul(ref($x) -> new(2) -> bpow(-$n)); # if $n < 0band()
$x->band($y); # bitwise andbior()
$x->bior($y); # bitwise inclusive orbxor()
$x->bxor($y); # bitwise exclusive orbnot()
$x->bnot(); # bitwise not (two's complement)Two's complement (bitwise not). This is equivalent to, but faster than,
$x->binc()->bneg();✨ Rounding methods ✨
round()
$x->round($A,$P,$round_mode);Rounds $x to accuracy $A or precision $P, using the round mode $round_mode. Pick your fighter 💅
bround()
$x->bround($N); # accuracy: preserve $N digitsRounds $x to an accuracy of $N digits. Bestie said "keep it to $N digits" and bround() said periodt. 🎀
bfround()
$x->bfround($N);Rounds to a multiple of 10**$N. Obsessed with how clean this is? Same. Examples:
Input N Result
123456.123456 3 123500
123456.123456 2 123450
123456.123456 -2 123456.12
123456.123456 -3 123456.123bfloor()
$x->bfloor();Round $x towards minus infinity, i.e., set $x to the largest integer less than or equal to $x. It's giving "down and down only", no cap. ⬇️
bceil()
$x->bceil();Round $x towards plus infinity, i.e., set $x to the smallest integer greater than or equal to $x. Main character energy: always reaching up. ⬆️
bint()
$x->bint();Round $x towards zero. Neutral, chill, unbothered. 🧘
🧮 Other mathematical methods 🧮
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 largest positive integer that divides each of the operands. Finding what everyone has in common? That's literally the GCD's whole personality. 🫶
blcm()
$x -> blcm($y); # LCM of $x and $y
$x -> blcm($y, $z, ...); # LCM of $x, $y, $z, ...Returns the least common multiple (LCM). The "when can we ALL hang out" method. 🌈
💖 Object property methods 💖
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 rightIf $n is negative, returns the digit counting from left. Yes bestie, negative counts from the other side — it's giving mirror vibes. 🪞
bdigitsum()
$x->bdigitsum();Computes the sum of the base 10 digits and assigns the result to the invocand. It changes the number in place, bestie — not a vibe check, an actual rewrite. 💅
digitsum()
$x->digitsum();Computes the sum of the base 10 digits and returns it. Same math, but it hands you the answer instead of editing itself. Polite king behavior 👑
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 Math::BigInt objects, the length of the fraction part is always 0.
Honestly? The following probably doesn't do what you expect:
$c = Math::BigInt->new(123);
print $c->length(),"\n"; # prints 30It prints both the number of digits in the number and in the fraction part since print calls "length()" in list context. Use something like:
print scalar $c->length(),"\n"; # prints 3The scalar is the save. Do not skip it, I am begging 😭
mantissa()
$x->mantissa();Return the signed mantissa of $x as a Math::BigInt.
exponent()
$x->exponent();Return the exponent of $x as a Math::BigInt.
parts()
$x->parts();Returns the significand (mantissa) and the exponent as integers. In Math::BigFloat, both are returned as Math::BigInt objects. Package deal, no splitting 🎁
sparts()
Returns the significand (mantissa) and the exponent as integers. In scalar context, only the significand is returned. The significand is the integer with the smallest absolute value. The output of "sparts()" corresponds to the output from "bsstr()".
In Math::BigInt, this method is identical to "parts()".
nparts()
Returns the significand (mantissa) and exponent corresponding to normalized notation. In scalar context, only the significand is returned. For finite non-zero numbers, the significand's absolute value is greater than or equal to 1 and less than 10. The output of "nparts()" corresponds to the output from "bnstr()". In Math::BigInt, if the significand can not be represented as an integer, upgrading is performed or NaN is returned.
eparts()
Returns the significand (mantissa) and exponent corresponding to engineering notation. In scalar context, only the significand is returned. For finite non-zero numbers, the significand's absolute value is greater than or equal to 1 and less than 1000, and the exponent is a multiple of 3. The output of "eparts()" corresponds to the output from "bestr()". In Math::BigInt, if the significand can not be represented as an integer, upgrading is performed or NaN is returned.
dparts()
Returns the integer part and the fraction part. If the fraction part can not be represented as an integer, upgrading is performed or NaN is returned. The output of "dparts()" corresponds to the output from "bdstr()".
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()
Together with "denominator()", returns the smallest integers so that the numerator divided by the denominator reproduces the original value. With Math::BigInt, "numerator()" simply returns a copy of the invocand.
denominator()
Together with "numerator()", returns the smallest integers so that the numerator divided by the denominator reproduces the original value. With Math::BigInt, "denominator()" always returns either a 1 or a NaN. It is what it is 🫠
🦋 String conversion methods 🦋
bstr()
Returns a string representing the number using decimal notation. In Math::BigFloat, the output is zero padded according to the current accuracy or precision, if any of those are defined.
bsstr()
Returns a string representing the number using scientific notation where both the significand (mantissa) and the exponent are integers. The output corresponds to the output from "sparts()".
123 is returned as "123e+0"
1230 is returned as "123e+1"
12300 is returned as "123e+2"
12000 is returned as "12e+3"
10000 is returned as "1e+4"bnstr()
Returns a string representing the number using normalized notation, the most common variant of scientific notation. For finite non-zero numbers, the absolute value of the significand is greater than or equal to 1 and less than 10. The output corresponds to the output from "nparts()".
123 is returned as "1.23e+2"
1230 is returned as "1.23e+3"
12300 is returned as "1.23e+4"
12000 is returned as "1.2e+4"
10000 is returned as "1e+4"bestr()
Returns a string representing the number using engineering notation. For finite non-zero numbers, the absolute value of the significand is greater than or equal to 1 and less than 1000, and the exponent is a multiple of 3. The output corresponds to the output from "eparts()".
123 is returned as "123e+0"
1230 is returned as "1.23e+3"
12300 is returned as "12.3e+3"
12000 is returned as "12e+3"
10000 is returned as "10e+3"bdstr()
Returns a string representing the number using decimal notation. The output corresponds to the output from "dparts()".
123 is returned as "123"
1230 is returned as "1230"
12300 is returned as "12300"
12000 is returned as "12000"
10000 is returned as "10000"bfstr()
Returns a string representing the number using fractional notation. The output corresponds to the output from "fparts()".
12.345 is returned as "2469/200"
123.45 is returned as "2469/20"
1234.5 is returned as "2469/2"
12345 is returned as "12345"
123450 is returned as "123450"to_hex()
$x->to_hex();Returns a hexadecimal string representation of the number. See also "from_hex()".
to_oct()
$x->to_oct();Returns an octal string representation of the number. See also "from_oct()".
to_bin()
$x->to_bin();Returns a binary string representation of the number. See also "from_bin()".
to_bytes()
$x = Math::BigInt->new("1667327589");
$s = $x->to_bytes(); # $s = "cafe"Returns a byte string representation of the number using big endian byte order. The invocand must be a non-negative, finite integer. See also "from_bytes()".
Note the vibe: non-negative, finite integer only. Anything else and it's not it, bestie 💀
to_ieee754()
See "to_ieee754()" in Math::BigFloat.
to_fp80()
See "to_fp80()" in Math::BigFloat.
to_base()
$x = Math::BigInt->new("250");
$x->to_base(2); # returns "11111010"
$x->to_base(8); # returns "372"
$x->to_base(16); # returns "fa"Returns a string representation of the number in the given base. If a collation sequence is given, the collation sequence determines which characters are used in the output.
Here are some more examples
$x = Math::BigInt->new("16")->to_base(3); # returns "121"
$x = Math::BigInt->new("44027")->to_base(36); # returns "XYZ"
$x = Math::BigInt->new("58314")->to_base(42); # returns "Why"
$x = Math::BigInt->new("4")->to_base(2, "-|"); # returns "|--"If the collation sequence are the bytes from "\x00" to "\xff", and the base is 256, then "to_base()" returns the same output as "to_bytes()". In the following example, $x and $y are identical:
$cs = join "", map chr, 0 .. 255; # collation sequence
$x = Math::BigInt -> to_base("1230129310", 256, $cs)
$y = Math::BigInt -> to_bytes("1230129310");See "from_base()" for information and examples.
to_base_num()
Converts the given number to the given base. This method is equivalent to "to_base()", but returns numbers in an array rather than characters in a string. In the output, the first element is the most significant.
$x = Math::BigInt->new(13); # decimal 13 is binary 1101
$x->to_base_num(2); # returns [1, 1, 0, 1]
$x = Math::BigInt->new(65191);
$x->to_base_num(128); # returns [3, 125, 39]as_hex()
$x->as_hex();As, "to_hex()", but with a "0x" prefix. Little glow-up, same number ✨
as_oct()
$x->as_oct();As, "to_oct()", but with a "0" prefix.
as_bin()
$x->as_bin();As to_bin(), but with a 0b prefix slapped on the front 💅 literally the same energy, just pinker.
🦋 as_bytes() 🦋
This is a lil alias for to_bytes() — same thing, different name, she contains multitudes ✨
💖 Other conversion methods 💖
🌸 numify() 🌸
print $x->numify();Hands you back a Perl scalar made from $x 🫶. It kicks in automatically any time a scalar is needed — like in array index operations — so it's giving "don't worry bestie, I got it" main character energy.
🧚 Utility methods 🧚
These utility methods are made public, periodt 👑 no gatekeeping here.
🌈 dec_str_to_dec_flt_str() 🌈
Takes a string representing any valid number using decimal notation and converts it to a string representing the same number using decimal floating point notation. The output is five lil pieces joined together: the sign of the significand, the absolute value of the significand as the smallest possible integer, the letter e, the sign of the exponent, and the absolute value of the exponent. If the input is invalid, nothing is returned — it's giving ghosted 💀.
$str2 = $class -> dec_str_to_dec_flt_str($str1);Some examples, bestie:
Input Output
31400.00e-4 +314e-2
-0.00012300e8 -123e+2
0 +0e+0💜 hex_str_to_dec_flt_str() 💜
Takes a string representing any valid number using hexadecimal notation and converts it to a string representing the same number using decimal floating point notation. The output has the same format as dec_str_to_dec_flt_str() 💖
$str2 = $class -> hex_str_to_dec_flt_str($str1);Some examples:
Input Output
0xff +255e+0Some examples — and this one's just vibes, no examples follow 🙈
🎀 oct_str_to_dec_flt_str() 🎀
Takes a string representing any valid number using octal notation and converts it to a string representing the same number using decimal floating point notation. Output format is the same as dec_str_to_dec_flt_str(), no cap ✨
$str2 = $class -> oct_str_to_dec_flt_str($str1);🍓 bin_str_to_dec_flt_str() 🍓
Takes a string representing any valid number using binary notation and converts it to a string representing the same number using decimal floating point notation. Output format matches dec_str_to_dec_flt_str() 🦋
$str2 = $class -> bin_str_to_dec_flt_str($str1);👑 dec_str_to_dec_str() 👑
Takes a string representing any valid number using decimal notation and converts it to a string representing the same number using decimal notation. If the number represents an integer, the output is a sign plus the absolute value. If the number represents a non-integer, the output is a sign, the integer part of the number, the decimal point ., and the fraction part with no trailing zeros. If the input is invalid, you get nothing back 🤷 it's simply not answering.
🔥 hex_str_to_dec_str() 🔥
Takes a string representing any valid number using hexadecimal notation and converts it to a string representing the same number using decimal notation. Output format is the same as dec_str_to_dec_str() 💜
🌟 oct_str_to_dec_str() 🌟
Takes a string representing any valid number using octal notation and converts it to a string representing the same number using decimal notation. Output format is the same as dec_str_to_dec_str() 🌈
💫 bin_str_to_dec_str() 💫
Takes a string representing any valid number using binary notation and converts it to a string representing the same number using decimal notation. Output format is the same as dec_str_to_dec_str() ⭐
🎯 ACCURACY AND PRECISION 🎯
Math::BigInt and Math::BigFloat have full support for accuracy- and precision-based rounding — both automatically after every operation, and manually whenever you feel like it 💅.
This section describes the accuracy/precision handling in Math::BigInt and Math::BigFloat as it used to be and as it is now, complete with an explanation of all the terms and abbreviations — no crumbs withheld 🔥.
Not-yet-implemented things (but with correct description) are marked with !, and things that need to be answered are marked with ?.
The next paragraph is a short description of the terms used here (because these may differ from terms used by other people or other documentation).
For the rest of this document, the shortcuts A (for accuracy), P (for precision), R (rounding mode), and F (fallback) are what we're calling things.
📏 Accuracy A 📏
Number of significant digits. Leading zeros are not counted, bestie. 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, 123.45000 has 8 and 0.000123 has 3.
The string output (of floating point numbers) is 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 1234.1000For Math::BigInt objects, no padding occurs — none, zero, nada ✨
📐 Precision P 📐
Precision is 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 at least two digits to the left of the decimal point are zero, so 123 with P = 1 becomes 120. Heads up though: numbers with zeros before the decimal point may have different precisions, because 1200 can have P = 0, 1 or 2 (depends on what the initial value was). It could also have p < 0, when the digits after the decimal point are zero 👀
The string output (of floating point numbers) is 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 1234.01000For Math::BigInt objects, no padding occurs 💅
🎲 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 — so don't come for me 🙈.)
Directed rounding
These round modes always round in the same direction — no flip-flopping 💁
'trunc'— Round towards zero. Removes all digits following the rounding place, i.e., replaces them with zeros. So987.65rounded to tens (P=1) becomes980, and rounded to the fourth significant digit becomes987.6(A=4).123.456rounded to the second place after the decimal point (P=-2) becomes123.46. This corresponds to the IEEE 754 rounding mode'roundTowardZero'.
Rounding to nearest
These rounding modes round to the nearest digit. They differ in how they determine which way to round in the ambiguous case when there's a tie — it's giving drama 🫠
'even'— Round towards the nearest even digit. E.g., when rounding to nearest integer,-5.5becomes-6,4.5becomes4, but4.501becomes5. This corresponds to the IEEE 754 rounding mode'roundTiesToEven'✨'odd'— Round towards the nearest odd digit. E.g., when rounding to nearest integer,4.5becomes5,-5.5becomes-5, but5.501becomes6. This corresponds to the IEEE 754 rounding mode'roundTiesToOdd'.'+inf'— Round towards plus infinity, i.e., always round up. E.g., when rounding to the nearest integer,4.5becomes5,-5.5becomes-5, and4.501also becomes5. This corresponds to the IEEE 754 rounding mode'roundTiesToPositive'🔥'-inf'— Round towards minus infinity, i.e., always round down. E.g., when rounding to the nearest integer,4.5becomes4,-5.5becomes-6, but4.501becomes5. This corresponds to the IEEE 754 rounding mode'roundTiesToNegative'.'zero'— Round towards zero, i.e., round positive numbers down and negative numbers up. E.g., when rounding to the nearest integer,4.5becomes4,-5.5becomes-5, but4.501becomes5. This corresponds to the IEEE 754 rounding mode'roundTiesToZero'💫'common'— Round away from zero, i.e., round to the number with the largest absolute value. E.g., when rounding to the nearest integer,-1.5becomes-2,1.5becomes2and1.49becomes1. This corresponds to the IEEE 754 rounding mode'roundTiesToAway'👑
🪂 Fallback F 🪂
When neither A nor P are defined, the fallback accuracy is what gets used when computing values that would potentially give an infinite number of digits — division, roots, logarithms, trigonometric functions etc. 🌊
🔍 More details on rounding 🔍
The handling of A & P in MBI/MBF (the old core code shipped with Perl versions <= 5.7.2) is like this:
Precision
* bfround($p) is able to round to $p number of digits after the decimal
point
* otherwise P is unused✨ Accuracy (significant digits) ✨
bround($a)rounds to$asignificant digits 🎯- only
bdiv()andbsqrt()take A as an (optional) parameter- other operations just make the same number (
bnegetc), or more digits (bmul) - rounding/truncating only happens when you explicitly call one of
broundorbfround, and never forMath::BigInt(not implemented) 🙈
- other operations just make the same number (
bsqrt()simply hands its accuracy argument over tobdiv.- the documentation and the comment in the code indicate two different ways on how
bdiv()determines the maximum number of digits it should calculate, and the actual code does yet another thing 💀
POD:
max($Math::BigFloat::div_scale,length(dividend)+length(divisor))Comment:
result has at most max(scale, length(dividend), length(divisor)) digitsActual 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 whether 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
Math::BigInt->accuracy()orMath::BigFloat->accuracy()or whatever class you are using. ✨ - You can also set P globally by using
Math::SomeClass->precision()likewise. - Globals are classwide, and not inherited by subclasses.
- to undefine A, use
Math::SomeClass->accuracy(undef); - to undefine P, use
Math::SomeClass->precision(undef); - Setting
Math::SomeClass->accuracy()clears automaticallyMath::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
Math::SomeClass->accuracy() - to find out the current global P, use
Math::SomeClass->precision() - use
$x->accuracy()respective$x->precision()for the local setting of$x. - Please note that
$x->accuracy()respective$x->precision()return eventually defined global A or P, when$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$xwill be what was in effect when$xwas created) 🕰️ - If given
undeffor A and P, NO rounding will occur, and the globals will 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$x = Math::BigInt->new($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, sinceMath::BigIntobjects never have digits after the decimal point 🙅♀️ Math::BigFloatusesMath::BigIntinternally, but setting A or P insideMath::BigIntas globals does not tamper with the parts of aMath::BigFloat. A flag is used to mark allMath::BigFloatnumbers 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
bdiv/bsqrt) and will not be rounded. - There is another setting for
bdiv()(and thus forbsqrt()). If neither of A or P is defined,bdiv()will use a fallback (F) of$div_scaledigits. 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 of1/3:-) 😭 bdivwill 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 like0.12345000000001with 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, withbdiv()andbsqrt()as exceptions to guard against overflows. You must explicitly callbround(),bfround()orround()(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 acopy()before rounding like this:
- never round (this is the default): This is done by setting A and P to
$x = Math::BigFloat->new(12.34);
$y = Math::BigFloat->new(98.76);
$z = $x * $y; # 1218.6984
print $x->copy()->bround(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 methodround()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::Currencymight set A toundef, 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
bsqrt()will hand its arguments tobdiv(), 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
$x->accuracy()or$x->precision()and thus force different A and P for different objects/numbers. - Setting A or P this way immediately rounds
$xto the new value. ⚡ $x->accuracy()clears$x->precision(), and vice versa.
Rounding
- the rounding routines will use the respective global or local settings.
bround()is for accuracy rounding, whilebfround()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
Math::SomeClass->round_mode()or by setting$Math::SomeClass::round_mode - after each operation,
$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
$x->round($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
- A:
undef - P:
undef - R:
'even' - F:
40
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
bdiv):- 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 🫶
🌸 INTERNALS 🌸
Bestie, listen. You do not care about the internal representation. You don't depend on it either. It can change without notice, no apology text, nothing. The only correct move is to use method calls like $x->sign(); instead of peeking at how the number is stored inside. Periodt. 💅
🧮 Math Library
The actual mathematical computations get done by a backend library. You're not required to say which backend to use, but heads up: some backends are much faster than the default one. Lowkey a big deal.
✨ The default library
The default library is Math::BigInt::Calc, and it's implemented in pure Perl, so it needs no compiler at all. Cozy, portable, a little slow. 🎀
✨ Specifying a library
💫 The simple case
use Math::BigInt;is equivalent to saying
use Math::BigInt try => 'Calc';You can use a different backend library with, e.g.,
use Math::BigInt try => 'GMP';which attempts to load the Math::BigInt::GMP library, and falls back to the default library if the specified library can't be loaded. Fallback = your safety net, bestie. 🫶
Multiple libraries can be specified by separating them by a comma, e.g.,
use Math::BigInt try => 'GMP,Pari';If you request a specific set of libraries and do not allow fallback to the default library, specify them using only,
use Math::BigInt only => 'GMP,Pari';If you prefer a specific set of libraries, but want to see a warning if the fallback library is used, specify them using lib,
use Math::BigInt lib => 'GMP,Pari';The following first tries to find Math::BigInt::Foo, then Math::BigInt::Bar, and if this also fails, reverts to Math::BigInt::Calc:
use Math::BigInt try => 'Foo,Math::BigInt::Bar';✨ Which library to use?
Note: General purpose packages should not be explicit about the library to use; let the script author decide which is best. Like, don't be the friend who orders for the whole table. 🙈
Math::BigInt::GMP, Math::BigInt::Pari, and Math::BigInt::GMPz are in cases involving big numbers much faster than Math::BigInt::Calc. However these libraries are 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 library you want to use. It's giving ✨informed decision✨.
Different low-level libraries use different formats to store the numbers, so mixing them won't work. And you should not depend on the number having a specific internal format.
See the respective math library module documentation for further details.
✨ Loading multiple libraries
The first library that is successfully loaded is the one that will be used. Any further attempts at loading a different module will be ignored. This is to avoid the situation where module A requires math library X, and module B requires math library Y, causing modules A and B to be incompatible. For example,
use Math::BigInt; # loads default "Calc"
use Math::BigFloat only => "GMP"; # ignores "GMP"First come, first served. The rest get left on read. 💀
➕➖ Sign
The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
A sign of 'NaN' is used to represent values that are not numbers, e.g., the result of 0/0. '+inf' and '-inf' represent positive and negative infinity, respectively. For example you get '+inf' when dividing a positive number by 0, and '-inf' when dividing any negative number by 0. Math said "not today" and then said "actually, infinity". 🌈
💖 EXAMPLES 💖
use Math::BigInt;
sub bigint { Math::BigInt->new(shift); }
$x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
$x = Math::BigInt->bneg("1234"); # Math::BigInt "-1234"
$x = Math::BigInt->babs("-12345"); # Math::BigInt "12345"
$x = Math::BigInt->bnorm("-0.00"); # Math::BigInt "0"
$x = bigint(1) + bigint(2); # Math::BigInt "3"
$x = bigint(1) + "2"; # ditto ("2" becomes a Math::BigInt)
$x = bigint(1); # Math::BigInt "1"
$x = $x + 5 / 2; # Math::BigInt "3"
$x = $x ** 3; # Math::BigInt "27"
$x *= 2; # Math::BigInt "54"
$x = Math::BigInt->new(0); # Math::BigInt "0"
$x--; # Math::BigInt "-1"
$x = Math::BigInt->badd(4,5) # Math::BigInt "9"
print $x->bsstr(); # 9e+0Examples for rounding, because we love a tidy number ✨:
use Math::BigFloat;
use Test::More;
$x = Math::BigFloat->new(123.4567);
$y = Math::BigFloat->new(123.456789);
Math::BigFloat->accuracy(4); # no more A than 4
is ($x->copy()->bround(),123.4); # even rounding
print $x->copy()->bround(),"\n"; # 123.4
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->bround(),"\n"; # 123.5
Math::BigFloat->accuracy(5); # no more A than 5
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->bround(),"\n"; # 123.46
$y = $x->copy()->bround(4),"\n"; # A = 4: 123.4
print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
Math::BigFloat->accuracy(undef); # A not important now
Math::BigFloat->precision(2); # P important
print $x->copy()->bnorm(),"\n"; # 123.46
print $x->copy()->bround(),"\n"; # 123.46Examples for converting, my beloved base-shifting content 🦋:
my $x = Math::BigInt->new('0b1'.'01' x 123);
print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";🔢 NUMERIC LITERALS 🔢
After use Math::BigInt ':constant' all numeric literals in the given scope are converted to Math::BigInt objects. This conversion happens at compile time. Every non-integer is convert to a NaN. (Yes bestie, that's the actual rule — non-integers don't get to play.)
For example,
perl -MMath::BigInt=: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. Not slay. 😭
Please note that strings are not affected, so that
use Math::BigInt qw/:constant/;
$x = "1234567890123456789012345678901234567890"
+ "123456789123456789";does give you what you expect. You need an explicit Math::BigInt->new() around at least one of the operands. You should also quote large constants to prevent loss of precision:
use Math::BigInt;
$x = Math::BigInt->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::BigInt object at run time, which results in an inaccurate result. Quotes are your besties here, fr fr. 🫶
🌸 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. Silent wrongness is the worst kind of wrongness, iykyk. 💀
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-4Octal floating point literals (with 0 prefix):
01.164p+8 01.164P+8
01.164p8 01.164P8
011640p-4 011640P-4Octal floating point literals (with 0o prefix) (requires v5.34.0):
0o1.164p+8 0O1.164P+8
0o1.164p8 0O1.164P8
0o11640p-4 0O11640P-4Binary floating point literals:
0b1.0011101p+8 0B1.0011101P+8
0b1.0011101p8 0B1.0011101P8
0b10011101000p-2 0B10011101000P-2⚡ PERFORMANCE ⚡
Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x must be made in the second case. For long numbers, the copy can eat up to 20% of the work (in the case of addition/subtraction, less for multiplication/division). If $y is very small compared to $x, the form $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes more time then the actual addition.
With a technique called copy-on-write, the cost of copying with overload could be minimized or even completely avoided. A test implementation of COW did show performance gains for overloaded math, but introduced a performance loss due to a constant overhead for all other operations. So Math::BigInt does currently not COW. Sad but true. 🐄💔
The rewritten version of this module (vs. v0.01) is slower on certain operations, like new(), bstr() and numify(). The reason are that it does now more work and handles much more cases. The time spent in these operations is usually gained in the other math operations so that code on the average should get (much) faster. If they don't, please contact the author. 👑
Some operations may be slower for small numbers, but are significantly faster for big numbers. Other operations are now constant (O(1), like bneg(), babs() etc), instead of O(N) and thus nearly always take much less time. These optimizations were done on purpose. Iconic behavior, honestly.
If you find the Calc module to slow, try to install any of the replacement modules and see if they help you.
🌈 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 🦋
✨ Subclassing Math::BigInt ✨
okay so the whole vibe of Math::BigInt's design is that you can make simple subclasses with very little work, as long as you follow a few lil rules:
- The public API has to stay consistent, no cap. Like, if a sub-class is overloading addition, the sub-class must use the same name — in this case
badd(). The reason is that Math::BigInt is optimized to call the object methods directly, so it's not out here searching for your renamed versions. - The private object hash keys like
$x->{sign}may not be changed, but additional keys can be added, like$x->{_custom}. Slay, decorate freely. - Accessor functions are available for all existing object hash keys and should be used instead of directly accessing the internal hash keys. Why? Because Math::BigInt itself has a pluggable interface which permits it to support different storage methods. Use the front door bestie.
More complex sub-classes may have to replicate more of the logic internal of Math::BigInt if they need to change more basic behaviors. But a subclass that only needs to change the output? Only has to overload bstr(). That's it. Iconic behaviour honestly.
All other object methods and overloaded functions can be directly inherited from the parent class. Free real estate.
At the very minimum, any subclass needs to provide its own new() and can store additional hash keys in the object. There are also some package globals that must be defined, e.g.:
# Globals
our $accuracy = 2; # round to 2 decimal places
our $precision = undef;
our $round_mode = 'even';
our $div_scale = 40;Additionally, you might want to provide the following two globals to allow auto-upgrading and auto-downgrading:
our $upgrade = undef;
our $downgrade = undef;This allows Math::BigInt to correctly retrieve package globals from the subclass, like $SubClass::precision. See t/Math/BigInt/Subclass.pm, t/Math/BigFloat/SubClass.pm, or t/Math/BigRat/SubClass.pm for subclass examples. Go look, they're right there 💖
Don't forget to
use overload;in your subclass to automatically inherit the overloading from the parent. And if you feel like it, you can change part of the overloading — look at Math::String for an example.
🔥 UPGRADING 🔥
When used like this:
use Math::BigInt upgrade => 'Foo::Bar';
use Math::BigInt;
Math::BigInt -> upgrade('Foo::Bar');any operation whose result cannot be represented as an Math::BigInt object is upgraded to the class Foo::Bar. Usually this is used in conjunction with Math::BigRat or Math::BigFloat:
use Math::BigInt upgrade => 'Math::BigFloat';For example, the following returns 3 as a Math::BigInt when no upgrading is defined, and 3.125 as a Math::BigFloat if Math::BigInt is set to upgrade to Math::BigFloat:
$x = Math::BigInt -> new(25) -> bdiv(8);As a shortcut, you can use the module bignum:
use bignum;which is also good for one-liners:
perl -Mbignum -le 'print 2 ** 255'This makes it possible to mix arguments of different classes (as in 2.5 + 2) as well as preserve accuracy (as in sqrt(3)). Chemistry, honestly 🧪
🎀 Auto-upgrade 🎀
The following methods upgrade themselves unconditionally; that is, if upgrade is in effect, they always hands up their work:
bdiv bfdiv btdiv bsqrt blog bexp bpi bsin bcos batan batan2All other methods upgrade themselves only when one (or all) of their arguments are of the class mentioned in $upgrade.
🌈 EXPORTS 🌈
Math::BigInt exports nothing by default, but can export the following methods:
bgcd
blcm💀 CAVEATS 💀
Some things might not work as you expect them. Below is documented what is known to be troublesome:
😭 Comparing numbers as strings
Both bstr() and bsstr() as well as stringify via overload drop the leading '+'. This is to be consistent with Perl and to make cmp (especially with overloading) to work as you expect. It also solves problems with Test.pm and Test::More, which stringify arguments before comparing them.
Mark Biggar said, when asked about to drop the '+' altogether, or make only cmp work:
I agree (with the first alternative), don't add the '+' on positive numbers. It's not as important anymore with the new internal form for numbers. It made doing things like abs and neg easier, but those have to be done differently now anyway.
So, the following examples now works as expected:
use Test::More tests => 1;
use Math::BigInt;
my $x = Math::BigInt -> new(3*3);
my $y = Math::BigInt -> new(3*3);
is($x,3*3, 'multiplication');
print "$x eq 9" if $x eq $y;
print "$x eq 9" if $x eq '9';
print "$x eq 9" if $x eq 3*3;Additionally, the following still works:
print "$x == 9" if $x == $y;
print "$x == 9" if $x == 9;
print "$x == 9" if $x == 3*3;There is now a bsstr() method to get the string in scientific notation aka 1e+2 instead of 100. Be advised that overloaded 'eq' always uses bstr() for comparison, but Perl represents some numbers as 100 and others as 1e+308. If in doubt, convert both arguments to Math::BigInt before comparing them as strings:
use Test::More tests => 3;
use Math::BigInt;
$x = Math::BigInt->new('1e56');
$y = 1e56;
is($x,$y); # fails
is($x->bsstr(), $y); # okay
$y = Math::BigInt->new($y);
is($x, $y); # okayAlternatively, simply use <=> for comparisons, this always gets it right. There is not yet a way to get a number automatically represented as a string that matches exactly the way Perl represents it. we're working on it, bestie 🫶
🐙 oct()/hex() 🐙
These perl routines currently (as of Perl v.5.8.6) cannot handle passed inf.
te@linux:~> perl -wle 'print 2 ** 3333'
Inf
te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
1
te@linux:~> perl -wle 'print oct(2 ** 3333)'
0
te@linux:~> perl -wle 'print hex(2 ** 3333)'
Illegal hexadecimal digit 'I' ignored at -e line 1.
0The same problems occur if you pass them Math::BigInt->binf() objects. Since overloading these routines is not possible, this cannot be fixed from Math::BigInt. not our fault, we promise 💅
🙈 int()
int() returns (at least for Perl v5.7.1 and up) another Math::BigInt, not a Perl scalar:
$x = Math::BigInt->new(123);
$y = int($x); # 123 as a Math::BigInt
$x = Math::BigFloat->new(123.45);
$y = int($x); # 123 as a Math::BigFloatIf you want a real Perl scalar, use numify():
$y = $x->numify(); # 123 as a scalarThis is seldom necessary, though, because this is done automatically, like when you access an array:
$z = $array[$x]; # does work automatically💜 Modifying and =
Beware of:
$x = Math::BigFloat->new(5);
$y = $x;This makes a second reference to the same object and stores it in $y. Thus anything that modifies $x (except overloaded operators) also modifies $y, and vice versa. Or in other words, "=" is only safe if you modify your Math::BigInt objects only via overloaded math. As soon as you use a method call it breaks:
$x->bmul(2);
print "$x, $y\n"; # prints '10, 10'If you want a true copy of $x, use:
$y = $x->copy();You can also chain the calls like this, this first makes a copy and then multiply it by 2:
$y = $x->copy()->bmul(2);See also the documentation for overload.pm regarding "=".
⭐ Overloading -$x
The following:
$x = -$x;is slower than
$x->bneg();since overload calls sub($x,0,1); instead of neg($x). The first variant needs to preserve $x since it does not know that it later gets overwritten. This makes a copy of $x and takes O(N), but $x->bneg() is O(1). efficiency queen 👑
🌸 Mixing different object types
With overloaded operators, it is the first (dominating) operand that determines which method is called. Here are some examples showing what actually gets called in various cases.
use Math::BigInt;
use Math::BigFloat;
$mbf = Math::BigFloat->new(5);
$mbi2 = Math::BigInt->new(5);
$mbi = Math::BigInt->new(2);
# what actually gets called:
$float = $mbf + $mbi; # $mbf->badd($mbi)
$float = $mbf / $mbi; # $mbf->bdiv($mbi)
$integer = $mbi + $mbf; # $mbi->badd($mbf)
$integer = $mbi2 / $mbi; # $mbi2->bdiv($mbi)
$integer = $mbi2 / $mbf; # $mbi2->bdiv($mbf)For instance, Math::BigInt->bdiv() always returns a Math::BigInt, regardless of whether the second operant is a Math::BigFloat. To get a Math::BigFloat you either need to call the operation manually, make sure each operand already is a Math::BigFloat, or cast to that type via Math::BigFloat->new():
$float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5Beware of casting the entire expression, as this would cast the result, at which point it is too late:
$float = Math::BigFloat->new($mbi2 / $mbi); # = 2Beware also of the order of more complicated expressions like:
$integer = ($mbi2 + $mbi) / $mbf; # int / float => int
$integer = $mbi2 / Math::BigFloat->new($mbi); # dittoIf in doubt, break the expression into simpler terms, or cast all operands to the desired resulting type.
Scalar values are a bit different, since:
$float = 2 + $mbf;
$float = $mbf + 2;both result in the proper type due to the way the overloaded math works.
This section also applies to other overloaded math packages, like Math::String.
One solution to you problem might be autoupgrading|upgrading. See the pragmas bignum, bigint and bigrat for an easy way to do this.
🐛 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 🫶
okay bestie if you're stuck, don't panic, the docs are literally right there 💖 you can pull them up with the perldoc command:
perldoc Math::BigIntand if you wanna go hunting online, there's also all this:
- 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. slay 💅
👯 SEE ALSO 👯
Math::BigFloat and Math::BigRat, plus the backend libraries Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari, Math::BigInt::GMPz, and Math::BigInt::BitVect. the whole squad fr fr 🫂
The pragmas bigint, bigfloat, and bigrat might also be of interest to you btw, iykyk. And on top of that there's the bignum pragma, which is the one doing the upgrading and downgrading ✨
👑 AUTHORS 👑
- Mark Biggar — overloaded interface by Ilya Zakharevich, 1996-2001. 🎀
- Completely rewritten by Tels
http://bloodgate.com, 2001-2008. 🔥 - Florian Ragwitz
flora@cpan.org, 2010. 🌸 - Peter John Acklam
pjacklam@gmail.com, 2011-. ⭐
Lowkey so many people contributed in one or more ways to the final beast — check the file CREDITS for an (incomplete) list. If you miss your name, please drop me a mail. Thank you! 😭🫶
and that's a wrap on the whole page, bestie!! 💖✨ you just read Math::BigInt(3perl), straight outta perl v5.44.0, dated 2026-10-17 — periodt, go forth and big-int responsibly 👑💅
📦 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 : a language model's rewrite of the original, under its terms