struct BigInt
Overview
A BigInt
can represent arbitrarily large integers.
It is implemented under the hood with GMP.
Included Modules
- Comparable(Float)
- Comparable(BigInt)
- Comparable(UInt128 | UInt16 | UInt32 | UInt64 | UInt8)
- Comparable(Int128 | Int16 | Int32 | Int64 | Int8)
Defined in:
big.crbig/big_int.cr
big/number.cr
Constructors
-
.new(str : String, base = 10)
Creates a
BigInt
with the value denoted by str in the given base. -
.new(num : Int::Signed)
Creates a
BigInt
from the given num. -
.new(num : Int::Unsigned)
Creates a
BigInt
from the given num. -
.new(num : Float::Primitive)
Creates a
BigInt
from the given num. -
.new(num : BigFloat)
Creates a
BigInt
from the given num. -
.new(num : BigDecimal)
Creates a
BigInt
from the given num. -
.new(num : BigRational)
Creates a
BigInt
from the given num. -
.new(num : BigInt)
Returns num.
-
.new
Creates a
BigInt
with the value zero.
Instance Method Summary
-
#%(other : Int) : BigInt
Returns
self
modulo other. - #&(other : Int) : BigInt
- #&*(other) : BigInt
- #&+(other) : BigInt
- #&-(other) : BigInt
- #*(other : Int) : BigInt
- #*(other : LibGMP::IntPrimitiveUnsigned) : BigInt
- #*(other : LibGMP::IntPrimitiveSigned) : BigInt
- #*(other : BigInt) : BigInt
-
#**(other : Int) : BigInt
Returns the value of raising
self
to the power of exponent. - #+(other : Int) : BigInt
- #+(other : BigInt) : BigInt
- #- : BigInt
- #-(other : Int) : BigInt
- #-(other : BigInt) : BigInt
- #/(other : UInt128) : BigFloat
- #/(other : Int128) : BigFloat
- #/(other : Float32) : BigFloat
- #/(other : UInt64) : BigFloat
- #/(other : Int64) : BigFloat
- #/(other : UInt32) : BigFloat
- #/(other : Int32) : BigFloat
- #/(other : UInt16) : BigFloat
- #/(other : Int16) : BigFloat
- #/(other : Int8) : BigFloat
- #/(other : BigRational) : BigRational
- #/(other : BigDecimal) : BigDecimal
- #/(other : BigInt) : BigFloat
- #/(other : UInt8) : BigFloat
- #/(other : Float64) : BigFloat
- #//(other : Int::Unsigned) : BigInt
- #//(other : Int) : BigInt
-
#<<(other : Int) : BigInt
Returns the result of shifting this number's bits count positions to the left.
- #<=>(other : BigInt)
-
#<=>(other : Float)
The comparison operator.
- #<=>(other : Int::Unsigned)
- #<=>(other : Int::Signed)
-
#>>(other : Int) : BigInt
Returns the result of shifting this number's bits count positions to the right.
- #^(other : Int) : BigInt
-
#abs : BigInt
Returns the absolute value of this number.
-
#bit_length : Int32
Returns the number of bits of this int value.
- #clone
- #divmod(number : Int::Unsigned)
- #divmod(number : Int::Signed)
- #divmod(number : LibGMP::ULong)
- #divmod(number : BigInt)
- #factorial : BigInt
-
#gcd(other : Int) : Int
Returns the greatest common divisor of
self
and other. -
#gcd(other : BigInt) : BigInt
Returns the greatest common divisor of
self
and other. -
#hash(hasher)
TODO check hash equality for numbers >= 2**63
-
#lcm(other : Int) : BigInt
Returns the least common multiple of
self
and other. -
#lcm(other : BigInt) : BigInt
Returns the least common multiple of
self
and other. -
#popcount
Counts
1
-bits in the binary representation of this integer. -
#remainder(other : Int) : BigInt
Returns
self
remainder other. -
#tdiv(other : Int) : BigInt
Divides
self
by other using truncated division. -
#to_big_d
Converts
self
toBigDecimal
. - #to_big_f
-
#to_big_i
Returns a
BigInt
representing this integer. -
#to_big_r
Returns a
BigRational
representing this integer. - #to_f
- #to_f!
- #to_f32
- #to_f32!
- #to_f64
- #to_f64!
- #to_i
- #to_i!
- #to_i16
- #to_i16!
- #to_i32
- #to_i32!
- #to_i64
- #to_i64!
- #to_i8
- #to_i8!
-
#to_s : String
Returns a string representation of self.
-
#to_s(base : Int) : String
Returns a string containing the representation of big radix base (2 through 36).
-
#to_s(io : IO) : Nil
Returns a string representation of self.
- #to_u
- #to_u!
- #to_u16
- #to_u16!
- #to_u32
- #to_u32!
- #to_u64
- #to_u64!
- #to_u8
- #to_u8!
- #to_unsafe
-
#trailing_zeros_count
Returns the number of trailing
0
-bits. - #unsafe_floored_div(other : BigInt) : BigInt
- #unsafe_floored_div(other : Int) : BigInt
- #unsafe_floored_divmod(number : LibGMP::ULong)
- #unsafe_floored_divmod(number : BigInt)
- #unsafe_floored_mod(other : Int) : BigInt
- #unsafe_floored_mod(other : BigInt) : BigInt
- #unsafe_truncated_div(other : Int) : BigInt
- #unsafe_truncated_div(other : BigInt) : BigInt
- #unsafe_truncated_divmod(number : BigInt)
- #unsafe_truncated_divmod(number : LibGMP::ULong)
- #unsafe_truncated_mod(other : Int) : BigInt
- #unsafe_truncated_mod(other : BigInt) : BigInt
- #unsafe_truncated_mod(other : LibGMP::IntPrimitive) : BigInt
- #|(other : Int) : BigInt
- #~ : BigInt
Instance methods inherited from module Comparable(Float)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigInt)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(UInt128 | UInt16 | UInt32 | UInt64 | UInt8)
<(other : T | T | T | T | T)
<,
<=(other : T | T | T | T | T)
<=,
<=>(other : T | T | T | T | T)
<=>,
==(other : T | T | T | T | T)
==,
>(other : T | T | T | T | T)
>,
>=(other : T | T | T | T | T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(Int128 | Int16 | Int32 | Int64 | Int8)
<(other : T | T | T | T | T)
<,
<=(other : T | T | T | T | T)
<=,
<=>(other : T | T | T | T | T)
<=>,
==(other : T | T | T | T | T)
==,
>(other : T | T | T | T | T)
>,
>=(other : T | T | T | T | T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from struct Int
%(other : BigInt) : BigInt%(other : Int) %, &*(other : BigInt) : BigInt &*, &**(exponent : Int) : self &**, &+(other : BigInt) : BigInt &+, &-(other : BigInt) : BigInt &-, *(other : BigDecimal)
*(other : BigInt) : BigInt
*(other : BigRational) *, **(exponent : Float) : Float64
**(exponent : Int) : self **, +(other : BigDecimal)
+(other : BigInt) : BigInt
+(other : BigRational) +, -(other : BigDecimal)
-(other : BigInt) : BigInt
-(other : BigRational) -, /(other : BigRational) /, //(other : Int::Primitive) //, <<(count : Int) <<, <=>(other : BigDecimal)
<=>(other : BigRational)
<=>(other : Int) : Int32
<=>(other : BigInt) <=>, ===(char : Char) ===, >>(count : Int) >>, abs abs, bit(bit) bit, bit_length : Int32 bit_length, bits(range : Range) bits, bits_set?(mask) bits_set?, ceil ceil, chr chr, day : Time::Span day, days : Time::Span days, digits(base = 10) : Array(Int32) digits, divisible_by?(num) divisible_by?, downto(to)
downto(to, &block : self -> ) : Nil downto, even? even?, fdiv(other) fdiv, floor floor, gcd(other : self) : self
gcd(other : BigInt) : Int gcd, hash(hasher) hash, hour : Time::Span hour, hours : Time::Span hours, humanize_bytes(precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : String
humanize_bytes(io : IO, precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : Nil humanize_bytes, lcm(other : BigInt) : BigInt
lcm(other : Int) lcm, microsecond : Time::Span microsecond, microseconds : Time::Span microseconds, millisecond : Time::Span millisecond, milliseconds : Time::Span milliseconds, minute : Time::Span minute, minutes : Time::Span minutes, modulo(other) modulo, month : Time::MonthSpan month, months : Time::MonthSpan months, nanosecond : Time::Span nanosecond, nanoseconds : Time::Span nanoseconds, odd? odd?, popcount popcount, pred pred, remainder(other : Int) remainder, round(mode : RoundingMode) : self round, round_away round_away, round_even : self round_even, second : Time::Span second, seconds : Time::Span seconds, succ succ, tdiv(other : Int) tdiv, times(&block : self -> ) : Nil
times times, to(to, &block : self -> ) : Nil
to(to) to, to_big_d to_big_d, to_big_i : BigInt to_big_i, to_big_r to_big_r, to_io(io : IO, format : IO::ByteFormat) to_io, to_json(json : JSON::Builder) to_json, to_json_object_key to_json_object_key, to_s(io : IO, base : Int = 10, *, upcase : Bool = false) : Nil
to_s(base : Int = 10, *, upcase : Bool = false) : String to_s, trailing_zeros_count trailing_zeros_count, trunc trunc, upto(to, &block : self -> ) : Nil
upto(to) upto, week : Time::Span week, weeks : Time::Span weeks, year : Time::MonthSpan year, years : Time::MonthSpan years, ~ ~
Constructor methods inherited from struct Int
from_io(io : IO, format : IO::ByteFormat) : self
from_io
Instance methods inherited from module Comparable(BigDecimal)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigRational)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigInt)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from struct Number
*(other : Complex)*(other : BigFloat) *, +(other : BigFloat)
+(other : Complex)
+ +, -(other : Complex)
-(other : BigFloat) -, /(other : Complex)
/(other : BigFloat) /, //(other) //, <=>(other : BigFloat)
<=>(other) : Int32? <=>, ==(other : Complex) ==, abs abs, abs2 abs2, cis cis, divmod(number) divmod, format(separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : String
format(io : IO, separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : Nil format, humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Indexable = SI_PREFIXES) : Nil
humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes = SI_PREFIXES) : String
humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, &prefixes : Int32, Float64 -> Tuple(Int32, _) | Tuple(Int32, _, Bool)) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, &) : String
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil humanize, i i, round(digits : Number, base = 10, *, mode : RoundingMode = :ties_even)
round(mode : RoundingMode = :ties_even) : self round, sign sign, significant(digits, base = 10) significant, step(*, to limit = nil, exclusive : Bool = false)
step(*, to limit = nil, by step, exclusive : Bool = false)
step(*, to limit = nil, exclusive : Bool = false, &) : Nil
step(*, to limit = nil, by step, exclusive : Bool = false, &) : Nil step, to_big_f to_big_f, to_c to_c, to_yaml(yaml : YAML::Nodes::Builder) to_yaml, zero? : Bool zero?
Constructor methods inherited from struct Number
additive_identity : self
additive_identity,
multiplicative_identity : self
multiplicative_identity,
zero : self
zero
Class methods inherited from struct Number
si_prefix(magnitude : Int, prefixes = SI_PREFIXES) : Char?
si_prefix
Instance methods inherited from module Comparable(BigFloat)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(Number)
<(other : T)
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T)
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from struct Value
==(other : JSON::Any)==(other : YAML::Any)
==(other) ==, dup dup
Instance methods inherited from class Object
! : Bool
!,
!=(other)
!=,
!~(other)
!~,
==(other)
==,
===(other : JSON::Any)===(other : YAML::Any)
===(other) ===, =~(other) =~, as(type : Class) as, as?(type : Class) as?, class class, dup dup, hash(hasher)
hash hash, in?(*values : Object) : Bool
in?(collection) : Bool in?, inspect : String
inspect(io : IO) : Nil inspect, is_a?(type : Class) : Bool is_a?, itself itself, nil? : Bool nil?, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, responds_to?(name : Symbol) : Bool responds_to?, tap(&) tap, to_json(io : IO)
to_json to_json, to_pretty_json(io : IO, indent : String = " ")
to_pretty_json(indent : String = " ") to_pretty_json, to_s : String
to_s(io : IO) : Nil to_s, to_yaml(io : IO)
to_yaml to_yaml, try(&) try, unsafe_as(type : T.class) forall T unsafe_as
Class methods inherited from class Object
from_json(string_or_io, root : String)from_json(string_or_io) from_json, from_yaml(string_or_io : String | IO) from_yaml
Constructor Detail
Creates a BigInt
with the value denoted by str in the given base.
Raises ArgumentError
if the string doesn't denote a valid integer.
require "big"
BigInt.new("123456789123456789123456789123456789") # => 123456789123456789123456789123456789
BigInt.new("123_456_789_123_456_789_123_456_789") # => 123456789123456789123456789
BigInt.new("1234567890ABCDEF", base: 16) # => 1311768467294899695
Returns num. Useful for generic code that does T.new(...)
with T
being a Number
.
Instance Method Detail
Returns self
modulo other.
This uses floored division.
See Int#/
for more details.
Returns the value of raising self
to the power of exponent.
Raises ArgumentError
if exponent is negative: if this is needed,
either use a float base or a float exponent.
Raises OverflowError
in case of overflow.
2 ** 3 # => 8
2 ** 0 # => 1
2 ** -1 # ArgumentError
Returns the result of shifting this number's bits count positions to the left.
- If count is greater than the number of bits of this integer, returns 0
- If count is negative, a right shift is performed
8000 << 1 # => 16000
8000 << 2 # => 32000
8000 << 32 # => 0
8000 << -1 # => 4000
The comparison operator. Returns 0
if the two objects are equal,
a negative number if this object is considered less than other,
a positive number if this object is considered greater than other,
or nil
if the two objects are not comparable.
Subclasses define this method to provide class-specific ordering.
The comparison operator is usually used to sort values:
# Sort in a descending way:
[3, 1, 2].sort { |x, y| y <=> x } # => [3, 2, 1]
# Sort in an ascending way:
[3, 1, 2].sort { |x, y| x <=> y } # => [1, 2, 3]
Returns the result of shifting this number's bits count positions to the right. Also known as arithmetic right shift.
- If count is greater than the number of bits of this integer, returns 0
- If count is negative, a left shift is performed
8000 >> 1 # => 4000
8000 >> 2 # => 2000
8000 >> 32 # => 0
8000 >> -1 # => 16000
-8000 >> 1 # => -4000
Returns the absolute value of this number.
123.abs # => 123
-123.abs # => 123
Returns the number of bits of this int value.
“The number of bits” means that the bit position of the highest bit which is different to the sign bit. (The bit position of the bit 2**n is n+1.) If there is no such bit (zero or minus one), zero is returned.
I.e. This method returns ceil(log2(self < 0 ? -self : self + 1))
.
0.bit_length # => 0
1.bit_length # => 1
2.bit_length # => 2
3.bit_length # => 2
4.bit_length # => 3
5.bit_length # => 3
# The above is the same as
0b0.bit_length # => 0
0b1.bit_length # => 1
0b10.bit_length # => 2
0b11.bit_length # => 2
0b100.bit_length # => 3
0b101.bit_length # => 3
Returns the greatest common divisor of self
and other.
Returns the least common multiple of self
and other.
Counts 1
-bits in the binary representation of this integer.
5.popcount # => 2
-15.popcount # => 29
Returns self
remainder other.
This uses truncated division.
See Int#tdiv
for more details.
Divides self
by other using truncated division.
In truncated division, given two integers x and y:
q = x.tdiv(y)
is rounded toward zeror = x.remainder(y)
has the sign of the first argumentx == q*y + r
For example:
x y x / y x % y
5 3 1 2
-5 3 -1 -2
5 -3 -1 2
-5 -3 1 -2
Raises if other is 0
, or if other is -1
and
self
is signed and is the minimum value for that
integer type.
Converts self
to BigDecimal
.
require "big"
12123415151254124124.to_big_d
Returns a BigInt
representing this integer.
require "big"
123.to_big_i
Returns a BigRational
representing this integer.
require "big"
123.to_big_r
Returns a string representation of self.
require "big"
BigInt.new("123456789101101987654321").to_s # => 123456789101101987654321
Returns a string containing the representation of big radix base (2 through 36).
require "big"
BigInt.new("123456789101101987654321").to_s(8) # => "32111154373025463465765261"
BigInt.new("123456789101101987654321").to_s(16) # => "1a249b1f61599cd7eab1"
BigInt.new("123456789101101987654321").to_s(36) # => "k3qmt029k48nmpd"
Returns a string representation of self.
require "big"
BigInt.new("123456789101101987654321").to_s # => 123456789101101987654321