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
BigIntwith the value denoted by str in the given base. -
.new(num : Int::Signed)
Creates a
BigIntfrom the given num. -
.new(num : Int::Unsigned)
Creates a
BigIntfrom the given num. -
.new(num : Float::Primitive)
Creates a
BigIntfrom the given num. -
.new(num : BigFloat)
Creates a
BigIntfrom the given num. -
.new(num : BigDecimal)
Creates a
BigIntfrom the given num. -
.new(num : BigRational)
Creates a
BigIntfrom the given num. -
.new(num : BigInt)
Returns num.
-
.new
Creates a
BigIntwith the value zero.
Instance Method Summary
-
#%(other : Int) : BigInt
Returns
selfmodulo other. - #&(other : Int) : BigInt
- #&*(other) : BigInt
- #&+(other) : BigInt
- #&-(other) : BigInt
- #*(other : BigInt) : BigInt
- #*(other : LibGMP::IntPrimitiveSigned) : BigInt
- #*(other : LibGMP::IntPrimitiveUnsigned) : BigInt
- #*(other : Int) : BigInt
-
#**(other : Int) : BigInt
Returns the value of raising
selfto the power of exponent. - #+(other : BigInt) : BigInt
- #+(other : Int) : BigInt
- #-(other : BigInt) : BigInt
- #-(other : Int) : BigInt
- #- : BigInt
- #/(other : BigInt) : BigFloat
- #/(other : BigDecimal) : BigDecimal
- #/(other : BigRational) : BigRational
- #/(other : Int8) : BigFloat
- #/(other : UInt8) : BigFloat
- #/(other : Int16) : BigFloat
- #/(other : UInt16) : BigFloat
- #/(other : Int32) : BigFloat
- #/(other : UInt32) : BigFloat
- #/(other : Int64) : BigFloat
- #/(other : UInt64) : BigFloat
- #/(other : Int128) : BigFloat
- #/(other : UInt128) : BigFloat
- #/(other : Float32) : 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 : Int::Signed)
- #<=>(other : Int::Unsigned)
-
#<=>(other : Float)
The comparison operator.
-
#>>(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 : BigInt) : Tuple(BigInt, BigInt)
- #divmod(number : LibGMP::ULong)
- #divmod(number : Int::Signed) : Tuple(BigInt, BigInt)
- #divmod(number : Int::Unsigned)
- #factorial : BigInt
-
#gcd(other : BigInt) : BigInt
Returns the greatest common divisor of
selfand other. -
#gcd(other : Int) : Int
Returns the greatest common divisor of
selfand other. -
#hash(hasher)
TODO check hash equality for numbers >= 2**63
-
#lcm(other : BigInt) : BigInt
Returns the least common multiple of
selfand other. -
#lcm(other : Int) : BigInt
Returns the least common multiple of
selfand other. -
#popcount : Int
Counts
1-bits in the binary representation of this integer. -
#remainder(other : Int) : BigInt
Returns
selfremainder other. -
#tdiv(other : Int) : BigInt
Divides
selfby other using truncated division. -
#to_big_d : BigDecimal
Converts
selftoBigDecimal. - #to_big_f : BigFloat
-
#to_big_i : BigInt
Returns a
BigIntrepresenting this integer. -
#to_big_r : BigRational
Returns a
BigRationalrepresenting this integer. - #to_f : Float64
- #to_f!
- #to_f32 : Float32
- #to_f32!
- #to_f64 : Float64
- #to_f64!
- #to_i : Int32
- #to_i!
- #to_i16 : Int16
- #to_i16! : Int16
- #to_i32 : Int32
- #to_i32! : Int32
- #to_i64 : Int64
- #to_i64! : Int64
- #to_i8 : Int8
- #to_i8! : Int8
-
#to_s(io : IO) : Nil
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 : String
Returns a string representation of self.
- #to_u : UInt32
- #to_u!
- #to_u16 : UInt16
- #to_u16! : UInt16
- #to_u32 : UInt32
- #to_u32! : UInt32
- #to_u64 : UInt64
- #to_u64! : UInt64
- #to_u8 : UInt8
- #to_u8! : UInt8
- #to_unsafe
-
#trailing_zeros_count : Int
Returns the number of trailing
0-bits. - #unsafe_floored_div(other : BigInt) : BigInt
- #unsafe_floored_div(other : Int) : BigInt
- #unsafe_floored_divmod(number : BigInt) : Tuple(BigInt, BigInt)
- #unsafe_floored_divmod(number : LibGMP::ULong) : Tuple(BigInt, BigInt)
- #unsafe_floored_mod(other : BigInt) : BigInt
- #unsafe_floored_mod(other : Int) : BigInt
- #unsafe_truncated_div(other : BigInt) : BigInt
- #unsafe_truncated_div(other : Int) : BigInt
- #unsafe_truncated_divmod(number : BigInt)
- #unsafe_truncated_divmod(number : LibGMP::ULong)
- #unsafe_truncated_mod(other : BigInt) : BigInt
- #unsafe_truncated_mod(other : LibGMP::IntPrimitive) : BigInt
- #unsafe_truncated_mod(other : Int) : BigInt
- #|(other : Int) : BigInt
- #~ : BigInt
Instance methods inherited from module Comparable(Float)
<(other : T) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigInt)
<(other : T) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(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) : Bool
<,
<=(other : T | T | T | T | T)
<=,
<=>(other : T | T | T | T | T)
<=>,
==(other : T | T | T | T | T)
==,
>(other : T | T | T | T | T) : Bool
>,
>=(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) : Bool
<,
<=(other : T | T | T | T | T)
<=,
<=>(other : T | T | T | T | T)
<=>,
==(other : T | T | T | T | T)
==,
>(other : T | T | T | T | T) : Bool
>,
>=(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 : BigInt) : BigInt
*(other : BigRational) : BigRational
*(other : BigDecimal) : BigDecimal *, **(exponent : Int) : self
**(exponent : Float) : Float64 **, +(other : BigInt) : BigInt
+(other : BigRational) : BigRational
+(other : BigDecimal) : BigDecimal +, -(other : BigInt) : BigInt
-(other : BigRational) : BigRational
-(other : BigDecimal) : BigDecimal -, /(other : BigRational) /, //(other : Int::Primitive) //, <<(count : Int) <<, <=>(other : BigInt)
<=>(other : Int) : Int32
<=>(other : BigRational)
<=>(other : BigDecimal) <=>, ===(char : Char) ===, >>(count : Int) >>, abs : self abs, bit(bit) bit, bit_length : Int32 bit_length, bits(range : Range) bits, bits_set?(mask) : Bool bits_set?, ceil : self ceil, chr : Char chr, day : Time::Span day, days : Time::Span days, digits(base = 10) : Array(Int32) digits, divisible_by?(num) : Bool divisible_by?, downto(to, &block : self -> ) : Nil
downto(to) downto, even? : Bool even?, fdiv(other) : Float64 fdiv, floor : self floor, gcd(other : self) : self
gcd(other : BigInt) : Int gcd, hash(hasher) hash, hour : Time::Span hour, hours : Time::Span hours, humanize_bytes(io : IO, precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : Nil
humanize_bytes(precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : String 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? : Bool odd?, popcount popcount, pred : self 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 : self succ, tdiv(other : Int) tdiv, times(&block : self -> ) : Nil
times times, to(to, &block : self -> ) : Nil
to(to) to, to_big_d : BigDecimal to_big_d, to_big_i : BigInt to_big_i, to_big_r : BigRational to_big_r, to_io(io : IO, format : IO::ByteFormat) : Nil to_io, to_json(json : JSON::Builder) to_json, to_json_object_key : String 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 : self 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) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigRational)
<(other : T) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Comparable(BigInt)
<(other : T) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from struct Number
*(other : BigFloat) : BigFloat*(other : Complex) : Complex *, +(other : BigFloat)
+(other : Complex) : Complex
+ +, -(other : BigFloat)
-(other : Complex) : Complex -, /(other : BigFloat) : BigFloat
/(other : Complex) : Complex /, //(other) //, <=>(other : BigFloat)
<=>(other) : Int32? <=>, ==(other : Complex) ==, abs : self abs, abs2 abs2, cis : Complex cis, divmod(number) divmod, format(io : IO, separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : Nil
format(separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : String 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) : String humanize, i : Complex i, negative? : Bool negative?, positive? : Bool positive?, round(mode : RoundingMode = :ties_even) : self
round(digits : Number, base = 10, *, mode : RoundingMode = :ties_even) round, sign : Int32 sign, significant(digits, base = 10) significant, step(*, to limit = nil, exclusive : Bool = false, &) : Nil
step(*, to limit = nil, exclusive : Bool = false) step, to_big_f : BigFloat to_big_f, to_c : Complex to_c, to_yaml(yaml : YAML::Nodes::Builder) : Nil 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) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(other : T)
>=,
clamp(min, max)clamp(range : Range) clamp
Instance methods inherited from module Steppable
step(*, to limit = nil, by step, exclusive : Bool = false, &) : Nilstep(*, to limit = nil, by step, exclusive : Bool = false) step
Instance methods inherited from module Comparable(Number)
<(other : T) : Bool
<,
<=(other : T)
<=,
<=>(other : T)
<=>,
==(other : T)
==,
>(other : T) : Bool
>,
>=(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?(collection : Object) : Bool
in?(*values : Object) : Bool in?, inspect(io : IO) : Nil
inspect : String 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) : Nil
to_json : String to_json, to_pretty_json(indent : String = " ") : String
to_pretty_json(io : IO, indent : String = " ") : Nil to_pretty_json, to_s(io : IO) : Nil
to_s : String to_s, to_yaml(io : IO) : Nil
to_yaml : String 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) # => 1311768467294899695Returns num. Useful for generic code that does T.new(...) with T
being a Number.
Instance Method Detail
Description copied from struct Int
Returns self modulo other.
This uses floored division.
See Int#/ for more details.
Description copied from struct Int
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
Description copied from struct Int
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
Description copied from module Comparable(Float)
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]
Description copied from struct Int
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
Description copied from struct Number
Returns the absolute value of this number.
123.abs # => 123
-123.abs # => 123
Description copied from struct Int
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 # => 3Returns the greatest common divisor of self and other.
Returns the least common multiple of self and other.
Description copied from struct Int
Counts 1-bits in the binary representation of this integer.
5.popcount # => 2
-15.popcount # => 29
Description copied from struct Int
Returns self remainder other.
This uses truncated division.
See Int#tdiv for more details.
Description copied from struct Int
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 -2Raises if other is 0, or if other is -1 and
self is signed and is the minimum value for that
integer type.
def to_big_d : BigDecimal
#
Description copied from struct Int
Converts self to BigDecimal.
require "big"
12123415151254124124.to_big_d
Description copied from struct Int
Returns a BigInt representing this integer.
require "big"
123.to_big_i
def to_big_r : BigRational
#
Description copied from struct Int
Returns a BigRational representing this integer.
require "big"
123.to_big_rReturns a string representation of self.
require "big"
BigInt.new("123456789101101987654321").to_s # => 123456789101101987654321Returns 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
Description copied from struct Int
Returns the number of trailing 0-bits.