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int.cr
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int.cr
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# Int is the base type of all integer types.
#
# There are four signed integer types: `Int8`, `Int16`, `Int32` and `Int64`,
# being able to represent numbers of 8, 16, 32 and 64 bits respectively.
# There are four unsigned integer types: `UInt8`, `UInt16`, `UInt32` and `UInt64`.
#
# An integer literal is an optional `+` or `-` sign, followed by
# a sequence of digits and underscores, optionally followed by a suffix.
# If no suffix is present, the literal's type is the lowest between `Int32`, `Int64` and `UInt64`
# in which the number fits:
#
# ```
# 1 # Int32
#
# 1_i8 # Int8
# 1_i16 # Int16
# 1_i32 # Int32
# 1_i64 # Int64
#
# 1_u8 # UInt8
# 1_u16 # UInt16
# 1_u32 # UInt32
# 1_u64 # UInt64
#
# +10 # Int32
# -20 # Int32
#
# 2147483648 # Int64
# 9223372036854775808 # UInt64
# ```
#
# The underscore `_` before the suffix is optional.
#
# Underscores can be used to make some numbers more readable:
#
# ```
# 1_000_000 # better than 1000000
# ```
#
# Binary numbers start with `0b`:
#
# ```
# 0b1101 # == 13
# ```
#
# Octal numbers start with `0o`:
#
# ```
# 0o123 # == 83
# ```
#
# Hexadecimal numbers start with `0x`:
#
# ```
# 0xFE012D # == 16646445
# 0xfe012d # == 16646445
# ```
struct Int
alias Signed = Int8 | Int16 | Int32 | Int64
alias Unsigned = UInt8 | UInt16 | UInt32 | UInt64
alias Primitive = Signed | Unsigned
# Returns a `Char` that has the unicode codepoint of `self`.
#
# Raises `ArgumentError` if this integer's value doesn't fit a char's range (`0..0x10ffff`).
#
# ```
# 97.chr # => 'a'
# ```
def chr
unless 0 <= self <= Char::MAX_CODEPOINT
raise ArgumentError.new("#{self} out of char range")
end
unsafe_chr
end
def ~
self ^ -1
end
# Divides `self` by *other* using floored division.
#
# In floored division, given two integers x and y:
# * q = x / y is rounded toward negative infinity
# * r = x % y has the sign of the second argument
# * x == q*y + r
#
# For example:
#
# ```text
# x y x / y x % y
# 5 3 1 2
# -5 3 -2 1
# 5 -3 -2 -1
# -5 -3 1 -2
# ```
#
# Raises if *other* is zero, or if *other* is -1 and
# `self` is signed and is the minimum value for that
# integer type.
def /(other : Int)
check_div_argument other
div = unsafe_div other
mod = unsafe_mod other
div -= 1 if other > 0 ? mod < 0 : mod > 0
div
end
# Divides `self` by *other* using truncated division.
#
# In truncated division, given two integers x and y:
# * `q = x.tdiv(y)` is rounded toward zero
# * `r = x.remainder(y)` has the sign of the first argument
# * `x == q*y + r`
#
# For example:
#
# ```text
# 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.
def tdiv(other : Int)
check_div_argument other
unsafe_div other
end
private def check_div_argument(other)
if other == 0
raise DivisionByZero.new
end
{% begin %}
if self < 0 && self == {{@type}}::MIN && other == -1
raise ArgumentError.new "Overflow: {{@type}}::MIN / -1"
end
{% end %}
end
def fdiv(other)
to_f / other
end
# Returns `self` modulo *other*.
#
# This uses floored division.
#
# See `Int#/` for more details.
def %(other : Int)
if other == 0
raise DivisionByZero.new
elsif (self ^ other) >= 0
self.unsafe_mod(other)
else
me = self.unsafe_mod(other)
me == 0 ? me : me + other
end
end
# Returns `self` remainder *other*.
#
# This uses truncated division.
#
# See `Int#div` for more details.
def remainder(other : Int)
if other == 0
raise DivisionByZero.new
else
unsafe_mod other
end
end
# 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
# ```
def >>(count : Int)
if count < 0
self << count.abs
elsif count < sizeof(self) * 8
self.unsafe_shr(count)
else
self.class.zero
end
end
# 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
# ```
def <<(count : Int)
if count < 0
self >> count.abs
elsif count < sizeof(self) * 8
self.unsafe_shl(count)
else
self.class.zero
end
end
def abs
self >= 0 ? self : -self
end
def ceil
self
end
def floor
self
end
def round
self
end
def trunc
self
end
# 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.
#
# ```
# 2 ** 3 # => 8
# 2 ** 0 # => 1
# 2 ** -1 # ArgumentError
# ```
def **(exponent : Int) : self
if exponent < 0
raise ArgumentError.new "Cannot raise an integer to a negative integer power, use floats for that"
end
result = self.class.new(1)
k = self
while exponent > 0
result *= k if exponent & 0b1 != 0
k *= k
exponent = exponent.unsafe_shr(1)
end
result
end
# Returns the value of raising `self` to the power of *exponent*.
#
# ```
# 2 ** 3.0 # => 8.0
# 2 ** 0.0 # => 1.0
# 2 ** -1.0 # => 0.5
# ```
def **(exponent : Float) : Float64
to_f ** exponent
end
def ===(char : Char)
self === char.ord
end
# Returns this number's *bit*th bit, starting with the least-significant.
#
# ```
# 11.bit(0) # => 1
# 11.bit(1) # => 1
# 11.bit(2) # => 0
# 11.bit(3) # => 1
# 11.bit(4) # => 0
# ```
def bit(bit)
self >> bit & 1
end
def gcd(other : Int)
self == 0 ? other.abs : (other % self).gcd(self)
end
def lcm(other : Int)
(self * other).abs / gcd(other)
end
def divisible_by?(num)
self % num == 0
end
def even?
divisible_by? 2
end
def odd?
!even?
end
def hash
self
end
def succ
self + 1
end
def pred
self - 1
end
def times(&block : self ->) : Nil
i = self ^ self
while i < self
yield i
i += 1
end
end
def times
TimesIterator(typeof(self)).new(self)
end
def upto(to, &block : self ->) : Nil
x = self
while x <= to
yield x
x += 1
end
end
def upto(to)
UptoIterator(typeof(self), typeof(to)).new(self, to)
end
def downto(to, &block : self ->) : Nil
x = self
while x >= to
yield x
x -= 1
end
end
def downto(to)
DowntoIterator(typeof(self), typeof(to)).new(self, to)
end
def to(to, &block : self ->) : Nil
if self < to
upto(to) { |i| yield i }
elsif self > to
downto(to) { |i| yield i }
else
yield self
end
end
def to(to)
self <= to ? upto(to) : downto(to)
end
def modulo(other)
self % other
end
private DIGITS_DOWNCASE = "0123456789abcdefghijklmnopqrstuvwxyz"
private DIGITS_UPCASE = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
private DIGITS_BASE62 = "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
def to_s
to_s(10)
end
def to_s(io : IO)
to_s(10, io)
end
def to_s(base : Int, upcase : Bool = false)
raise ArgumentError.new("Invalid base #{base}") unless 2 <= base <= 36 || base == 62
raise ArgumentError.new("upcase must be false for base 62") if upcase && base == 62
case self
when 0
return "0"
when 1
return "1"
end
internal_to_s(base, upcase) do |ptr, count|
String.new(ptr, count, count)
end
end
def to_s(base : Int, io : IO, upcase : Bool = false)
raise ArgumentError.new("Invalid base #{base}") unless 2 <= base <= 36 || base == 62
raise ArgumentError.new("upcase must be false for base 62") if upcase && base == 62
case self
when 0
io << '0'
return
when 1
io << '1'
return
end
internal_to_s(base, upcase) do |ptr, count|
io.write_utf8 Slice.new(ptr, count)
end
end
private def internal_to_s(base, upcase = false)
chars = uninitialized UInt8[65]
ptr_end = chars.to_unsafe + 64
ptr = ptr_end
num = self
neg = num < 0
digits = (base == 62 ? DIGITS_BASE62 : (upcase ? DIGITS_UPCASE : DIGITS_DOWNCASE)).to_unsafe
while num != 0
ptr -= 1
ptr.value = digits[num.remainder(base).abs]
num = num.tdiv(base)
end
if neg
ptr -= 1
ptr.value = '-'.ord.to_u8
end
count = (ptr_end - ptr).to_i32
yield ptr, count
end
# Writes this integer to the given *io* in the given *format*.
#
# See also: `IO#write_bytes`.
def to_io(io : IO, format : IO::ByteFormat)
format.encode(self, io)
end
# Reads an integer from the given *io* in the given *format*.
#
# See also: `IO#read_bytes`.
def self.from_io(io : IO, format : IO::ByteFormat)
format.decode(self, io)
end
# Counts `1`-bits in the binary representation of this integer.
#
# ```
# 5.popcount # => 2
# -15.popcount # => 29
# ```
abstract def popcount
private class TimesIterator(T)
include Iterator(T)
@n : T
@index : Int32
def initialize(@n : T, @index = 0)
end
def next
if @index < @n
value = @index
@index += 1
value
else
stop
end
end
def rewind
@index = 0
self
end
end
private class UptoIterator(T, N)
include Iterator(T)
@from : T
@to : N
@current : T
def initialize(@from : T, @to : N)
@current = @from
end
def next
if @current > @to
stop
else
value = @current
@current += 1
value
end
end
def rewind
@current = @from
self
end
end
private class DowntoIterator(T, N)
include Iterator(T)
@from : T
@to : N
@current : T
def initialize(@from : T, @to : N)
@current = @from
end
def next
if @current < @to
stop
else
value = @current
@current -= 1
value
end
end
def rewind
@current = @from
self
end
end
end
struct Int8
MIN = -128_i8
MAX = 127_i8
# Returns an `Int8` by invoking `to_i8` on *value*.
def self.new(value)
value.to_i8
end
def -
0_i8 - self
end
def popcount
Intrinsics.popcount8(self)
end
def clone
self
end
end
struct Int16
MIN = -32768_i16
MAX = 32767_i16
# Returns an `Int16` by invoking `to_i16` on *value*.
def self.new(value)
value.to_i16
end
def -
0_i16 - self
end
def popcount
Intrinsics.popcount16(self)
end
def clone
self
end
end
struct Int32
MIN = -2147483648_i32
MAX = 2147483647_i32
# Returns an `Int32` by invoking `to_i32` on *value*.
def self.new(value)
value.to_i32
end
def -
0 - self
end
def popcount
Intrinsics.popcount32(self)
end
def clone
self
end
end
struct Int64
MIN = -9223372036854775808_i64
MAX = 9223372036854775807_i64
# Returns an `Int64` by invoking `to_i64` on *value*.
def self.new(value)
value.to_i64
end
def -
0_i64 - self
end
def popcount
Intrinsics.popcount64(self)
end
def clone
self
end
end
struct UInt8
MIN = 0_u8
MAX = 255_u8
# Returns an `UInt8` by invoking `to_u8` on *value*.
def self.new(value)
value.to_u8
end
def abs
self
end
def popcount
Intrinsics.popcount8(self)
end
def clone
self
end
end
struct UInt16
MIN = 0_u16
MAX = 65535_u16
# Returns an `UInt16` by invoking `to_u16` on *value*.
def self.new(value)
value.to_u16
end
def abs
self
end
def popcount
Intrinsics.popcount16(self)
end
def clone
self
end
end
struct UInt32
MIN = 0_u32
MAX = 4294967295_u32
# Returns an `UInt32` by invoking `to_u32` on *value*.
def self.new(value)
value.to_u32
end
def abs
self
end
def popcount
Intrinsics.popcount32(self)
end
def clone
self
end
end
struct UInt64
MIN = 0_u64
MAX = 18446744073709551615_u64
# Returns an `UInt64` by invoking `to_u64` on *value*.
def self.new(value)
value.to_u64
end
def abs
self
end
def popcount
Intrinsics.popcount64(self)
end
def clone
self
end
end