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big_decimal.cr
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big_decimal.cr
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require "big"
# A `BigDecimal` represents arbitrary precision decimals.
#
# It is internally represented by a pair of `BigInt` and `UInt64`: value and scale.
# Value contains the actual value, and scale tells the decimal point place.
# e.g. value=1234, scale=2 => 12.34
#
# The general idea and some of the arithmetic algorithms were adapted from
# the MIT/APACHE -licensed https://github.com/akubera/bigdecimal-rs
class InvalidBigDecimalException < Exception
def initialize(big_decimal_str : String, reason : String)
super("Invalid BigDecimal: #{big_decimal_str} (#{reason})")
end
end
struct BigDecimal < Number
ZERO = BigInt.new(0)
TEN = BigInt.new(10)
DEFAULT_MAX_DIV_ITERATIONS = 100_u64
include Comparable(Int)
include Comparable(Float)
include Comparable(BigRational)
include Comparable(BigDecimal)
getter value : BigInt
getter scale : UInt64
# Creates a new `BigDecimal` from `Float`.
#
# NOTE: Floats are fundamentally less precise than BigDecimals,
# which makes initialization from them risky.
def self.new(num : Float)
new(num.to_s)
end
# Creates a new `BigDecimal` from `BigRational`.
def self.new(num : BigRational)
num.numerator.to_big_d / num.denominator.to_big_d
end
# Returns *num*. Useful for generic code that does `T.new(...)` with `T`
# being a `Number`.
def self.new(num : BigDecimal)
num
end
# Creates a new `BigDecimal` from `BigInt` *value* and `UInt64` *scale*,
# which matches the internal representation.
def initialize(@value : BigInt, @scale : UInt64)
end
# Creates a new `BigDecimal` from `Int`.
def initialize(num : Int = 0, scale : Int = 0)
initialize(num.to_big_i, scale.to_u64)
end
# Creates a new `BigDecimal` from a `String`.
#
# Allows only valid number strings with an optional negative sign.
def initialize(str : String)
# Strip leading '+' char to smooth out cases with strings like "+123"
str = str.lchop('+')
# Strip '_' to make it compatible with int literals like "1_000_000"
str = str.delete('_')
raise InvalidBigDecimalException.new(str, "Zero size") if str.bytesize == 0
# Check str's validity and find index of '.'
decimal_index = nil
# Check str's validity and find index of 'e'
exponent_index = nil
str.each_char_with_index do |char, index|
case char
when '-'
unless index == 0 || exponent_index == index - 1
raise InvalidBigDecimalException.new(str, "Unexpected '-' character")
end
when '+'
unless exponent_index == index - 1
raise InvalidBigDecimalException.new(str, "Unexpected '+' character")
end
when '.'
if decimal_index
raise InvalidBigDecimalException.new(str, "Unexpected '.' character")
end
decimal_index = index
when 'e', 'E'
if exponent_index
raise InvalidBigDecimalException.new(str, "Unexpected #{char.inspect} character")
end
exponent_index = index
when '0'..'9'
# Pass
else
raise InvalidBigDecimalException.new(str, "Unexpected #{char.inspect} character")
end
end
decimal_end_index = (exponent_index || str.bytesize) - 1
if decimal_index
decimal_count = (decimal_end_index - decimal_index).to_u64
value_str = String.build do |builder|
# We know this is ASCII, so we can slice by index
builder.write(str.to_slice[0, decimal_index])
builder.write(str.to_slice[decimal_index + 1, decimal_count])
end
@value = value_str.to_big_i
else
decimal_count = 0_u64
@value = str[0..decimal_end_index].to_big_i
end
if exponent_index
exponent_postfix = str[exponent_index + 1]
case exponent_postfix
when '+', '-'
exponent_positive = exponent_postfix == '+'
exponent = str[(exponent_index + 2)..-1].to_u64
else
exponent_positive = true
exponent = str[(exponent_index + 1)..-1].to_u64
end
@scale = exponent
if exponent_positive
if @scale < decimal_count
@scale = decimal_count - @scale
else
@scale -= decimal_count
@value *= 10.to_big_i ** @scale
@scale = 0_u64
end
else
@scale += decimal_count
end
else
@scale = decimal_count
end
end
def - : BigDecimal
BigDecimal.new(-@value, @scale)
end
def +(other : BigDecimal) : BigDecimal
if @scale > other.scale
scaled = other.scale_to(self)
BigDecimal.new(@value + scaled.value, @scale)
elsif @scale < other.scale
scaled = scale_to(other)
BigDecimal.new(scaled.value + other.value, other.scale)
else
BigDecimal.new(@value + other.value, @scale)
end
end
def +(other : Int)
self + BigDecimal.new(other)
end
def -(other : BigDecimal) : BigDecimal
if @scale > other.scale
scaled = other.scale_to(self)
BigDecimal.new(@value - scaled.value, @scale)
elsif @scale < other.scale
scaled = scale_to(other)
BigDecimal.new(scaled.value - other.value, other.scale)
else
BigDecimal.new(@value - other.value, @scale)
end
end
def -(other : Int)
self - BigDecimal.new(other)
end
def *(other : BigDecimal) : BigDecimal
BigDecimal.new(@value * other.value, @scale + other.scale)
end
def *(other : Int)
self * BigDecimal.new(other)
end
def /(other : BigDecimal) : BigDecimal
div other
end
def /(other : Int)
self / BigDecimal.new(other)
end
def //(other)
(self / other).floor
end
# Divides `self` with another `BigDecimal`, with a optionally configurable *max_div_iterations*, which
# defines a maximum number of iterations in case the division is not exact.
#
# ```
# BigDecimal.new(1).div(BigDecimal.new(2)) # => BigDecimal(@value=5, @scale=2)
# BigDecimal.new(1).div(BigDecimal.new(3), 5) # => BigDecimal(@value=33333, @scale=5)
# ```
def div(other : BigDecimal, max_div_iterations = DEFAULT_MAX_DIV_ITERATIONS) : BigDecimal
check_division_by_zero other
other.factor_powers_of_ten
scale = @scale - other.scale
numerator, denominator = @value, other.@value
quotient, remainder = numerator.divmod(denominator)
if remainder == ZERO
return BigDecimal.new(normalize_quotient(other, quotient), scale)
end
remainder = remainder * TEN
i = 0
while remainder != ZERO && i < max_div_iterations
inner_quotient, inner_remainder = remainder.divmod(denominator)
quotient = quotient * TEN + inner_quotient
remainder = inner_remainder * TEN
i += 1
end
BigDecimal.new(normalize_quotient(other, quotient), scale + i)
end
def <=>(other : BigDecimal) : Int32
if @scale > other.scale
@value <=> other.scale_to(self).value
elsif @scale < other.scale
scale_to(other).value <=> other.value
else
@value <=> other.value
end
end
def <=>(other : Int | Float | BigRational)
self <=> BigDecimal.new(other)
end
def ==(other : BigDecimal) : Bool
case @scale
when .>(other.scale)
scaled = other.value * power_ten_to(@scale - other.scale)
@value == scaled
when .<(other.scale)
scaled = @value * power_ten_to(other.scale - @scale)
scaled == other.value
else
@value == other.value
end
end
# Scales a `BigDecimal` to another `BigDecimal`, so they can be
# computed easier.
def scale_to(new_scale : BigDecimal) : BigDecimal
in_scale(new_scale.scale)
end
private def in_scale(new_scale : UInt64) : BigDecimal
if @value == 0
BigDecimal.new(0.to_big_i, new_scale)
elsif @scale > new_scale
scale_diff = @scale - new_scale.to_big_i
BigDecimal.new(@value // power_ten_to(scale_diff), new_scale)
elsif @scale < new_scale
scale_diff = new_scale - @scale.to_big_i
BigDecimal.new(@value * power_ten_to(scale_diff), new_scale)
else
self
end
end
# Raises the decimal to the *other*th power
#
# ```
# require "big"
#
# BigDecimal.new(1234, 2) ** 2 # => 152.2756
# ```
def **(other : Int) : BigDecimal
if other < 0
raise ArgumentError.new("Negative exponent isn't supported")
end
BigDecimal.new(@value ** other, @scale * other)
end
def ceil : BigDecimal
mask = power_ten_to(@scale)
diff = (mask - @value % mask) % mask
(self + BigDecimal.new(diff, @scale))
end
def floor : BigDecimal
in_scale(0)
end
def trunc : BigDecimal
self < 0 ? ceil : floor
end
def to_s(io : IO) : Nil
factor_powers_of_ten
s = @value.to_s
if @scale == 0
io << s
return
end
if @scale >= s.size && @value >= 0
io << "0."
(@scale - s.size).times do
io << '0'
end
io << s
elsif @scale >= s.size && @value < 0
io << "-0.0"
(@scale - s.size).times do
io << '0'
end
io << s[1..-1]
else
offset = s.size - @scale
io << s[0...offset] << '.' << s[offset..-1]
end
end
def to_big_d
self
end
# Converts to `BigInt`. Truncates anything on the right side of the decimal point.
def to_big_i
if @value >= 0
(@value // TEN ** @scale)
else
-(@value.abs // TEN ** @scale)
end
end
# Converts to `Int64`. Truncates anything on the right side of the decimal point.
# Raises `OverflowError` in case of overflow.
def to_i64
to_big_i.to_i64
end
# Converts to `Int32`. Truncates anything on the right side of the decimal point.
# Raises `OverflowError` in case of overflow.
def to_i32
to_big_i.to_i32
end
# Converts to `Int16`. Truncates anything on the right side of the decimal point.
# Raises `OverflowError` in case of overflow.
def to_i16
to_big_i.to_i16
end
# Converts to `Int8`. Truncates anything on the right side of the decimal point.
# Raises `OverflowError` in case of overflow.
def to_i8
to_big_i.to_i8
end
# Converts to `Int32`. Truncates anything on the right side of the decimal point.
# Raises `OverflowError` in case of overflow.
def to_i
to_i32
end
# Converts to `Int8`. Truncates anything on the right side of the decimal point.
# In case of overflow a wrapping is performed.
def to_i8!
to_big_i.to_i8!
end
# Converts to `Int16`. Truncates anything on the right side of the decimal point.
# In case of overflow a wrapping is performed.
def to_i16!
to_big_i.to_i16!
end
# Converts to `Int32`. Truncates anything on the right side of the decimal point.
# In case of overflow a wrapping is performed.
def to_i32!
to_big_i.to_i32!
end
# Converts to `Int64`. Truncates anything on the right side of the decimal point.
# In case of overflow a wrapping is performed.
def to_i64!
to_big_i.to_i64!
end
# Converts to `Int32`. Truncates anything on the right side of the decimal point.
# In case of overflow a wrapping is performed.
def to_i!
to_i32!
end
private def to_big_u
(@value.abs // TEN ** @scale)
end
# Converts to `UInt64`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# Raises `OverflowError` in case of overflow.
def to_u64
to_big_u.to_u64
end
# Converts to `UInt32`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# Raises `OverflowError` in case of overflow.
def to_u32
to_big_u.to_u32
end
# Converts to `UInt16`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# Raises `OverflowError` in case of overflow.
def to_u16
to_big_u.to_u16
end
# Converts to `UInt8`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# Raises `OverflowError` in case of overflow.
def to_u8
to_big_u.to_u8
end
# Converts to `UInt32`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# Raises `OverflowError` in case of overflow.
def to_u
to_u32
end
# Converts to `UInt8`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# In case of overflow a wrapping is performed.
def to_u8!
to_big_u.to_u8!
end
# Converts to `UInt16`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# In case of overflow a wrapping is performed.
def to_u16!
to_big_u.to_u16!
end
# Converts to `UInt32`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# In case of overflow a wrapping is performed.
def to_u32!
to_big_u.to_u32!
end
# Converts to `UInt64`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# In case of overflow a wrapping is performed.
def to_u64!
to_big_u.to_u64!
end
# Converts to `UInt32`. Truncates anything on the right side of the decimal point,
# converting negative to positive.
# In case of overflow a wrapping is performed.
def to_u!
to_u32!
end
# Converts to `Float64`.
# Raises `OverflowError` in case of overflow.
def to_f64
to_s.to_f64
end
# Converts to `Float32`.
# Raises `OverflowError` in case of overflow.
def to_f32
to_f64.to_f32
end
# Converts to `Float64`.
# Raises `OverflowError` in case of overflow.
def to_f
to_f64
end
# Converts to `Float32`.
# In case of overflow a wrapping is performed.
def to_f32!
to_f64.to_f32!
end
# Converts to `Float64`.
# In case of overflow a wrapping is performed.
def to_f64!
to_f64
end
# Converts to `Float64`.
# In case of overflow a wrapping is performed.
def to_f!
to_f64!
end
# Converts to `BigFloat`.
def to_big_f
BigFloat.new(to_s)
end
def clone
self
end
def hash(hasher)
hasher.string(to_s)
end
# Returns the *quotient* as absolutely negative if `self` and *other* have
# different signs, otherwise returns the *quotient*.
def normalize_quotient(other : BigDecimal, quotient : BigInt) : BigInt
if (@value < 0 && other.value > 0) || (other.value < 0 && @value > 0)
-quotient.abs
else
quotient
end
end
private def check_division_by_zero(bd : BigDecimal)
raise DivisionByZeroError.new if bd.value == 0
end
private def power_ten_to(x : Int) : Int
TEN ** x
end
# Factors out any extra powers of ten in the internal representation.
# For instance, value=100 scale=2 => value=1 scale=0
protected def factor_powers_of_ten
while @scale > 0
quotient, remainder = value.divmod(TEN)
break if remainder != 0
@value = quotient
@scale = @scale - 1
end
end
end
struct Int
include Comparable(BigDecimal)
# Converts `self` to `BigDecimal`.
# ```
# require "big"
# 12123415151254124124.to_big_d
# ```
def to_big_d
BigDecimal.new(self)
end
def <=>(other : BigDecimal)
to_big_d <=> other
end
def +(other : BigDecimal)
other + self
end
def -(other : BigDecimal)
to_big_d - other
end
def *(other : BigDecimal)
other * self
end
def /(other : BigDecimal)
to_big_d / other
end
def //(other : BigDecimal)
to_big_d // other
end
end
struct Float
include Comparable(BigDecimal)
def <=>(other : BigDecimal)
to_big_d <=> other
end
# Converts `self` to `BigDecimal`.
#
# NOTE: Floats are fundamentally less precise than BigDecimals,
# which makes conversion to them risky.
# ```
# require "big"
# 1212341515125412412412421.0.to_big_d
# ```
def to_big_d
BigDecimal.new(self)
end
end
struct BigRational
include Comparable(BigDecimal)
def <=>(other : BigDecimal)
to_big_d <=> other
end
# Converts `self` to `BigDecimal`.
def to_big_d
BigDecimal.new(self)
end
end
class String
# Converts `self` to `BigDecimal`.
# ```
# require "big"
# "1212341515125412412412421".to_big_d
# ```
def to_big_d
BigDecimal.new(self)
end
end