# struct BigDecimal

- BigDecimal
- Number
- Value
- Object

##
Overview

A `BigDecimal` can represent arbitrarily large 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. when value is `1234` and scale `2`, the result is `12.34`.

The general idea and some of the arithmetic algorithms were adapted from the MIT/APACHE-licensed bigdecimal-rs.

##
Included Modules

- Comparable(BigDecimal)
- Comparable(BigRational)
- Comparable(Float)
- Comparable(Int)

##
Defined in:

##
Constant Summary

DEFAULT_MAX_DIV_ITERATIONS = `100_u64`
TEN = `BigInt.new(10)`
ZERO = `BigInt.new(0)`

##
Constructors

- .new(value : BigInt, scale : UInt64)

  Creates a new `BigDecimal` from `BigInt` value and `UInt64` scale, which matches the internal representation.

- .new(num : Float)

  Creates a new `BigDecimal` from `Float`.

- .new(num : BigRational)

  Creates a new `BigDecimal` from `BigRational`.

- .new(num : BigDecimal)

  Returns num.

- .new(num : Int = 0, scale : Int = 0)

  Creates a new `BigDecimal` from `Int`.

- .new(str : String)

  Creates a new `BigDecimal` from a `String`.

##
Instance Method Summary

- #*(other : BigDecimal) : BigDecimal
- #*(other : Int)
- #**(other : Int) : BigDecimal

  Raises the decimal to the otherth power

- #+(other : BigDecimal) : BigDecimal
- #+(other : Int)
- #-(other : BigDecimal) : BigDecimal
- #-(other : Int)
- #- : BigDecimal
- #/(other : UInt16) : BigDecimal
- #/(other : Float32) : BigDecimal
- #/(other : UInt128) : BigDecimal
- #/(other : Int128) : BigDecimal
- #/(other : UInt64) : BigDecimal
- #/(other : Int64) : BigDecimal
- #/(other : UInt32) : BigDecimal
- #/(other : Int32) : BigDecimal
- #/(other : Int16) : BigDecimal
- #/(other : UInt8) : BigDecimal
- #/(other : Int8) : BigDecimal
- #/(other : BigRational) : BigRational
- #/(other : BigFloat) : BigDecimal
- #/(other : BigInt) : BigDecimal
- #/(other : BigDecimal) : BigDecimal
- #/(other : Float64) : BigDecimal
- #<=>(other : BigDecimal) : Int32

  The comparison operator.

- #<=>(other : Int | Float | BigRational)
- #==(other : BigDecimal) : Bool

  Compares this object to other based on the receiver’s `#<=>` method, returning `true` if it returns `0`.

- #ceil : BigDecimal
- #clone
- #div(other : BigDecimal, max_div_iterations = DEFAULT_MAX_DIV_ITERATIONS) : BigDecimal

  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.

- #floor : BigDecimal
- #hash(hasher)

  Appends this object's value to hasher, and returns the modified hasher.

- #normalize_quotient(other : BigDecimal, quotient : BigInt) : BigInt

  Returns the quotient as absolutely negative if `self` and other have different signs, otherwise returns the quotient.

- #scale : UInt64
- #scale_to(new_scale : BigDecimal) : BigDecimal

  Scales a `BigDecimal` to another `BigDecimal`, so they can be computed easier.

- #to_big_d
- #to_big_f

  Converts to `BigFloat`.

- #to_big_i

  Converts to `BigInt`.

- #to_big_r
- #to_f

  Converts to `Float64`.

- #to_f!

  Converts to `Float64`.

- #to_f32

  Converts to `Float32`.

- #to_f32!

  Converts to `Float32`.

- #to_f64

  Converts to `Float64`.

- #to_f64!

  Converts to `Float64`.

- #to_i

  Converts to `Int32`.

- #to_i!

  Converts to `Int32`.

- #to_i16

  Converts to `Int16`.

- #to_i16!

  Converts to `Int16`.

- #to_i32

  Converts to `Int32`.

- #to_i32!

  Converts to `Int32`.

- #to_i64

  Converts to `Int64`.

- #to_i64!

  Converts to `Int64`.

- #to_i8

  Converts to `Int8`.

- #to_i8!

  Converts to `Int8`.

- #to_s(io : IO) : Nil

  Appends a `String` representation of this object to the given `IO` object.

- #to_u

  Converts to `UInt32`.

- #to_u!

  Converts to `UInt32`.

- #to_u16

  Converts to `UInt16`.

- #to_u16!

  Converts to `UInt16`.

- #to_u32

  Converts to `UInt32`.

- #to_u32!

  Converts to `UInt32`.

- #to_u64

  Converts to `UInt64`.

- #to_u64!

  Converts to `UInt64`.

- #to_u8

  Converts to `UInt8`.

- #to_u8!

  Converts to `UInt8`.

- #trunc : BigDecimal
- #value : BigInt

### 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(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(Int)`

<(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(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, &) : 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, prefixes = SI_PREFIXES) : String
humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil humanize, i i, round(digits = 0, base = 10) round, sign sign, significant(digits, base = 10) significant, step(*, to = nil, by = 1)
step(*, to = nil, by = 1, &) 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`

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`

!=(other) !=, !~(other) !~, ==(other) ==, ===(other : JSON::Any)
===(other : YAML::Any)
===(other) ===, =~(other) =~, __crystal_pseudo_! : Bool __crystal_pseudo_!, __crystal_pseudo_as(type : Class) __crystal_pseudo_as, __crystal_pseudo_as?(type : Class) __crystal_pseudo_as?, __crystal_pseudo_is_a?(type : Class) : Bool __crystal_pseudo_is_a?, __crystal_pseudo_nil? : Bool __crystal_pseudo_nil?, __crystal_pseudo_responds_to?(name : Symbol) : Bool __crystal_pseudo_responds_to?, class class, dup dup, hash(hasher)
hash hash, inspect : String
inspect(io : IO) : Nil inspect, itself itself, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, tap(&) tap, to_json(io : IO)
to_json to_json, to_pretty_json(indent : String = " ")
to_pretty_json(io : IO, 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

def self.new(value : BigInt, scale : UInt64) #

Creates a new `BigDecimal` from `BigInt` value and `UInt64` scale, which matches the internal representation.

def self.new(num : Float) #

Creates a new `BigDecimal` from `Float`.

NOTE Floats are fundamentally less precise than BigDecimals, which makes initialization from them risky.

def self.new(num : BigRational) #

Creates a new `BigDecimal` from `BigRational`.

NOTE BigRational are fundamentally more precise than BigDecimals, which makes initialization from them risky.

def self.new(num : BigDecimal) #

Returns num. Useful for generic code that does `T.new(...)` with `T` being a `Number`.

def self.new(num : Int = 0, scale : Int = 0) #

Creates a new `BigDecimal` from `Int`.

def self.new(str : String) #

Creates a new `BigDecimal` from a `String`.

Allows only valid number strings with an optional negative sign.

##
Instance Method Detail

def *(other : BigDecimal) : BigDecimal #
def *(other : Int) #
def **(other : Int) : BigDecimal #

Raises the decimal to the otherth power

    require "big"

    BigDecimal.new(1234, 2) ** 2 # => 152.2756

def +(other : BigDecimal) : BigDecimal #
def +(other : Int) #
def -(other : BigDecimal) : BigDecimal #
def -(other : Int) #
def - : BigDecimal #
def /(other : UInt16) : BigDecimal #
def /(other : Float32) : BigDecimal #
def /(other : UInt128) : BigDecimal #
def /(other : Int128) : BigDecimal #
def /(other : UInt64) : BigDecimal #
def /(other : Int64) : BigDecimal #
def /(other : UInt32) : BigDecimal #
def /(other : Int32) : BigDecimal #
def /(other : Int16) : BigDecimal #
def /(other : UInt8) : BigDecimal #
def /(other : Int8) : BigDecimal #
def /(other : BigRational) : BigRational #
def /(other : BigFloat) : BigDecimal #
def /(other : BigInt) : BigDecimal #
def /(other : BigDecimal) : BigDecimal #
def /(other : Float64) : BigDecimal #
def <=>(other : BigDecimal) : Int32 #
Description copied from module Comparable(BigDecimal)

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 greter 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]

def <=>(other : Int | Float | BigRational) #
def ==(other : BigDecimal) : Bool #
Description copied from module Comparable(BigDecimal)

Compares this object to other based on the receiver’s `#<=>` method, returning `true` if it returns `0`.

Also returns `true` if this and other are the same object.

def ceil : BigDecimal #
def clone #
def div(other : BigDecimal, max_div_iterations = DEFAULT_MAX_DIV_ITERATIONS) : BigDecimal #

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 floor : BigDecimal #
def hash(hasher) #
Description copied from class Object

Appends this object's value to hasher, and returns the modified hasher.

Usually the macro `def_hash` can be used to generate this method. Otherwise, invoke `#hash(hasher)` on each object's instance variables to accumulate the result:

    def hash(hasher)
      hasher = @some_ivar.hash(hasher)
      hasher = @some_other_ivar.hash(hasher)
      hasher
    end

def normalize_quotient(other : BigDecimal, quotient : BigInt) : BigInt #

Returns the quotient as absolutely negative if `self` and other have different signs, otherwise returns the quotient.

def scale : UInt64 #
def scale_to(new_scale : BigDecimal) : BigDecimal #

Scales a `BigDecimal` to another `BigDecimal`, so they can be computed easier.

def to_big_d #
def to_big_f #

Converts to `BigFloat`.

def to_big_i #

Converts to `BigInt`. Truncates anything on the right side of the decimal point.

def to_big_r #
def to_f #

Converts to `Float64`. Raises `OverflowError` in case of overflow.

def to_f! #

Converts to `Float64`. In case of overflow a wrapping is performed.

def to_f32 #

Converts to `Float32`. Raises `OverflowError` in case of overflow.

def to_f32! #

Converts to `Float32`. In case of overflow a wrapping is performed.

def to_f64 #

Converts to `Float64`. Raises `OverflowError` in case of overflow.

def to_f64! #

Converts to `Float64`. In case of overflow a wrapping is performed.

def to_i #

Converts to `Int32`. Truncates anything on the right side of the decimal point. Raises `OverflowError` in case of overflow.

def to_i! #

Converts to `Int32`. Truncates anything on the right side of the decimal point. In case of overflow a wrapping is performed.

def to_i16 #

Converts to `Int16`. Truncates anything on the right side of the decimal point. Raises `OverflowError` in case of overflow.

def to_i16! #

Converts to `Int16`. Truncates anything on the right side of the decimal point. In case of overflow a wrapping is performed.

def to_i32 #

Converts to `Int32`. Truncates anything on the right side of the decimal point. Raises `OverflowError` in case of overflow.

def to_i32! #

Converts to `Int32`. Truncates anything on the right side of the decimal point. In case of overflow a wrapping is performed.

def to_i64 #

Converts to `Int64`. Truncates anything on the right side of the decimal point. Raises `OverflowError` in case of overflow.

def to_i64! #

Converts to `Int64`. Truncates anything on the right side of the decimal point. In case of overflow a wrapping is performed.

def to_i8 #

Converts to `Int8`. Truncates anything on the right side of the decimal point. Raises `OverflowError` in case of overflow.

def to_i8! #

Converts to `Int8`. Truncates anything on the right side of the decimal point. In case of overflow a wrapping is performed.

def to_s(io : IO) : Nil #
Description copied from class Object

Appends a `String` representation of this object to the given `IO` object.

An object must never append itself to the io argument, as this will in turn call `#to_s(io)` on it.

def to_u #

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! #

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_u16 #

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! #

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_u32 #

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! #

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_u64 #

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! #

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_u8 #

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! #

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 trunc : BigDecimal #
def value : BigInt #