# BigDecimal

Class

`BigDecimal` provides arbitrary-precision floating point decimal arithmetic.

## Introduction

Ruby provides built-in support for arbitrary precision integer arithmetic.

For example:

```42**13  #=>   1265437718438866624512
```

`BigDecimal` provides similar support for very large or very accurate floating point numbers.

Decimal arithmetic is also useful for general calculation, because it provides the correct answers people expect–whereas normal binary floating point arithmetic often introduces subtle errors because of the conversion between base 10 and base 2.

For example, try:

```sum = 0
10_000.times do
sum = sum + 0.0001
end
print sum #=> 0.9999999999999062
```

and contrast with the output from:

```require 'bigdecimal'

sum = BigDecimal.new("0")
10_000.times do
sum = sum + BigDecimal.new("0.0001")
end
print sum #=> 0.1E1
```

Similarly:

```(BigDecimal.new("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") #=> true

(1.2 - 1.0) == 0.2 #=> false
```

## Special features of accurate decimal arithmetic

Because `BigDecimal` is more accurate than normal binary floating point arithmetic, it requires some special values.

### Infinity

`BigDecimal` sometimes needs to return infinity, for example if you divide a value by zero.

```BigDecimal.new("1.0") / BigDecimal.new("0.0")  #=> Infinity
BigDecimal.new("-1.0") / BigDecimal.new("0.0")  #=> -Infinity
```

You can represent infinite numbers to `BigDecimal` using the strings `'Infinity'`, `'+Infinity'` and `'-Infinity'` (case-sensitive)

### Not a Number

When a computation results in an undefined value, the special value `NaN` (for ‘not a number’) is returned.

Example:

```BigDecimal.new("0.0") / BigDecimal.new("0.0") #=> NaN
```

You can also create undefined values.

NaN is never considered to be the same as any other value, even NaN itself:

```n = BigDecimal.new('NaN')
n == 0.0 #=> false
n == n #=> false
```

### Positive and negative zero

If a computation results in a value which is too small to be represented as a `BigDecimal` within the currently specified limits of precision, zero must be returned.

If the value which is too small to be represented is negative, a `BigDecimal` value of negative zero is returned.

```BigDecimal.new("1.0") / BigDecimal.new("-Infinity") #=> -0.0
```

If the value is positive, a value of positive zero is returned.

```BigDecimal.new("1.0") / BigDecimal.new("Infinity") #=> 0.0
```

(See `BigDecimal.mode` for how to specify limits of precision.)

Note that `-0.0` and `0.0` are considered to be the same for the purposes of comparison.

Note also that in mathematics, there is no particular concept of negative or positive zero; true mathematical zero has no sign.

`BigDecimal` is released under the Ruby and 2-clause BSD licenses. See LICENSE.txt for details.

Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.

Documented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and many other contributors.

`BigDecimal` extends the native `Numeric` class to provide the `to_digits` and `to_d` methods.

When you require `BigDecimal` in your application, this method will be available on `BigDecimal` objects.

Constants

#### BASE

Base value used in internal calculations. On a 32 bit system, `BASE` is 10000, indicating that calculation is done in groups of 4 digits. (If it were larger, BASE**2 wouldn’t fit in 32 bits, so you couldn’t guarantee that two groups could always be multiplied together without overflow.)

#### EXCEPTION_ALL

Determines whether overflow, underflow or zero divide result in an exception being thrown. See `BigDecimal.mode`.

#### EXCEPTION_NaN

Determines what happens when the result of a computation is not a number (NaN). See `BigDecimal.mode`.

#### EXCEPTION_INFINITY

Determines what happens when the result of a computation is infinity. See `BigDecimal.mode`.

#### EXCEPTION_UNDERFLOW

Determines what happens when the result of a computation is an underflow (a result too small to be represented). See `BigDecimal.mode`.

#### EXCEPTION_OVERFLOW

Determines what happens when the result of a computation is an overflow (a result too large to be represented). See `BigDecimal.mode`.

#### EXCEPTION_ZERODIVIDE

Determines what happens when a division by zero is performed. See `BigDecimal.mode`.

#### ROUND_MODE

Determines what happens when a result must be rounded in order to fit in the appropriate number of significant digits. See `BigDecimal.mode`.

#### ROUND_UP

Indicates that values should be rounded away from zero. See `BigDecimal.mode`.

#### ROUND_DOWN

Indicates that values should be rounded towards zero. See `BigDecimal.mode`.

#### ROUND_HALF_UP

Indicates that digits >= 5 should be rounded up, others rounded down. See `BigDecimal.mode`.

#### ROUND_HALF_DOWN

Indicates that digits >= 6 should be rounded up, others rounded down. See `BigDecimal.mode`.

#### ROUND_CEILING

Round towards +Infinity. See `BigDecimal.mode`.

#### ROUND_FLOOR

Round towards -Infinity. See `BigDecimal.mode`.

#### ROUND_HALF_EVEN

Round towards the even neighbor. See `BigDecimal.mode`.

#### SIGN_NaN

Indicates that a value is not a number. See `BigDecimal.sign`.

#### SIGN_POSITIVE_ZERO

Indicates that a value is +0. See `BigDecimal.sign`.

#### SIGN_NEGATIVE_ZERO

Indicates that a value is -0. See `BigDecimal.sign`.

#### SIGN_POSITIVE_FINITE

Indicates that a value is positive and finite. See `BigDecimal.sign`.

#### SIGN_NEGATIVE_FINITE

Indicates that a value is negative and finite. See `BigDecimal.sign`.

#### SIGN_POSITIVE_INFINITE

Indicates that a value is positive and infinite. See `BigDecimal.sign`.

#### SIGN_NEGATIVE_INFINITE

Indicates that a value is negative and infinite. See `BigDecimal.sign`.

#### INFINITY

Positive infinity value.

#### NAN

‘Not a Number’ value.

Class Methods

Internal method used to provide marshalling support. See the `Marshal` module.

The `BigDecimal.double_fig` class method returns the number of digits a `Float` number is allowed to have. The result depends upon the CPU and OS in use.

Import a `JSON` Marshalled object.

method used for `JSON` marshalling support.

Limit the number of significant digits in newly created `BigDecimal` numbers to the specified value. Rounding is performed as necessary, as specified by `BigDecimal.mode`.

A limit of 0, the default, means no upper limit.

The limit specified by this method takes less priority over any limit specified to instance methods such as ceil, floor, truncate, or round.

Controls handling of arithmetic exceptions and rounding. If no value is supplied, the current value is returned.

Six values of the mode parameter control the handling of arithmetic exceptions:

For each mode parameter above, if the value set is false, computation continues after an arithmetic exception of the appropriate type. When computation continues, results are as follows:

`EXCEPTION_NaN`

NaN

`EXCEPTION_INFINITY`

+Infinity or -Infinity

`EXCEPTION_UNDERFLOW`

0

`EXCEPTION_OVERFLOW`

+Infinity or -Infinity

`EXCEPTION_ZERODIVIDE`

+Infinity or -Infinity

One value of the mode parameter controls the rounding of numeric values: `BigDecimal::ROUND_MODE`. The values it can take are:

`ROUND_UP`, :up

round away from zero

`ROUND_DOWN`, :down, :truncate

round towards zero (truncate)

`ROUND_HALF_UP`, :half_up, :default

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round away from zero. (default)

`ROUND_HALF_DOWN`, :half_down

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards zero.

`ROUND_HALF_EVEN`, :half_even, :banker

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards the even neighbor (Banker’s rounding)

`ROUND_CEILING`, :ceiling, :ceil

round towards positive infinity (ceil)

`ROUND_FLOOR`, :floor

round towards negative infinity (floor)

Create a new `BigDecimal` object.

initial

The initial value, as an `Integer`, a `Float`, a `Rational`, a `BigDecimal`, or a String.

If it is a String, spaces are ignored and unrecognized characters terminate the value.

digits

The number of significant digits, as a `Fixnum`. If omitted or 0, the number of significant digits is determined from the initial value.

The actual number of significant digits used in computation is usually larger than the specified number.

#### Exceptions

`TypeError`

If the `initial` type is neither `Fixnum`, `Bignum`, `Float`, `Rational`, nor `BigDecimal`, this exception is raised.

`TypeError`

If the `digits` is not a `Fixnum`, this exception is raised.

`ArgumentError`

If `initial` is a `Float`, and the `digits` is larger than Float::DIG + 1, this exception is raised.

`ArgumentError`

If the `initial` is a `Float` or `Rational`, and the `digits` value is omitted, this exception is raised.

Execute the provided block, but preserve the exception mode

```BigDecimal.save_exception_mode do
BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, false)
BigDecimal.mode(BigDecimal::EXCEPTION_NaN, false)

BigDecimal.new(BigDecimal('Infinity'))
BigDecimal.new(BigDecimal('-Infinity'))
BigDecimal(BigDecimal.new('NaN'))
end
```

For use with the BigDecimal::EXCEPTION_*

Execute the provided block, but preserve the precision limit

```BigDecimal.limit(100)
puts BigDecimal.limit
BigDecimal.save_limit do
BigDecimal.limit(200)
puts BigDecimal.limit
end
puts BigDecimal.limit
```

Execute the provided block, but preserve the rounding mode

```BigDecimal.save_rounding_mode do
BigDecimal.mode(BigDecimal::ROUND_MODE, :up)
puts BigDecimal.mode(BigDecimal::ROUND_MODE)
end
```

For use with the BigDecimal::ROUND_*

Returns the `BigDecimal` version number.

Instance Methods

Returns the modulus from dividing by b.

Multiply by the specified value.

e.g.

```c = a.mult(b,n)
c = a * b
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

Returns the value raised to the power of n.

e.g.

```c = a.add(b,n)
c = a + b
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

Return self.

e.g.

```b = +a  # b == a
```

Subtract the specified value.

e.g.

```c = a - b
```

The precision of the result value depends on the type of `b`.

If `b` is a `Float`, the precision of the result is Float::DIG+1.

If `b` is a `BigDecimal`, the precision of the result is `b`‘s precision of internal representation from platform. So, it’s return value is platform dependent.

Return the negation of self.

e.g.

```b = -a
b == a * -1
```

Divide by the specified value.

e.g.

```c = a.div(b,n)
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

If digits is 0, the result is the same as the / operator. If not, the result is an integer `BigDecimal`, by analogy with `Float#div`.

The alias quo is provided since `div(value, 0)` is the same as computing the quotient; see `BigDecimal#divmod`.

Returns true if a is less than b.

Values may be coerced to perform the comparison (see ==, `BigDecimal#coerce`).

Returns true if a is less than or equal to b.

Values may be coerced to perform the comparison (see ==, `BigDecimal#coerce`).

The comparison operator. a <=> b is 0 if a == b, 1 if a > b, -1 if a < b.

Tests for value equality; returns true if the values are equal.

The == and === operators and the eql? method have the same implementation for `BigDecimal`.

Values may be coerced to perform the comparison:

```BigDecimal.new('1.0') == 1.0  #=> true
```
An alias for ==

Returns true if a is greater than b.

Values may be coerced to perform the comparison (see ==, `BigDecimal#coerce`).

Returns true if a is greater than or equal to b.

Values may be coerced to perform the comparison (see ==, `BigDecimal#coerce`)

`Method` used to provide marshalling support.

```inf = BigDecimal.new('Infinity')
#=> #<BigDecimal:1e16fa8,'Infinity',9(9)>
#=> #<BigDecimal:1df8dc8,'Infinity',9(9)>
```

See the `Marshal` module.

Returns the absolute value, as a `BigDecimal`.

```BigDecimal('5').abs #=> 5
BigDecimal('-3').abs #=> 3
```

e.g.

```c = a.add(b,n)
c = a + b
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

`Marshal` the object to `JSON`.

method used for `JSON` marshalling support.

Return the smallest integer greater than or equal to the value, as a `BigDecimal`.

```BigDecimal('3.14159').ceil #=> 4
BigDecimal('-9.1').ceil #=> -9
```

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

```BigDecimal('3.14159').ceil(3) #=> 3.142
BigDecimal('13345.234').ceil(-2) #=> 13400.0
```

The coerce method provides support for Ruby type coercion. It is not enabled by default.

This means that binary operations like + * / or - can often be performed on a `BigDecimal` and an object of another type, if the other object can be coerced into a `BigDecimal` value.

e.g.

```a = BigDecimal.new("1.0")
b = a / 2.0 #=> 0.5
```

Note that coercing a String to a `BigDecimal` is not supported by default; it requires a special compile-time option when building Ruby.

No documentation available

Divides by the specified value, and returns the quotient and modulus as `BigDecimal` numbers. The quotient is rounded towards negative infinity.

For example:

```require 'bigdecimal'

a = BigDecimal.new("42")
b = BigDecimal.new("9")

q, m = a.divmod(b)

c = q * b + m

a == c  #=> true
```

The quotient q is (a/b).floor, and the modulus is the amount that must be added to q * b to get a.

An alias for ==

Returns the exponent of the `BigDecimal` number, as an `Integer`.

If the number can be represented as 0.xxxxxx*10**n where xxxxxx is a string of digits with no leading zeros, then n is the exponent.

Returns True if the value is finite (not NaN or infinite).

Return the integer part of the number, as a `BigDecimal`.

Return the largest integer less than or equal to the value, as a `BigDecimal`.

```BigDecimal('3.14159').floor #=> 3
BigDecimal('-9.1').floor #=> -10
```

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

```BigDecimal('3.14159').floor(3) #=> 3.141
BigDecimal('13345.234').floor(-2) #=> 13300.0
```

Return the fractional part of the number, as a `BigDecimal`.

Creates a hash for this `BigDecimal`.

Two BigDecimals with equal sign, fractional part and exponent have the same hash.

Returns nil, -1, or +1 depending on whether the value is finite, -Infinity, or +Infinity.

Returns debugging information about the value as a string of comma-separated values in angle brackets with a leading #:

```BigDecimal.new("1234.5678").inspect
#=> "#<BigDecimal:b7ea1130,'0.12345678E4',8(12)>"
```

The first part is the address, the second is the value as a string, and the final part ss(mm) is the current number of significant digits and the maximum number of significant digits, respectively.

An alias for %

Multiply by the specified value.

e.g.

```c = a.mult(b,n)
c = a * b
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

Returns True if the value is Not a Number.

Returns self if the value is non-zero, nil otherwise.

Returns the value raised to the power of n.

Note that n must be an `Integer`.

Also available as the operator **.

Returns an Array of two `Integer` values.

The first value is the current number of significant digits in the `BigDecimal`. The second value is the maximum number of significant digits for the `BigDecimal`.

An alias for /

Returns the remainder from dividing by the value.

x.remainder(y) means x-y*(x/y).truncate

Round to the nearest integer (by default), returning the result as a `BigDecimal`.

```BigDecimal('3.14159').round #=> 3
BigDecimal('8.7').round #=> 9
BigDecimal('-9.9').round #=> -10
```

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

```BigDecimal('3.14159').round(3) #=> 3.142
BigDecimal('13345.234').round(-2) #=> 13300.0
```

The value of the optional mode argument can be used to determine how rounding is performed; see `BigDecimal.mode`.

Returns the sign of the value.

Returns a positive value if > 0, a negative value if < 0, and a zero if == 0.

The specific value returned indicates the type and sign of the `BigDecimal`, as follows:

`BigDecimal::SIGN_NaN`

value is Not a Number

`BigDecimal::SIGN_POSITIVE_ZERO`

value is +0

`BigDecimal::SIGN_NEGATIVE_ZERO`

value is -0

`BigDecimal::SIGN_POSITIVE_INFINITE`

value is +Infinity

`BigDecimal::SIGN_NEGATIVE_INFINITE`

value is -Infinity

`BigDecimal::SIGN_POSITIVE_FINITE`

value is positive

`BigDecimal::SIGN_NEGATIVE_FINITE`

value is negative

Splits a `BigDecimal` number into four parts, returned as an array of values.

The first value represents the sign of the `BigDecimal`, and is -1 or 1, or 0 if the `BigDecimal` is Not a Number.

The second value is a string representing the significant digits of the `BigDecimal`, with no leading zeros.

The third value is the base used for arithmetic (currently always 10) as an `Integer`.

The fourth value is an `Integer` exponent.

If the `BigDecimal` can be represented as 0.xxxxxx*10**n, then xxxxxx is the string of significant digits with no leading zeros, and n is the exponent.

From these values, you can translate a `BigDecimal` to a float as follows:

```sign, significant_digits, base, exponent = a.split
f = sign * "0.#{significant_digits}".to_f * (base ** exponent)
```

(Note that the `to_f` method is provided as a more convenient way to translate a `BigDecimal` to a `Float`.)

Returns the square root of the value.

Result has at least n significant digits.

Subtract the specified value.

e.g.

```c = a.sub(b,n)
```
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to `BigDecimal.mode`.

Returns self.

Converts a `BigDecimal` to a String of the form “nnnnnn.mmm”. This method is deprecated; use `BigDecimal#to_s`(“F”) instead.

```require 'bigdecimal'
require 'bigdecimal/util'

d = BigDecimal.new("3.14")
d.to_digits
# => "3.14"
```

Returns a new `Float` object having approximately the same value as the `BigDecimal` number. Normal accuracy limits and built-in errors of binary `Float` arithmetic apply.

Returns the value as an integer (`Fixnum` or `Bignum`).

If the BigNumber is infinity or NaN, raises `FloatDomainError`.

An alias for to_i

return the `JSON` value

Converts the value to a string.

The default format looks like 0.xxxxEnn.

The optional parameter s consists of either an integer; or an optional ‘+’ or ‘ ’, followed by an optional number, followed by an optional ‘E’ or ‘F’.

If there is a ‘+’ at the start of s, positive values are returned with a leading ‘+’.

A space at the start of s returns positive values with a leading space.

If s contains a number, a space is inserted after each group of that many fractional digits.

If s ends with an ‘E’, engineering notation (0.xxxxEnn) is used.

If s ends with an ‘F’, conventional floating point notation is used.

Examples:

```BigDecimal.new('-123.45678901234567890').to_s('5F')
#=> '-123.45678 90123 45678 9'

BigDecimal.new('123.45678901234567890').to_s('+8F')
#=> '+123.45678901 23456789'

BigDecimal.new('123.45678901234567890').to_s(' F')
#=> ' 123.4567890123456789'
```

Truncate to the nearest integer (by default), returning the result as a `BigDecimal`.

```BigDecimal('3.14159').truncate #=> 3
BigDecimal('8.7').truncate #=> 8
BigDecimal('-9.9').truncate #=> -9
```

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

```BigDecimal('3.14159').truncate(3) #=> 3.141
BigDecimal('13345.234').truncate(-2) #=> 13300.0
```

Returns True if the value is zero.