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

Similarly:

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

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

For a calculation using a BigDecimal and another `value`, the precision of the result depends on the type of `value`:

• If `value` is a Float, the precision is Float::DIG + 1.

• If `value` is a Rational, the precision is larger than Float::DIG + 1.

• If `value` is a BigDecimal, the precision is `value`‘s precision in the internal representation, which is platform-dependent.

• If `value` is other object, the precision is determined by the result of +BigDecimal(value)+.

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

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

```BigDecimal("1.0") / BigDecimal("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/util

When you require `bigdecimal/util`, the `to_d` method will be available on `BigDecimal` and the native `Integer`, `Float`, `Rational`, and `String` classes:

```require 'bigdecimal/util'

42.to_d         # => 0.42e2
0.5.to_d        # => 0.5e0
(2/3r).to_d(3)  # => 0.667e0
"0.5".to_d      # => 0.5e0
```

`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.

Constants

#### VERSION

The version of bigdecimal library

#### 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

Special value constants

#### NAN

No documentation available
Class Methods

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

Returns the number of digits a `Float` object is allowed to have; the result is system-dependent:

```BigDecimal.double_fig # => 16
```
No documentation available

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.

Returns an integer representing the mode settings for exception handling and rounding.

These modes control exception handling:

• BigDecimal::EXCEPTION_NaN.

• BigDecimal::EXCEPTION_INFINITY.

• BigDecimal::EXCEPTION_UNDERFLOW.

• BigDecimal::EXCEPTION_OVERFLOW.

• BigDecimal::EXCEPTION_ZERODIVIDE.

• BigDecimal::EXCEPTION_ALL.

Values for `setting` for exception handling:

• `true`: sets the given `mode` to `true`.

• `false`: sets the given `mode` to `false`.

• `nil`: does not modify the mode settings.

You can use method `BigDecimal.save_exception_mode` to temporarily change, and then automatically restore, exception modes.

For clarity, some examples below begin by setting all exception modes to `false`.

This mode controls the way rounding is to be performed:

• BigDecimal::ROUND_MODE

You can use method `BigDecimal.save_rounding_mode` to temporarily change, and then automatically restore, the rounding mode.

NaNs

Mode BigDecimal::EXCEPTION_NaN controls behavior when a BigDecimal NaN is created.

Settings:

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal('NaN')                                 # => NaN
BigDecimal.mode(BigDecimal::EXCEPTION_NaN, true)  # => 2
BigDecimal('NaN') # Raises FloatDomainError
```

Infinities

Mode BigDecimal::EXCEPTION_INFINITY controls behavior when a BigDecimal Infinity or -Infinity is created. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
BigDecimal('Infinity')                                # => Infinity
BigDecimal('-Infinity')                               # => -Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_INFINITY, true) # => 1
BigDecimal('Infinity')  # Raises FloatDomainError
BigDecimal('-Infinity') # Raises FloatDomainError
```

Underflow

Mode BigDecimal::EXCEPTION_UNDERFLOW controls behavior when a BigDecimal underflow occurs. Settings:

• `false` (default): Returns `BigDecimal('0')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)      # => 0
def flow_under
x = BigDecimal('0.1')
100.times { x *= x }
end
flow_under                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_UNDERFLOW, true) # => 4
flow_under # Raises FloatDomainError
```

Overflow

Mode BigDecimal::EXCEPTION_OVERFLOW controls behavior when a BigDecimal overflow occurs. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
def flow_over
x = BigDecimal('10')
100.times { x *= x }
end
flow_over                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, true) # => 1
flow_over # Raises FloatDomainError
```

Zero Division

Mode BigDecimal::EXCEPTION_ZERODIVIDE controls behavior when a zero-division occurs. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)       # => 0
one = BigDecimal('1')
zero = BigDecimal('0')
one / zero                                              # => Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_ZERODIVIDE, true) # => 16
one / zero # Raises FloatDomainError
```

All Exceptions

Mode BigDecimal::EXCEPTION_ALL controls all of the above:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal.mode(BigDecimal::EXCEPTION_ALL, true)  # => 23
```

Rounding

Mode BigDecimal::ROUND_MODE controls the way rounding is to be performed; its `setting` values are:

• `ROUND_UP`: Round away from zero. Aliased as `:up`.

• `ROUND_DOWN`: Round toward zero. Aliased as `:down` and `:truncate`.

• `ROUND_HALF_UP`: Round toward the nearest neighbor; if the neighbors are equidistant, round away from zero. Aliased as `:half_up` and `:default`.

• `ROUND_HALF_DOWN`: Round toward the nearest neighbor; if the neighbors are equidistant, round toward zero. Aliased as `:half_down`.

• `ROUND_HALF_EVEN` (Banker’s rounding): Round toward the nearest neighbor; if the neighbors are equidistant, round toward the even neighbor. Aliased as `:half_even` and `:banker`.

• `ROUND_CEILING`: Round toward positive infinity. Aliased as `:ceiling` and `:ceil`.

• `ROUND_FLOOR`: Round toward negative infinity. Aliased as `:floor:`.

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(BigDecimal('Infinity'))
BigDecimal(BigDecimal('-Infinity'))
BigDecimal(BigDecimal('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_*

Instance Methods

Returns the modulus from dividing by b.

No documentation available

Returns the BigDecimal value of `self` raised to power `other`:

```b = BigDecimal('3.14')
b ** 2              # => 0.98596e1
b ** 2.0            # => 0.98596e1
b ** Rational(2, 1) # => 0.98596e1
```

Related: `BigDecimal#power`.

Returns the BigDecimal sum of `self` and `value`:

```b = BigDecimal('111111.111') # => 0.111111111e6
b + 2                        # => 0.111113111e6
b + 2.0                      # => 0.111113111e6
b + Rational(2, 1)           # => 0.111113111e6
b + Complex(2, 0)            # => (0.111113111e6+0i)
```

Returns `self`:

```+BigDecimal(5)  # => 0.5e1
+BigDecimal(-5) # => -0.5e1
```

Returns the BigDecimal difference of `self` and `value`:

```b = BigDecimal('333333.333') # => 0.333333333e6
b - 2                        # => 0.333331333e6
b - 2.0                      # => 0.333331333e6
b - Rational(2, 1)           # => 0.333331333e6
b - Complex(2, 0)            # => (0.333331333e6+0i)
```

Returns the BigDecimal negation of self:

```b0 = BigDecimal('1.5')
b1 = -b0 # => -0.15e1
b2 = -b1 # => 0.15e1
```

Divide by the specified value.

The result precision will be the precision of the larger operand, but its minimum is 2*Float::DIG.

Returns `true` if `self` is less than `other`, `false` otherwise:

```b = BigDecimal('1.5') # => 0.15e1
b < 2                 # => true
b < 2.0               # => true
b < Rational(2, 1)    # => true
b < 1.5               # => false
```

Raises an exception if the comparison cannot be made.

Returns `true` if `self` is less or equal to than `other`, `false` otherwise:

```b = BigDecimal('1.5') # => 0.15e1
b <= 2                # => true
b <= 2.0              # => true
b <= Rational(2, 1)   # => true
b <= 1.5              # => true
b < 1                 # => false
```

Raises an exception if the comparison cannot be made.

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

Returns `true` if `self` is greater than `other`, `false` otherwise:

```b = BigDecimal('1.5')
b > 1              # => true
b > 1.0            # => true
b > Rational(1, 1) # => true
b > 2              # => false
```

Raises an exception if the comparison cannot be made.

Returns `true` if `self` is greater than or equal to `other`, `false` otherwise:

```b = BigDecimal('1.5')
b >= 1              # => true
b >= 1.0            # => true
b >= Rational(1, 1) # => true
b >= 1.5            # => true
b > 2               # => false
```

Raises an exception if the comparison cannot be made.

Returns a string representing the marshalling of `self`. See module `Marshal`.

```inf = BigDecimal('Infinity') # => Infinity
dumped = inf._dump           # => "9:Infinity"
```

Returns the BigDecimal absolute value of `self`:

```BigDecimal('5').abs  # => 0.5e1
BigDecimal('-3').abs # => 0.3e1
```

Returns the BigDecimal sum of `self` and `value` with a precision of `ndigits` decimal digits.

When `ndigits` is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see `BigDecimal.mode`.

Examples:

```# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('111111.111')
b.add(Rational(1, 1), 15) # => 0.111112111e6
```

`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
```
No documentation available

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("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.

Divide by the specified value.

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 for the / operator or `quo`.

If digits is not specified, the result is an integer, by analogy with `Float#div`; see also `BigDecimal#divmod`.

Examples:

```a = BigDecimal("4")
b = BigDecimal("3")

a.div(b, 3)  # => 0.133e1

a.div(b, 0)  # => 0.1333333333333333333e1
a / b        # => 0.1333333333333333333e1
a.quo(b)     # => 0.1333333333333333333e1

a.div(b)     # => 1
```

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("42")
b = BigDecimal("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 clone
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`.

Returns the integer hash value for `self`.

Two instances of BigDecimal have the same hash value if and only if they have equal:

• Sign.

• Fractional part.

• Exponent.

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

Returns a string representation of self.

```BigDecimal("1234.5678").inspect
#=> "0.12345678e4"
```
An alias for %

Returns the BigDecimal product of `self` and `value` with a precision of `ndigits` decimal digits.

When `ndigits` is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see `BigDecimal.mode`.

Examples:

```# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('555555.555')
b.mult(3, 0)              # => 0.1666666665e7
b.mult(3, 3)              # => 0.167e7
b.mult(3, 6)              # => 0.166667e7
b.mult(3, 15)             # => 0.1666666665e7
b.mult(3.0, 0)            # => 0.1666666665e7
b.mult(Rational(3, 1), 0) # => 0.1666666665e7
b.mult(Complex(3, 0), 0)  # => (0.1666666665e7+0.0i)
```

Returns the number of decimal significant digits in `self`.

```BigDecimal("0").scale         # => 0
BigDecimal("1").scale         # => 1
BigDecimal("1.1").scale       # => 2
BigDecimal("3.1415").scale    # => 5
BigDecimal("-1e20").precision # => 1
BigDecimal("1e-20").precision # => 1
BigDecimal("Infinity").scale  # => 0
BigDecimal("-Infinity").scale # => 0
BigDecimal("NaN").scale       # => 0
```

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 the number of decimal digits in `self`:

```BigDecimal("0").precision         # => 0
BigDecimal("1").precision         # => 1
BigDecimal("1.1").precision       # => 2
BigDecimal("3.1415").precision    # => 5
BigDecimal("-1e20").precision     # => 21
BigDecimal("1e-20").precision     # => 20
BigDecimal("Infinity").precision  # => 0
BigDecimal("-Infinity").precision # => 0
BigDecimal("NaN").precision       # => 0
```

Returns a 2-length array; the first item is the result of `BigDecimal#precision` and the second one is of `BigDecimal#scale`.

Returns an `Array` of two `Integer` values that represent platform-dependent internal storage properties.

This method is deprecated and will be removed in the future. Instead, use `BigDecimal#n_significant_digits` for obtaining the number of significant digits in scientific notation, and `BigDecimal#precision` for obtaining the number of digits in decimal notation.

Divide by the specified value.

digits

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

If digits is 0 or omitted, the result is the same as for the / operator.

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` if n is specified, or as an `Integer` if it isn’t.

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

BigDecimal('3.14159').round(2).class.name #=> "BigDecimal"
BigDecimal('3.14159').round.class.name #=> "Integer"
```

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, and return value will be an `Integer`.

```BigDecimal('3.14159').round(3) #=> 3.142
BigDecimal('13345.234').round(-2) #=> 13300
```

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

Returns the number of decimal digits following the decimal digits in `self`.

```BigDecimal("0").scale         # => 0
BigDecimal("1").scale         # => 1
BigDecimal("1.1").scale       # => 1
BigDecimal("3.1415").scale    # => 4
BigDecimal("-1e20").precision # => 0
BigDecimal("1e-20").precision # => 20
BigDecimal("Infinity").scale  # => 0
BigDecimal("-Infinity").scale # => 0
BigDecimal("NaN").scale       # => 0
```

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.

```require 'bigdecimal/util'

d = BigDecimal("3.14")
d.to_d                       # => 0.314e1
```

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

```require 'bigdecimal/util'

d = BigDecimal("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`.

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

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

BigDecimal('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.