# Float

Class

`BigDecimal` extends the native `Float` class to provide the `to_d` method.

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

`Float` objects represent inexact real numbers using the native architecture’s double-precision floating point representation.

Floating point has a different arithmetic and is an inexact number. So you should know its esoteric system. see following:

Constants

#### ROUNDS

Represents the rounding mode for floating point addition.

Usually defaults to 1, rounding to the nearest number.

Other modes include:

-1

Indeterminable

0

Rounding towards zero

1

Rounding to the nearest number

2

Rounding towards positive infinity

3

Rounding towards negative infinity

The base of the floating point, or number of unique digits used to represent the number.

Usually defaults to 2 on most systems, which would represent a base-10 decimal.

#### MANT_DIG

The number of base digits for the `double` data type.

Usually defaults to 53.

#### DIG

The minimum number of significant decimal digits in a double-precision floating point.

Usually defaults to 15.

#### MIN_EXP

The smallest posable exponent value in a double-precision floating point.

Usually defaults to -1021.

#### MAX_EXP

The largest possible exponent value in a double-precision floating point.

Usually defaults to 1024.

#### MIN_10_EXP

The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.

Usually defaults to -307.

#### MAX_10_EXP

The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.

Usually defaults to 308.

#### MIN

The smallest positive normalized number in a double-precision floating point.

Usually defaults to 2.2250738585072014e-308.

If the platform supports denormalized numbers, there are numbers between zero and `Float::MIN`. 0.0.next_float returns the smallest positive floating point number including denormalized numbers.

#### MAX

The largest possible integer in a double-precision floating point number.

Usually defaults to 1.7976931348623157e+308.

#### EPSILON

The difference between 1 and the smallest double-precision floating point number greater than 1.

Usually defaults to 2.2204460492503131e-16.

#### INFINITY

An expression representing positive infinity.

#### NAN

An expression representing a value which is “not a number”.

Instance Methods

Return the modulo after division of `float` by `other`.

```6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996
```

Returns a new float which is the product of `float` and `other`.

`float ** other  ->  float`

Raises `float` to the power of `other`.

```2.0**3      #=> 8.0
```

Returns a new float which is the sum of `float` and `other`.

Returns a new float which is the difference of `float` and `other`.

Returns float, negated.

Returns a new float which is the result of dividing `float` by `other`.

Returns `true` if `float` is less than `real`.

The result of `NaN < NaN` is undefined, so the implementation-dependent value is returned.

Returns `true` if `float` is less than or equal to `real`.

The result of `NaN <= NaN` is undefined, so the implementation-dependent value is returned.

Returns -1, 0, +1 or nil depending on whether `float` is less than, equal to, or greater than `real`. This is the basis for the tests in `Comparable`.

The result of `NaN <=> NaN` is undefined, so the implementation-dependent value is returned.

`nil` is returned if the two values are incomparable.

Returns `true` only if `obj` has the same value as `float`. Contrast this with `Float#eql?`, which requires obj to be a `Float`.

The result of `NaN == NaN` is undefined, so the implementation-dependent value is returned.

```1.0 == 1   #=> true
```
An alias for ==

Returns `true` if `float` is greater than `real`.

The result of `NaN > NaN` is undefined, so the implementation-dependent value is returned.

Returns `true` if `float` is greater than or equal to `real`.

The result of `NaN >= NaN` is undefined, so the implementation-dependent value is returned.

Returns the absolute value of `float`.

```(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
```
An alias for arg

Returns 0 if the value is positive, pi otherwise.

Returns the smallest `Integer` greater than or equal to `float`.

```1.2.ceil      #=> 2
2.0.ceil      #=> 2
(-1.2).ceil   #=> -1
(-2.0).ceil   #=> -2
```

Returns an array with both a `numeric` and a `float` represented as `Float` objects.

This is achieved by converting a `numeric` to a `Float`.

```1.2.coerce(3)       #=> [3.0, 1.2]
2.5.coerce(1.1)     #=> [1.1, 2.5]
```

provides a unified `clone` operation, for `REXML::XPathParser` to use across multiple `Object` types

Returns the denominator (always positive). The result is machine dependent.

See numerator.

```42.0.divmod 6 #=> [7, 0.0]
42.0.divmod 5 #=> [8, 2.0]
```

Returns `true` only if `obj` is a `Float` with the same value as `float`. Contrast this with `Float#==`, which performs type conversions.

The result of `NaN.eql?(NaN)` is undefined, so the implementation-dependent value is returned.

```1.0.eql?(1)   #=> false
```
An alias for quo

Returns `true` if `float` is a valid IEEE floating point number (it is not infinite, and `Float#nan?` is `false`).

Returns the largest integer less than or equal to `float`.

```1.2.floor      #=> 1
2.0.floor      #=> 2
(-1.2).floor   #=> -2
(-2.0).floor   #=> -2
```

Returns a hash code for this float.

See also `Object#hash`.

Return values corresponding to the value of `float`:

`finite`

`nil`

`-Infinity`

`-1`

`+Infinity`

`1`

For example:

```(0.0).infinite?        #=> nil
(-1.0/0.0).infinite?   #=> -1
(+1.0/0.0).infinite?   #=> 1
```
An alias for to_s
An alias for abs
An alias for %

Returns `true` if `float` is an invalid IEEE floating point number.

```a = -1.0      #=> -1.0
a.nan?        #=> false
a = 0.0/0.0   #=> NaN
a.nan?        #=> true
```

Returns `true` if `float` is less than 0.

Returns the next representable floating-point number.

Float::MAX.next_float and Float::INFINITY.next_float is `Float::INFINITY`.

Float::NAN.next_float is `Float::NAN`.

For example:

```p 0.01.next_float  #=> 0.010000000000000002
p 1.0.next_float   #=> 1.0000000000000002
p 100.0.next_float #=> 100.00000000000001

p 0.01.next_float - 0.01   #=> 1.734723475976807e-18
p 1.0.next_float - 1.0     #=> 2.220446049250313e-16
p 100.0.next_float - 100.0 #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147cp-7 0.010000000000000002
#   0x1.47ae147ae147dp-7 0.010000000000000004
#   0x1.47ae147ae147ep-7 0.010000000000000005
#   0x1.47ae147ae147fp-7 0.010000000000000007
#   0x1.47ae147ae148p-7  0.010000000000000009
#   0x1.47ae147ae1481p-7 0.01000000000000001
#   0x1.47ae147ae1482p-7 0.010000000000000012
#   0x1.47ae147ae1483p-7 0.010000000000000014
#   0x1.47ae147ae1484p-7 0.010000000000000016
#   0x1.47ae147ae1485p-7 0.010000000000000018
#   0x1.47ae147ae1486p-7 0.01000000000000002
#   0x1.47ae147ae1487p-7 0.010000000000000021
#   0x1.47ae147ae1488p-7 0.010000000000000023
#   0x1.47ae147ae1489p-7 0.010000000000000024
#   0x1.47ae147ae148ap-7 0.010000000000000026
#   0x1.47ae147ae148bp-7 0.010000000000000028
#   0x1.47ae147ae148cp-7 0.01000000000000003
#   0x1.47ae147ae148dp-7 0.010000000000000031
#   0x1.47ae147ae148ep-7 0.010000000000000033

f = 0.0
100.times { f += 0.1 }
p f                            #=> 9.99999999999998       # should be 10.0 in the ideal world.
p 10-f                         #=> 1.9539925233402755e-14 # the floating-point error.
p(10.0.next_float-10)          #=> 1.7763568394002505e-15 # 1 ulp (units in the last place).
p((10-f)/(10.0.next_float-10)) #=> 11.0                   # the error is 11 ulp.
p((10-f)/(10*Float::EPSILON))  #=> 8.8                    # approximation of the above.
p "%a" % f                     #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5.  16 - 5 = 11 ulp.
```

Returns the numerator. The result is machine dependent.

```n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3
```
An alias for arg

Returns `true` if `float` is greater than 0.

Returns the previous representable floating-point number.

(-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY.

Float::NAN.prev_float is `Float::NAN`.

For example:

```p 0.01.prev_float  #=> 0.009999999999999998
p 1.0.prev_float   #=> 0.9999999999999999
p 100.0.prev_float #=> 99.99999999999999

p 0.01 - 0.01.prev_float   #=> 1.734723475976807e-18
p 1.0 - 1.0.prev_float     #=> 1.1102230246251565e-16
p 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147ap-7 0.009999999999999998
#   0x1.47ae147ae1479p-7 0.009999999999999997
#   0x1.47ae147ae1478p-7 0.009999999999999995
#   0x1.47ae147ae1477p-7 0.009999999999999993
#   0x1.47ae147ae1476p-7 0.009999999999999992
#   0x1.47ae147ae1475p-7 0.00999999999999999
#   0x1.47ae147ae1474p-7 0.009999999999999988
#   0x1.47ae147ae1473p-7 0.009999999999999986
#   0x1.47ae147ae1472p-7 0.009999999999999985
#   0x1.47ae147ae1471p-7 0.009999999999999983
#   0x1.47ae147ae147p-7  0.009999999999999981
#   0x1.47ae147ae146fp-7 0.00999999999999998
#   0x1.47ae147ae146ep-7 0.009999999999999978
#   0x1.47ae147ae146dp-7 0.009999999999999976
#   0x1.47ae147ae146cp-7 0.009999999999999974
#   0x1.47ae147ae146bp-7 0.009999999999999972
#   0x1.47ae147ae146ap-7 0.00999999999999997
#   0x1.47ae147ae1469p-7 0.009999999999999969
#   0x1.47ae147ae1468p-7 0.009999999999999967
```

Returns `float / numeric`, same as `Float#/`.

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). if the optional eps is not given, it will be chosen automatically.

```0.3.rationalize          #=> (3/10)
1.333.rationalize        #=> (1333/1000)
1.333.rationalize(0.01)  #=> (4/3)
```

See to_r.

Rounds `float` to a given precision in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is more than zero.

```1.4.round      #=> 1
1.5.round      #=> 2
1.6.round      #=> 2
(-1.5).round   #=> -2

1.234567.round(2)  #=> 1.23
1.234567.round(3)  #=> 1.235
1.234567.round(4)  #=> 1.2346
1.234567.round(5)  #=> 1.23457

34567.89.round(-5) #=> 0
34567.89.round(-4) #=> 30000
34567.89.round(-3) #=> 35000
34567.89.round(-2) #=> 34600
34567.89.round(-1) #=> 34570
34567.89.round(0)  #=> 34568
34567.89.round(1)  #=> 34567.9
34567.89.round(2)  #=> 34567.89
34567.89.round(3)  #=> 34567.89
```

Convert `flt` to a `BigDecimal` and return it.

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

0.5.to_d
# => #<BigDecimal:1dc69e0,'0.5E0',9(18)>
```

Since `float` is already a float, returns `self`.

Returns the `float` truncated to an `Integer`.

Synonyms are `to_i`, `to_int`, and `truncate`.

An alias for to_i

Returns the value as a rational.

NOTE: 0.3.to_r isn’t the same as ‘0.3’.to_r. The latter is equivalent to ‘3/10’.to_r, but the former isn’t so.

```2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)
```

See rationalize.

Returns a string containing a representation of self. As well as a fixed or exponential form of the `float`, the call may return `NaN`, `Infinity`, and `-Infinity`.

An alias for to_i

Returns `true` if `float` is 0.0.