# View Source Float (Elixir v1.13.0-rc.0)

Functions for working with floating-point numbers.

## Kernel functions

There are functions related to floating-point numbers on the `Kernel`

module
too. Here is a list of them:

`Kernel.round/1`

: rounds a number to the nearest integer.`Kernel.trunc/1`

: returns the integer part of a number.

## Known issues

There are some very well known problems with floating-point numbers and arithmetics due to the fact most decimal fractions cannot be represented by a floating-point binary and most operations are not exact, but operate on approximations. Those issues are not specific to Elixir, they are a property of floating point representation itself.

For example, the numbers 0.1 and 0.01 are two of them, what means the result of squaring 0.1 does not give 0.01 neither the closest representable. Here is what happens in this case:

- The closest representable number to 0.1 is 0.1000000014
- The closest representable number to 0.01 is 0.0099999997
- Doing 0.1 * 0.1 should return 0.01, but because 0.1 is actually 0.1000000014, the result is 0.010000000000000002, and because this is not the closest representable number to 0.01, you'll get the wrong result for this operation

There are also other known problems like flooring or rounding numbers. See
`round/2`

and `floor/2`

for more details about them.

To learn more about floating-point arithmetic visit:

# Link to this section Summary

## Functions

Rounds a float to the smallest integer greater than or equal to `num`

.

Rounds a float to the largest number less than or equal to `num`

.

Parses a binary into a float.

Computes `base`

raised to power of `exponent`

.

Returns a pair of integers whose ratio is exactly equal to the original float and with a positive denominator.

Rounds a floating-point value to an arbitrary number of fractional digits (between 0 and 15).

Returns a charlist which corresponds to the text representation of the given float.

Returns a binary which corresponds to the text representation of the given float.

# Link to this section Types

`@type precision_range() :: 0..15`

# Link to this section Functions

@spec ceil(float(), precision_range()) :: float()

Rounds a float to the smallest integer greater than or equal to `num`

.

`ceil/2`

also accepts a precision to round a floating-point value down
to an arbitrary number of fractional digits (between 0 and 15).

The operation is performed on the binary floating point, without a conversion to decimal.

The behaviour of `ceil/2`

for floats can be surprising. For example:

```
iex> Float.ceil(-12.52, 2)
-12.51
```

One may have expected it to ceil to -12.52. This is not a bug. Most decimal fractions cannot be represented as a binary floating point and therefore the number above is internally represented as -12.51999999, which explains the behaviour above.

This function always returns floats. `Kernel.trunc/1`

may be used instead to
truncate the result to an integer afterwards.

## Examples

```
iex> Float.ceil(34.25)
35.0
iex> Float.ceil(-56.5)
-56.0
iex> Float.ceil(34.251, 2)
34.26
```

@spec floor(float(), precision_range()) :: float()

Rounds a float to the largest number less than or equal to `num`

.

`floor/2`

also accepts a precision to round a floating-point value down
to an arbitrary number of fractional digits (between 0 and 15).
The operation is performed on the binary floating point, without a
conversion to decimal.

This function always returns a float. `Kernel.trunc/1`

may be used instead to
truncate the result to an integer afterwards.

## Known issues

The behaviour of `floor/2`

for floats can be surprising. For example:

```
iex> Float.floor(12.52, 2)
12.51
```

One may have expected it to floor to 12.52. This is not a bug. Most decimal fractions cannot be represented as a binary floating point and therefore the number above is internally represented as 12.51999999, which explains the behaviour above.

## Examples

```
iex> Float.floor(34.25)
34.0
iex> Float.floor(-56.5)
-57.0
iex> Float.floor(34.259, 2)
34.25
```

Parses a binary into a float.

If successful, returns a tuple in the form of `{float, remainder_of_binary}`

;
when the binary cannot be coerced into a valid float, the atom `:error`

is
returned.

If the size of float exceeds the maximum size of `1.7976931348623157e+308`

,
the `ArgumentError`

exception is raised.

If you want to convert a string-formatted float directly to a float,
`String.to_float/1`

can be used instead.

## Examples

```
iex> Float.parse("34")
{34.0, ""}
iex> Float.parse("34.25")
{34.25, ""}
iex> Float.parse("56.5xyz")
{56.5, "xyz"}
iex> Float.parse("pi")
:error
```

Computes `base`

raised to power of `exponent`

.

`base`

must be a float and `exponent`

can be any number.
However, if a negative base and a fractional exponent
are given, it raises `ArithmeticError`

.

It always returns a float. See `Integer.pow/2`

for
exponentiation that returns integers.

## Examples

```
iex> Float.pow(2.0, 0)
1.0
iex> Float.pow(2.0, 1)
2.0
iex> Float.pow(2.0, 10)
1024.0
iex> Float.pow(2.0, -1)
0.5
iex> Float.pow(2.0, -3)
0.125
iex> Float.pow(3.0, 1.5)
5.196152422706632
iex> Float.pow(-2.0, 3)
-8.0
iex> Float.pow(-2.0, 4)
16.0
iex> Float.pow(-1.0, 0.5)
** (ArithmeticError) bad argument in arithmetic expression
```

@spec ratio(float()) :: {integer(), pos_integer()}

Returns a pair of integers whose ratio is exactly equal to the original float and with a positive denominator.

## Examples

```
iex> Float.ratio(0.0)
{0, 1}
iex> Float.ratio(3.14)
{7070651414971679, 2251799813685248}
iex> Float.ratio(-3.14)
{-7070651414971679, 2251799813685248}
iex> Float.ratio(1.5)
{3, 2}
iex> Float.ratio(-1.5)
{-3, 2}
iex> Float.ratio(16.0)
{16, 1}
iex> Float.ratio(-16.0)
{-16, 1}
```

@spec round(float(), precision_range()) :: float()

Rounds a floating-point value to an arbitrary number of fractional digits (between 0 and 15).

The rounding direction always ties to half up. The operation is performed on the binary floating point, without a conversion to decimal.

This function only accepts floats and always returns a float. Use
`Kernel.round/1`

if you want a function that accepts both floats
and integers and always returns an integer.

## Known issues

The behaviour of `round/2`

for floats can be surprising. For example:

```
iex> Float.round(5.5675, 3)
5.567
```

One may have expected it to round to the half up 5.568. This is not a bug. Most decimal fractions cannot be represented as a binary floating point and therefore the number above is internally represented as 5.567499999, which explains the behaviour above. If you want exact rounding for decimals, you must use a decimal library. The behaviour above is also in accordance to reference implementations, such as "Correctly Rounded Binary-Decimal and Decimal-Binary Conversions" by David M. Gay.

## Examples

```
iex> Float.round(12.5)
13.0
iex> Float.round(5.5674, 3)
5.567
iex> Float.round(5.5675, 3)
5.567
iex> Float.round(-5.5674, 3)
-5.567
iex> Float.round(-5.5675)
-6.0
iex> Float.round(12.341444444444441, 15)
12.341444444444441
```

Returns a charlist which corresponds to the text representation of the given float.

It uses the shortest representation according to algorithm described in "Printing Floating-Point Numbers Quickly and Accurately" in Proceedings of the SIGPLAN '96 Conference on Programming Language Design and Implementation.

## Examples

```
iex> Float.to_charlist(7.0)
'7.0'
```

Returns a binary which corresponds to the text representation of the given float.

It uses the shortest representation according to algorithm described in "Printing Floating-Point Numbers Quickly and Accurately" in Proceedings of the SIGPLAN '96 Conference on Programming Language Design and Implementation.

## Examples

```
iex> Float.to_string(7.0)
"7.0"
```