Functions for working with floating-point numbers.
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.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:
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:
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.
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.
precision_range() :: 0..15
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.
iex> Float.ceil(34.25) 35.0 iex> Float.ceil(-56.5) -56.0 iex> Float.ceil(34.251, 2) 34.26
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.
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.
iex> Float.floor(34.25) 34.0 iex> Float.floor(-56.5) -57.0 iex> Float.floor(34.259, 2) 34.25
parse(binary()) :: {float(), binary()} | :error
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.
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
ratio(float()) :: {integer(), pos_integer()}
Returns a pair of integers whose ratio is exactly equal to the original float and with a positive denominator.
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}
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.
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.
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
to_charlist(float()) :: charlist()
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.
iex> Float.to_charlist(7.0) '7.0'
to_string(float()) :: String.t()
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.
iex> Float.to_string(7.0) "7.0"
© 2012 Plataformatec
Licensed under the Apache License, Version 2.0.
https://hexdocs.pm/elixir/1.11.2/Float.html