# Decimal v1.5.0 Decimal View Source

Decimal arithmetic on arbitrary precision floating-point numbers.

A number is represented by a signed coefficient and exponent such that: ```
sign
* coefficient * 10 ^ exponent
```

. All numbers are represented and calculated
exactly, but the result of an operation may be rounded depending on the
context the operation is performed with, see: `Decimal.Context`

. Trailing
zeros in the coefficient are never truncated to preserve the number of
significant digits unless explicitly done so.

There are also special values such as NaN (not a number) and ±Infinity.
-0 and +0 are two distinct values.
Some operation results are not defined and will return NaN.
This kind of NaN is quiet, any operation returning a number will return
NaN when given a quiet NaN (the NaN value will flow through all operations).
The other kind of NaN is signalling which is the value that can be reached
in `result`

field on `Decimal.Error`

when the result is NaN. Any operation
given a signalling NaN return will signal `:invalid_operation`

.

Exceptional conditions are grouped into signals, each signal has a flag and a
trap enabler in the context. Whenever a signal is triggered it’s flag is set
in the context and will be set until explicitly cleared. If the signal is trap
enabled `Decimal.Error`

will be raised.

## Specifications

This implementation follows the above standards as closely as possible. But at some places the implementation diverges from the specification. The reasons are different for each case but may be that the specification doesn’t map to this environment, ease of implementation or that API will be nicer. Still, the implementation is close enough that the specifications can be seen as additional documentation that can be used when things are unclear.

The specification models the sign of the number as 1, for a negative number,
and 0 for a positive number. Internally this implementation models the sign as
1 or -1 such that the complete number will be ```
sign * coefficient *
10 ^ exponent
```

and will refer to the sign in documentation as either *positive*
or *negative*.

There is currently no maximum or minimum values for the exponent. Because of that all numbers are “normal”. This means that when an operation should, according to the specification, return a number that “underflow” 0 is returned instead of Etiny. This may happen when dividing a number with infinity. Additionally, overflow, underflow and clamped may never be signalled.

# Link to this section Summary

## Types

The coefficient of the power of `10`

. Non-negative because the sign is stored separately in `sign`

The exponent to which `10`

is raised

`1`

for positive`-1`

for negative

This implementation models the `sign`

as `1`

or `-1`

such that the complete number will be: `sign * coef * 10 ^ exp`

## Functions

The absolute value of given number. Sets the number’s sign to positive

Adds two numbers together

Compares two numbers numerically. If the first number is greater than the second
`:gt`

is returned, if less than `:lt`

is returned, if both numbers are equal
`:eq`

is returned

Compares two numbers numerically. If the first number is greater than the second
`#Decimal<1>`

is returned, if less than `#Decimal<-1>`

is returned. Otherwise,
if both numbers are equal `#Decimal<0>`

is returned. If either number is a quiet
NaN, then that number is returned

Returns `true`

if argument is a decimal number, otherwise `false`

Divides two numbers

Divides two numbers and returns the integer part

Compares two numbers numerically and returns `true`

if they are equal,
otherwise `false`

Creates a new decimal number from a floating point number

Gets the process’ context

Returns `true`

if number is ±Infinity, otherwise `false`

Compares two values numerically and returns the maximum. Unlike most other
functions in `Decimal`

if a number is NaN the result will be the other number.
Only if both numbers are NaN will NaN be returned

Compares two values numerically and returns the minimum. Unlike most other
functions in `Decimal`

if a number is NaN the result will be the other number.
Only if both numbers are NaN will NaN be returned

Negates the given number

Multiplies two numbers

Returns `true`

if number is NaN, otherwise `false`

Check if given number is negative

Creates a new decimal number from an integer or a string representation

Creates a new decimal number from the sign, coefficient and exponent such that
the number will be: `sign * coefficient * 10 ^ exponent`

Parses a binary into a decimal

Applies the context to the given number rounding it to specified precision

Check if given number is positive

Reduces the given number. Removes trailing zeros from coefficient while keeping the number numerically equivalent by increasing the exponent

Remainder of integer division of two numbers. The result will have the sign of the first number

Rounds the given number to specified decimal places with the given strategy (default is to round to nearest one). If places is negative, at least that many digits to the left of the decimal point will be zero

Set the process’ context

Subtracts second number from the first. Equivalent to `Decimal.add/2`

when the
second number’s sign is negated

Returns the decimal converted to a float

Returns the decimal represented as an integer

Converts given number to its string representation

Update the process’ context

Runs function with given context

# Link to this section Types

coefficient() :: non_neg_integer() | :qNaN | :sNaN | :inf

The coefficient of the power of `10`

. Non-negative because the sign is stored separately in `sign`

.

`non_neg_integer`

- when the`t`

represents a number, instead of one of the special values below.`:qNaN`

- a quiet NaN was produced by a previous operation. Quiet NaNs propagate quietly, unlike signaling NaNs that return errors (based on the`Decimal.Context`

).`:sNaN`

- signalling NaN that indicated an error occurred that should stop the next operation with an error (based on the`Decimal.Context`

).`:inf`

- Infinity.

The exponent to which `10`

is raised.

rounding() :: :down | :half_up | :half_even | :ceiling | :floor | :half_down | :up

`1`

for positive`-1`

for negative

signal() :: :invalid_operation | :division_by_zero | :rounded | :inexact

t() :: %Decimal{coef: coefficient(), exp: exponent(), sign: sign()}

This implementation models the `sign`

as `1`

or `-1`

such that the complete number will be: `sign * coef * 10 ^ exp`

.

`coef`

- the coefficient of the power of`10`

.`exp`

- the exponent of the power of`10`

.`sign`

-`1`

for positive,`-1`

for negative.

# Link to this section Functions

The absolute value of given number. Sets the number’s sign to positive.

Adds two numbers together.

## Exceptional conditions

- If one number is -Infinity and the other +Infinity
`:invalid_operation`

will be signalled.

## Examples

```
iex> Decimal.add(1, "1.1")
#Decimal<2.1>
iex> Decimal.add(1, "Inf")
#Decimal<Infinity>
```

Compares two numbers numerically. If the first number is greater than the second
`:gt`

is returned, if less than `:lt`

is returned, if both numbers are equal
`:eq`

is returned.

Neither number can be a NaN. If you need to handle quiet NaNs, use `compare/2`

.

## Examples

```
iex> Decimal.cmp("1.0", 1)
:eq
iex> Decimal.cmp("Inf", -1)
:gt
```

Compares two numbers numerically. If the first number is greater than the second
`#Decimal<1>`

is returned, if less than `#Decimal<-1>`

is returned. Otherwise,
if both numbers are equal `#Decimal<0>`

is returned. If either number is a quiet
NaN, then that number is returned.

## Examples

```
iex> Decimal.compare("1.0", 1)
#Decimal<0>
iex> Decimal.compare("Inf", -1)
#Decimal<1>
```

Returns `true`

if argument is a decimal number, otherwise `false`

.

Divides two numbers.

## Exceptional conditions

- If both numbers are ±Infinity
`:invalid_operation`

is signalled. - If both numbers are ±0
`:invalid_operation`

is signalled. - If second number (denominator) is ±0
`:division_by_zero`

is signalled.

## Examples

```
iex> Decimal.div(3, 4)
#Decimal<0.75>
iex> Decimal.div("Inf", -1)
#Decimal<-Infinity>
```

Divides two numbers and returns the integer part.

## Exceptional conditions

- If both numbers are ±Infinity
`:invalid_operation`

is signalled. - If both numbers are ±0
`:invalid_operation`

is signalled. - If second number (denominator) is ±0
`:division_by_zero`

is signalled.

## Examples

```
iex> Decimal.div_int(5, 2)
#Decimal<2>
iex> Decimal.div_int("Inf", -1)
#Decimal<-Infinity>
```

Integer division of two numbers and the remainder. Should be used when both
`div_int/2`

and `rem/2`

is needed. Equivalent to: ```
{Decimal.div_int(x, y),
Decimal.rem(x, y)}
```

.

## Exceptional conditions

- If both numbers are ±Infinity
`:invalid_operation`

is signalled. - If both numbers are ±0
`:invalid_operation`

is signalled. - If second number (denominator) is ±0
`:division_by_zero`

is signalled.

## Examples

```
iex> Decimal.div_rem(5, 2)
{Decimal.new(2), Decimal.new(1)}
```

Compares two numbers numerically and returns `true`

if they are equal,
otherwise `false`

.

## Examples

```
iex> Decimal.equal?("1.0", 1)
true
iex> Decimal.equal?(1, -1)
false
```

Creates a new decimal number from a floating point number.

Floating point numbers will be converted to decimal numbers with
`:io_lib_format.fwrite_g/1`

. Since this conversion is not exact it is
recommended to give an integer or a string via `new/1`

instead.

## Examples

```
iex> Decimal.from_float(3.14)
#Decimal<3.14>
```

Gets the process’ context.

Returns `true`

if number is ±Infinity, otherwise `false`

.

Compares two values numerically and returns the maximum. Unlike most other
functions in `Decimal`

if a number is NaN the result will be the other number.
Only if both numbers are NaN will NaN be returned.

## Examples

```
iex> Decimal.max(1, "2.0")
#Decimal<2.0>
iex> Decimal.max(1, "NaN")
#Decimal<1>
iex> Decimal.max("NaN", "NaN")
#Decimal<NaN>
```

Compares two values numerically and returns the minimum. Unlike most other
functions in `Decimal`

if a number is NaN the result will be the other number.
Only if both numbers are NaN will NaN be returned.

## Examples

```
iex> Decimal.min(1, "2.0")
#Decimal<1>
iex> Decimal.min(1, "NaN")
#Decimal<1>
iex> Decimal.min("NaN", "NaN")
#Decimal<NaN>
```

Negates the given number.

## Examples

```
iex> Decimal.minus(1)
#Decimal<-1>
iex> Decimal.minus("-Inf")
#Decimal<Infinity>
```

Multiplies two numbers.

## Exceptional conditions

- If one number is ±0 and the other is ±Infinity
`:invalid_operation`

is signalled.

## Examples

```
iex> Decimal.mult("0.5", 3)
#Decimal<1.5>
iex> Decimal.mult("Inf", -1)
#Decimal<-Infinity>
```

Returns `true`

if number is NaN, otherwise `false`

.

Check if given number is negative

Creates a new decimal number from an integer or a string representation.

A decimal number will always be created exactly as specified with all digits kept - it will not be rounded with the context.

## Backus–Naur form

```
sign ::= "+" | "-"
digit ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
indicator ::= "e" | "E"
digits ::= digit [digit]...
decimal-part ::= digits "." [digits] | ["."] digits
exponent-part ::= indicator [sign] digits
infinity ::= "Infinity" | "Inf"
nan ::= "NaN" [digits] | "sNaN" [digits]
numeric-value ::= decimal-part [exponent-part] | infinity
numeric-string ::= [sign] numeric-value | [sign] nan
```

## Examples

```
iex> Decimal.new(1)
#Decimal<1>
iex> Decimal.new("3.14")
#Decimal<3.14>
```

new(1 | -1, non_neg_integer() | :qNaN | :sNaN | :inf, integer()) :: t()

Creates a new decimal number from the sign, coefficient and exponent such that
the number will be: `sign * coefficient * 10 ^ exponent`

.

A decimal number will always be created exactly as specified with all digits kept - it will not be rounded with the context.

Parses a binary into a decimal.

If successful, returns a tuple in the form of `{:ok, decimal}`

,
otherwise `:error`

.

## Examples

```
iex> Decimal.parse("3.14")
{:ok, %Decimal{coef: 314, exp: -2, sign: 1}}
iex> Decimal.parse("-1.1e3")
{:ok, %Decimal{coef: 11, exp: 2, sign: -1}}
iex> Decimal.parse("bad")
:error
```

Applies the context to the given number rounding it to specified precision.

Check if given number is positive

Reduces the given number. Removes trailing zeros from coefficient while keeping the number numerically equivalent by increasing the exponent.

Remainder of integer division of two numbers. The result will have the sign of the first number.

## Exceptional conditions

- If both numbers are ±Infinity
`:invalid_operation`

is signalled. - If both numbers are ±0
`:invalid_operation`

is signalled. - If second number (denominator) is ±0
`:division_by_zero`

is signalled.

## Examples

```
iex> Decimal.rem(5, 2)
#Decimal<1>
```

Rounds the given number to specified decimal places with the given strategy (default is to round to nearest one). If places is negative, at least that many digits to the left of the decimal point will be zero.

## Examples

```
iex> Decimal.round("1.234")
#Decimal<1>
iex> Decimal.round("1.234", 1)
#Decimal<1.2>
```

Set the process’ context.

Subtracts second number from the first. Equivalent to `Decimal.add/2`

when the
second number’s sign is negated.

## Exceptional conditions

- If one number is -Infinity and the other +Infinity
`:invalid_operation`

will be signalled.

## Examples

```
iex> Decimal.sub(1, "0.1")
#Decimal<0.9>
iex> Decimal.sub(1, "Inf")
#Decimal<-Infinity>
```

Returns the decimal converted to a float.

The returned float may have lower precision than the decimal. Fails if the decimal cannot be converted to a float.

Returns the decimal represented as an integer.

Fails when loss of precision will occur.

Converts given number to its string representation.

## Options

`:scientific`

- number converted to scientific notation.`:normal`

- number converted without a exponent.`:raw`

- number converted to its raw, internal format.

update_context((Decimal.Context.t() -> Decimal.Context.t())) :: :ok

Update the process’ context.

with_context(Decimal.Context.t(), (() -> x)) :: x when x: var

Runs function with given context.