`enum FloatingPointRoundingRule`

A rule for rounding a floating-point number.

### Cases

Round to the closest allowed value that is less than or equal to the source.

The following example shows the results of rounding numbers using this rule:

```
(5.2).rounded(.down)
// 5.0
(5.5).rounded(.down)
// 5.0
(-5.2).rounded(.down)
// -6.0
(-5.5).rounded(.down)
// -6.0
```

This rule is equivalent to the C `floor`

function and implements the
`roundToIntegralTowardNegative`

operation defined by the IEEE 754
specification.

#### Declaration

`case down`

Round to the closest allowed value; if two values are equally close, the one with greater magnitude is chosen.

This rounding rule is also known as "schoolbook rounding." The following example shows the results of rounding numbers using this rule:

```
(5.2).rounded(.toNearestOrAwayFromZero)
// 5.0
(5.5).rounded(.toNearestOrAwayFromZero)
// 6.0
(-5.2).rounded(.toNearestOrAwayFromZero)
// -5.0
(-5.5).rounded(.toNearestOrAwayFromZero)
// -6.0
```

This rule is equivalent to the C `round`

function and implements the
`roundToIntegralTiesToAway`

operation defined by the IEEE 754
specification.

#### Declaration

`case toNearestOrAwayFromZero`

Round to the closest allowed value; if two values are equally close, the even one is chosen.

This rounding rule is also known as "bankers rounding," and is the default IEEE 754 rounding mode for arithmetic. The following example shows the results of rounding numbers using this rule:

```
(5.2).rounded(.toNearestOrEven)
// 5.0
(5.5).rounded(.toNearestOrEven)
// 6.0
(4.5).rounded(.toNearestOrEven)
// 4.0
```

This rule implements the `roundToIntegralTiesToEven`

operation defined by
the IEEE 754 specification.

#### Declaration

`case toNearestOrEven`

Round to the closest allowed value whose magnitude is less than or equal to that of the source.

The following example shows the results of rounding numbers using this rule:

```
(5.2).rounded(.towardZero)
// 5.0
(5.5).rounded(.towardZero)
// 5.0
(-5.2).rounded(.towardZero)
// -5.0
(-5.5).rounded(.towardZero)
// -5.0
```

This rule is equivalent to the C `trunc`

function and implements the
`roundToIntegralTowardZero`

operation defined by the IEEE 754
specification.

#### Declaration

`case towardZero`

Round to the closest allowed value that is greater than or equal to the source.

The following example shows the results of rounding numbers using this rule:

```
(5.2).rounded(.up)
// 6.0
(5.5).rounded(.up)
// 6.0
(-5.2).rounded(.up)
// -5.0
(-5.5).rounded(.up)
// -5.0
```

This rule is equivalent to the C `ceil`

function and implements the
`roundToIntegralTowardPositive`

operation defined by the IEEE 754
specification.

#### Declaration

`case up`

Round to the closest allowed value whose magnitude is greater than or equal to that of the source.

The following example shows the results of rounding numbers using this rule:

## Declaration

`case awayFromZero`