# Documentation

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# ceil

Round toward positive infinity

## Syntax

`y = ceil(a)`

## Description

`y = ceil(a)` rounds `fi` object `a` to the nearest integer in the direction of positive infinity and returns the result in `fi` object `y`.

`y` and `a` have the same `fimath` object and `DataType` property.

When the `DataType` property of `a` is `single`, `double`, or `boolean`, the `numerictype` of `y` is the same as that of `a`.

When the fraction length of `a` is zero or negative, `a` is already an integer, and the `numerictype` of `y` is the same as that of `a`.

When the fraction length of `a` is positive, the fraction length of `y` is `0`, its sign is the same as that of `a`, and its word length is the difference between the word length and the fraction length of `a` plus one bit. If `a` is signed, then the minimum word length of `y` is `2`. If `a` is unsigned, then the minimum word length of `y` is `1`.

For complex `fi` objects, the imaginary and real parts are rounded independently.

`ceil` does not support `fi` objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0.

## Examples

### Example 1

The following example demonstrates how the `ceil` function affects the `numerictype` properties of a signed `fi` object with a word length of 8 and a fraction length of 3.

```a = fi(pi, 1, 8, 3) a = 3.1250 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 8 FractionLength: 3 y = ceil(a) y = 4 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 0 ```

### Example 2

The following example demonstrates how the `ceil` function affects the `numerictype` properties of a signed `fi` object with a word length of 8 and a fraction length of 12.

```a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 8 FractionLength: 12 y = ceil(a) y = 1 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 2 FractionLength: 0 ```

### Example 3

The functions `ceil`, `fix`, and `floor` differ in the way they round `fi` objects:

• The `ceil` function rounds values to the nearest integer toward positive infinity

• The `fix` function rounds values toward zero

• The `floor` function rounds values to the nearest integer toward negative infinity

The following table illustrates these differences for a given `fi` object `a`.

aceil(a)fix(a)floor(a)
– 2.5–2–2–3
–1.75–1–1–2
–1.25–1–1–2
–0.500–1
0.5100
1.25211
1.75211
2.5322