# Documentation

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# `ceil`

Round up to the next integer

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

For the `ceil` function in MATLAB®, see `ceil`.

## Syntax

```ceil(`x`)
```

## Description

`ceil` rounds a number to the next larger integer.

For complex arguments, `ceil` rounds the real and the imaginary parts separately.

For real numbers and exact expressions representing real numbers, `ceil` returns integers.

For arguments that contain symbolic identifiers, `ceil` returns unevaluated function calls.

For floating-point intervals, `ceil` returns floating-point intervals containing all the results of applying `ceil` to the real or complex numbers inside the interval.

### Note

If the argument is a floating-point number of absolute value larger than 10DIGITS, the resulting integer is affected by internal non-significant digits. See Example 2.

### Note

Internally, exact numerical expressions that are neither integers nor rational numbers are approximated by floating-point numbers before rounding. Thus, the resulting integer depends on the current `DIGITS` setting. See Example 3.

## Environment Interactions

The functions are sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

Round the following real and complex numbers:

`ceil(3.5), ceil(-7/2), ceil(3 + 5/2*I)`

Round the following symbolic expression representing a number:

`ceil(PI*I + 7*sin(exp(2)))`

Rounding of expressions with symbolic identifiers produces unevaluated function calls:

` ceil(x)`

### Example 2

Rounding floating-point numbers of large absolute value is affected by internal non-significant digits:

`x := 10^30/3.0`

Note that only the first 10 decimal digits are “significant”. Further digits are subject to round-off effects caused by the internal binary representation. These “insignificant” digits are part of the integer produced by rounding:

`ceil(x)`

`delete x:`

### Example 3

Exact numerical expressions are internally converted to floating-point numbers before rounding. Consequently, the current setting of `DIGITS` can affect the result:

`x := 10^30 - exp(30)^ln(10)`

Note that the exact value of this number is 0. Floating-point evaluation is subject to severe cancellations:

```DIGITS := 10: float(x), ceil(x)```

The floating-point result is more accurate when calculated with a higher precision. The rounded values change accordingly:

```DIGITS := 20: float(x), ceil(x)```

```DIGITS := 30: float(x), ceil(x)```

`delete x, DIGITS:`

### Example 4

On floating-point intervals, `ceil` behaves as follows:

`ceil(3.5...6.7)`

This interval containa the results of `ceil(x)` for all .

Because there are finite numbers represented as `RD_INF` and `RD_NINF`, respectively, `ceil` returns very small or large representable numbers in certain cases:

`ceil(RD_NINF...RD_NINF)`

## Parameters

 `x`

## Return Values

Arithmetical expression.

`x`