ceil() and log() are used in mathematical computing scenarios

M66 2025-06-02

In PHP programming, when dealing with mathematical calculations, we often encounter situations where we need to round up and logarithmic operations. The ceil() function and the log() function are two very practical mathematical functions. They are used in combination in many scenarios to help us achieve more accurate results.

This article will explain in detail how to use PHP's ceil() and log() functions for mathematical calculations, and demonstrate their specific usage through sample code.

Introduction to ceil() and log() functions in PHP

ceil(float $value): float
The ceil() function is used to round upwards, that is, to return the smallest integer greater than or equal to the parameter.
log(float $value, float $base = M_E): float
The log() function is used to calculate logarithm, and the default is to calculate natural logarithm (base with e). The second parameter is optional and is used to specify the base of logarithm.

Why use ceil() and log() in combination?

Suppose we need to calculate the logarithm of a certain value based on certain data and then round the result upwards. This operation is very common when calculating the number of pages, batches, or data structure capacity in computer science.

For example, when paging is displayed, if $10$ of data is displayed per page and the total number is $95$, we need to calculate the total number of pages:

 $totalItems = 95;
$itemsPerPage = 10;
$totalPages = ceil($totalItems / $itemsPerPage); // turn out 10

If you combine ceil() when using logarithmic calculations, you can get an accurate rounding result.

Combined with examples: Calculate the minimum power number

Suppose we want to calculate a number $n$ and find the smallest integer $k$ so that $b^k \geq n$, where $b$ is the base number. This problem can be solved by logarithmic and upward rounding:

The formula is:

k = \lceil \log_b n \rceil

Use PHP to implement the following:

 <?php
function minPower($n, $base) {
    return (int) ceil(log($n, $base));
}

// Example
$n = 1000;
$base = 10;
$result = minPower($n, $base);
echo "The smallest k Make {$base}^k >= {$n} yes: " . $result;
?>

Run output:

 The smallest k Make 10^k >= 1000 yes: 3

This indicates that $10^3 = 1000$ is satisfied.

More complex application scenarios

Suppose you are designing a cache system, and the cache capacity is powered by 2. In order to ensure that the cache capacity is at least the upper limit of the number of requests, you need to calculate the power index of the cache capacity:

 <?php
function getCacheSize($requestCount) {
    // Calculate at least the power index required
    $exponent = (int) ceil(log($requestCount, 2));
    // Calculate cache capacity
    return pow(2, $exponent);
}

// Example
$requestCount = 150;
$cacheSize = getCacheSize($requestCount);
echo "To satisfy the number of requests {$requestCount}，The cache capacity should be: {$cacheSize}";
?>

Output:

 To satisfy the number of requests 150，The cache capacity should be: 256

Here we calculate the required exponent through logarithm, and then round it up with ceil() to ensure that the cache capacity is sufficient.

summary

Use the log() function to calculate logarithm, and you can flexibly process logarithm operations of various cardinalities.
Use the ceil() function to round the result upward to avoid insufficient capacity or insufficient page count due to decimals.
When combined, it can easily solve the mathematical calculation problems that need to be rounded in actual development.

For more information about PHP mathematical functions, please refer to the PHP official manual .

ceil
log