PHP: Understanding scientific notation (e.g. 1.2e3)

Introduction

Grasping the concept of scientific notation in PHP enhances the ability to handle very large or small numbers efficiently. This tutorial will guide you through the basics to more advanced uses of scientific notation in PHP.

Understanding Scientific Notation

In scientific notation, a number is represented as a product of a number (between 1 and 10) and a power of ten. In PHP, this is written in a shorthand format using the letter ‘e’, where ‘e’ is short for exponent. For instance, 1.2e3 stands for 1.2 * 10³, or 1200.

$a = 1.2e3;
echo $a; // Outputs: 1200

This notation is especially useful when dealing with very large or very small numbers that may be cumbersome to write out in full.

Basic Usage in PHP

PHP understands both lowercase (e) and uppercase (E) to represent scientific notation. To use scientific notation in PHP, follow this structure:

$veryLargeNumber = 5e9;
echo $veryLargeNumber; // Outputs: 5000000000
$verySmallNumber = 5e-9;
echo $verySmallNumber; // Outputs: 0.000000005

It’s important to note that PHP automatically converts numbers in scientific notation into their corresponding float representations.

Floating Point Precision

One of the complexities of working with floating-point numbers is precision. PHP has a default precision of 14 which you can adjust using ini_set().

ini_set('precision', 20);
$number = 2.5e-10;
echo $number; // Outputs: 2.5e-10 with increased precision

Increasing the precision allows more exact representation of numbers but can lead to slower computations and increased memory usage.

Converting to Scientific Notation

To convert a standard float number to scientific notation, you can use the sprintf() function or number_format() depending on your preference and requirements:

$num = 123456789123456;
echo sprintf('%.4e', $num); // Outputs: 1.2346e+14
echo number_format($num, 0, '', ''); // Outputs: 123456789123456

However, keep in mind that sprintf() return scientific notation as a string, which may not be suitable for further calculations.

Multiplying and Dividing in Scientific Notation

Multiplying and dividing numbers in scientific notation works just like with normal floating points.

$value1 = 5e3; // 5000
$value2 = 2e4; // 20000
echo $value1 * $value2; // 1.0e+8 which is 100000000

Remember that PHP’s floating-point arithmetic follows the same rules as most programming languages and is affected by the same precision limitations.

Advanced Operations

For more advanced purposes, PHP provides a set of mathematical functions that can be applied to numbers in scientific notation:

$logarithm = log(1e3); // Natural logarithm of 1000
echo $logarithm; // Outputs: 6.9077552789821

Other functions include exp(), pow(), and many others that support float numbers and can be used with numbers written in scientific notation.

Best Practices

When using scientific notation in PHP:

• Be wary of precision and internal floating-point representation.
• Always validate your outputs to ensure correctness, especially if the scientific notation is used for display purposes.
• Ensure your code is readable by providing comments or using variables in a self-explanatory way.

Conclusion

Scientific Notation in PHP makes handling of certain numbers straightforward. Through understanding and practicing with this handy shortcut, developers can work with large-scale calculations efficiently. As always, considering precision and context is key to successful implementation.