How to avoid statistical errors caused by floating point accuracy?

Floating point accuracy problems are a common pitfall during programming, especially when it comes to mathematical calculations. Floating point numbers are represented in computers in a limited way, which can lead to subtle errors when performing numerical calculations. In PHP, we usually encounter floating point accuracy problems, especially when it comes to statistics and calculations. So, how can we avoid statistical errors caused by floating point accuracy problems? This article will discuss how to solve these problems and ensure that the statistical results are accurate when using PHP's array_count_values ​​function.

1. Overview of floating point accuracy problems

Floating point accuracy problems are usually caused by limitations in the representation of floating point numbers inside the computer. Since computers can only represent floating-point numbers in finite memory, and the accuracy of floating-point numbers is finite, this means that floating-point numbers may not be accurately represented when performing certain calculations. For example, expressing 0.1 + 0.2 may result in an approximation, rather than an exact 0.3 .

Such problems are particularly important in the statistical process, because any subtle error can lead to deviations in the final result and affect the accuracy of data analysis.

2. Common ways to avoid floating point accuracy problems

In order to avoid errors caused by floating point accuracy problems, we can adopt the following methods:

1. Use integers instead of floating-point numbers : If possible, convert the floating-point number into integers for calculation. For example, if you need to deal with the amount, you can convert it into "minutes" instead of "member", which can avoid the accuracy of floating point numbers.

    $amount = 0.1 * 100;  // Become an integer
   $amount = round($amount);  // Avoid floating errors
   

2. Using bcmath function : PHP provides bcmath extension, which is specially used for high-precision mathematical calculations, which can avoid the accuracy of floating-point numbers. Through this expansion, we can accurately control the number of digits after the decimal point, thereby avoiding floating errors.

    $result = bcadd('0.1', '0.2', 2);  // usebcmathFunction calculation
   echo $result;  // Output 0.3
   

3. Set precision : The ini_set() function in PHP allows us to set the output precision of floating point numbers. By setting higher accuracy, we can reduce the impact of floating point error in some application scenarios.

    ini_set('precision', 14);
   

3. Ensure the array_count_values ​​statistical results are accurate

array_count_values ​​is a very useful function in PHP. It can count the occurrences of all values ​​in an array and return an associative array. The key of the array is the value and the value of the array is the number of occurrences of the value.

However, floating point accuracy issues may affect the statistical results of the array_count_values ​​function, especially when including floating point values ​​in an array. To ensure accurate statistical results, the following measures are recommended:

1. Rounding floating point values : For floating point values, you can round before calling array_count_values . Use the round() function to round the floating point value to a certain number of decimal places to ensure consistency of the statistical results.

    $numbers = [0.1, 0.2, 0.1, 0.2, 0.3];
   $roundedNumbers = array_map(function($value) {
       return round($value, 2);
   }, $numbers);
   
   $counts = array_count_values($roundedNumbers);
   print_r($counts);
   

   In this way, even if there are slight errors in the calculation of floating point numbers, the final statistical results will be accurate.

2. Unified formatting of floating point values : If the floating point values ​​in the array contain many decimal places, and you only care about the accuracy of a certain decimal place, you can first format these floating point values ​​into a unified format before counting.

    $numbers = [0.1, 0.1000000001, 0.2000000001];
   $formattedNumbers = array_map(function($value) {
       return number_format($value, 2, '.', '');
   }, $numbers);
   
   $counts = array_count_values($formattedNumbers);
   print_r($counts);
   

3. Handle large-scale floating errors : If there are many floating errors in the data, you can consider limiting the floating range to a certain range to reduce the impact of floating errors on statistical results.

    $numbers = [0.1000001, 0.1000002, 0.2000001, 0.2000002];
   $adjustedNumbers = array_map(function($value) {
       return round($value, 6);  // Only six decimal places are retained
   }, $numbers);
   
   $counts = array_count_values($adjustedNumbers);
   print_r($counts);
   

4. Summary

In PHP, floating point accuracy problems are an important reason for statistical errors. When using array_count_values ​​for statistics, slight errors in floating-point numbers may affect the final result. Therefore, we can avoid this problem in the following ways:

• Convert floating point numbers to integers for processing.

• Use high-precision bcmath extensions.

• Round or format floating point numbers to ensure consistency.

By taking these measures, we can ensure the accuracy of statistical results and avoid problems caused by floating errors.