Current Location: Home> Latest Articles> The difference between the calculation result of bcsqrt function and the sqrt function

The difference between the calculation result of bcsqrt function and the sqrt function

gitbox 2025-05-27

1. Function introduction

1. sqrt() function

sqrt() is a built-in function in PHP that returns the square root of a number. The syntax is as follows:

 sqrt(float $num): float

For example:

 echo sqrt(2); // Output 1.4142135623731

This function returns a floating point number, based on the system's underlying double precision floating point number (double).

2. bcsqrt() function

bcsqrt() is a function provided by the BC Math extension to calculate square roots in high precision. The syntax is as follows:

 bcsqrt(string $operand, int $scale = 0): string

For example:

 echo bcsqrt('2', 50); 
// Output 1.4142135623730950488016887242096980785696718753769480732

Unlike sqrt() , bcsqrt() returns a string type value, which can specify the number of decimal places ( scale parameter) of the result.

2. The accuracy difference of calculation results

The floating point numbers used by sqrt() have natural limitations in terms of accuracy. The floating point accuracy of PHP is generally around 14 bits, which is suitable for most daily application scenarios. However, in scenarios involving finance, scientific computing or encryption algorithms, limited accuracy will lead to inaccurate results.

bcsqrt() is a high-precision mathematical operation based on strings, and the accuracy is completely controlled by the developer. For example, we can easily calculate the square root of a 100 decimal place, which is crucial for programs that require precise calculations.

Comparative example:

 $num = '2';

echo 'sqrt: ' . sqrt((float)$num) . PHP_EOL;
echo 'bcsqrt: ' . bcsqrt($num, 100) . PHP_EOL;

The output may be as follows:

 sqrt: 1.4142135623731
bcsqrt: 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573

It can be seen that the results provided by bcsqrt() are much more accurate than sqrt() .

3. Summary of the advantages of bcsqrt()

  1. High-precision calculation <br> Allow developers to control the accuracy of decimals by themselves to avoid floating point errors.

  2. Higher stability <br> For very small or very large numbers, bcsqrt() behaves more stably and is less prone to overflow or rounding errors.

  3. Wide range of application <br> It is particularly important in applications involving financial operations (such as interest calculation, currency exchange) and scientific engineering.

  4. Type Safety <br> The return value is a string, which is conducive to maintaining the integrity and consistency of the original data and avoiding floating-point rounding errors.

4. Application scenario example: High-precision interest rate calculation

Suppose we have a cryptocurrency application that requires complex interest rate calculations for user deposits. In this scenario, we cannot tolerate any accuracy error.

 $principal = '10000.00';
$rate = '0.05'; // 5%
$years = '3';

// Calculate the final compound interest value：FV = P * (1 + r)^n
$growth = bcpow(bcadd('1', $rate, 10), $years, 20);
$final = bcmul($principal, $growth, 20);

echo 'Final amount after 3 years: ' . $final;

The above code completely avoids floating point calculations, ensures the accuracy of interest calculations, and is suitable for the financial application module on https://gitbox.net .

Related