Are floating point operations in PHP accurate?

No, there are errors in floating point operations under PHP. In PHP, floating point numbers have limited precision; although depending on the system, PHP generally uses the IEEE 754 double precision format, the maximum relative error due to rounding is "1.11e-16"; non-basic math operations may give A larger error will occur, and the error propagation when performing composite operations must be taken into account.

The operating environment of this tutorial: windows7 system, PHP8 version, DELL G3 computer

The "pot" of floating-point number operations ”

//加
$a = 0.1;
$b = 0.7;
$c = intval(($a + $b) * 10);
echo $c."<br>";
//输出：7

//减
$a = 100;
$b = 99.98;
$c = $a - $b;
echo $c."<br>";
//输出：0.019999999999996

//乘
$a = 0.58;
$b = 100;
$c = intval($a * $b);
echo $c."<br>";
//输出：57

//除
$a = 0.7;
$b = 0.1;
$c = intval($a / $b);
echo $c."<br>";
//输出：6

The above result is obviously not what we want!

The PHP official manual explains it as follows:

Floating point numbers have limited precision. Although it depends on the system, PHP usually uses the IEEE 754 double format, so the maximum relative error due to rounding is 1.11e-16. Non-basic mathematical operations may give larger errors, and error propagation when doing compound operations needs to be taken into account. Never trust a floating-point result to the last digit, and never compare two floating-point numbers for equality. If you really need higher precision, you should use the arbitrary precision math function or the gmp function.

The key here is that the decimal of the floating point number is expressed in binary. The process is as follows:

• Multiply the decimal by 2 and take the integer part to represent the first digit;
• Multiply the decimal part by 2, take the integer part to represent the second digit;
• Multiply the decimal part by 2, take the integer part to represent the third digit;
• .. . And so on, until the decimal part is 0;

Example: 0.58

• 0.58 * 2 = 1.16 ---> 1
• 0.16 * 2 = 0.32 ---> 0
• 0.32 * 2 = 0.64 ---> 0
• 0.64 * 2 = 1.28 ---> 1
• 0.28 * 2 = 0.56 ---> 0
• 0.56 * 2 = 1.12 ---> 1
• 0.12 * 2 = 0.24 ---> 0
• 0.24 * 2 = 0.48 ---> 0
• 0.48 * 2 = 0.96 ---> 0
• 0.96 * 2 = 1.92 ---> 1
• ...

We will get an infinite loop of binary decimals:

0.1001010001...

There is a loop in the decimal part, and the limited binary digits cannot be accurate represents a decimal, which is the reason for errors in decimal operations.

Next, I will introduce to you Arbitrary precision mathematical functions.

Arbitrary-precision math functions

For arbitrary-precision math, PHP provides binary calculations that support numbers of any size and precision represented by strings.

BCMath: BC is the abbreviation of Binary Calculator.

Official manual: http://php.net/manual/zh/book.bc.php

Before using it, please confirm whether bcmath has been installed .

//加
$a = 0.1;
$b = 0.7;
$c = intval(bcadd($a, $b, 1) * 10);
echo $c."<br>";
//输出：8

//减
$a = 100;
$b = 99.98;
$c = bcsub($a, $b, 2);
echo $c."<br>";
//输出：0.02

//乘
$a = 0.58;
$b = 100;
$c = intval(bcmul($a, $b));
echo $c."<br>";
//输出：58

//除
$a = 0.7;
$b = 0.1;
$c = intval(bcdiv($a, $b));
echo $c."<br>";
//输出：7

In addition to addition, subtraction, multiplication and division, bcmath also provides the following methods:

• bccomp Compares two arbitrary-precision numbers
• bcmod Modulo an arbitrary-precision number
• bcpow The power of arbitrary precision numbers
• bcpowmod The modulus of the power of high-precision numbers
• bcscale Sets the default decimal point retention digits for all bc math functions
• bcsqrt The quadratic root of arbitrary precision numbers

Common numerical processing solutions

Rounding method (rounding down)

echo floor(5.1);
//输出：5

echo floor(8.8);
//输出：8

Rounding method (rounding up)

echo ceil(5.1);
//输出：6

echo ceil(8.8);
//输出：9

Ordinary rounding method

echo round(5.1);
//输出：5

echo round(8.8);
//输出：9

//保留两位小数并且进行四舍五入
echo round(5.123, 2);
//输出：5.12

echo round(8.888, 2);
//输出：8.89

//保留两位小数并且不进行四舍五入
echo substr(round(5.12345, 3), 0, -1);
//输出：5.12

echo substr(round(8.88888, 3), 0, -1);
//输出：8.88

Bank Family rounding method

Consider rounding to five. If the last five is not empty, add one. If the last five is empty, look at the odd or even number. If the first five is even, it should be discarded. If the first five is odd, add one. .

Retain two decimal places, for example:

• 1.2849 = 1.28 -> Round
• 1.2866 = 1.29 -> Six entries
• 1.2851 = 1.29 -> If the last five is not empty, add one
• 1.2850 = 1.28 -> If the last five is empty, look at the odd or even number, and if the first five is even, discard it
• 1.2750 = 1.28 -> ; If the last five is empty, look at the odd and even numbers, and if the first five are odd, then advance to one

The implementation code is as follows:

echo round(1.2849, 2, PHP_ROUND_HALF_EVEN);
//输出：1.28

echo round(1.2866, 2, PHP_ROUND_HALF_EVEN);
//输出：1.29

echo round(1.2851, 2, PHP_ROUND_HALF_EVEN);
//输出：1.29

echo round(1.2850, 2, PHP_ROUND_HALF_EVEN);
//输出：1.28

echo round(1.2750, 2, PHP_ROUND_HALF_EVEN);
//输出：1.28

For more round usage instructions, please check the official manual: http ://php.net/manual/zh/function.round.php

Numeric formatting (thousands grouping)

Apply to the display of amounts , such as the bank card balance that we often look at.

echo number_format('10000.98', 2, '.', ',');
//输出：10,000.98

echo number_format('340888999', 2, '.', ',');
//输出：340,888,999.00

Extension

MySQL floating point field

In MySQL, there is also a floating point type when creating table fields.

Floating-point number types include single-precision floating-point numbers (float) and double-precision floating-point numbers (double).

Similarly, it is not recommended to use floating point number type! ! !

There are errors in floating-point numbers. When we use precision-sensitive data, we should use fixed-point numbers (decimal) for storage.

Summary

Through the issue of floating-point number precision, we learned that decimals of floating-point numbers are represented in binary.

shared the use of PHP arbitrary precision mathematical functions to perform high-precision operations.

At the same time, common numerical processing solutions are shared, such as rounding, rounding, banker's rounding, numerical formatting, etc.

Finally, let’s think of MySQL’s float through PHP’s float.

In the future, when using floating point calculations, you must be cautious, details determine success or failure.

Recommended learning: "PHP Video Tutorial"

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