Floating point calculation problem in php_PHP tutorial

If you use PHP’s +-*/ to calculate floating point numbers, you may encounter some problems with incorrect calculation results. For example, echo intval(0.58*100); will print 57 instead of 58. This is actually It is a bug that the underlying binary of the computer cannot accurately represent floating point numbers. It is cross-language. I also encountered this problem when using Python. Therefore, basically most languages ​​​​provide class libraries or function libraries for precise calculations. For example, PHP has a BC high-precision function library. Below, PHP training teacher Dane will introduce the use of some commonly used BC high-precision functions.

Example

代码如下

Why is the output 57? Is it a PHP bug?

I believe that many students have had such questions, because there are many people asking me similar questions, not to mention that people often ask on bugs.php.net...

To understand this reason, first we need to know the representation of floating point numbers (IEEE 754):

Floating point numbers, taking 64-bit length (double precision) as an example, will be represented by 1 sign bit (E), 11 exponent bits (Q), and 52-bit mantissa (M) (a total of 64 bits).

Sign bit: The highest bit represents the sign of the data, 0 represents a positive number, and 1 represents a negative number.

Exponent bit: represents the data raised to the power of base 2, and the exponent is represented by an offset code

Mantissa: Indicates the significant digits after the decimal point of the data.

The key point here is the representation of decimals in binary. As for how decimals are represented in binary, you can search on Baidu. I won’t go into details here. The key thing we need to understand is that for binary representation, 0.58 is infinite. Long values ​​(numbers below omit the implicit 1)..

The binary representation of 0.58 (52 bits) is basically: 00101000111101011100001010001111010111000010100011110.57 The binary representation (52 bits) is basically: 001000111101011100001010001 111010111000010100011110 And the binary numbers of the two, if calculated only through these 52 bits, are: www.111cn. net

　0.58 -> 0.579999999999999960.57 -> 0.5699999999999999 As for the specific floating point multiplication of 0.58 * 100, we do not consider it in detail. Those who are interested can look at it (Floating point), we will look at it vaguely with mental arithmetic... 0.58 * 100 = 57.999999999

Then if you intval it, it will naturally be 57…

It can be seen that the key point of this problem is: "Your seemingly finite decimal is actually infinite in the binary representation of the computer"

So, don’t think this is a PHP bug anymore, this is what it is…

PHP floating point type has an inaccuracy in +-*%/

For example:

　1.

　$a = 0.1;

　$b = 0.7;

　var_dump(($a + $b) == 0.8);

The printed value is boolean false

Why is this? The PHP manual has the following warning message for floating point numbers:

Warning

Floating point precision

Apparently simple decimal fractions like 0.1 or 0.7 cannot be converted to the internal binary format without losing a bit of precision. This can lead to confusing results: for example, floor((0.1+0.7)*10) will usually return 7 instead of the expected 8, because the internal representation of the result is something like 7.9999999999….

This is related to the fact that it is impossible to express certain decimal fractions accurately with a finite number of digits. For example, 1/3 in decimal becomes 0.3333333. . .

So never believe that the floating point number result is accurate to the last digit, and never compare whether two floating point numbers are equal. If you really need higher precision, you should use arbitrary precision math functions or the gmp function

The code is as follows
代码如下
$a = 0.1; $b = 0.7; var_dump(bcadd($a,$b,2) == 0.8);

$a = 0.1;
$b = 0.7;
var_dump(bcadd($a,$b,2) == 0.8);

bcadd — Add two high-precision numbers

bccomp — Compares two high-precision numbers, returns -1, 0, 1

bcdiv — divide two high-precision numbers

bcmod — Find the remainder of a high-precision number

bcmul — Multiply two high-precision numbers

bcpow — Find the power of high-precision numbers

bcpowmod — Find high-precision numerical power and modulus, very commonly used in number theory

bcscale — Configure the default number of decimal points, which is equivalent to "scale="

in Linux bc

bcsqrt — Find the square root of a high-precision number

bcsub — Subtract two high-precision numbers

Organized some examples

PHP BC high-precision function library includes: addition, comparison, division, subtraction, remainder, multiplication, nth power, configure the default number of decimal points, and square. These functions are more useful when it comes to monetary calculations, such as e-commerce price calculations.

代码如下

/**   * 两个高精度数比较   *    * @access global   * @param float $left   * @param float $right   * @param int $scale 精确到的小数点位数   *    * @return int $left==$right 返回 0 | $left$right 返回 1   */ var_dump(bccomp($left=4.45, $right=5.54, 2)); // -1     /**   * 两个高精度数相加   *    * @access global   * @param float $left   * @param float $right   * @param int $scale 精确到的小数点位数   *    * @return string    */ var_dump(bcadd($left=1.0321456, $right=0.0243456, 2)); //1.04     /**   * 两个高精度数相减   *    * @access global   * @param float $left   * @param float $right   * @param int $scale 精确到的小数点位数   *    * @return string    */ var_dump(bcsub($left=1.0321456, $right=3.0123456, 2)); //-1.98     /**   * 两个高精度数相除   *    * @access global   * @param float $left   * @param float $right   * @param int $scale 精确到的小数点位数   *    * @return string    */ var_dump(bcdiv($left=6, $right=5, 2)); //1.20    /**   * 两个高精度数相乘   *    * @access global   * @param float $left   * @param float $right   * @param int $scale 精确到的小数点位数   *    * @return string    */ var_dump(bcmul($left=3.1415926, $right=2.4569874566, 2)); //7.71    /**   * 设置bc函数的小数点位数   *    * @access global   * @param int $scale 精确到的小数点位数   *    * @return void    */  bcscale(3); var_dump(bcdiv('105', '6.55957'));  // 16.007

Note: Regarding the number of digits set, the excess is discarded instead of rounded.

http://www.bkjia.com/PHPjc/730239.htmlwww.bkjia.comtruehttp: //www.bkjia.com/PHPjc/730239.htmlTechArticleIf you use PHP’s +-*/ to calculate floating point numbers, you may encounter some problems with incorrect calculation results. , for example, echo intval(0.58*100); will print 57 instead of 58. This is actually the bottom of the computer...