PHP high precision computing

One 、 There is a pit ahead

php When using operators such as addition, subtraction, multiplication and division to calculate floating-point numbers , There are often unexpected results , Especially with regard to the calculation of financial data , Caused a lot of trouble to many engineers . For example, today's work finally arrived in a case ：

$a = 2586;

$b = 2585.98;

var_dump($a-$b);

The expected result is ：float(0.02)

The actual result ：

float(0.019999999999982)

There are pits in life , Beware of everywhere

Two 、 Pit prevention strategy ：

1、 By riding 100 The way is transformed into integer addition and subtraction , And then divide by 100 Convert back ……

2、 Use number_format Convert to string , And then use （float） Strong turn back ……

3、php It provides a function library for high-precision calculation , In fact, it is born to solve the problem of floating-point calculation .

The main functions are ：

bcadd — Add two high-precision numbers

bccomp — Compare two high-precision numbers , return -1, 0, 1

bcdiv — Divide two high-precision numbers

bcmod — Find high precision digital remainder

bcmul — Multiply two high-precision numbers

bcpow — Find a high-precision digital power

bcpowmod — To find high precision digital power and modulus , It's very common in number theory

bcscale — Configure default decimal places , It's equivalent to Linux bc Medium ”scale=”

bcsqrt — Find the square root of high precision figures

bcsub — Subtract two high-precision numbers

The first two rogue methods are not tested , Use bcsub Test the third example of subtracting two numbers ,

First look at bcsub usage （ From official website ）

string bcsub ( string $left_operand , string $right_operand [, int $scale = int ] )

Parameters

left_operand Left operand of string type .

right_operand Right operand of string type .

scale This optional parameter is used to set the number of decimal places after the decimal point in the result . You can also use bcscale() To set the global default decimal places , For all functions .

Return value Returns the result of subtraction as a string .

Test code ：

var_dump(bcsub($a,$b,2));

result

0.02

For other functions, please refer to PHP Official website

3、 ... and 、 Why are there pits ：

php Of bug? No , This is a problem that almost all languages encounter , Therefore, most languages basically provide class libraries or function libraries for accurate calculation .

To understand why , First of all, we need to know the representation of floating-point numbers (IEEE 754):

Floating point numbers , With 64 The length of bits ( Double precision ) For example , Will be used 1 Bit sign bit (E), 11 Exponential position (Q), 52 Potential mantissa (M) Express ( altogether 64 position ).

Sign bit ： The highest bit indicates the positive and negative of the data ,0 It means a positive number ,1 A negative number .

Exponential position ： Represent data with 2 The power of the bottom , The exponent is represented by an offset code

mantissa ： Represents the significant number after the decimal point of the data .

The key point here is , The representation of decimals in binary , How to convert decimal into binary ？

The algorithm is multiplied by 2 Until there are no decimals . Here's an example ,0.9 Expressed as a binary number

0.9*2=1.8 Take the whole part 1

0.8(1.8 Decimal part of )*2=1.6 Take the whole part 1

0.6*2=1.2 Take the whole part 1

0.2*2=0.4 Take the whole part 0

0.4*2=0.8 Take the whole part 0

0.8*2=1.6 Take the whole part 1

0.6*2=1.2 Take the whole part 0

.........

0.9 Binary representation as ( From the top down ): 1100100100100......

Be careful ： The above calculation cycle , in other words *2 It's never possible to eliminate the decimal part , This algorithm will go on indefinitely . Obviously , The binary representation of decimals is sometimes impossible to be exact . In fact, it's very simple , Can decimal system accurately express 1/3 Well ？ The binary system also can't express exactly 1/10. This explains why floating-point subtraction occurs " It can't be reduced " The loss of accuracy problem .

let me put it another way ： We see decimal decimals , What is stored in the computer is not an exact number , It's impossible to be accurate . So there are unexpected results after digital addition, subtraction, multiplication and division .

Four 、 Pit prevention tips

For the above reasons , So never believe that floating-point results are accurate to the last place , Never compare two floating-point numbers for equality . If higher precision is really needed , You should use any precision mathematical function or gmp function