解決JS浮點數(小數)計算加減乘除的BUG


在JavaScript中輸出下面這些數值(注意不能作為字符串輸出):0.1000000000000000000000000001(28位小數)、0.100000000000000000000000001(27位小數)、0.1000000000000000000000000456(28位小數)、0.09999999999999999999999(23位小數),顯示出來的結果都是數值0.1。又如,如果輸出1/3的有理數表達式,結果是0.3333333333333333。 document.write(.1 + .2) // 0.3000000000000004

document.write(.3 + .6) // 0.8999999999999999

Some statistics related to this famous double precision question. I used this code.

When adding all values (a+b) using a step of 0.1 (from 0.1 to 100) we have ~15% chance of precision error. Here are some examples (for full .txt results here):

0.1 + 0.2 = 0.30000000000000004
0.1 + 0.7 = 0.7999999999999999
...
1.7 + 1.9 = 3.5999999999999996
1.7 + 2.2 = 3.9000000000000004
...
3.2 + 3.6 = 6.800000000000001
3.2 + 4.4 = 7.6000000000000005

When subtracting all values (a-b where a>b) using a step of 0.1 (from 100 to 0.1) we have ~34% chance of precision error. Here are some examples (for full .txt results here):

0.6 - 0.2 = 0.39999999999999997
0.5 - 0.4 = 0.09999999999999998
...
2.1 - 0.2 = 1.9000000000000001
2.0 - 1.9 = 0.10000000000000009
...
100 - 99.9 = 0.09999999999999432
100 - 99.8 = 0.20000000000000284

*I was surprised with these 15% and 34%.. they are huge, so always use BigDecimal when precision is of big importance. With 2 decimal digits (step 0.01) the situation worsens a bit more (18% and 36%).

 
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 1 /**
 2  ** 加法函數,用來得到精確的加法結果
 3  ** 說明:javascript的加法結果會有誤差,在兩個浮點數相加的時候會比較明顯。這個函數返回較為精確的加法結果。
 4  ** 調用:accAdd(arg1,arg2)
 5  ** 返回值:arg1加上arg2的精確結果
 6  **/
 7 function accAdd(arg1, arg2) {
 8     var r1, r2, m, c;
 9     try {
10         r1 = arg1.toString().split(".")[1].length;
11     }
12     catch (e) {
13         r1 = 0;
14     }
15     try {
16         r2 = arg2.toString().split(".")[1].length;
17     }
18     catch (e) {
19         r2 = 0;
20     }
21     c = Math.abs(r1 - r2);
22     m = Math.pow(10, Math.max(r1, r2));
23     if (c > 0) {
24         var cm = Math.pow(10, c);
25         if (r1 > r2) {
26             arg1 = Number(arg1.toString().replace(".", ""));
27             arg2 = Number(arg2.toString().replace(".", "")) * cm;
28         } else {
29             arg1 = Number(arg1.toString().replace(".", "")) * cm;
30             arg2 = Number(arg2.toString().replace(".", ""));
31         }
32     } else {
33         arg1 = Number(arg1.toString().replace(".", ""));
34         arg2 = Number(arg2.toString().replace(".", ""));
35     }
36     return (arg1 + arg2) / m;
37 }
38 
39 //給Number類型增加一個add方法,調用起來更加方便。
40 Number.prototype.add = function (arg) {
41     return accAdd(arg, this);
42 };
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 1 /**
 2  ** 減法函數,用來得到精確的減法結果
 3  ** 說明:javascript的減法結果會有誤差,在兩個浮點數相減的時候會比較明顯。這個函數返回較為精確的減法結果。
 4  ** 調用:accSub(arg1,arg2)
 5  ** 返回值:arg1加上arg2的精確結果
 6  **/
 7 function accSub(arg1, arg2) {
 8     var r1, r2, m, n;
 9     try {
10         r1 = arg1.toString().split(".")[1].length;
11     }
12     catch (e) {
13         r1 = 0;
14     }
15     try {
16         r2 = arg2.toString().split(".")[1].length;
17     }
18     catch (e) {
19         r2 = 0;
20     }
21     m = Math.pow(10, Math.max(r1, r2)); //last modify by deeka //動態控制精度長度
22     n = (r1 >= r2) ? r1 : r2;
23     return ((arg1 * m - arg2 * m) / m).toFixed(n);
24 }
25 
26 // 給Number類型增加一個mul方法,調用起來更加方便。
27 Number.prototype.sub = function (arg) {
28     return accMul(arg, this);
29 };
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 1 /**
 2  ** 乘法函數,用來得到精確的乘法結果
 3  ** 說明:javascript的乘法結果會有誤差,在兩個浮點數相乘的時候會比較明顯。這個函數返回較為精確的乘法結果。
 4  ** 調用:accMul(arg1,arg2)
 5  ** 返回值:arg1乘以 arg2的精確結果
 6  **/
 7 function accMul(arg1, arg2) {
 8     var m = 0, s1 = arg1.toString(), s2 = arg2.toString();
 9     try {
10         m += s1.split(".")[1].length;
11     }
12     catch (e) {
13     }
14     try {
15         m += s2.split(".")[1].length;
16     }
17     catch (e) {
18     }
19     return Number(s1.replace(".", "")) * Number(s2.replace(".", "")) / Math.pow(10, m);
20 }
21 
22 // 給Number類型增加一個mul方法,調用起來更加方便。
23 Number.prototype.mul = function (arg) {
24     return accMul(arg, this);
25 };
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 1 /** 
 2  ** 除法函數,用來得到精確的除法結果
 3  ** 說明:javascript的除法結果會有誤差,在兩個浮點數相除的時候會比較明顯。這個函數返回較為精確的除法結果。
 4  ** 調用:accDiv(arg1,arg2)
 5  ** 返回值:arg1除以arg2的精確結果
 6  **/
 7 function accDiv(arg1, arg2) {
 8     var t1 = 0, t2 = 0, r1, r2;
 9     try {
10         t1 = arg1.toString().split(".")[1].length;
11     }
12     catch (e) {
13     }
14     try {
15         t2 = arg2.toString().split(".")[1].length;
16     }
17     catch (e) {
18     }
19     with (Math) {
20         r1 = Number(arg1.toString().replace(".", ""));
21         r2 = Number(arg2.toString().replace(".", ""));
22         return (r1 / r2) * pow(10, t2 - t1);
23     }
24 }
25 
26 //給Number類型增加一個div方法,調用起來更加方便。
27 Number.prototype.div = function (arg) {
28     return accDiv(this, arg);
29 };
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高級瀏覽器解決方法:
 
function strip(number) {
    return (parseFloat(number.toPrecision(12)));
}

 

Using 'toPrecision(12)' leaves trailing zeros which 'parseFloat()' removes. Assume it is accurate to plus/minus one on the least significant digit.

定義和用法

toPrecision() 方法可在對象的值超出指定位數時將其轉換為指數計數法。

語法

NumberObject.toPrecision(num)
參數 描述
num 必需。規定必須被轉換為指數計數法的最小位數。該參數是 1 ~ 21 之間(且包括 1 和 21)的值。有效實現允許有選擇地支持更大或更小的 num。如果省略了該參數,則調用方法 toString(),而不是把數字轉換成十進制的值。

返回值

返回 NumberObject 的字符串表示,包含 num 個有效數字。如果 num 足夠大,能夠包括 NumberObject 整數部分的所有數字,那么返回的字符串將采用定點計數法。否則,采用指數計數法,即小數點前有一位數字,小數點后有 num-1 位數字。必要時,該數字會被舍入或用 0 補足。

拋出

當 num 太小或太大時拋出異常 RangeError。1 ~ 21 之間的值不會引發該異常。有些實現支持更大范圍或更小范圍內的值。

當調用該方法的對象不是 Number 時拋出 TypeError 異常。

實例

在本例中,我們將把一個數字轉換為指數計數法:

Show 10,000 as an exponential notation:
<script type="text/javascript">
var num = new Number(10000);
document.write (num.toPrecision(4))
</script>

輸出:

Show 10,000 as an exponential notation:
1.000e+4

同時還可以使用一個https://github.com/MikeMcl/bignumber.js 插件來完成JS精度運算的BUG

Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
8 KB minified and gzipped
Simple API but full-featured
Works with numbers with or without fraction digits in bases from 2 to 64 inclusive
Replicates the toExponential, toFixed, toPrecision and toString methods of JavaScript's Number type
Includes a toFraction and a correctly-rounded squareRoot method
Supports cryptographically-secure pseudo-random number generation
No dependencies
Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
Comprehensive documentation and test set
API

If a smaller and simpler library is required see big.js. It's less than half the size but only works with decimal numbers and only has half the methods. It also does not allow NaN or Infinity, or have the configuration options of this library.

Use

In all examples below, var, semicolons and toString calls are not shown. If a commented-out value is in quotes it means toString has been called on the preceding expression.

The library exports a single function: BigNumber, the constructor of BigNumber instances.

It accepts a value of type number (up to 15 significant digits only), string or BigNumber object,

x = new BigNumber(123.4567)
y = BigNumber('123456.7e-3')
z = new BigNumber(x)
x.equals(y) && y.equals(z) && x.equals(z) // true
and a base from 2 to 64 inclusive can be specified.

x = new BigNumber(1011, 2) // "11"
y = new BigNumber('zz.9', 36) // "1295.25"
z = x.plus(y) // "1306.25"
A BigNumber is immutable in the sense that it is not changed by its methods.

0.3 - 0.1 // 0.19999999999999998
x = new BigNumber(0.3)
x.minus(0.1) // "0.2"
x // "0.3"
The methods that return a BigNumber can be chained.

x.dividedBy(y).plus(z).times(9).floor()
x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').ceil()
Many method names have a shorter alias.

x.squareRoot().dividedBy(y).toPower(3).equals(x.sqrt().div(y).pow(3)) // true
x.cmp(y.mod(z).neg()) == 1 && x.comparedTo(y.modulo(z).negated()) == 1 // true
Like JavaScript's number type, there are toExponential, toFixed and toPrecision methods

x = new BigNumber(255.5)
x.toExponential(5) // "2.55500e+2"
x.toFixed(5) // "255.50000"
x.toPrecision(5) // "255.50"
x.toNumber() // 255.5
and a base can be specified for toString.

x.toString(16) // "ff.8"
There is also a toFormat method which may be useful for internationalisation

y = new BigNumber('1234567.898765')
y.toFormat(2) // "1,234,567.90"
The maximum number of decimal places of the result of an operation involving division (i.e. a division, square root, base conversion or negative power operation) is set using the config method of the BigNumber constructor.

The other arithmetic operations always give the exact result.

BigNumber.config({ DECIMAL_PLACES: 10, ROUNDING_MODE: 4 })
// Alternatively, BigNumber.config( 10, 4 );

x = new BigNumber(2);
y = new BigNumber(3);
z = x.div(y) // "0.6666666667"
z.sqrt() // "0.8164965809"
z.pow(-3) // "3.3749999995"
z.toString(2) // "0.1010101011"
z.times(z) // "0.44444444448888888889"
z.times(z).round(10) // "0.4444444445"
There is a toFraction method with an optional maximum denominator argument

y = new BigNumber(355)
pi = y.dividedBy(113) // "3.1415929204"
pi.toFraction() // [ "7853982301", "2500000000" ]
pi.toFraction(1000) // [ "355", "113" ]
and isNaN and isFinite methods, as NaN and Infinity are valid BigNumber values.

x = new BigNumber(NaN) // "NaN"
y = new BigNumber(Infinity) // "Infinity"
x.isNaN() && !y.isNaN() && !x.isFinite() && !y.isFinite() // true
The value of a BigNumber is stored in a decimal floating point format in terms of a coefficient, exponent and sign.

x = new BigNumber(-123.456);
x.c // [ 123, 45600000000000 ] coefficient (i.e. significand)
x.e // 2 exponent
x.s // -1 sign
Multiple BigNumber constructors can be created, each with their own independent configuration which applies to all BigNumber's created from it.

// Set DECIMAL_PLACES for the original BigNumber constructor
BigNumber.config({ DECIMAL_PLACES: 10 })

// Create another BigNumber constructor, optionally passing in a configuration object
BN = BigNumber.another({ DECIMAL_PLACES: 5 })

x = new BigNumber(1)
y = new BN(1)

x.div(3) // '0.3333333333'
y.div(3) // '0.33333'
For futher information see the API reference in the doc directory.

 
分類:  JavaScript


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