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Detailed explanation of the implementation steps for calculating pi to 100 decimal places using JS
- php中世界最好的语言Original
- 2018-05-23 10:54:552610browse
This time I will bring you a detailed explanation of the implementation steps for calculating pi to 100 digits after the decimal point with JS. What are the precautions for calculating pi to 100 digits after the decimal point with JS. Here is a practical case. Let’s take a look. .
The significant digits of floating point numbers are 16. I made a large number class myself, which can store 100 significant digits and implement the basic operations of the large number class. I used it to calculate pi (circle cut method, that is, polygonal approximation), and got one hundred significant figures after the decimal point. I compared the calculation results with Machin's formula, and there was no error. It takes about 2 seconds.
The complete example is as follows:
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>js计算圆周率</title>
</head>
<body>
<script>
<!--
function BigNum(str, n, b)
{
/*
BigNum -- 大数类
私有成员：
data -- 119 位数字，放在长度为 17 的数组里，每个数组元素存放 7 位数字。
decimal_place -- 小数点的位置，从最左位开始算。
positive -- 是否是正数。
recalc() -- 为了尽可能存放最多的有效数位，去除前缀的 0，并重新计算小数点位置。
init() -- 部分初始化工作。
公有成员：
BigNum( String str, INT n, BOOL b) --
构造函数。参数：str -- 字符串，各个有效数位；n -- 整数，小数点位置，从最左位开始算，比如 BigNum("123", 2) = 12.3; BigNum("123", 0) = 0.123; BigNum("123", -2) = 0.00123；b -- 布尔值，是否是正数。
Add( BigNum num ) -- 加法。
Subtract( BigNum num ) -- 减法。
Multiply( BigNum num ) -- 乘法。
pide( BigNum num ) -- 除法。
SquareRoot() -- 平方根。
toString() -- 转换为字符串（包括小数点），以便以文本形式输出计算结果。
Clone() -- 复制。
*/
this.recalc = function() /* 去除前缀的 0，并重新计算小数点位置 */
{
for(var i = 0; i < 17; i ++)
{
if(this.data[0] != 0) break;
this.data.shift();
this.data.push(0);
this.decimal_place --;
}
}
this.init = function() /* 部分初始化工作 */
{
this.decimal_place = Math.ceil( n / 7 ); //小数点位置
this.data = new Array(17); //保存有效数位的数组
if(n % 7 > 0)
{
var arr = new Array( 8 - n % 7 );
}
else
{
var arr = new Array( 1 - n % 7 );
}
str = arr.join("0") + str;
if(str.length > 119)
{
str = str.substr(0, 119);
}
else if(str.length < 119)
{
var arr = new Array(120 - str.length);
str += arr.join("0");
}
for( var i = 0; i < 17; i ++ )
{
this.data[i] = parseInt( str.substr(i * 7, 7) , 10 );
}
}
/* 初始化开始 */
this.positive = b;
if( ! /^0*$/.test(str) )
{
this.init();
this.recalc();
}
else
{
this.data = new Array(17);
for( var i = 0; i < 17; i ++ )
{
this.data[i] = 0;
}
this.decimal_place = 0;
}
/* 初始化结束 */
this.Add = function(num) /* 加法 */
{
if(this.positive && !num.positive)
{
num.positive = true;
var result = this.Subtract(num);
num.positive = false;
return result;
}
else if(num.positive && !this.positive)
{
this.positive = true;
var result = num.Subtract(this);
this.positive = false;
return result;
}
var result = new BigNum("", 0, this.positive);
var num1,num2;
if(this.decimal_place >= num.decimal_place)
{
num1 = this;
num2 = num;
}
else
{
num1 = num;
num2 = this;
}
result.decimal_place = num1.decimal_place;
if(num1.decimal_place - num2.decimal_place >= 17)
{
for(var i = 0; i < 17; i ++)
{
result.data[i] = num1.data[i];
}
return result;
}
var nOffDec = num1.decimal_place - num2.decimal_place;
var nTmp = 0;
for( var i = 16; i >= 0; i -- )
{
var nTmp1 = i - nOffDec;
var nTmp2 = 0;
if(nTmp1 >= 0)
{
nTmp2 = num1.data[i] + num2.data[nTmp1];
}
else
{
nTmp2 = num1.data[i];
}
nTmp2 += nTmp;
nTmp = Math.floor(nTmp2 / 10000000);
result.data[i] = nTmp2 % 10000000;
}
if(nTmp > 0)
{
result.data.unshift(nTmp);
result.decimal_place ++;
}
return result;
}
this.Subtract = function(num) /* 减法 */
{
if(this.positive && !num.positive)
{
num.positive = true;
var result = this.Add(num);
num.positive = false;
return result;
}
else if(!this.positive && num.positive)
{
this.positive = true;
var result = this.Add(num);
result.positive = false;
this.positive = false;
return result;
}
else
{
var num1 = num2 = null;
var bPositive;
if(this.decimal_place > num.decimal_place)
{
num1 = this;
num2 = num;
bPositive = this.positive;
}
else if(this.decimal_place < num.decimal_place)
{
num1 = num;
num2 = this;
bPositive = !this.positive;
}
else
{
for( var i = 0; i < 17; i ++ )
{
if(this.data[i] > num.data[i])
{
num1 = this;
num2 = num;
bPositive = this.positive;
break;
}
else if(this.data[i] < num.data[i])
{
num1 = num;
num2 = this;
bPositive = !this.positive;
break;
}
}
}
if( num1 == null)
{
return new BigNum("", 0, true);
}
else
{
if(num1.decimal_place - num2.decimal_place >= 17)
{
var result = new BigNum("", 0, bPositive);
for(var i = 0; i < 17; i ++)
{
result.data[i] = num1.data[i];
}
result.decimal_place = num1.decimal_place;
return result;
}
var result = new BigNum("", 0, bPositive);
result.decimal_place = num1.decimal_place;
var nOffDec = num1.decimal_place - num2.decimal_place;
var nTmp = 0;
for( var i = 16; i >= 0; i -- )
{
var nTmp1 = i - nOffDec;
var nTmp2 = 0;
if(nTmp1 >= 0)
{
nTmp2 = 10000000 + nTmp + num1.data[i] - num2.data[nTmp1];
}
else
{
nTmp2 = 10000000 + nTmp + num1.data[i];
}
if(nTmp2 >= 10000000)
{
result.data[i] = nTmp2 - 10000000;
nTmp = 0;
}
else
{
result.data[i] = nTmp2;
nTmp = -1;
}
}
result.recalc();
return result;
}
}
}
this.Multiply = function(num) /* 乘法 */
{
var bPositive;
var nDecimalPlace = this.decimal_place + num.decimal_place - 1;
if(this.positive == num.positive)
{
bPositive = true;
}
else
{
bPositive = false;
}
var result = new BigNum("", 0, bPositive);
var nTmpData = 0;
for( var i = 16; i >= 0; i -- )
{
for( var j = 16; j >= 0; j -- )
{
if(isNaN(result.data[j + i]))
result.data[j + i] = 0;
result.data[j + i] += this.data[j] * num.data[i];
if(result.data[j + i] >= 10000000)
{
if( j + i -1 >= 0 )
{
result.data[j + i -1] += Math.floor(result.data[j + i] / 10000000);
}
else
{
nTmpData += Math.floor(result.data[j + i] / 10000000);
}
result.data[j + i] = result.data[j + i] % 10000000;
}
}
}
if(nTmpData > 0)
{
result.data.unshift(nTmpData);
result.data.pop();
nDecimalPlace ++;
}
result.decimal_place += nDecimalPlace;
return result;
}
this.pide = function(num) /* 除法 */
{
var bPositive;
var nDecimalPlace = this.decimal_place - num.decimal_place + 1;
if(this.positive == num.positive)
{
bPositive = true;
}
else
{
bPositive = false;
}
var result = new BigNum("", 0, bPositive);
var arrTemp = new Array(17);
for( var i = 0; i < 17; i ++ )
{
arrTemp[i] = this.data[i];
}
var bTest = true;
var nTest = 0;
for( var i = 0; i < 17; i ++ )
{
if(bTest)
{
nTest = Math.floor( ( arrTemp[0] * 10000000 + arrTemp[1] ) / ( num.data[0] * 10000000 + num.data[1] ) );
}
else
{
bTest = true;
}
if(nTest == 0)
{
result.data[i] = 0;
arrTemp[1] += arrTemp[0] * 10000000;
arrTemp.shift();
arrTemp.push(0);
continue;
}
var arrTemp1 = new Array(17);
for( var j = 0; j < 17; j ++ )
{
arrTemp1[j] = 0;
}
for( var j = 16; j >= 0; j -- )
{
arrTemp1[j] += nTest * num.data[j];
if(arrTemp1[j] >= 10000000)
{
if(j != 0)
{
arrTemp1[j - 1] += Math.floor( arrTemp1[j] / 10000000);
arrTemp1[j] = arrTemp1[j] % 10000000;
}
}
}
for( var j = 0; j < 17; j ++ )
{
if(arrTemp[j] < arrTemp1[j])
{
bTest = false;
break;
}
else if(arrTemp[j] > arrTemp1[j])
{
break;
}
}
if(bTest)
{
result.data[i] = nTest;
for( var j = 16; j >= 0; j -- )
{
if(arrTemp[j] >= arrTemp1[j])
{
arrTemp[j] -= arrTemp1[j];
}
else
{
arrTemp[j] = 10000000 + arrTemp[j] - arrTemp1[j];
arrTemp[j - 1] --;
}
}
}
else
{
nTest --;
i --;
continue;
}
arrTemp[1] += arrTemp[0] * 10000000;
arrTemp.shift();
arrTemp.push(0);
}
result.decimal_place = nDecimalPlace;
result.recalc();
return result;
}
this.SquareRoot = function() /* 平方根 */
{
var result = new BigNum("", 0, true);
nDecimalPlace = Math.ceil(this.decimal_place / 2);
var arrTemp = new Array(17);
for(var i = 0; i < 17; i ++)
{
arrTemp[i] = this.data[i];
}
var bTest = true;
for(var i = 0; i < 17; i ++)
{
if( i == 0 )
{
if(this.decimal_place % 2 == 0)
{
var nTemp = arrTemp[0] * 10000000 + arrTemp[1];
var nTemp1 = Math.floor( Math.sqrt( nTemp ) );
var nTemp2 = nTemp - nTemp1 * nTemp1;
arrTemp[0] = 0;
arrTemp[1] = nTemp2;
arrTemp.shift();
arrTemp.push(0);
}
else
{
var nTemp1 = Math.floor( Math.sqrt( arrTemp[0] ) );
var nTemp2 = arrTemp[0] - nTemp1 * nTemp1;
arrTemp[0] = nTemp2;
}
}
else
{
if(bTest)
{
if( i == 1 )
{
nTemp1 = Math.sqrt( (arrTemp[0] * 10000000 + arrTemp[1]) + 100000000000000 * Math.pow(result.data[0], 2) ) - 10000000 * result.data[0];
nTemp1 = Math.floor(nTemp1);
}
else
{
nTemp = result.data[0] * 10000000 + result.data[1];
nTemp1 = Math.floor( ( arrTemp[0] * 10000000 + arrTemp[1] ) / ( 2 * nTemp ) );
}
}
else
{
bTest = true;
}
var arrTemp1 = new Array(17);
var nTemp3 = 0
for( var j = i - 1; j >= 0; j -- )
{
arrTemp1[j] = result.data[j] * 2 + nTemp3;
if( arrTemp1[j] >= 10000000 && j > 0 )
{
nTemp3 = 1;
arrTemp1[j] = arrTemp1[j] % 10000000;
}
else
{
nTemp3 = 0;
}
}
arrTemp1[i] = nTemp1;
nTemp3 = 0;
for( var j = i; j >= 0; j -- )
{
arrTemp1[j] = arrTemp1[j] * nTemp1 + nTemp3;
if( arrTemp1[j] >= 10000000 && j > 0 )
{
nTemp3 = Math.floor( arrTemp1[j] / 10000000 );
arrTemp1[j] = arrTemp1[j] % 10000000;
}
else
{
nTemp3 = 0;
}
}
var arrTemp2 = new Array(17);
for( var j = 0; j < 17; j ++ )
{
arrTemp2[j] = arrTemp[j];
}
for( var j = i; j >= 0; j -- )
{
if( arrTemp2[j] >= arrTemp1[j] )
{
arrTemp2[j] -= arrTemp1[j];
}
else
{
if(j > 0)
{
arrTemp2[j] = arrTemp2[j] + 10000000 - arrTemp1[j];
arrTemp2[j - 1] --;
}
else
{
bTest = false;
break;
}
}
}
if(bTest)
{
arrTemp = arrTemp2;
}
else
{
nTemp1 --;
i --;
continue;
}
}
result.data[i] = nTemp1;
arrTemp[1] += arrTemp[0] * 10000000;
arrTemp.shift();
arrTemp.push(0);
}
result.decimal_place = nDecimalPlace;
result.recalc();
return result;
}
this.toString = function() /* 转换为字符串（包括小数点），以便以文本形式输出计算结果 */
{
var szData = "";
var szOutPut = "";
this.recalc();
for( var i = 0; i < 17; i ++ )
{
var szTmpData = this.data[i].toString()
var arr = new Array(8 - szTmpData.length);
szData += arr.join("0") + szTmpData;
}
if( /^0*$/.test(szData) )
{
return "0";
}
var n = this.decimal_place * 7;
for(var i = 0; i < 7; i++)
{
if(szData.substr(i, 1) != 0) break;
n --;
}
szData = szData.replace(/^0+/g,"");
szData = szData.substr(0, 101);
szData = szData.replace(/0+$/g,"");
if( n < 1 )
{
szOutPut = szData.substr(0, 1) +
( ( szData.length > 1 ) ? "." : "" ) +
szData.substr(1) + "e" + ( n - 1 ).toString();
}
else if(n == szData.length)
{
szOutPut = szData;
}
else if(n > szData.length)
{
szOutPut = szData.substr(0, 1) + "." + szData.substr(1) + "e+" + (n - 1).toString();
}
else
{
szOutPut = szData.substr(0, n) + "." + szData.substr(n);
}
return ( this.positive ? "" : "-" ) + szOutPut;
}
this.Clone = function() /* 复制 */
{
var result = new BigNum("", 0, true);
for( var i = 0; i < 17; i ++)
{
result.data[i] = this.data[i];
}
result.decimal_place = this.decimal_place;
result.positive = this.positive;
return result;
}
}
var a = new BigNum("1", 1, true)
var count = 168;
var nTwo = new BigNum("2", 1, true);
function loop(intTmpvar,intCount)
{
if(intCount == 0) return intTmpvar;
var v1 = intTmpvar.pide( nTwo );
var v11 = v1.Clone();
var nTemp = v1.Multiply( v11 );
var a1 = a.Clone();
a1 = a.Multiply(a1);
var nTemp1 = a1.Subtract( nTemp )
v2 = nTemp1.SquareRoot();
v3 = a.Subtract( v2 );
var v31 = v3.Clone();
var nTemp2 = v3.Multiply( v31 );
var nTemp3 = nTemp2.Add(nTemp);
v4 = nTemp3.SquareRoot();
return loop( v4 , -- intCount )
}
var a1 = a.Clone();
var nTemp = a.Multiply(a1);
var nTemp1 = nTemp.Clone();
nTemp = nTemp.Add(nTemp1);
nTemp = loop(nTemp.SquareRoot(), count);
var nFour = new BigNum("4", 1, true);
nTemp = nTemp.Multiply( nFour );
nTemp1 = new BigNum("2", 1, true);
var nTemp2 = new BigNum("2", 1, true);
for(var i = 0; i < count - 1; i ++)
{
nTemp1 = nTemp1.Multiply( nTemp2 );
}
nTemp = nTemp.Multiply( nTemp1 );
nTemp = nTemp.pide( nTwo );
nTemp = nTemp.pide( a );
document.write( nTemp )
//-->
</script>
</body>
</html>
Running result:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421 170679
I believe you have mastered the method after reading the case in this article. For more exciting information, please pay attention to php Other related articles on the Chinese website!
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