2012年3月14日20:37:40 今天是世界圆周率日 上Java算π的算法 1000位的

import java.math.BigDecimal;

public class PI {
public static void main(String args[]) throws NumberFormatException {
int digits = 1000; // 计算1000位
long begin = System.currentTimeMillis();
String pi = computePi(digits).toString();
long end = System.currentTimeMillis();
System.out.println(pi);
System.out.println((end - begin) + "ms");
}

/** constants used in pi computation */
private static final BigDecimal FOUR = BigDecimal.valueOf(4);

/** rounding mode to use during pi computation */
private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;

/**
* Compute the value of pi to the specified number of digits after the
* decimal point. The value is computed using Machin's formula:
*
* pi/4 = 4*arctan(1/5) - arctan(1/239)
*
* and a power series expansion of arctan(x) to sufficient precision.
*/
public static BigDecimal computePi(int digits) {
int scale = digits + 5;
BigDecimal arctan1_5 = arctan(5, scale);
BigDecimal arctan1_239 = arctan(239, scale);
BigDecimal pi = arctan1_5.multiply(FOUR).subtract(arctan1_239)
.multiply(FOUR);
return pi.setScale(digits, BigDecimal.ROUND_HALF_UP);
}

/**
* Compute the value, in radians, of the arctangent of the inverse of the
* supplied integer to the specified number of digits after the decimal
* point. The value is computed using the power series expansion for the arc
* tangent:
*
* arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + (x^9)/9 ...
*/
public static BigDecimal arctan(int inverseX, int scale) {
BigDecimal result, numer, term;
BigDecimal invX = BigDecimal.valueOf(inverseX);
BigDecimal invX2 = BigDecimal.valueOf(inverseX * inverseX);

numer = BigDecimal.ONE.divide(invX, scale, roundingMode);

result = numer;
int i = 1;
do {
numer = numer.divide(invX2, scale, roundingMode);
int denom = 2 * i + 1;
term = numer.divide(BigDecimal.valueOf(denom), scale, roundingMode);
if ((i % 2) != 0) {
result = result.subtract(term);
} else {
result = result.add(term);
}
i++;
} while (term.compareTo(BigDecimal.ZERO) != 0);
return result;
}
}

console:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

39ms