这看起来像在工作。我还没有进行详尽的测试，也没有进行任何时间的测试，但似乎运行时间合理。
public class Test { private int log10(BigInteger huge) { int digits = 0; int bits = huge.bitLength(); // Serious reductions. while (bits > 4) { // 4 > log[2](10) so we should not reduce it too far. int reduce = bits / 4; // Divide by 10^reduce huge = huge.divide(BigInteger.TEN.pow(reduce)); // Removed that many decimal digits. digits += reduce; // Recalculate bitLength bits = huge.bitLength(); } // Now 4 bits or less - add 1 if necessary. if ( huge.intValue() > 9 ) { digits += 1; } return digits; } // Random tests. Random rnd = new Random(); // Limit the bit length. int maxBits = BigInteger.TEN.pow(200000).bitLength(); public void test() { // 100 tests. for (int i = 1; i <= 100; i++) { BigInteger huge = new BigInteger((int)(Math.random() * maxBits), rnd); // Note start time. long start = System.currentTimeMillis(); // Do my method. int myLength = log10(huge); // Record my result. System.out.println("Digits: " + myLength+ " Took: " + (System.currentTimeMillis() - start)); // Check the result. int trueLength = huge.toString().length() - 1; if (trueLength != myLength) { System.out.println("WRONG!! " + (myLength - trueLength)); } } } public static void main(String args[]) { new Test().test(); }}在我的Celeron M笔记本电脑上花了大约3秒钟，因此它在某些不错的工具包上应该不到2秒钟。
