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Name: jl125535 Date: 03/04/2002 FULL PRODUCT VERSION : java version "1.4.0" Java(TM) 2 Runtime Environment, Standard Edition (build 1.4.0b92) Java HotSpot(TM) Client VM (build 1.4.0b92, mixed mode) FULL OPERATING SYSTEM VERSION : Microsoft Windows 2000 [Version 5.00.2195] ADDITIONAL OPERATING SYSTEMS : All A DESCRIPTION OF THE PROBLEM : The algorithm used by BigInteger.pow(int exponent) is extremely slow for large exponents, making it unusable for serious mathematical work. For example, calculating the value of the largest currentlyknown Mersenne prime, 2^13466917  1, takes about 104 minutes on an 800 MHz Pentium III. This is not the same bug as 4449911; that bug indicates a regression when porting a C library to Java for JDK 1.3. The regression was fixed. This bug is to address the fact that nonoptimal *algorithms* are still being used and critical optimizations are missed. Much faster algorithms exist, and the workaround below shows a very powerful optimization. For a Java implementation and analysis of more efficient algorithms, see http://www.cis.ksu.edu/~howell/calculator/comparison.html. This implementation, using a base 2 or base 10 radix (the radix is configurable) can calculate the value in 5 minutes, making it approximately 20 times faster than BigInteger. It achieves this performance improvement partially by using more efficient algorithms for multiplication. The current implementation also misses a simple and inexpensive optimization when the base is a power of 2 (which applies in this case:) If the base conatins a power of 2, the exponentiation can be significantly speeded by factoring out the largest power of two (by simply counting trailing zeros in the binary expansion, which is easy and fast) as indicated in the workaround below. For the case listed above, this performs the exponentiation in about .16 seconds or so, a factor of tens of thousands of times faster. The code I use to make this optimization is listed below. Again, this is critical if BigInteger is to be used for serious mathematical work. Related (but different bugs): 4641897 4449911 STEPS TO FOLLOW TO REPRODUCE THE PROBLEM : Compile and run the sample code below: 1. javac BigIntTest.java 2. java BigIntTest (wait over an hour) This bug can be reproduced always.  BEGIN SOURCE  import java.math.BigInteger; public class BigIntTest { /** This calculates the largestknown Mersenne Prime, 2^13466917  1 */ public static void main(String[] args) { int exponent = 13466917; System.out.println("Starting"); BigInteger b = new BigInteger("2"); BigInteger p; p = b.pow(exponent); // The shiftLeft() below does the same thing if the base is 2, and in // a fraction of a second. //p = b.shiftLeft(exponent  1); System.out.println("Exponentiation complete"); // Note: this takes a long time... over an hour. } }  END SOURCE  CUSTOMER WORKAROUND : One workaround is to use the KSU LargeInteger class used above. A missed optimization (that I use before calling pow) determines if the base contains a power of 2 and performs the shiftLeft optimization, which can be done very fast.) This could be done even faster if I had access to the internal fields, (without allocation of intermediates) and should not be used as the final implementation. It works if the base contains a power of 2, and could be easily extended to negative bases. It makes my particular application hundreds of times faster. BigInteger myPow(BigInteger big, int exponent) { // Note: this can be fixed to work with negative numbers if (big.signum() > 0) { // Get factor of two int bit = 0; // Count trailing zero bits while (big.testBit(bit) == false) bit++; // If there's a factor of 2, if (bit > 0) { // Factor the power of 2 out of the number // (quickly, by shifting right) big = big.shiftRight(bit); // This is the power of 2 we factored out raised // to the specified exponent BigInteger twoPower = BigInteger.ONE.shiftLeft(bit*exponent); // If the remainin number is exactly one, we're done if (big.equals(BigInteger.ONE)) return twoPower; else { // Raise the remaining part to the exponent big = big.pow(exponent); // multiply by the power of 2 return big.multiply(twoPower); } } } // If we fell through, do the normal exponent return big.pow(exponent); } (Review ID: 143631) ====================================================================== ###@###.### 20041111 22:25:55 GMT
