## Re: [PrimeNumbers] big numbers library

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• If it wasn t clear (and it wasn t,) the algorithm I just posted was one to speed up exponentiation. I use it as a wrapper around BigInteger.pow(BigInteger
Message 1 of 9 , Aug 7, 2005
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If it wasn't clear (and it wasn't,) the algorithm I just posted was
one to speed up exponentiation. I use it as a wrapper around
BigInteger.pow(BigInteger big, int exponent) in Java.

--
Alan Eliasen | "It is not enough to do your best;
eliasen@... | you must know what to do and THEN
http://futureboy.homeip.net/ | do your best." -- W. Edwards Deming
• Alan, Yes is clear .. Thanks. But, my problem still the same when the exponent is a prime 2... I m trying to find out the best (fastest) way to calculate it
Message 2 of 9 , Aug 21, 2005
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Alan,
Yes is clear .. Thanks.
But, my problem still the same when the exponent is a prime > 2...
I'm trying to find out the best (fastest) way to calculate it ...
I welcome any new ideas...
Regards
Faysal

-----Original Message-----
Behalf Of Alan Eliasen
Sent: Sunday, August 07, 2005 3:34 PM
To: fyatim
Cc: 'Jan van Oort'; 'Prime Number'
Subject: Re: [PrimeNumbers] big numbers library

fyatim wrote:
> I wrote a small method using a well known algorithm "Exponentiation by
> Squaring", but it still take horrible execution time.

That's because Sun's Java implementation still uses horrible O(n^2)
algorithms for multiplication. Their exponentiation routine already
does exponentiation by squaring, so you probably can't improve on it
without fixing multiplication.

> Where can I find the algorithm you are mentioning i.e. "bit shifting" ??

"Bit shifting" works when your base contains powers of 2. This is
because you can do powers of 2 by simply left-shifting the binary
representation by the appropriate number of bits. If you're doing
something like calculating large Mersenne numbers, this makes it about a
thousand times faster or more than Sun's implementation. It's an easy
and obvious optimization that Sun missed.

In short, here's a code snippet that does it. The base is expected
to be in a BigInteger called "big", and the exponent in an int called
"exponent". It factors out powers of two quickly by the call to
getLowestSetBit(), and does the exponentiation for powers of two rapidly
with shiftLeft() and then multiplies it by the remaining part that isn't
a power of 2.

This only helps if your base contains powers of 2.

if (big.signum() > 0)
{
// Get factor of two
int bit = big.getLowestSetBit();

if (bit > 0)
{
big = big.shiftRight(bit);
BigInteger twoPower = FrinkBigInteger.ONE.shiftLeft(bit*exponent);
if (big.equals(FrinkBigInteger.ONE))
return FrinkInteger.construct(twoPower);
else
{
big = big.pow(exponent);
return FrinkInteger.construct(big.multiply(twoPower));
}
}
}

--
Alan Eliasen | "It is not enough to do your best;
eliasen@... | you must know what to do and THEN
http://futureboy.homeip.net/ | do your best." -- W. Edwards Deming

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