Hi Ranchers, I'm trying to find the result of 2^1000. With "double x = Math.pow(2,1000)". The result is deviating, i mean its rounding it off at a particular limit and I need the full values. Can someone please help?

@Shamsudeen - More specifically, something like:
private static final BigInteger TWO = BigInteger.valueOf(2L); (I don't know why BigInteger doesn't define this constant itself)
and then elsewhere in your code:
TWO.pow(1000);

Winston

Isn't it funny how there's always time and money enough to do it WRONG?
Articles by Winston can be found here

Shamsudeen Akanbi wrote: . . . With "double x = Math.pow(2,1000)". The result is deviating, i mean its rounding it off at a particular limit . . .

All the primitives have limits of range, and the floating-point types have limits to their precision, too. The limits are clearly stated in the Java Language Specification and Java Tutorials, and you can find more by Googling for IEEE754. 2 to the 1000 is actually inside the range of a double, so you won’t get infinitiy, but it will tell you it is only precise to 15 or 16 Significant figures. Floating-point arithmetic is designed for engineers to use.

When I was an undergraduate:

What’t an engineer?

He’s somebody you ask “What’s 2×2?”, and he gets his slide‑rule and says, “ . . . two by two . . . three point nine nine . . . that’s four, near as makes no difference.”

Floating-point arithmetic is intended for people who don’t mind such imprecision. You have already been given the correct solution, twice, with and without spelling errors

BTW: If you fancy it (and you have the memory space and - possibly more importantly - time )
try:
BigInteger FOUR = new BigInteger.valueOf(4L);
System.out.println(FOUR.pow(1073741824).bitLength());

I've never got it to work; probably because my heap memory is too small (possibilities run to anywhere around 3Gb, depending on efficiency) and I can't be bothered to fix it; but I suspect very strongly that it will display a negative number..SILENTLY. And this after repeated queries about it to Oracle and Sun.

Winston

Campbell Ritchie
Sheriff

Joined: Oct 13, 2005
Posts: 41098

29

posted

0

You already know its bit length. I can tell you it free. 2147483649.

Campbell Ritchie wrote:2147483649. Presumably rounded with the ROUND_PEG_SQUARE_HOLE algorithm, to the nearest int.
. . . And how long does it take to run? (Or crash?)

Actually, nanoseconds; unless the number is negative and an exact power of 2; so, on average...

My objection is theoretical: bitLength() returns an int, which has a limit of 23^31 -1. The magnitude of a BigInteger is held in an int[], which can hold up to ≈2^36 bits. I've just never been able to prove that it does what I think it will.

Winston

Campbell Ritchie
Sheriff

Joined: Oct 13, 2005
Posts: 41098

29

posted

0

Winston Gutkowski wrote: . . . unless the number is negative and an exact power of 2; so, on average... . . .

How can a number be negative and an exact power of 2?

I did work out that something would go wrong, so I said it would use the ROUND_PEG_SQUARE_HOLE algorithm. I have had the d*mn thing running for several hours with no sign of any output yet.

Winston Gutkowski wrote: . . . unless the number is negative and an exact power of 2; so, on average... . . .

How can a number be negative and an exact power of 2?

I guess I should have said -(2^n).

BigIntegers hold their values in sign/magnitude form, and bitLength() is defined as returning:
"the number of bits in the minimal two's-complement representation of this BigInteger, excluding [the] sign bit."

I take that to mean "the number of bits from the first one in the 2's-C form that differs from the sign bit"; otherwise the check doesn't make much sense.
Personally, I think they could've saved themselves a lot of bother by simply returning the bit length of the absolute value, but maybe they had their reasons.

BTW: How did your attempt work out?

Winston

Campbell Ritchie
Sheriff

Joined: Oct 13, 2005
Posts: 41098

29

posted

0

I gave up after it had a day, on and off, and still hadn’t completed. I had to close the shell to terminate it; even ctrl-C didn’t seem to stop it