Quick n-th Square of BigInteger

[Jan Burse]

Dear All,

What is your favorite algorithm to compute the n-th Square of
a BigInteger, i.e.

Given: x, n
Compute: y = max { z | z^n =< x }

Bye

 

[Gene Wirchenko]

Dear All,

What is your favorite algorithm to compute the n-th Square of
a BigInteger, i.e.

Given: x, n
Compute: y = max { z | z^n =< x }

Do you mean the integer part of the nth *root* of z given integer
x and n?

I do not have a favourite or even an algorithm. If I had to come
up with something, I would probably try a first approximation with
logarithms.

Sincerely,

Gene Wirchenko

 

[Jan Burse]

Do you mean the integer part of the nth *root* of z given integer
x and n?

I do not have a favourite or even an algorithm. If I had to come
up with something, I would probably try a first approximation with
logarithms.

Sincerely,

Gene Wirchenko

Sorry, yes root, and z integer.

 

[markspace]

Sorry, yes root, and z integer.

Positive integers? Do you want the complex roots too? ;-) You ask big
questions Jan, but I think you need to ask them a little more thoughtfully.

I'm confused about the max, the z |, and the =< x. Care to explain
what those signify in your question? If you want something besides the
real, positive nth root of A=z^n, what do you want? I think "nth root
of A" is the correct phrasing, which leads to the wonder what the other
mathematical verbiage signifies.

 

[Jan Burse]

Dear All,

What is your favorite algorithm to compute the n-th Square of
a BigInteger, i.e.

Given: x, n
Compute: y = max { z | z^n =< x }

Bye

Clarification:

Given: x BigInteger positive non-zero, n int positive non-zero

Compute: y BigInteger = max { z BigInteger | z^n =< x }

(In words: y is the biggest BigInteger z such that
z raised to the power of n is less or equal x)

(Mathematically this is would be floor(root(x,n)))

Bye

 

[Eric Sosman]

Dear All,

What is your favorite algorithm to compute the n-th Square of
a BigInteger, i.e.

Given: x, n
Compute: y = max { z | z^n =< x }

(I'm assuming you mean n'th root, which is what your final
line seems to imply.)

It's not something I've found a need to do, so I have no
"favorite" algorithm. For positive `x' I think I'd start
by observing that

x.bitCount()-1 <= lg(x) < x.bitCount()

hence the lg() of the desired root is between

floor((x.bitCount()-1)/n) <= lg(root) < ceil(x.bitCount()/n)

From this you can get lower and upper bounds on the root itself,
something like (just typed in free-hand)

BigInteger lo = BigInteger.ONE.shiftLeft(
Math.floor((x.bitCount()-1)/n));
BitInteger hi = BigInteger.ONE.shiftLeft(
Math.ceil(x.bitCount()/n));

.... and then do a binary search between those extrema. (Looks like
they'd differ by a factor of two usually, maybe a factor of four
occasionally -- but I might be wrong about that.)

Simplifications might be possible if `n' is known to be an
integer.

For negative `x' and odd integer `n' you could find the bounds
for -x, negate and interchange them, and then do the same binary
search.

For negative `x' and `n' even or non-integer, I think you're
out of luck.

 

[glen herrmannsfeldt]

(snip)

Positive integers? Do you want the complex roots too? ;-)
You ask big questions Jan, but I think you need to ask them
a little more thoughtfully.

I will guess that the OP isn't a native English speaker, and
is not translating so well.

I had to look it up as I didn't know, .fm seems to be Micronesia.

It looks like he wants the nth root rounded down to the next
integer value.

I do remember when first learning Fortran wondering why no
ISQRT function.

One possibility is to do exactly as written, binary search
for the largest z such that z**n <= x. (No exclusive or operators
are needed here.)

-- glen

 

[Jan Burse]

... and then do a binary search between those extrema. (Looks like
they'd differ by a factor of two usually, maybe a factor of four
occasionally -- but I might be wrong about that.)

Binary search would use (x.bitCount()-1)/n steps in the
extrem, and in each step calculating pow(). Is this
effective?

 

[Jan Burse]

I will guess that the OP isn't a native English speaker, and
is not translating so well. I had to look it up as I didn't know,
.fm seems to be Micronesia.

Ha Ha

fastmail.fm = messagingengine.com

 

[Jan Burse]

I'm confused about the max, the z |, and the =< x.

For those who don't know, there exists a set builder notation:

http://en.wikipedia.org/wiki/Set-builder_notation#Z_notation

max is then a higher order function from a set to an element.

Forgot where this is taught, in elementary school?

Bye

 

[Eric Sosman]

Binary search would use (x.bitCount()-1)/n steps in the
extrem, and in each step calculating pow(). Is this
effective?

In light of your abusiveness in responding to other people who've
tried to help, I decline to assist you any further. Have a nice life.

 

[Jan Burse]

In light of your abusiveness in responding to other people who've
tried to help, I decline to assist you any further. Have a nice life.

Problem is I scribbled the exact same solution on
a back of an envelope, but I have doubt that it is
a good solution for small n, like n=2.

Bye

 

[Lew]

For those who don't know, there exists a set builder notation:

http://en.wikipedia.org/wiki/Set-builder_notation#Z_notation

max is then a higher order function from a set to an element.

Forgot where this is taught, in elementary school?

Riiiight. As nations and smaller school districts remove evolution from
their textbooks, they're going to teach mathematical logic and set
theory in elementary school?

In any event, this being a Java forum, the notation '=<' (shown nowhere
in your reference link, BTW) is rather odd, as we are used to '<='. Given
that '=<' apparently is not part of the "Set Builder" notation, how about
we stick with the Java (also C, Fortran, C++, C#, Javascript, BASIC, SQL,
Python, shell, ...) idiom?

 

[Jan Burse]

In any event, this being a Java forum, the notation '=<' (shown nowhere
in your reference link, BTW) is rather odd, as we are used to '<='. Given
that '=<' apparently is not part of the "Set Builder" notation, how about
we stick with the Java (also C, Fortran, C++, C#, Javascript, BASIC, SQL,
Python, shell, ...) idiom?

It was not Java, it was a math spec. When one writes:

Given: xxx
Compute: yyy

Then xxx and yyy are not necessarely needed to follow
the Java language specification.

Do you want me to start counting the trolls that will
now make their appearance in this thread? You are
number 3 so far. I guess there will follow some more...

Bye

 

[Jan Burse]

Do you want me to start counting the trolls that will
now make their appearance in this thread? You are
number 3 so far. I guess there will follow some more...

But still comp.lang.java.programmer is too small
I guess so that a shitstorm will rise. And there are
still some that want to profit.

Bye

 

[Lew]

Problem is I scribbled the exact same solution on
a back of an envelope, but I have doubt that it is
a good solution for small n, like n=2.

For n == 2, just use any of the standard algorithms for square root, like
<http://stackoverflow.com/questions/...-a-biginteger-system-numerics-biginteger?rq=1>
found in about 10 minutes of online searching.

 

[Lew]

It was not Java, it was a math spec. When one writes:

Given: xxx
Compute: yyy

Then xxx and yyy are not necessarely needed to follow
the Java language specification.

Do you want me to start counting the trolls that will
now make their appearance in this thread? You are
number 3 so far. I guess there will follow some more...

A troll is not someone who suggests that you be clear in
your communication, but someone who gets personally
abusive as you did when given such a suggestion.

Oh, darn, I forgot. You're the same person who suggests
that one perform a sex act on you when they try to engage
in any technical discussion with you. How do you feel you have
the moral authority to accuse anyone else of being a troll?

Because you don't.

Matthew 7:5.

 

[Jan Burse]

A troll is not someone who suggests that you be clear in
your communication, but someone who gets personally
abusive as you did when given such a suggestion.

=< should be cristal clear, = = equal and < = less.
And if it is not cristal clear on first sight, it will
become clear from reading the context. In the present
case a troll is somebody who pretends not understand
a post, when he does.

Bye

 

[Lew]

=< should be cristal clear, = = equal and < = less.
And if it is not cristal clear on first sight, it will
become clear from reading the context. In the present
case a troll is somebody who pretends not understand
a post, when he does.

I don't know whom you mean. No one here pretended not
to understand it, only suggested that you follow the conventions
appropriate to the forum.

Stop being so nasty and confrontational, Jan. If you can't play
nice, stay off the playground. You're being mean without any
need.

 

[Jan Burse]

Stop being so nasty and confrontational, Jan. If you can't play
nice, stay off the playground. You're being mean without any
need.

Stop your peer pressure. I told you already once:

Suck my dick, shut up and **** off.