On Wed, 23 Jul 2025 21:11:16 GMT, fabioromano1 wrote:
>> I noticed the usage of exp() and log(), thanks for the change.
>>
>> My concerns about using transcendental are rooted in [this
>> paper](https://members.loria.fr/PZimmermann/papers/accuracy.pdf).
>> The Javadoc claims an error of 1 ulp f
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request with a new target base due to a merge
or a rebase. The pull request now contains 84 commits:
- Merge branch 'openjdk:master' into nth-root-branch
- Revision changes
- More
On Wed, 23 Jul 2025 19:49:51 GMT, Raffaello Giulietti
wrote:
>> @rgiulietti I've changed the formula that computes the initial estimate, now
>> it does not use `Math.pow()` anymore, but `Math.exp()` and `Math.log()`
>> instead, which are guaranteed to have always an error less than 1 ulp by
On Wed, 23 Jul 2025 17:40:22 GMT, fabioromano1 wrote:
>> Can you please provide a succinct "proof" in form of a comment? Needs to be
>> convincing, although not necessarily rigorous.
>
> @rgiulietti I've changed the formula that computes the initial estimate, now
> it does not use `Math.pow()`
On Wed, 23 Jul 2025 17:05:07 GMT, Raffaello Giulietti
wrote:
>> @rgiulietti Now that I checked the recurrence better, it seems to me that it
>> should give an overestimate if `rLong` is an underestimate, without modify
>> it.
>
> Can you please provide a succinct "proof" in form of a comment?
On Wed, 23 Jul 2025 16:11:20 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> More accurate lower bound for doubles val
On Mon, 14 Jul 2025 16:41:15 GMT, fabioromano1 wrote:
>> This is my hunch as well.
>> So while the use of `nextUp()` and `ceil()` certainly help to achieve an
>> overestimate, I'm less sure that this is sufficient when using `pow()`. If
>> the latter has some error bigger than a few ulps, then
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
More accurate lower bound for doubles values tests
-
Changes:
- all: https://git.openjdk.or
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
No need to ceiling the initial estimate if not shifted
-
Changes:
- all: https://git.openjd
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Ensure an initial overestimate of the root
Ensure an initial overestimate of the root, using Math.exp(
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Merge branch 'nth-root-branch' of https://github.com/fabioromano1/jdk into
nth-root-branch
- Refinement
On Tue, 22 Jul 2025 18:38:28 GMT, fabioromano1 wrote:
> The cases in which the method throws correspond to the cases in which the
> integer root is not defined.
Yes, that's why it should be part of the definition: like in "the largest
integer ..., if it exists; otherwise the result is undefine
On Tue, 22 Jul 2025 15:26:25 GMT, Raffaello Giulietti
wrote:
>> I think this is probably what you are searching for.
>>
>> If x ≥ 0 there's at most one integer y ≥ 0 meeting y^n ≤ x < (y+1)^n.
>> If x < 0 there's at most one integer y ≤ 0 meeting y^n ≥ x > (y-1)^n.
>> The method returns y if it
On Wed, 16 Jul 2025 14:40:53 GMT, Raffaello Giulietti
wrote:
>> I don't know other ways to define it that don't involve the clause `!(x < 0
>> && n % 2 == 0)`. If the first definition is confusing, the only solution I
>> see is to remove it, and leave only the formula `(x.signum() *
>> floor(
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Added bug id
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new: https:
On Tue, 22 Jul 2025 11:21:46 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> No need to check for root's shift overflo
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
No need to check for root's shift overflow
-
Changes:
- all: https://git.openjdk.org/jdk/pu
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Include one more possible correct bit in initial estimate
-
Changes:
- all: https://git.ope
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Added tests for nth root
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
-
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Revert "Make sure to round up"
This reverts commit e305c9f68914553421f2fdd8b4389eaf03946fea.
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Make sure to round up
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- ne
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Discard wrong bits from the initial estimate
-
Changes:
- all: https://git.openjdk.org/jdk/
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Formatting changes
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Minor change
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new: https:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Minor change
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new: https:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Removed trailingwhitespace
- Revision changes
Revision changes, with explanation comment for init
On Wed, 16 Jul 2025 10:32:41 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/BigInteger.java line 2755:
>>
>>> 2753: * is even and this BigInteger is negative, an {@code
>>> ArithmeticException} will be
>>> 2754: * thrown.
>>> 2755: *
>>
>> I think this specifi
On Wed, 16 Jul 2025 10:01:00 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Removed useless instruction
>
> src/java.base/share/classes/java/math/BigInteger.java line 2755:
>
>> 2753:
On Sat, 12 Jul 2025 09:18:27 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Removed useless instruction
src/java.bas
On Mon, Jul 14, 2025 at 10:14 AM fabioromano1 wrote:
>
> On Sat, 12 Jul 2025 09:18:27 GMT, fabioromano1 wrote:
>
> >> This PR implements nth root computation for BigIntegers using Newton
method.
> >
> > fabioromano1 has updated the pull request incrementally with one
additional commit since the l
On Mon, 14 Jul 2025 15:43:58 GMT, Raffaello Giulietti
wrote:
>> @rgiulietti The convergence of the recurrence is guaranteed if the initial
>> estimate is larger than or equal to the exact value, AFAIK no guarantee is
>> given when the estimate is smaller than the exact value.
>
> This is my hu
On Sat, 12 Jul 2025 09:18:27 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Removed useless instruction
The integers
On Mon, 14 Jul 2025 15:52:19 GMT, fabioromano1 wrote:
> This is my hunch as well. So while the use of `nextUp()` and `ceil()`
> certainly help to achieve an overestimate, I'm less sure that this is
> sufficient when using `pow()`. If the latter has some error bigger than a few
> ulps, then we
On Fri, Jul 11, 2025 at 11:44 AM fabioromano1 wrote:
>
> On Fri, 11 Jul 2025 18:07:31 GMT, fabioromano1 wrote:
>
> >> This PR implements nth root computation for BigIntegers using Newton
method.
> >
> > fabioromano1 has updated the pull request incrementally with one
additional commit since the l
On Mon, 14 Jul 2025 15:43:58 GMT, Raffaello Giulietti
wrote:
> This is my hunch as well. So while the use of `nextUp()` and `ceil()`
> certainly help to achieve an overestimate, I'm less sure that this is
> sufficient when using `pow()`. If the latter has some error bigger than a few
> ulps,
On Mon, 14 Jul 2025 15:46:47 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 1936:
>>
>>> 1934: * where {@code nthRoot(., n)} denotes the mathematical {@code
>>> n}th root.
>>> 1935: * The contents of {@code this} are not changed. The
>>>
On Mon, 14 Jul 2025 14:32:45 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Removed useless instruction
>
> src/java.base/share/classes/java/math/MutableBigInteger.java line 1936:
>
>> 1
On Mon, 14 Jul 2025 15:40:18 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 1964:
>>
>>> 1962: final double rad = Math.nextUp(x >= 0 ? x : x + 0x1p64);
>>> 1963: final double approx = n == 3 ? Math.cbrt(rad) :
>>> Math.pow(r
On Mon, 14 Jul 2025 14:33:26 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Removed useless instruction
>
> src/java.base/share/classes/java/math/MutableBigInteger.java line 1964:
>
>> 1
On Sat, 12 Jul 2025 09:18:27 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Removed useless instruction
I'm looking
On Sat, 12 Jul 2025 09:18:27 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Removed useless instruction
I agree that
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Removed useless instruction
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Code simplification
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
small change for readability
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
On Fri, 11 Jul 2025 18:07:31 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Avoid to discard fraction bits in the ini
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Avoid to discard fraction bits in the initial estimate
-
Changes:
- all: https://git.openjd
Apologies if this has been discussed before.
The explanation for the exception for negative n ("This would cause
the operation to yield a non-integer value.") feels wrong to me. I think
the definition of the result as: x.signum() * floor(abs(nthRoot(x, n)))
works fine for that case, if nthRoot(x,-
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Optimize the computation of the input's shift
Optimize the computation of the input's shift, in order
On Fri, 6 Jun 2025 08:08:09 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Update "since" version
Right.
--
On Fri, 11 Jul 2025 12:38:56 GMT, Raffaello Giulietti
wrote:
> On the other hand, the code contains about 80 lines just to find the initial
> estimate. To ensure that the code is readable and maintainable, it either
> needs to be documented better, possibly with math, or simplified so that the
On Fri, 6 Jun 2025 08:08:09 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Update "since" version
Sure, the initial
On Thu, 10 Jul 2025 15:21:10 GMT, Raffaello Giulietti
wrote:
>> @rgiulietti Regarding the tests for _n_-th root, the tests for `sqrt()`
>> could be extended in order to test also `nthRoot()`.
>
> @fabioromano1 IIUC, the bulk of the code in the PR is aimed at finding a good
> starting estimate.
On Sat, 17 May 2025 11:25:58 GMT, fabioromano1 wrote:
>> The [Rampdown Phase One](https://openjdk.org/projects/jdk/25/) for JDK 25 is
>> about 3 weeks from now.
>>
>> I think it's a bit too late for API additions to be approved in due time.
>> And even if we could rush this work for 25, it mak
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Update "since" version
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- n
On Sat, 17 May 2025 11:25:58 GMT, fabioromano1 wrote:
>> The [Rampdown Phase One](https://openjdk.org/projects/jdk/25/) for JDK 25 is
>> about 3 weeks from now.
>>
>> I think it's a bit too late for API additions to be approved in due time.
>> And even if we could rush this work for 25, it mak
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Code simplification
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Do first refinement loop only if shift == 0
-
Changes:
- all: https://git.openjdk.org/jdk/p
On Wed, 14 May 2025 18:48:50 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Revert "Use type long for bitLength instead of int"
>>
>> This reverts commit c8e1b8159206d9fb5532df7ccdf9
On Wed, 14 May 2025 18:48:50 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Revert "Use type long for bitLength instead of int"
>>
>> This reverts commit c8e1b8159206d9fb5532df7ccdf9
On Wed, 14 May 2025 18:07:08 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Revert "Use type long for bitLength inste
On Wed, 14 May 2025 18:27:28 GMT, Raffaello Giulietti
wrote:
> I doubt that the AKS primality test is of any practical relevance, although
> it's a _great_ theoretical achievement.
Yes, indeed it was just an example, but the exact power detection can be used
also as a test apart from the enti
On Wed, 14 May 2025 18:07:08 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with one additional
> commit since the last revision:
>
> Revert "Use type long for bitLength inste
On Wed, 14 May 2025 17:59:59 GMT, Raffaello Giulietti
wrote:
> I guess this work will be the basis for a future work on `BigDecimal` _n_-th
> root?
@rgiulietti Yes, it is. Some use cases could be primality testing, like AKS,
where part of the algorithm detect composite numbers by checking whe
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Revert "Use type long for bitLength instead of int"
This reverts commit c8e1b8159206d9fb5532df7ccdf98a
On Mon, 12 May 2025 19:23:16 GMT, fabioromano1 wrote:
>> @fabioromano1 Is [this
>> proof](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
>> still relevant?
>
> @rgiulietti No, the proof of the recurrence used is the one by Zimmermann
> linked in the code
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Use type long for bitLength instead of int
-
Changes:
- all: https://git.openjdk.org/jdk/pu
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Code simplification
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new:
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Merge branch 'nth-root-branch' of https://github.com/fabioromano1/jdk into
nth-root-branch
- Compute re
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Avoid needless box/unbox conversion
-
Changes:
- all: https://git.openjdk.org/jdk/pull/2489
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Merge branch 'nth-root-branch' of https://github.com/fabioromano1/jdk into
nth-root-branch
- correct an
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Removed useless code
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
correct typos
-
Changes:
- all: https://git.openjdk.org/jdk/pull/24898/files
- new: https
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Factor out newton's recurrence in a separate method
-
Changes:
- all: https://git.openjdk.o
On Mon, 12 May 2025 17:37:54 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with two additional
>> commits since the last revision:
>>
>> - Merge branch 'nth-root-branch' of https://github.com/fabioromano1/jdk
>> into nth-root-branch
>> - Restore
On Sat, 10 May 2025 11:57:32 GMT, fabioromano1 wrote:
>> This PR implements nth root computation for BigIntegers using Newton method.
>
> fabioromano1 has updated the pull request incrementally with two additional
> commits since the last revision:
>
> - Merge branch 'nth-root-branch' of https
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Merge branch 'nth-root-branch' of https://github.com/fabioromano1/jdk into
nth-root-branch
- Restore nt
> This PR implements nth root computation for BigIntegers using Newton method.
fabioromano1 has updated the pull request with a new target base due to a merge
or a rebase. The pull request now contains 44 commits:
- Merge branch 'openjdk:master' into nth-root-branch
- Update to resolve conflic
> This PR implements nth root computation for BigIntegers using Newton method.
> This PR is dependent by this [PR](https://github.com/openjdk/jdk/pull/24690).
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
An optimization
-
> This PR implements nth root computation for BigIntegers using Newton method.
> This PR is dependent by this [PR](https://github.com/openjdk/jdk/pull/24690).
fabioromano1 has updated the pull request incrementally with one additional
commit since the last revision:
Correct unsigned division
> This PR implements nth root computation for BigIntegers using Newton method.
> This PR is dependent by this [PR](https://github.com/openjdk/jdk/pull/24690).
fabioromano1 has updated the pull request incrementally with two additional
commits since the last revision:
- Correct typo in comment
> This PR optimizes `BigInteger.pow(int)` method. The primary enhancement in
> `pow()` is not concerned most on execution time, but rather in memory
> optimization, because the PR implementation does the "shift of the exponent"
> squaring the result rather than the base, so the base is not squar
This PR implements nth root computation for BigIntegers using Newton method.
This PR is dependent by this [PR](https://github.com/openjdk/jdk/pull/24690).
-
Commit messages:
- Merge branch 'openjdk:master' into BigInteger-nth-root
- Optimized nth root iteration loop
- Systematizat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
fabioromano1 has updated the pull request with a new target base due to a merge
or a rebase. The incremental webrev excludes the unrelated changes brought in
by the merg
On Thu, 24 Apr 2025 20:18:42 GMT, fabioromano1 wrote:
>> @fabioromano1 I just had a cursory glance at this PR.
>>
>> AFAIU, there are two main contributions here:
>>
>> - Performance enhancements in `pow()`, which is of general interest and does
>> not require submitting a [CSR](https://wiki.o
On Thu, 24 Apr 2025 18:17:38 GMT, Raffaello Giulietti
wrote:
> * Performance enhancements in `pow()`, which is of general interest and does
> not require submitting a [CSR](https://wiki.openjdk.org/display/csr/Main).
@rgiulietti Yes, but here, the primary enhancement in `pow()` is not concerne
On Mon, 21 Apr 2025 11:47:30 GMT, fabioromano1 wrote:
>>> [Here is a proof of convergence of the recurrence
>>> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
>>
>> That's very nice. It would be even nicer if this was a permalink into the
>> JDK r
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
> This PR implements nth root computation for `BigInteger`s using Newton method
> and optimizes `BigInteger.pow(int)` method.
> [Here is a proof of convergence of the recurrence
> used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
fabioromano1 has updat
On Mon, 21 Apr 2025 10:14:05 GMT, Andrew Haley wrote:
> That's very nice. It would be even nicer if this was a permalink into the JDK
> repo, and a reference in the source code.
@theRealAph Ok. It would be useful to have a link to an explanation on how this
can be done, if there is one. Thanks
On Mon, 21 Apr 2025 10:05:21 GMT, Andrew Haley wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Code simplification
>
> src/java.base/share/classes/java/math/MutableBigInteger.java line 1924:
>
>> 1922: * @imp
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