> I have implemented the Zimmermann's square root algorithm, available in works
> [here](https://inria.hal.science/inria-00072854/en/) and
> [here](https://www.researchgate.net/publication/220532560_A_proof_of_GMP_square_root).
>
> The algorithm is proved to be asymptotically faster than the New
On Tue, 9 Jul 2024 20:06:40 GMT, fabioromano1 wrote:
>> I have implemented the Zimmermann's square root algorithm, available in
>> works [here](https://inria.hal.science/inria-00072854/en/) and
>> [here](https://www.researchgate.net/publication/220532560_A_proof_of_GMP_square_root).
>>
>> The
On Wed, 10 Jul 2024 12:13:32 GMT, Raffaello Giulietti
wrote:
> Yes, thanks, I saw it.
If some other clarifications are needed, please let me know.
-
PR Comment: https://git.openjdk.org/jdk/pull/19710#issuecomment-2220362708
On Tue, 9 Jul 2024 20:06:40 GMT, fabioromano1 wrote:
>> I have implemented the Zimmermann's square root algorithm, available in
>> works [here](https://inria.hal.science/inria-00072854/en/) and
>> [here](https://www.researchgate.net/publication/220532560_A_proof_of_GMP_square_root).
>>
>> The
On Fri, 12 Jul 2024 13:04:42 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:28:14 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 128:
>>
>>> 126: intLen = 2;
>>> 127: value[0] = hi;
>>> 128: value[1] = (int) val;
>>
>> Suggestion:
>>
>> value = new int
On Fri, 12 Jul 2024 13:06:35 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:06:46 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:43:29 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 1941:
>>
>>> 1939:
>>> 1940: // Initial estimate is the square root of the unsigned
>>> long value.
>>> 1941: long s = (long) Math.sqrt(x > 0 ? x :
On Fri, 12 Jul 2024 13:07:02 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:49:55 GMT, Raffaello Giulietti
wrote:
>> The proof has been made simply by exaustive experiment: for every long value
>> `s` in [0, 2^32) such that `x == s * s`, it is true that `s == (long)
>> Math.sqrt(x >= 0 ? x : x + 0x1p64)`. This can be verified directly by a Java
On Fri, 12 Jul 2024 13:07:39 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:07:51 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:08:29 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 14:16:38 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 2040:
>>
>>> 2038: sqrt.add(q);
>>> 2039:
>>> 2040: MutableBigInteger chunk = u;
>>
>> I don't get the need for `chunk`. It should be possible to use `u` d
On Fri, 12 Jul 2024 13:08:37 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:08:59 GMT, Raffaello Giulietti
wrote:
>> fabioromano1 has updated the pull request incrementally with one additional
>> commit since the last revision:
>>
>> Added comment on normalization in MutableBigInteger.sqrtRemZimmermann()
>
> src/java.base/share/classes/java/ma
On Fri, 12 Jul 2024 13:57:55 GMT, fabioromano1 wrote:
>> (Yes, I proved it to myself in this way.)
>>
>> A similar explanation should be in a comment in the code, not here. The
>> source of truth is the code, not the comments on GitHub ;-)
>
> I would keep zero as the only special case, so as n
On Fri, 12 Jul 2024 13:51:24 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 1967:
>>
>>> 1965: MutableBigInteger[] sqrtRem = x.sqrtRemZimmermann(x.intLen,
>>> needRemainder);
>>> 1966:
>>> 1967: // Unnormalize
>>
>> This unnormali
On Fri, 12 Jul 2024 14:20:23 GMT, fabioromano1 wrote:
>> Ok, but what should the name be?
>
> Like `u_a0`? It is the most "mathematical" name that comes to my mind.
In the paper `u` is called R'', so I'd rename it as `rpp` (for R prime prime).
Generally, the more the names in the code match the
On Fri, 12 Jul 2024 14:42:33 GMT, Raffaello Giulietti
wrote:
>> Like `u_a0`? It is the most "mathematical" name that comes to my mind.
>
> In the paper `u` is called R'', so I'd rename it as `rpp` (for R prime
> prime). Generally, the more the names in the code match the ones in the
> paper, t
On Fri, 12 Jul 2024 14:55:19 GMT, fabioromano1 wrote:
>> In the paper `u` is called R'', so I'd rename it as `rpp` (for R prime
>> prime). Generally, the more the names in the code match the ones in the
>> paper, the easier it becomes to read the code with the paper at hand.
>>
>> Then you can
On Fri, 12 Jul 2024 14:22:33 GMT, fabioromano1 wrote:
>> src/java.base/share/classes/java/math/MutableBigInteger.java line 2054:
>>
>>> 2052:
>>> 2053: rem.add(ONE);
>>> 2054: rem.subtract(twiceSqrt);
>>
>> Shouldn't these be `rem + twiceSqrt - 1`?
>
> No, becau
On Fri, 12 Jul 2024 14:39:51 GMT, Raffaello Giulietti
wrote:
>> The full explanation for the unnormalization is in the second paper, "A
>> proof of GMP square root", par. 3.2 at page 11.
>
> Well, I have to compare that section, which is clear to me, with the code
> again.
@rgiulietti I notic
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