sha512 optimisation

[shramee]

Pull Request type

Please check the type of change your PR introduces:

• Bugfix
• Feature
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Build-related changes
• Documentation content changes
• Other (please describe):

What is the current behavior?

Collected 3 test(s) from alexandria_math package
Running 3 test(s) from src/
[PASS] alexandria_math::tests::sha512_test::test_size_zero (gas: ~20074)
-        steps: 2165513
+        steps: 735949
        memory holes: 353718
        builtins: ("range_check_builtin": 501826, "bitwise_builtin": 2025)
        syscalls: ()
        
[PASS] alexandria_math::tests::sha512_test::test_sha512_size_one (gas: ~20073)
-        steps: 2165490
+        steps: 735926
        memory holes: 353718
        builtins: ("range_check_builtin": 501823, "bitwise_builtin": 2025)
        syscalls: ()
        
[PASS] alexandria_math::tests::sha512_test::test_sha512_lorem_ipsum (gas: ~59599)
-        steps: 6427014
+        steps: 2149930
        memory holes: 1055226
        builtins: ("range_check_builtin": 1489975, "bitwise_builtin": 5929)
        syscalls: ()
        
Tests: 3 passed, 0 failed, 0 skipped, 0 ignored, 145 filtered out

Does this introduce a breaking change?

• Yes
• No

[tdelabro]

can you:

• add doc to the functions you use/create
• add an explanation of the optimisation you are doing in your PR description (I have no clue what is going on)
• add comments in your code explaining the algorithm you are using, a maybe a link to the Wikipedia page of the algo, or the paper describing this optimization

[shramee]

Apologies for not adding the details,

I mostly did common dev sense optimisations on this one, I noticed a loooot of power ops.

fpow(base: u128, power: u128) -> u128

This one does a modulo op and a divide op, behind the scenes both these ops use a div_mod op. So we can just do it once saving one div_mod call on each iteration.

fn two_pow(power: u128) -> u128

Among pow ops, most were pow of 2. There are only so many powers of 2 you can have in a u128. So I wrote two_pow with cached 2 pow squarings saving a square op in each iteration.
I'll add some docs on this one.

These two things make it 3x faster to do SHA512.

About renaming single letter variables, as an outside optimiser, I'd refrain from changing var names coz they might hold significance beyond my understanding.

[tdelabro]

About renaming single letter variables, as an outside optimiser, I'd refrain from changing var names coz they might hold significance beyond my understanding.

Ok no worry then, I have been asked to do a cleanup of the codebase before audit. Renaming to more explicit var name will be part of it