make some calculations 250-500 times faster

[Safari77]

Before:
$ time ./fend 2^1555.555|b3sum
0567ac5de698ba87f79145ebf29c1ab169d37b185e76ddd4b8ecc2de2c82d4de -

real 1m42,334s
user 1m41,908s
sys 0m0,032s

Afer:
$ time ./fend 2^1555.555|b3sum
0567ac5de698ba87f79145ebf29c1ab169d37b185e76ddd4b8ecc2de2c82d4de -

real 0m0,401s
user 0m0,401s
sys 0m0,004s

And for the gcd:

Before:
$ time ./fend 0.9911^192|b3sum
315e6e5e5b9716413c0e6cbe347ed8a7e2923b3cec6290db7d88ff9710aea09e -

real    0m19,810s
user    0m19,757s
sys     0m0,005s

After:
$ time ./fend 0.9911^192|b3sum
315e6e5e5b9716413c0e6cbe347ed8a7e2923b3cec6290db7d88ff9710aea09e -

real    0m0,049s
user    0m0,040s

System information: rust 1.92.0, LLVM 20.1.8 x86_64-redhat-linux-gnu, Intel i5-13600K, opt-level=3, ~/.cargo/config.toml contents: [build]
rustflags = ["-C", "target-cpu=native"]

Functions changed:

add_assign_internal: Replaces high-level get/set overhead with efficient, vectorizable slice iteration using .zip() to eliminate bounds checks in the hot loop.

sub: Optimizes borrowing logic using u128 overflow detection and safely clamps loop ranges to handle unnormalized inputs without panicking.

sub_assign: Performs subtraction in-place on mutable buffers to eliminate expensive memory allocations during the Karatsuba recombination step.

mul: Dispatches to Karatsuba multiplication for inputs larger than 64 limbs (4096 bits) to reduce algorithmic complexity from O(N²) to O(N^¹·⁵⁸⁵).

mul_karatsuba_slice: Recursively computes Karatsuba products using &[u64] slices instead of cloning BigUint vectors, significantly reducing memory churn.

mul_internal_slice: Provides a highly optimized Schoolbook (O(N²)) multiplication base case that operates directly on slices for maximum cache efficiency.

div_rem_knuth (called by divmod): Replaces slow bit-by-bit binary division with Knuth's Algorithm D (base-2⁶⁴), reducing the number of division steps by a factor of 64.

root_n: Replaces Binary Search (linear convergence) with Newton's Method (quadratic convergence), reducing iteration count from thousands to dozens for large roots.

lshift / rshift: Moves interrupt checks outside the loop and simplifies carry logic to allow the compiler to generate efficient block memory moves.

add_assign_shifted: A specialized helper for Karatsuba that performs a "shift-and-add" operation in one pass without creating intermediate shifted values.

gcd: Replaces the division-heavy Euclidean algorithm with Stein's Algorithm (Binary GCD),
utilizing efficient bitwise shifts and subtraction to eliminate expensive modulo operations during
fraction simplification.

[codecov]

Codecov Report

❌ Patch coverage is 75.47974% with 115 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.17%. Comparing base (9636b16) to head (6a52ead).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
core/src/num/biguint.rs	75.47%	115 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #372      +/-   ##
==========================================
- Coverage   81.47%   81.17%   -0.30%     
==========================================
  Files          52       52              
  Lines       14717    15032     +315     
==========================================
+ Hits        11990    12202     +212     
- Misses       2727     2830     +103     

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[printfn]

Thank you!