Add genus-2 split model (not_char2, arbitrary, char2; both reduced bases) - #1
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Ports the not-characteristic-2 split (two points at infinity) genus 2
divisor arithmetic from the Magma negReduced + posReduced formulas:
- precompute(): curve constants, Vpl/Vn, degree-0 adjust divisor
- negative basis: add_neg, double_neg
- positive basis: add_pos, double_pos
Divisors use the 4-coordinate balanced Mumford representation with an
integer balance weight n (DivisorCoords{u2,u1,u0,v1,v0,n}).
Verification mirrors the original Magma testers, checking against the
generic Cantor reference in src/generic/split.rs (no Magma needed):
- random divisor pairs over F7/F31/F127/F8191 (cf. *_random.mag)
- whitebox vectors auto-extracted from the GF(5)/GF(7) tester blocks
- test-only branch instrumentation proving all 154 formula branches
(ADD/DBL neg + PADD/PDBL pos) are exercised
cargo test --release: 203 passing (177 prior + 26 split).
- generic/split.rs: rewrite Add/Double/Adjust_SPLIT_{NEG,POS} to faithfully
match Magma with h threaded throughout (previously h=0-only). Factors the
shared compose/normalize/reduce. nch2 (h=0) regresses cleanly.
- g2/split/arbitrary.rs: arbitrary-characteristic split model (any field incl.
char 2 and 3), both reduced bases, ADD + DBL, ported from arb_splitG2_*.mag.
precompute takes a caller-supplied root y3 of x²+h3x−f6 (the ∞ points).
- arb_tests.rs: cross-checks vs the h-aware oracle over odd fields with h≠0;
all 18+59 branches per basis exercised.
cargo test --release: 218 passing.
Char-2 split genus 2 divisor arithmetic over GF(2^k), in the normalized form h = x³ + h1·x + h0, f = f6·x⁶ + f2·x² + f1·x + f0. Both reduced bases, ADD + DBL, ported from ch2_splitG2_*.mag with XOR-based char-2 arithmetic (no /2). precompute takes a caller-supplied root y3 of x²+x+f6 (the two ∞ points). Tested over GF(2^4/2^6/2^8) against the h-aware generic Cantor oracle: - A0 harness validation (round-trip incl. n, oracle well-formedness) - explicit add/double cross-checks (neg + pos) - branch coverage incl. an exhaustive deg-1 doubling sweep; the only branches not reached by testing are 13 double-degenerate ADD cases that return a trivial neutral constant (allowlisted; char2 whitebox vectors can't be ported because Magma's GF(2^k) uses a different irreducible than BinaryExtField). Fixed 4 transliteration bugs in the u=up special cases (CDBL09, CPDBL09, CADD13, CADD38) that returned degree 1 instead of the degree-2 u². cargo test --release: 226 passing.
- benches: representative degree-2 add/double benchmarks for the split model (nch2, arbitrary, char2), building valid divisors via the generic oracle then timing the explicit formulas. - README: document the split model + a split performance table. - scripts/test.sh: run the g2::split suites. - split mod docs: list all three variants.
Rebased onto current main (which added cargo fmt + clippy cleanup). Apply rustfmt, satisfy `clippy --all-targets -- -D warnings` (assign-op patterns, drop a dead s_deg store, module-level allow(too_many_arguments) for the coordinate-formula modules), and adopt main's generic/mod.rs (re-applying the h-threading edits). All four CI gates pass: test, fmt, clippy, doc.
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Summary
Implements explicit divisor arithmetic for the genus-2 split model (curves with two points at infinity,
y² + h·y = f,deg f = 6), ported from the Magma reference in salindne/divisorArithmetic. This fills insrc/g2/split/, which was previously a// TODOstub.Divisors use the balanced 4-coordinate Mumford representation with an integer balance weight
n, in both the positive (Vpl) and negative (Vn = −Vpl − h) reduced bases.What's added
g2::split::not_char2— odd characteristic,h = 0g2::split::arbitrary— any characteristic (incl. 2 and 3), generalhg2::split::char2— characteristic 2 overGF(2^k), XOR-basedprecompute+add_neg/double_neg+add_pos/double_pos.generic::splitgeneralized to threadhthroughAdd/Double/Adjust_SPLIT_{NEG,POS}(wash = 0-only), so it's a faithful Cantor reference for every characteristic.scripts/test.shruns the split suites.How it's verified
Mirroring the original Magma testers, every explicit formula is cross-checked against the generic Cantor reference (no Magma needed):
F7..F8191,GF(2^4..2^8)),DBLnn/ADDnnlabels).cargo test --release: 226 passing. Clippy (-D warnings), rustfmt, rustdoc, andcargo bench --no-runall clean.Notes
precomputeforarbitrary/char2takes a caller-supplied rooty3ofx² + h3·x − f6(the points at infinity); tests construct splitting curves with a knowny3.GF(2^k)uses a different irreducible than this crate'sBinaryExtField. Correctness of those branches follows by direct correspondence to the oracle-verified nch2/arb analogs.Out of scope: the genus-3 split model (
src/g3/remains a stub).Commits
generic::splitoracle forh≠0+ arbitrary-characteristic model