uber / h3-go / 27736586680

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master: 100%

Pull #133

github

perf: fold projection trig into precomputed tables and fused IJK descent

Two hot transforms behind nearly every geometry call are reworked.

toVec3 (the inverse gnomonic projection behind CellToLatLng, CellToBoundary,
CellArea*, EdgeLength*, vertex/edge boundaries, and the polygon paths) computed
five transcendental calls per invocation (atan2 + atan + two sin/cos pairs).
Replace them with algebra:
  - cos/sin of the in-plane angle taken directly from the vector (no atan2);
  - per-face azimuth and the Class III rotation folded in via angle-addition
    against precomputed cos/sin tables;
  - the inverse gnomonic via cos(atan r)=1/sqrt(1+r^2), sin(atan r)=r/sqrt(1+r^2)
    (one sqrt, no atan/sin/cos).

toFaceIjkWithInitializedFijk (the forward path behind LatLngToCell,
PolygonToCells, and local-IJ) fuses the per-resolution Class II/III digit
descent so each digit does a single coordIJK normalize, instead of normalizing
the rotated and the translated coordinates separately.

Both transforms are algebraically exact; output differs from C only at the ULP
level, well within the parity suite's 1e-5 relative tolerance. All white-box and
parity tests pass.

benchstat, pure-Go, f5c493f -> toVec3 fold (Apple M3 Max, count=10):

                              │    sec/op    │   sec/op     vs base                │
CellToLatLng-16                  160.4n ± 2%   126.4n ± 1%  -21.20% (p=0.000 n=10)
CellLatLng-16                    160.6n ± 0%   126.4n ± 2%  -21.35% (p=0.000 n=10)
CellToBoundary-16                648.1n ± 1%   438.9n ± 2%  -32.28% (p=0.000 n=10)
CellBoundary-16                  647.2n ± 1%   463.8n ± 3%  -28.35% (p=0.000 n=10)
CellAreaRads2-16                 813.8n ± 0%   631.3n ± 3%  -22.43% (p=0.000 n=10)
CellAreaKm2-16                   814.5n ± 1%   612.9n ± 2%  -24.76% (p=0.000 n=10)
CellAreaM2-16                    823.4n ± 3%   610.4n ± 1%  -25.87% (p=0.000 n=10)
EdgeLengthRads-16                394.0n ± 1%   329.4n ± 3%  -16.38% (p=0.000 n=... (continued)

58 of 58 new or added lines in 2 files covered. (100.0%)

4266 of 4266 relevant lines covered (100.0%)

3090181.95 hits per line