uber / h3-go / 27738291857

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master: 100%

Pull #134

github

perf: fold forward gnomonic projection (toHex2d) into algebra

toHex2d is the forward gnomonic projection behind LatLngToCell, PolygonToCells,
and local-IJ -> cell. Like the earlier toVec3 work it computed the angle and
radius with transcendentals: acos for the angular distance, atan2 (inside
azimuthRads) for the azimuth, tan for the gnomonic scaling, and a final sin/cos
pair, plus two vec3d.normalize() sqrts (the tangent basis and the projection).

Replace them with algebra:
  - the azimuth's cos/sin come straight from the tangent-plane components
    (cosAz = N/hyp, sinAz = E/hyp) instead of atan2 -> cos/sin; because only the
    N/E ratio is used, neither the tangent basis nor the projection needs
    normalizing -- both scale by the same factor, which cancels (drops 2 sqrt);
  - the per-face azimuth offset and the Class III rotation fold in via
    angle-subtraction against the precomputed faceAxis0Cos/Sin and ap7Rot tables;
  - the gnomonic tan(acos x) reduces to sqrt(1-x^2)/x with x = 1 - sqd/2, written
    as sqrt((sqd/2)(2-sqd/2))/x = (1-x)(1+x) to avoid cancellation near center.

Five transcendentals + 2 normalize sqrts become 2 sqrt. The transform is
algebraically exact; output differs from C only at the ULP level, within the
parity suite's 1e-5 tolerance. azimuthRads and posAngleRads are now unused and
removed. All white-box and parity tests pass; package stays at 100% coverage.

NOTE on the face-center guard: the old `acos(1-sqd/2) < epsilon` short-circuit
(the azimuth is singular at the face center, where the tangent projection
vanishes) is re-expressed on sqd as `sqd < epsilon*epsilon`. The exact form
2(1-cos epsilon) underflows to 0 at epsilon=1e-16 (cos(1e-16) rounds to 1), so
its leading-order equivalent epsilon^2 is used; without a working guard a point
exactly on a face center divides 0/0 and yields NaN coordinates.

benchstat, pure-Go, 4953a75 -> this commit (Apple M3 Max, count=10):

                              │   sec/op    │  ... (continued)

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