fix(nl): NL(87°) returns 2 per DO-260B §A.1.7.2, not 1#2
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The first threshold in nl_double() was 86.99999999999998578914, which is the largest IEEE 754 double strictly below 87.0. This caused fabs(87.0) > 86.999... to evaluate as true, returning NL=1 for the exact 87° latitude point. DO-260B §A.1.7.2 defines the following boundary points explicitly: NL(+87°) = 2, NL(−87°) = 2 NL(lat > +87°) = 1, NL(lat < −87°) = 1 The standard therefore includes 87° in the NL=2 zone. The correct threshold is exactly 87.0, so that the boundary point itself falls through to NL=2 and only strictly polar latitudes return NL=1. Finder: @mrksngl
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Problem
nl_double(87.0)returnsNL=1but RTCA DO-260B §A.1.7.2 mandatesNL(87°) = 2.The first comparison threshold was
86.99999999999998578914— this isnextafter(87.0, 0.0)in IEEE 754, the largest representable double strictly less than 87.0. Thereforefabs(87.0) > 86.9999...istrue, and the function misclassifies the exact 87° boundary point into the polar-cap zone (NL=1) instead of the adjacent zone (NL=2).Standard reference
RTCA DO-260B / EUROCAE ED-102A, §A.1.7.2 defines these points explicitly:
NL(+87°) = 2NL(−87°) = 2NL(lat > +87°) = 1NL(lat < −87°) = 1The 87° point belongs to the NL=2 zone; only latitudes strictly above 87° return NL=1.
Fix
Change the threshold to exactly
87.0:87.0is exactly representable in IEEE 754 double precision (it is a small integer), so there is no precision loss. The comment added to the source cites the standard section so the intent is unambiguous.Testing
Verify with a simple unit check:
Closes #1
Credit
Bug discovered by @mrksngl.