3D/4D vector Length() with int/short/byte storage is one too low on perfect squares: Position3D<int>.FromMeter(6, 41, 42).Length() returns 58, not 59 #537

What's wrong

For storage types that IsRoundedThroughDouble sends through double (byte, sbyte, short, ushort, int, uint), the 3- and 4-component StorageMath.Hypot overloads nest two double.Hypot calls and then truncate the result:

// Semantics.Quantities/StorageMath.cs:322-328
return T.CreateChecked(double.Hypot(double.Hypot(dx, dy), dz));
// Semantics.Quantities/StorageMath.cs:364-371
return T.CreateChecked(double.Hypot(double.Hypot(dx, dy), double.Hypot(dz, dw)));

Each Hypot call rounds, so an exact integer length can come back 1 ulp low, for example 58.99999999999999. CreateChecked then truncates it to 58. The method's documented contract is "the floor for an integer type". The true floor of √3481 is 59.

All generated Length(), Magnitude(), Distance() and DistanceTo() members on 3D and 4D vector forms go through this code (for example Velocity3D.g.cs:115-120).

Reproduction

Verified by running against the built assemblies at ff736ff:

A brute force over components 0..60 in 3D and 0..20 in 4D found 3 wrong results in 3D and 20 in 4D. Other examples: (14,39,42) gives 58, (27,28,36) gives 52, (2,3,4,14) gives 14 instead of 15, and (1,4,8,12) gives 14 instead of 15. The 2-component Hypot<int> was correct on every Pythagorean triple below 46000.

Why it matters

This is a regression from 5f727f0, the #327 overflow fix. The previous code summed the squares and took a single Math.Sqrt, which is exact for perfect squares in range. The existing tests only use vectors with one non-zero component, such as (65536, 0, 0), so no test catches it. Callers comparing integer distances, for example distance <= radius on a grid, get off-by-one answers exactly on the boundary.

Suggested fix

• Send the narrow integer primitives through the exact integer path rather than the double round trip. For example, widen them to long/Int128, use HypotOfWideInteger or an integer sum of squares plus an integer square root, then T.CreateChecked back.
• Keep the double.Hypot route only for float, double and Half. For double itself the same 1-ulp error appears (Position3D<double>(6, 41, 42).Length() returns 58.99999999999999), which is less serious but worth the same review.
• Add tests on perfect-square triples and quadruples: (6,41,42) → 59 and (3,3,3,3) → 6, for both int and short.

Related, lower priority: generated Distance() subtracts the components in T before calling Hypot (QuantitiesGenerator.cs:1935), so the difference can wrap without any error. Position3D<int>.FromMeter(int.MaxValue, 0, 0).Distance(FromMeter(-2, 0, 0)) returns 2147483647. That matches the type's unchecked - operator, but it is not the OverflowException the #520 Hypot contract describes, so it is worth deciding on while this code is open.