mathlib-fp 1.4.0

Release date: 2026-07-25

Highlights

• GeometryLib.Geometry now provides natural arithmetic for fixed-size
  TVector2D and TVector3D value records.
• Vector magnitude and normalization are scale-safe for finite extreme-scale
  components.
• The geometry walkthrough includes a compact Theodorus-spiral construction
  using Radius := Radius + Step, symmetric 3-D arithmetic, and runnable
  extreme-scale normalization.

Vector arithmetic

Both vector types provide componentwise addition, binary subtraction, unary
negation, scalar multiplication in either operand order, and vector/scalar
division:

V2 := -((V2 + Step) / 2.0);
V3 := 3.0 * (V3 - Offset);

The two types expose the same arithmetic operator set. TVector2D keeps its
existing Perpendicular helper as the intentional dimensional difference.
The operations return independent record values, allocate no storage, and do
not modify their operands, including when a caller assigns an expression back
to one of its inputs.

All fixed-size arithmetic and numeric vector operations are O(1), allocation-
free on successful calls, and reentrant. Concurrent calls are safe when the
same record storage is not being modified by another thread.

Magnitude and normalization

Magnitude scales components before accumulating their squares, avoiding
premature overflow and underflow for representable finite results. Infinity
takes precedence over NaN in the magnitude, matching hypot-style behavior.
Normalise now accepts finite non-zero vectors at tiny and large scales and
returns a new value even when the unnormalised magnitude is too large for
Double. It raises EGeometryError for exact-zero, NaN, or infinite vectors.

Floating-point behavior

The operators apply ordinary IEEE-754 Double arithmetic to each coordinate.
They preserve normal target behavior for signed zero, NaN, infinity, and
overflow rather than rejecting those values. Finite overflow produces signed
infinity; a non-zero finite coordinate divided by signed zero produces the
corresponding signed infinity; zero divided by zero produces NaN. Arithmetic
operators do not raise EGeometryError for these cases and do not alter the
caller's FPU exception mask. The described result values apply with the related
IEEE status exceptions masked; an unmasked FPU exception is reported according
to the caller's configured FPU mode.

Compatibility

This is an additive API change. Existing GeometryLib record fields, methods,
and callers remain source-compatible. Point/vector translation operators are
not included: points and displacement vectors continue to be distinct types
until coordinate-transform semantics have their own documented design. The
existing normalization API now treats small finite non-zero vectors as valid
and reports non-finite vectors explicitly instead of returning indeterminate
coordinates.

Validation

Focused tests cover both dimensions, ordinary arithmetic, value/alias
semantics, additive identity and inverse, distributivity, scale inversion,
2-D/3-D agreement, signed zero, zero-scalar division, NaN, infinity, and
overflow. Extreme-scale magnitude and normalization tests cover large and tiny
finite vectors, zero vectors, and non-finite inputs. Dot linearity and magnitude
scaling connect the operators to the established vector methods. The public-API
smoke suite compiles each new operator form. See the
GeometryLib reference and run
examples/12_geometry.pas for arithmetic,
Theodorus construction, and scale-safe normalization examples.