Features

Vectorial Calculus Algebra

• Cross product via .cross. infix operator
• Dot product via .dot. infix operator
• Parallel projection via .paral. infix operator
• Orthogonal projection via .ortho. infix operator
• Matrix product via .matrix. infix operator
• Triangle face normals: face_normal3 (also as stand-alone procedure)
• Quad face normals: face_normal4 (also as stand-alone procedure) — norm equals face area

Arithmetic Operators

All standard operators work between two vectors and between a vector and any scalar:

• +, -, *, / between two vector objects
• +, -, *, / between a vector and a numeric scalar of any supported kind (left and right)
• Unary + and -
• All operators resolved at compile time via generic interfaces — no runtime dispatch overhead

Comparison Operators

Vectors are compared by their L2 norm:

• <, <=, ==, /=, >=, > — work between two vectors and between a vector and any numeric scalar

Geometry Methods

• normL2() — Euclidean (L2) norm
• sq_norm() — squared norm (avoids a square root when only ordering is needed)
• normalize() — normalize the vector in-place (subroutine); falls back to zero vector if norm is zero
• normalized() — return the normalized vector (function)
• angle(vec) — angle between two vectors in radians
• rotate(axis, angle) — rotate the vector around a given axis by the given angle
• mirror(plane_normal) — mirror the vector across a plane defined by its normal
• distance_to_line(pt, dir) — distance from the vector (treated as a point) to a line
• distance_to_plane(pt, normal) — distance from the vector to a plane
• projection_onto_plane(normal) — orthogonal projection onto a plane
• is_collinear(v1, v2) — test collinearity of three vectors (as points)
• is_concyclic(v1, v2, v3) — test whether four vectors lie on a common circle

I/O and Printing

• print — formatted output of x, y, z components to any Fortran unit
• save / load — binary I/O for vector data (sequential and stream access)
• iolen() — returns the record length needed for direct-access I/O

Multi-Precision Support

Type	Kind	Precision
vector / vector_R8P	R8P = selected_real_kind(15,307)	64-bit, ~15 digits
vector_R4P	R4P = selected_real_kind(6,37)	32-bit, ~6 digits
vector_R16P	R16P = selected_real_kind(33,4931)	128-bit, ~33 digits (if compiler supports it)

The single use vecfor statement re-exports all precision variants and the corresponding Cartesian versors (ex, ey, ez for each kind).

Mixed-Kind Operands

All operators accept mixed-kind arguments. Supported scalar kinds:

Kind	Type	Width
R16P	real	128-bit
R8P	real	64-bit
R4P	real	32-bit
I8P	integer	64-bit
I4P	integer	32-bit
I2P	integer	16-bit
I1P	integer	8-bit

Compiler Support

Compiler	Status
GNU gfortran ≥ 4.9.2	Supported
Intel Fortran ≥ 12.x	Supported
NVIDIA nvfortran	Supported
IBM XL Fortran	Not tested
g95	Not tested
NAG Fortran	Not tested

Design Principles

• Pure Fortran — no C extensions, no system calls beyond standard I/O
• OOP — a single vector derived type exposes all functionality as type-bound procedures and operators
• TDD — every public procedure is exercised by automated doctests in src/tests/
• KISS — simple, focused API; the entire library fits in one file
• Thread-safe — all procedures are pure or elemental
• Free & Open Source — multi-licensed for FOSS and commercial use