This PR does the following;

• ✨ add (optional) efficient support for f16 (through the half package)
• 🧹 some minor refactoring (using macro's to avoid duplicate code)
• 🤖 add CI-CD (not yet tested)

P.S. f16 is supported through converting it to (what I call) i16ord - which is an ordinal (i.e., monotonic) mapping of f16 to i16;

The ord transformation:

ord_transform(v: i16) = ((v >> 15) & 0x7FFF) ^ v)

(to apply this on a f16, just transmute f16 to i16 first)

Some useful properties of this transformation

• 🙌 As ordinality is preserved, we can use fast built-in i16 (SIMD) instructions for comparison.
• ↔️ As the transformation is symmetric we can - as long as we don't change the i16(ord) values - transform the outcome back to f16 without needing a lookup table.
• ⚡ (bonus): transformation only performs binary (bitwise) operations, ensuring minimal overhead
  => these operations can easily implemented in SIMD instructions 🎉

Visualization of the transformation

Illustration of ord_transform on all possible float16 numbers.
You can observe the montonic rising slope 🥳

Illustration of the symmetry propetry.
When applying the ord_transform twice on the same value, we get back the original value!!

Limitations

• NaN values and infs are not supported in this transformation

Benchmarks

The f16 support that leverages the ord_transform:

• f16 SIMD ~ 2x faster than f32 SIMD 🔥
• f16 scalar ~ 1.25x slower than f32 scalar (:face_exhaling:)
  • 🐎 ~10x faster than generic scalar code (which f32 uses) on half::f16
  • 🤯 ~3x faster than f32 upcasting (i.e., replacing ord_transform with to_f32 in the implementation)