If NEON support is not planned then repository and project description should be updated, reflecting the x86-only goals.

It would be great to have some optimized BLAS-like kernels for vector/matrix operations, both SoA and AoS styles.

Backends

• Scalar
• SSE2 (in-progress)
• SSE4.2 (in-progress)
• AVX (in-progress)
• AVX2
• AVX512F
• WASM SIMD
• ARM/aarch64 NEON

Extra data types

• i16/u16
• i8/u8

These can use 128-bit registers even on AVX/AVX2, and 256-bit registers on AVX512

Polyfills

• Emulated FMA on older platforms
  • For f32, promote to f64 and back.
  • For f64, implement this method

Iterator library

• Prototype

Vectorized math library

Currently fully implemented for single and double-precision:
sin, cos, tan, asin, acos, atan, atan2, sinh, cosh, tanh, asinh, acosh, atanh, exp, exp2, exph (0.5 * exp), exp10, exp_m1, cbrt, powf, ln, ln_1p, ln2, ln10, erf, erfinv, tgamma, lgamma, next_float, prev_float

Precision-agnostic implementations: lerp, scale, fmod, powi (single and vector exponents), poly, poly_f, poly_rational, summation_f, product_f, smoothstep, smootherstep, smootheststep, hermite (single and vector degrees), jacobi, legendre, bessel_y

TODO:

• Beta function
• Zeta function
• Digamma function

Bessel functions:

• Bessel J_n for n > 1, n=0 and n=1 are implemented.
• Bessel J_f (Bessel function of the first kind with real order)
• Bessel Y_f (Bessel function of the second kind with real order)
• Bessel I_n (Modified Bessel function of the first kind)
• Bessel K_n (Modified Bessel function of the second kind)
• Hankel function?

Complex and Dual number libraries

• Make difficult parts branchless, ideally.

Precision Improvements

• Improve precision of lgamma where possible.
  • Should it fallback to ln(tgamma(x)) when we know it won't overflow?
• Improve precision of trig functions when angle is a product of π (sin(x*π), etc.)
• Compensated float fallbacks on platforms without FMA

Performance improvements:

• Investigate ways to improve non-FMA operations.
• Look for ways to simplify more expressions algebraically.
• Experiment with the "crush denormals" trick to remove denormal inputs?
  • 1 - (1 - x) is the trick.

Policy improvements:

• Improve codegen size for Size policy, especially when WASM support is added (both scalar and SIMD)

Testing

• Structured tests for all vector types and backends (some partial tests exist, but I need to clean them up)
• Tests for the math library