GPGPU Programming for Games and Science

302 GPGPU Programming for Games and Science

uses only multiplications and additions and has no branching. For applica-

tions that make heavy use of SLERP, the approximation provides a decent

approximation with a significant speedup.

An alternative that is faster and more robust is presented in [10], which in-

volves a two-variable polynomial approximation. The algorithm uses only mul-

tiplication, addition, and subtraction and does not require division, branching,

or testing for special conditions. It is also friendly to SIMD.

The coefficient sin(tθ)/ sin(θ) in Equation (6.92) is evaluated for t ∈ [0, 1].

It has the same form as sin(nθ)/ sin(θ) for nonneg ...