Vertex shader, one of the core parts in 3D graphics systems, is to speed up the operations of coordinate transformation and lighting in 3D graphics pipeline, and vector ALU is the key part of a vertex shader. This thesis proposes several unified architectures that integrate the floating-point vector arithmetic unit and special function unit in order to share some hardware resource. We propose three different architectures for the design of the unified vector ALU. The first architecture includes a single-instruction-multiple-data (SIMD) vector arithmetic unit, and uses table-based method with first-order approximation to calculate some special functions. The second architecture use higher-order approximation to reduce the table sizes and share the floating-point multipliers in the SIMD vector unit. The proposed third architecture has two copies of hardware that can compute two dot-product operations in parallel and thus increase the throughput of the matrix computation by a factor of two. Furthermore, the two dot-product units can be used to perform the interpolation for special function calculation.