State Machines in VHDL Trigonometric Functions Vol. 4: State Machine Design for Arithmetic Processes
Synopsis "State Machines in VHDL Trigonometric Functions Vol. 4: State Machine Design for Arithmetic Processes"
A digital designer's book devoted entirely to trigonometry, first of its kind. Relevant theory and graphical illustrations are also provided. Table-based solutions include all core functions and their reciprocals, as well as inverse functions and their reciprocals. Each with an implementation in both degrees and radians, twenty-four in all. The list includes: sine, cosine, and tangent, and their reciprocals: cosecant, secant, and cotangent. Inverse functions: arcsine, arccosine, and arctangent, as well as their reciprocals: arccosecant, arcsecant, and arccotangent. Real-Time solutions provide high to very high precision utilizing Taylor polynomials for core functions and Borchardt-Gauss using iterated means (variant of Arithmetic-Geometric Mean) for their inverse functions, radians only. Included are: sine, cosine, tangent, and their inverse arcsine, arccosine, and arctangent. All designs are fully coded utilizing state machines in VHDL. Each have associated diagrams, tables, and operational parameters. Implementations are fixed-point and have scalable operands based on constants.
