Elementary function

Abstract: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and square-root The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated The only operations required are shifting, adding, subtracting and the recall of prestored constants The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculations

Abstract: The author presents a simple integral expression for calculating the exact probability of a symbol error for an arbitrary array of signal points. The integrand contains only elementary functions and the range of integration is finite. The approach is introduced by applying it to M-ary phase shift keying (MPSK). The special case of M=2 gives novel and possibly useful expressions for calculating the Gaussian tail probability function and the related complementary error function. The approach is outlined for polygonal decision regions, and results are given for 16-point signal constellations. A method of obtaining, not exact, but even simpler and highly accurate expressions for symbol error probability when the latter is less than a few hundredths is presented. >

Abstract: Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration. Theta Functions and the Arithmetic-Geometric Mean Iteration. Jacobi's Triple-Product and Some Number Theoretic Applications. Higher Order Transformations. Modular Equations and Algebraic Approximations to pi. The Complexity of Algebraic Functions. Algorithms for the Elementary Functions. General Means and Iterations. Some Additional Applications. Other Approaches to the Elementary Functions. Pi. Bibliography. Symbol List. Index.