Arithmetic and Function Evaluation Routines

by Irwin D. Greenwald


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A description of the programming of arithmetic and function evaluation routines for JOSS form a programmer's point of view. JOSS functions are divided into three groups: arithmetic operations (including exponential and square root), elementary transcendental functions, and number dissection functions. The four arithmetic operations (add, subtract, multiply, divide) and square root treat the operands as exact nine-digit numbers and produce true results rounded to nine digits. Descriptions of the arithmetic routines are presented in gross verbal flow-charts, amplified by commentaries. The discussion of the transcendental functions emphasizes the analysis done to achieve almost nine-significant-digit accuracy in the results and shows how special cases are handled to hit certain "magic" values on the nose. Program flows of the number dissection functions demonstrate how a sophisticated tool may be supplied to the user with trivial expenditure of programming effort.

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