Table-driven implementation of the logarithm function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Radian reduction for trigonometric functions
ACM SIGNUM Newsletter
Handling floating-point exceptions in numeric programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Technical report for floating-point exception handling
ACM SIGPLAN Fortran Forum - Special issue: draft technical reports
Implementing the complex arcsine and arccosine functions using exception handling
ACM Transactions on Mathematical Software (TOMS)
Algorithm 786: multiple-precision complex arithmetic and functions
ACM Transactions on Mathematical Software (TOMS)
On computing givens rotations reliably and efficiently
ACM Transactions on Mathematical Software (TOMS)
Complex Square Root with Operand Prescaling
Journal of VLSI Signal Processing Systems
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Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in FORTRAN 77 and FORTRAN 9, namely, cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding FORTRAN programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results of these tests are included in the paper, but the FORTRAN programs are not.