Remark on remarks on algorithm 48: of a complex number
Communications of the ACM
Algorithm 243: Logarithm of a complex number[B3] rewrite of algorithm 48
Communications of the ACM
Algorithm 48: logarithm of a complex number
Communications of the ACM
Certification of Algorithm 48: Logarithm of a complex number
Communications of the ACM
Remark on Algorithm 48: Logarithm of a complex number
Communications of the ACM
Notation for complex "part" functions
ACM SIGAPL APL Quote Quad
Extension of APL primitive functions to the complex domain
ACM SIGAPL APL Quote Quad
Design choices for complex APL
ACM SIGAPL APL Quote Quad
Complex APL: comments from the APL community
ACM SIGAPL APL Quote Quad
APL '79 Proceedings of the international conference on APL: part 1
Revised report on the algorithmic language scheme
ACM SIGPLAN Notices
Proposed standard for a generic package of complex elementary functions
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
Rationale for the proposed standard for a generic package of complex elementary functions
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
Report on the programming language Haskell: a non-strict, purely functional language version 1.2
ACM SIGPLAN Notices - Haskell special issue
Complex Gaussian integers for “Gaussian graphics”
ACM SIGPLAN Notices
Revised report on the algorithmic language scheme
ACM SIGPLAN Lisp Pointers
Revised Report on the Algorithmic Language Scheme
Higher-Order and Symbolic Computation
APL '82 Proceedings of the international conference on APL
Journal of Functional Programming
Handling of Complex Numbers in the $C^H$ Programming Language
Scientific Programming
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Complex numbers are useful in science and engineering and, through analogy to the complex plane, in two-dimensional graphics, such as those for integrated-circuit layouts. The extension of APL to complex numbers requires many decisions. Almost all have been discussed in detail in a recent series of papers. One topic requiring further discussion is the choice of branch cuts and principal values for the primitive APL functions that require them. Conventional mathematical notation and the experience of other computer languages are of only moderate help. For example, one cannot find in the mathematics or computer-science literature a definitive value for the principal value of the arcsin of 3. The extension of APL to the complex domain presents a unique opportunity to define a set of choices that will best serve APL and other languages. This paper recommends locations of all branch cuts, directions of continuity of the branch cuts, and values at the branch points. It also recommends that comparison tolerance be used in the selection of principal values. The results apply to APL, other languages, applications packages, and VLSI hardware for complex calculations.