Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Mathematica: a system for doing mathematics by computer
Mathematica: a system for doing mathematics by computer
Common LISP: the language (2nd ed.)
Common LISP: the language (2nd ed.)
The C programming language
The C++ programming language (2nd ed.)
The C++ programming language (2nd ed.)
Rationale for the proposed standard for a generic package of elementary functions for Ada
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
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
Less complex elementary functions
ACM SIGPLAN Notices
Communications of the ACM
Principal values and branch cuts in complex APL
APL '81 Proceedings of the international conference on APL
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The handling of complex numbers in the $C^H$ programming language will be described in this paper. Complex is a built-in data type in $C^H$. The I/O, arithmetic and relational operations, and built-in mathematical functions are defined for both regular complex numbers and complex metanumbers of ComplexZero, Complexlnf, and ComplexNaN. Due to polymorphism, the syntax of complex arithmetic and relational operations and built-in mathematical functions are the same as those for real numbers. Besides polymorphism, the built-in mathematical functions are implemented with a variable number of arguments that greatly simplify computations of different branches of multiple-valued complex functions. The valid lvalues related to complex numbers are defined. Rationales for the design of complex features in $C^H$ are discussed from language design, implementation, and application points of views. Sample $C^H$ programs show that a computer language that does not distinguish the sign of zeros in complex numbers can also handle the branch cuts of multiple-valued complex functions effectively so long as it is appropriately designed and implemented.