William Kahan and J. W. Thomas. Augmenting a programming language with complex arithmetics. Technical Report No. 91/667, University of California at Berkeley, Department of Computer Science, December 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of side effects in case of exceptions. A related question of extending a language with a primitive type can emulate value class semantics by means of pass by value mechanisms. complex is whether there should be a separate primitive type for imaginary numbers as well, as proposed by Kahan [9]. It is debated whether and how such a separate imaginary type should be included in the C9X proposal [2] To avoid the complexity of an extra type, our work only adds the type complex although future extensions might have the imaginary type as well. 3 Complex numbers in cj Cj extends the set of ....

William Kahan and J. W. Thomas. Augmenting a programming language with complex arithmetics. Technical Report No. 91/667, University of California at Berkeley, Department of Computer Science, December 1991.

....of side effects in case of exceptions. A related question of extending a language with a primitive type 1 C can emulate value class semantics by means of pass by value mechanisms. complex is whether there should be a separate primitive type for imaginary numbers as well, as proposed by Kahan [9]. It is debated whether and how such a separate imaginary type should be included in the C9X proposal [2] To avoid the complexity of an extra type, our work only adds the type complex although future extensions might have the imaginary type as well. 3 Complex numbers in cj Cj extends the set of ....

William Kahan and J. W. Thomas. Augmenting a programming language with complex arithmetics. Technical Report No. 91/667, University of California at Berkeley, Department of Computer Science, December 1991.

....Unfortunately, such promotion creates a zero imaginary component which has adverse consequences for complex arithmetic in some applications; spurious overflows and underflows can occur and some complex number identities are violated. Using a separate imaginary type and the formulas discussed in [63] gives fewer computational irregularities. Example code for a portion of the Complex class is listed in section 6.9.6.1. 6.5. Floating Point System Properties Processor designers have created three distinct families of IEEE 754 compliant machines. The first class of machines takes a ....

....of the lower case hexadecimal ASCII code of each operator character. For example, op is represented as op 2b 54 . 6.9.6. Operator Overloading Examples The following examples demonstrate a number of uses of Borneo operator overloading. 6.9.6.1. Complex and Imaginary Classes As discussed in [63], having separate Complex and Imaginary types gives better numerical properties to complex arithmetic. The following code is a partial implementation of a Complex class; overloaded equality and assignment operators are shown as well as various addition operators. An Imaginary value class is ....

William Kahan and J.W. Thomas, "Augmenting A Programming Language with Complex Arithmetic," Report No. UCB/CSD 91/667, December 1991.

....unless x or y is an infinity. However, if x is infinity, y is finite, and v is nonzero (say, positive) the result should be vy i, but instead we get NaN i, since multiplication of zero and infinity yields a NaN ( Not a Number ) in IEEE arithmetic, and NaNs propagate through addition. See [Kahan 91] A similar situation can be demonstrated for the multiplication of a complex value and a pure real value, but in that case we expect to have such a mixed mode operation, and if we use it the generation of the NaN is avoided. Another subtle problem occurs when the imaginary value iv is added to ....

....occurs when the imaginary value iv is added to the complex value x iy. The result, of course, should be x i(y v) Without an imaginary type, we have to represent the imaginary value as the complex value 0.0 iv and perform a full complex addition, yielding (x 0. 0) i(y v) The problem here [Kahan 91] is that if x is a negative zero, the real component of the result of the full complex addition will have the wrong sign; it will be a positive zero instead of the expected negative zero. This phenomenon, also a consequence of the rules of IEEE arithmetic, can and does occur in existing Ada 83 ....

W. Kahan and J. W. Thomas. Augmenting a Programming Language with Complex Arithmetic. Technical Report UCB/CSD 91/667, Univ. of Calif. at Berkeley, December, 1991.

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William Kahan and J. W. Thomas. Augmenting a programming language with complex arithmetics. Technical Report No. 91/667, University of California at Berkeley, Department of Computer Science, December 1991.

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