Cleanup Issue COMPLEX-RATIONAL-RESULT

Status
Version 3 passed Jun89 X3J13 (Version 1 passed March 89, but had problems)
Category
CLARIFICATION
References
CLtL p.203

Problem Description

Referring to irrational and transcendental functions, CLtL says:

When the arguments to a function in this section are all rational and the true mathematical result is also (mathematically) rational, then unless otherwise noted an implementation is free to return either an accurate result of type rational or a single-precision floating-point approximation. If the arguments are all rational but the result cannot be expressed as a rational number, then a single-precision floating-point approximation is always returned.

Referring to EXPT, CLtL says:

If the base-number is of type RATIONAL and the power-number is an INTEGER, the calculation will be exact and the result will be of type RATIONAL; otherwise a floating-point approximation may result.

What about arguments of type (complex rational)?

Proposal (EXTEND)

Extend the paragraph quoted above as follows to cover the components of complex numbers. If the arguments to a function are all of type (OR RATIONAL (COMPLEX RATIONAL)) and the true mathematical result is (mathematically) a complex number with rational real and imaginary parts, then unless otherwise noted an implementation is free to return either an accurate result of type (OR RATIONAL (COMPLEX RATIONAL)) or a single-precision floating-point approximation of type SINGLE-FLOAT (permissible only if the imaginary part of the true mathematical result is zero) or (COMPLEX SINGLE-FLOAT). If the arguments are all of type (OR RATIONAL (COMPLEX RATIONAL)) but the result cannot be expressed as a rational or complex rational number, then the returned value will be of type SINGLE-FLOAT (permissible only if the imaginary part of the true mathematical result is zero) or (COMPLEX SINGLE-FLOAT).

For EXPT of a (COMPLEX RATIONAL) to an integer power, the calculation must be exact and the result will be of type (OR RATIONAL (COMPLEX RATIONAL)).

Examples

[a]  (log #c(-16 16) #c(2 2)) => 3 or approximately #c(3.0 0.0)
			           or approximately 3.0 (unlikely)
[b]  (abs #c(3/5 4/5)) => 1 or approximately 1.0
[c]  (expt #c(2 2) 3) => #c(-16 16)
[d]  (expt #c(2 2) 4) => -64 

Rationale

This seems most consistent with the treatment of real numbers.

Current Practice

[a] [b] [c] [d] Symbolics Genera 7.4 #c(3.00... 1.40...e-7) 1 #c(-16 16) -64 Sun Common Lisp 3.0.1 #c(3.0 2.61...e-16) 1.0 #c(-16 16) -64 KCL of 9/16/86 on VAX #c(3.0s0 -1.40...s-7) 1.0s0 #c(-16 16) -64 Allegro CL (Mac II) #c(3.0 2.05...e-16) 1.0 #c(-16 16) -64

Cost to Implementors

Only EXPT would have to change, since the type of the other results is at the discretion of the implementation.

Cost to Users

Probably none, but it is hard to predict.

Cost of Non-Adoption

Slightly less self-consistent language.

Performance Impact

None of any significance.

Benefits/Esthetics

More self-consistent language.

Discussion

None.

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