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Issue COMPLEX-RATIONAL-RESULT Writeup

Issue:         COMPLEX-RATIONAL-RESULT

References: CLtL p.203

Category: CLARIFICATION

Edit history: Version 1, 20-Mar-89, by Moon

Version 2, 08-Apr-89, by Steele

Version 3, 28-Apr-89, by Steele

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 (COMPLEX-RATIONAL-RESULT: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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