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.