## Exact, inexact, and mixed complex numbers

Exact, inexact, and mixed complex number representations, where inexact and mixed numbers that are = are nevertheless distinct in the sense of eqv?: Gambit, Kawa, Chibi. (Also CLISP, Pure.)

Exact, inexact, and mixed complex number representations, where inexact and mixed numbers that are = are the same in the sense of eqv?: MIT, STklos.

Exact and inexact complex number representations only (mixed complex numbers become inexact): Racket, Chicken 4 with the numbers egg, Chicken 5, Scheme48/scsh, Kawa, Chez, Vicare, Larceny, Ypsilon, IronScheme, Spark, Wraith, Sagittarius. (Also ABCL, Allegro CL, Clozure CL, CMUCL, ECL, GNU CL, LispWorks, SBCL, Scieneer CL.)

Inexact complex number representations only: Gauche, Guile, SISC, SCM, KSi, S7, UMB, Stalin. (Also Fortran, C/C++, Python, etc.)

Exact complex number representations only: Owl Lisp (which has no inexact numbers).

No complex numbers: plain Chicken 4, Bigloo, Ikarus, NexJ, SigScheme, Shoe, TinyScheme, Scheme 9, Dream, RScheme, BDC, XLisp, Rep, Schemik, Elk, VX, Oaklisp, Llava, SXM, Sizzle, FemtoLisp, Dfsch, Inlab.

Mosh has a bug whereby numbers that are = are always eqv? even if they differ in exactness; it supports exact, inexact, and mixed complex number representations, but doesn't differentiate exact from inexact properly.

## The imaginary part of an inexact real number

The value of (imag-part 2.0) is exact 0: Racket, MIT, Gambit, plain Chicken, Guile, Kawa, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos, RScheme (but see below), Sizzle, Spark.

The value of (imag-part 2.0) is inexact 0.0: Gauche, Chicken with the numbers egg, Scheme48/scsh, SISC, Chibi, SCM, KSi, S7, UMB, SXM.

No imag-part procedure: Bigloo, NexJ, Shoe, TinyScheme, Scheme 9, BDC, XLisp, Rep, Schemik, Elk, VX, Llava, FemtoLisp, Dfsch, Inlab.

No inexact numbers: SigScheme, Dream, Oaklisp, Owl Lisp.

Integrating both sets of results, this means that Racket, Guile, Chez, Vicare, Larceny, Ypsilon, IronScheme, Spark behave *as if* they supported mixed-exactness complex numbers in the case where the real part is inexact and the imaginary part is exact 0, even though they do not support mixed-exactness complex numbers otherwise.

## Fake complex number support

Schemes that don't support non-real numbers can still fake support for real-part and imag-part by having the former return its argument and the latter return zero. As usual, some do and some don't:

Fake support: plain Chicken, RScheme

No support: Shoe, TinyScheme, BDC, XLisp, Sizzle, Bigloo, Scheme 9, Elk, Rep, Owl Lisp

## See also

See also NumericTower.