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Source for wiki ComplexLog version 6

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cowan

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127.11.51.1

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ComplexLog

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== Complex logarithm ==

Guy Steele's three-part smoke test for Common Lisp involves evaluating `(atanh -2)`.  Traditionally, a Lisp passes if it returns a complex number; if it returns the ''correct'' complex number, so much the better.  The `atanh` function is not provided in R7RS-small, so I defined it as follows:

{{{
(define (atanh x)
    (/ (- (log (+ 1 x))
          (log (- 1 x)))
       2))
}}}

(Note:  KSi already defines `atanh` and will not allow its redefinition.)

Returns `-0.5493061443340549+1.5707963267948966i`, the ''correct'' complex number:  Racket, Gauche, MIT, Chicken with the numbers egg, Scheme48, Guile, Kawa, Chibi, Chez, Vicare, Larceny, Ypsilon, !IronScheme, STklos, KSi, S7, Spark, Sagittarius

Returns NaN (i.e. it is attempting to use a real-number log function) when the argument is `2`, but returns the correct complex number when the argument is `2.0+0.0i`:  scsh, SISC, Mosh

Returns an incorrect complex number: SCM

No support for log of negative numbers: UMB, Owl Lisp

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

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2014-12-28 08:03:19