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  • #77
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Issue created Jan 01, 2020 by Raymond Toy@rtoyOwner

sqrt incorrect for exceptional values?

Kahan's paper (Branch Cuts for Elementary Functions) gives an algorithm for the complex square root and mentions the following special cases:

  • sqrt(-beta +/- i0) = +0 +/- sqrt(beta), beta >= 0
  • sqrt(x +/- i inf) = +inf +/- i inf for all finite x
  • sqrt(NaN + i beta) = NaN + i NaN
  • sqrt(beta + i NaN) = NaN + i NaN
  • sqrt(NaN + i NaN) = NaN + i NaN
  • sqrt(inf +/- i beta) = +inf +/- i0
  • sqrt(inf +/- i NaN) = +inf + i NaN
  • sqrt(-inf +/- i beta) = +0 +/- i inf
  • sqrt(-inf +/- i NaN) = NaN +/- i inf

Our implementation of sqrt doesn't satisfy these cases:

  • (sqrt (complex 4 ext:double-float-negative-infinity)) = #C(#.EXT:DOUBLE-FLOAT-POSITIVE-INFINITY #.EXT:DOUBLE-FLOAT-NEGATIVE-INFINITY)
  • (sqrt (complex ext:double-float-negative-infinity *nan*)) = #C(#<DOUBLE-FLOAT Quiet NaN> #.EXT:DOUBLE-FLOAT-NEGATIVE-INFINITY)
  • (sqrt (complex ext:double-float-negative-infinity (- *nan*))) = #C(#<DOUBLE-FLOAT Quiet NaN> #.EXT:DOUBLE-FLOAT-POSITIVE-INFINITY)

We should fix these and add tests for these cases.

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