[issue11658] complex sqrt error

[STINNER Victor]

STINNER Victor <victor.stinner at haypocalc.com> added the comment:

(-1)**.5 is the same than complex(-1,0)**.5, but it is computed differently than cmath.sqrt(-1).

-1.**0.5 computes:

  vabs = math.hypot(-1, 0)
  len = pow(vabs, 0.5)
  at = math.atan2(0, -1)
  phase = at * 0.5
  return complex(len*math.cos(phase), len*math.sin(phase))

whereas cmath.sqrt(-1) computes:

  ax = math.fabs(-1)
  ay = math.fabs(0)
  ax /= 8.
  s = 2. * math.sqrt(ax + math.hypot(ax, ay/8.))
  d = ay / (2.*s)
  return complex(d, math.copysign(s, 0))

Anyway, math.sqrt() and cmath.sqrt() are designed to be more precise than x**0.5.

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nosy: +haypo, mark.dickinson

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<http://bugs.python.org/issue11658>
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