Tim Peters <[email protected]> added the comment:
One more implication: since the quality of the initial square root doesn't
really much matter, instead of
result = sqrt(to_float(parts))
a, b = split(result)
parts = add_on(-a*a, parts)
parts = add_on(-2.0*a*b, parts)
parts = add_on(-b*b, parts)
x = to_float(parts)
result += x / (2.0 * result)
at the end, it should work just as well (in fact, probably a little better, due
to getting more beneficial cancellation) to do:
a = parts[0] - 1.0
result = sqrt(a)
x, y = split(result)
result += (a - x*x - 2.0*x*y - y*y + parts[1]) / (2.0 * result)
at the end. Although this crucially relies on the doing the last-line chain of
subtracts and adds "left to right".
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<https://bugs.python.org/issue41513>
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