Raymond Hettinger <raymond.hettin...@gmail.com> added the comment:
Per the referenced paper, here's what is involved in further reducing error:
def hypot(*coords):
# Corrected, unfused: https://arxiv.org/pdf/1904.09481.pdf
# Simplified version omits scaling and handling of wide ranges.
# Only handle the 2-dimensional cases.
# Has 1 ulp error 0.88% of the time (0.54% per the paper).
# Can be reduced to 0.00% with a reliable fused multiply-add.
a, b = map(fabs, coords)
h = sqrt(a*a + b*b)
if h <= 2*b:
delta = h - b
x = a*(2*delta - a) + (delta - 2*(a - b))*delta
else:
delta = h - a
x = 2*delta*(a - 2*b) + (4*delta - b)*b + delta*delta
return h - x/(2*h)
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<https://bugs.python.org/issue41513>
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