[issue41513] Scale by power of two in math.hypot()

[Raymond Hettinger]

Raymond Hettinger <raymond.hettinger at 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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