a more precise distance algorithm

[Brian Blais]

On Mon, May 25, 2015 at 11:11 PM, Steven D'Aprano <steve at pearwood.info> wrote:
>
> Let's compare three methods.
>
> def naive(a, b):
>     return math.sqrt(a**2 + b**2)
>
> def alternate(a, b):
>     a, b = min(a, b), max(a, b)
>     if a == 0:  return b
>     if b == 0:  return a
>     return a * math.sqrt(1 + b**2 / a**2)


>     d1 = naive(a, b)
>     d2 = alternate(a, b)
>     d3 = math.hypot(a, b)
>

> which shows that:
>
> (1) It's not hard to find mismatches;
> (2) It's not obvious which of the three methods is more accurate.
>

Bottom line: they all suck.  :)

I ran the program you posted, and, like you, got the following two examples:

for fun in [naive, alternate, math.hypot]:
    print '%.20f' % fun(222.44802484683657,680.255801504161)

715.70320611153294976248
715.70320611153283607564
715.70320611153283607564

and

for fun in [naive, alternate, math.hypot]:
    print '%.20f' % fun(376.47153302262484,943.1877995550265)

1015.54617837194291496417
1015.54617837194280127733
1015.54617837194291496417

but when comparing to Wolfram Alpha, which calculates these out many
more decimal places, we have for the two cases:

715.7032061115328768204988784125331443593766145937358347357252...
715.70320611153294976248
715.70320611153283607564
715.70320611153283607564

1015.546178371942943007625196455666280385821355370154991424749...
1015.54617837194291496417
1015.54617837194280127733
1015.54617837194291496417

where all of the methods deviate at the 13/14 decimal place.



bb


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