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Asked: 2026-05-15T18:58:59+00:00

please ignore this post, I misread algorithm, so the question is not relevant. However,

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please ignore this post, I misread algorithm, so the question is not relevant.
However, I cannot close post anymore.
Please vote to close

I have been using certain algorithm from numerical recipes, which converges to zero via underflow:

// all types are the same floating type
sum = 0
for (i in 0,N)
   sum += abs(V[i]);

my question, how does it happen? how does sum of small positive floating-point numbers converge to underflow/zero?

is there some condition where 0 + f = 0 , f > 0?

algorithm in question is Jacoby, http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f11-1.pdf, page 460.
It is quite possible I misunderstand how the convergence is achieved, if so, please correct me.

thank you

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1 Answer

  1. Editorial Team

    If V is an array of doubles and sum is a float (or single), you can certainly have values that are > 0 but when added to sum produces 0 if they are smaller than the smallest non-zero denormalized value representable in a float.

    How do you know sum is actually zero and not just really really close? Are all bits set to zero?

    EDIT: after reading the actual application, the underflow to zero remark is probably referring to repeated rotations around various axes to determine the eigenvalues and eigenvectors of a matrix. In that case, the algorithm only works if you can assume that repeated multiplications of very small numbers will clamp or underflow to zero. The actual sum won’t underflow itself, however.

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