> I have a problem with valgrind since I did convert
> my program to use long double instead double on
> critical points. Here is an example code:  [snipped]

> Due to that precision loss, I cannot further use valgrind. Some numeric
> integals etc. heavily depend on numeric precision...

valgrind handling only single- and double-precision floating point is
well documented.

If 53 bits of fractional precision are not enough, then the question
becomes, "Why are 64 bits enough?  Why aren't 2*53 bits, or 53+64 bits,
or 2*64 bits, or more, required?"

If you must have both such high precision and valgrind, then convert
to software double precision.  Represent each quantity by the sum of
two 'double's, such that the difference in exponents is near 53.
[Have fun with the many corner cases: exponent underflow, ...]

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