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Throughout UHD, we often do floating-point comparisons for frequency
ranges that require resilience to floating point rounding errors. Most
of the time the checks look like this:
```cpp
if (fp_compare_epsilon<double>(freq) > boundary) {
// ...
}
```
The exception is the N320 daughterboard control, which uses a custom
epsilon:
```cpp
if (fp_compare_epsilon<double>(freq,
RHODIUM_FREQ_COMPARE_EPSILON) > boundary) {
// ...
}
```
This was, for the most part, not by design, but because authors simply
didn't think about which epsilon value was appropriate for the frequency
comparison. This was complicated by the fact that fp_compare_epsilon
previously had some issues.
This patch introduces FREQ_COMPARE_EPSILON, which is a sensible default
value for fp_compare_epsilon when doing frequency comparisons (note that
fp_compare_delta already had such a value).
Also, it introduces freq_compare_epsilon(x), which is a shorthand for
fp_compare_epsilon<double>(x, FREQ_COMPARE_EPSILON).
We then replace all occurrences of fp_compare_epsilon<double> which are
specific to frequency checks with freq_compare_epsilon.
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UHD had an issue where the design of fp_compare_epsilon and its usage
differed. In fact, the *only* usage of fp_compare_epsilon outside of
unit tests was to do a fuzzy frequency comparison, and it always took
a form like this:
```cpp
// The argument EPSILON may be implied, i.e., using the default
if (fp_compare_epsilon<double>(test_freq, EPSILON) < boundary_freq) {
// ...
}
```
However, the API of fp_compare_epsilon was such that it would apply
DOUBLE_PRECISION_EPSILON to part of the frequency comparison, thus
rendering the argument EPSILON obsolete. When the default EPSILON was
used, this was OK, but only when the floating point type of
fp_compare_epsilon<> was `double`, and not `float`.
As an example, consider the following:
```
if (fp_compare_epsilon<double>(1e9 + x, LITTLE_EPSILON) == 1e9) {
// ....
}
double BIG_EPSILON = x * 10;
if (fp_compare_epsilon<double>(1e9 + x, BIG_EPSILON) == 1e9) {
// ....
}
```
If you expect the second comparison to pass even if the first failed,
then you are not alone. However, that's not what UHD would do. Because
of the aforementioned behaviour, it would use DOUBLE_PRECISION_EPSILON
for the right hand comparison, which would fail again.
Instead of fixing the instances of fp_compare_epsilon throughout UHD,
this patch changes the comparison algorithm from "very close with
tolerance epsilon" to "close enough with tolerance epsilon". This
requires only one side to be close to the other, using its own epsilon,
so the aforementioned example would always pass on the second check.
However, this exposed a second bug in fp_compare_epsilon. For
greater-/less-than comparisons, it would use epsilon like a delta value,
i.e., it would check if
a + epsilon < b - epsilon
That means that if a < b, but (b-a) < 2*epsilon, this check would return
"false", i.e., it would report that a >= b, which is incorrect. These
operators are now changed such that they first check equality of a and
b using the algorithm described in the code, and then compare the values
of a and b (ignoring epsilon) directly. A unit test for this case was
added.
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