Use std::atan (::atan is double-only)

[WOnder93]

::atan is the C version of the atan function and is not overloaded (it only works with doubles, ::atanf is for floats). Therefore the current code first casts the score to float, divides it by 128.0F, then converts it to double and the rest of the computation is done with double precision. The cast to float indicates that this was not the intended behavior (and it is also a waste).

This patch switches tostd::atan, which is the C++ version of this function and has overloads for both float and double and thus behaves as expected.

This seems to be a non-functional change (bench stays the same), although the resulting values might be slightly different in some corner case.

Compiler Explorer link (for assembly output difference)

[Stefano80]

What problems are solved by this patch exactly?

[WOnder93]

Current code is equivalent to:

float step1 = float(previousScore) / 128;
double step2 = double(step1);
double step3 = std::atan(step2);
double step4 = 48 * step3;
double step5 = std::round(step4);
ct += int(step5);

while the new code is simply:

float step1 = float(previousScore) / 128;
float step2 = std::atan(step1);
float step3 = 48 * step2;
float step4 = std::round(step3);
ct += int(step4);

[ceebo]

We could avoid conversions to float altogether using the expression:

ct += 88 * previousScore / (std::abs(previousScore) + 200);

It approximates the expression in master to within +/-5 over the range [-1000,1000] but it would be a functional change and require proper testing.

[gonlem]

Ceebo's formula don't use trigonometric function and is (subjectively) easier to understand. His formula is probably computationally faster than the atan version. Could it be considered as a simplification ?

https://docs.google.com/spreadsheets/d/1jPfg0sZeX-zgjxn9J9B9M4bNgsXh0740wDjPGO1oOIM/edit?usp=sharing

[vondele]

@ceebo I think your expression should be tested with [-3,1] bounds, getting rid of the floats and conversions altogether is a simplification in my opinion.

[snicolet]

The discussion has shifted to an alternative formula for dynamic contempt (again ?!?), but the use of atan is fine in current master, in my opinion. So I am closing this pull request about the use of "std::atan" against "atan".