Support ^ power operator and more TMath functions in TTree::Draw expressions

[Prafyl]

This Pull request:

In ROOT ^ is the power operator in draw expressions, but jsroot passes the expression straight into a js function where ^ is like the bitwise xor operator thing. So tree.Draw("x^2") gives a histogram of x XOR 2, it doesnt give error but gives just wrong numbers. Also only TMath::Exp/Abs/Prob/Gaus were mapped, so things like TMath::Sqrt(x) or TMath::Pi() throw a syntax error on the ::.

values at x=3 from a small tree (x = 0..9), compared with TTree::Draw in ROOT 6.40:

expression           root        jsroot before   jsroot after
x^2                  9           1               9
-x^2                 -9          -1              -9
(x+1)^2              16          6               16
x^0.5                1.7320508   3               1.7320508
x^-1                 0.33333333  -4              0.33333333
2*x^2+1              19          5               19
x^2^0.5              3           1               3
TMath::Power(x,2)    9           SyntaxError     9
TMath::Sqrt(x)       1.7320508   SyntaxError     1.7320508
TMath::Pi()*x        9.424778    SyntaxError     9.424778
TMath::Max(x,5.)     5           SyntaxError     5
TMath::Sin(x)^2      0.019914857 SyntaxError     0.019914857

Changes:

• ^ gets rewritten to ** before the expression is compiled. operands are taken as names, numbers, brackets or calls, so -x^2 stays -(x**2) and a^b^c goes frpm the left side to right side, both like ROOT does (2^3^2 is 64 in root).
• added the usual TMath functions (Sqrt, Power, Log, Log10, Sin/Cos/Tan, ASin/ACos/ATan/ATan2, SinH/CosH/TanH, Floor, Ceil, Max, Min) plus TMath::Pi() and TMath::E(), mapped to the js Math equivalents.

things like tree_draw, tree_dump, tree_selector and tree_staged give the same output as before.

Fixes:

draw expressions using ^ or common TMath functions now give the same values as ROOT instead of different wrong numbers or a syntax error.

[linev]

Do we need support of not existing TMath here?

It was done for TFormula/TF1 classes while there formula can be defined in C++ and should be supported on JavaScript.

But treeDraw() functionality fully defined in JavaScript and I see no reason to introduce artificial support of TMath methods

Same is about x^y. Why not use x**y or just Math.pow(x,y)

[Prafyl]

Fair point, i didnt notice the docs say draw expressions use js Math. I'll drop the TMath part.

The only reason i did ^ is that it doesnt fail, it silently gives xor. If someone copies an expression from a ROOT macro like x^2 they get a histogram that looks fine but has wrong numbers, and nothing tells them. If you'd rather not translate it i can just close this, or i could make ^ throw an error saying to use ** instead, whichever you prefer.

[linev]

We do not need mimic C++ functionality here.

But it is valid point for TFormula - there we should care about translating C++ code to JavaScript.
And if ^ used there - one should translate it to JavaScript syntax.

If you interested - you can try extend functionality in the modules/base/func.mjs

[Prafyl]

Thanks, that makes sense, i realize treeDraw doesnt need it since its all js. I'll close this one and look into TFormula in func.mjs instead.