performance tuning - Faster alternatives for DayOfWeek

It has been noticed on several occasions that DayOfWeek function is rather slow when applied to a large list of dates, e.g. in this recent question. What faster alternatives do we have in such situations?

Answer

Just a literal implementation of a formula for the day of the week:

Clear[dow];

dow[{year_, month_, day_, _ : 0, _ : 0, _ : 0}] :=
  Module[{Y = If[month == 1 || month == 2, year - 1, year], 
    m = Mod[month + 9, 12] + 1, y, c, 
    s = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}},
    y = Mod[Y, 100];
    c = Quotient[Y, 100];
    s[[Mod[day + Floor[2.6 m - 0.2] + y + Quotient[y, 4] + Quotient[c, 4] - 2 c, 7] + 1]]];

Seems to give a 5-fold speed increase:

d = RandomDates[100000];

DayOfWeek /@ d // Short // AbsoluteTiming
dow /@ d // Short // AbsoluteTiming

{19.5781250,{Thursday,Thursday,Sunday,Friday,<<99992>>,Tuesday,Saturday,Saturday,Thursday}}

{3.7968750,{Thursday,Thursday,Sunday,Friday,<<99992>>,Tuesday,Saturday,Saturday,Thursday}}

Addition

Your function is readily compilable:

dowc = Compile[{{year, _Integer}, {month, _Integer}, {day, _Integer}},

    Module[
        {Y, m, y, c, s},
        Y = If[month == 1 || month==2, year-1, year];
        m = Mod[month + 9, 12] + 1; 
        y = Mod[Y, 100]; c = Quotient[Y, 100];
        Mod[day + Floor[2.6 m-0.2] + y + Quotient[y, 4] + Quotient[c, 4]-2 c,7]+1
    ],
    CompilationTarget -> "C",
    RuntimeAttributes -> {Listable},
    Parallelization -> True

];

In[286]:= dowc @@@ d[[All, 1 ;; 3]] // Short // AbsoluteTiming
Out[286]= {0.136741,{6,4,5,2,4,5,3,7,<<99984>>,5,4,2,4,3,2,5,6}}

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