I will provide one solution which will be using Java and a simple Java reloader I recently introduced. This solution brings to the table up to 100-fold speed-up for large lists of dates.

I will borrow @Mike's functions to generate a random list of dates, from his code in his recent question

1. Load the Java reloader

2. Compile the following class:

    JCompileLoad@
      "import java.util.*;
       public class DayOfWeekCalculator {
           public static int[] getDaysOfWeek(int[][] dateDataList){
              Calendar calendar = new GregorianCalendar();
              int[] result = new int[dateDataList.length];
              int ctr = 0;
              for(int[] date: dateDataList){                        
                 calendar.set(date[0],date[1],date[2]);
                 result[ctr++]=calendar.get(Calendar.DAY_OF_WEEK);
              }
              return result;    
           }    
       }"
   

3. The actual function is then:

    Clear[dayOfWeek];
    dayOfWeek[dates_List] :=
       DayOfWeekCalculator`getDaysOfWeek@Transpose@
           {#[[All, 1]], #[[All, 2]] - 1, #[[All, 3]]} &@dates;
   

I will provide one solution which will be using Java and a simple Java reloader I recently introduced. This solution brings to the table up to 100-fold speed-up for large lists of dates.

I will borrow @Mike's functions to generate a random list of dates, from his code in his recent question

1. Load the Java reloader

2. Compile the following class:

    JCompileLoad@
      "import java.util.*;
       public class DayOfWeekCalculator {
           public static int[] getDaysOfWeek(int[][] dateDataList){
              Calendar calendar = new GregorianCalendar();
              int[] result = new int[dateDataList.length];
              int ctr = 0;
              for(int[] date: dateDataList){                        
                 calendar.set(date[0],date[1],date[2]);
                 result[ctr++]=calendar.get(Calendar.DAY_OF_WEEK);
              }
              return result;    
           }    
       }"
   

3. The actual function is then:

    Clear[dayOfWeek];
    dayOfWeek[dates_List] :=
       DayOfWeekCalculator`getDaysOfWeek@Transpose@
           {#[[All, 1]], #[[All, 2]] - 1, #[[All, 3]]} &@dates;
   

The input is a nested list of the type you construct randomly. I subtract 1 from month, to comply with the Java conventions.

There is a 100-fold speedup for this example. Note that there is a small constant overhead of calling Java, so the larger is your list of dates, the more you gain. You will have to convert days from numbers 1-7 to strings, but you can as well do that after binning.

• You have a large collection of Mathematica pbjects, which you want to process somehow.
• The top-level overhead of explicit looping is (very) large, but the problem is not easily amenable to Compile
• The functionality you seek for is readily available via Java libraries, or can be easily implemented using those.

The input is a nested list of the type we construct randomly, which is a natural date format as it appears in Mathematica. I subtract 1 from month, to comply with the Java conventions.

There is a 100-fold speedup for this example. Note that there is a small constant overhead of calling Java, so the larger is your list of dates, the more you gain.

• You have a large collection of Mathematica objects, which you want to process somehow.
• The top-level overhead of explicit looping is (very) large, but the problem is not easily amenable to Compile
• The functionality you seek for is readily available via Java libraries, or can be easily implemented using those.