How to do "bitwise or aggregation" on a column? (or how to run aggregates on substrings?)

[GeoffreyS]

I would like to understand if and how I could perform a "bitwise or aggregation" on a column, to calculate the bitwise or for all values in a specific column, to be included in a DAX measure. 

Simplified dataset to explain

The (simulated and drastically simplified) source data I have is daily data which consists of the following dimensional attributes 

• date in the form of day of month / month
• customer
• category
• product_group

and has many numerical metrics, in this example represented by value_1. 

In PowerBI I have many measures defined to which sum etc. on the value_xx columns which I can group / display across many of the dimensions. 

The problem

Due to load peformance I want to change the PowerBI dashboard to monthly aggregates, vs. daily data which in 99% of the cases is looked at on a monthly basis only.  I can do a lot of aggregations to monthly basis in the SQL load scripts, because the majority of my measures is summing anyhow. 

However one of the key measures I have is the distinct count of days per month, which nicely calculates in the PowerBI report across all the different dimensions, filters, etc.  because I have the individual days as my finest granularity. When I move up to monthly granularity, I will lose the ability to run these distinct days per month counts. 

Prepare data to monthly aggregate in my source system

To overcome this challenge I thought of generating a bit string of length 31 (representing day 1 - 31 in the month) as part of my datapreparations (simple pseudo formula: string(10^(day of month -1)) 

So:

• on day 1- bit 1 is set to 1
• on day  2, bit 2 is set to 1
• ...
• on day 31, bit 31 is set to 1

an example can be found in the 'day_of_month_bit_position' column in the sample data set below. 

since this is a string, I can also calculate the decimal reprenstation for this based on bin2dec conversions in my source system. 

that's what is found in day_of_month_bit_as_decimal. 

In my source I can also generate the bitwise or aggregates when grouping into my month aggregates, which practically means that for each position in the string the maximum value is taken across all observations I aggregate over. So the monthly aggregate will have 1s on the bits representing the days we had data for. 

Examle (with week bit string representing mo-sun, because 31 is a lot of 1s and zeroes in an example):

• aggregate 1, data on mon, wed and fri --> 1010100 (3 unique days)
• aggregate 2, data on wed, fri, sat and sun --> 0010111 (4 unique days)

the bitwise or of this results in 1010111 (5 unique days, mon, wed, fri, sat, sun) 

How to do this same aggregation in PowerBI using a measure?

I want to be able to do this same 'bitwise or aggregation' in PowerBI to count the unique days in my current context, to do so I thought of the following steps

• generate the 'bitwise or aggregated' bit string
• sum all 1s / bit_count the bit string 
• return this value as the unique days

Struggling to get it working

I have been banging my head against the wall now for some hours to get anywhere with this. Constantly ending up in dead ends 😞 .

To summarize (in the example below):

• when I aggregate
  • month 2
  • for customer_1 
• the bitwise or aggregate should result in 0000100100000100000000000000000
• summing over/bitcounting this bit string results in 3 unique days. 

Note: I know this is still daily data, I on purpose provided this example instead of the monthly_pre_aggregates which I can create from my source, because validation of the calculation is still possible, since day_of_month is present. 

[Greg_Deckler]

@GeoffreyS Can you post that data as text? There are a number of DAX bit operations that you can find here, including BITOR:

A-B Excel to DAX Translation - Microsoft Fabric Community

[GeoffreysS]

@Greg_Deckler 

copy paste from my other message below allows for reading in as tsv. 

for completeness here is .csv format as well. 

With regards to the bitwise functions available, they are meant for comparing two values bitwise, not so much to apply them in an aggregation ( i think 😉 ). 

If there is a way to do something like this pseudo code example in DAX it could be an option:

running_bitwise_or_agg = 0

for each value val_x in column x from all rows in table in context:
   running_bitwise_or_agg = BITOR(val_x, running_bitwise_or_agg)

csv

day_of_month,month,customer,category,product_group,value_1,day_of_month_bit_position,day_of_month_bit_as_decimal, ,day_of_month_bit_as_csv
24,2,customer_1,cat a,prod_group_1,62,0000000100000000000000000000000,8388608, ,"0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
27,2,customer_1,cat a,prod_group_2,67,0000100000000000000000000000000,67108864, ,"0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
18,2,customer_1,cat b,prod_group_3,20,0000000000000100000000000000000,131072, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
29,3,customer_1,cat c,prod_group_4,57,0010000000000000000000000000000,268435456, ,"0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
21,3,customer_1,cat a,prod_group_5,59,0000000000100000000000000000000,1048576, ,"0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
5,3,customer_1,cat b,prod_group_6,78,0000000000000000000000000010000,16, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0"
29,1,customer_2,cat b,prod_group_7,20,0010000000000000000000000000000,268435456, ,"0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
17,4,customer_2,cat c,prod_group_8,53,0000000000000010000000000000000,65536, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
10,5,customer_2,cat b,prod_group_6,46,0000000000000000000001000000000,512, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0"
10,1,customer_3,cat a,prod_group_5,81,0000000000000000000001000000000,512, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0"
17,1,customer_3,cat b,prod_group_3,22,0000000000000010000000000000000,65536, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
1,1,customer_3,cat c,prod_group_4,63,0000000000000000000000000000001,1, ,"0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1"
27,3,customer_3,cat c,prod_group_13,77,0000100000000000000000000000000,67108864, ,"0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"
30,3,customer_3,cat a,prod_group_5,41,0100000000000000000000000000000,536870912, ,"0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0"

[Greg_Deckler]

@GeoffreyS @GeoffreysS Hey, how about that, we invented something new! The XBITOR! See attached PBIX file below signature.

XBITOR = 
    VAR __RowCount = COUNTROWS('bitor')
    VAR __Length = LEN(MAX('bitor'[day_of_month_bit_position]))
    VAR __String = CONCATENATEX('bitor', [day_of_month_bit_position])
    VAR __Table = 
            ADDCOLUMNS(
                GENERATESERIES(0, __RowCount * (__Length - 1)),
                "__Bit", MID(__String, [Value]+1, 1) + 0,
                "__Mod", MOD([Value], __Length + 1)
            )
    VAR __Table1 = 
        ADDCOLUMNS(
            GENERATESERIES(0, __Length),
            "__BITOR", 
                    VAR __Index = [Value]
                    VAR __Sum = SUMX(FILTER(__Table, [__Mod] = __Index),[__Bit])
                    VAR __Result = IF(__Sum = 0, 0, 1)
                RETURN
                    __Result
        )
RETURN
    CONCATENATEX(__Table1, [__BITOR],,[Value],ASC)

[GeoffreysS]

Hi @Greg_Deckler 

Thanks a lot... that was fast 😉 

I am gonna check tomorrow... but it looks promising 😉 

I might be over asking here, but is there a fast way to get the sum of all the ones back as well? (that's the actual unique day count)

[Greg_Deckler]

@GeoffreysS Found a bug, fixed in these versions:

XBITOR = 
    VAR __RowCount = COUNTROWS('bitor')
    VAR __Length = LEN(MAX('bitor'[day_of_month_bit_position]))
    VAR __String = CONCATENATEX('bitor', [day_of_month_bit_position])
    VAR __Table = 
            ADDCOLUMNS(
                GENERATESERIES(0, __RowCount * __Length - 1),
                "__Bit", MID(__String, [Value]+1, 1) + 0,
                "__Mod", MOD([Value], __Length)
            )
    VAR __Table1 = 
        ADDCOLUMNS(
            GENERATESERIES(0, __Length - 1),
            "__BITOR", 
                    VAR __Index = [Value]
                    VAR __Sum = SUMX(FILTER(__Table, [__Mod] = __Index),[__Bit])
                    VAR __Result = IF(__Sum = 0, 0, 1)
                RETURN
                    __Result
        )
RETURN
    CONCATENATEX(__Table1, [__BITOR],,[Value],ASC)

XBITOR_DEC = 
    VAR __RowCount = COUNTROWS('bitor')
    VAR __Length = LEN(MAX('bitor'[day_of_month_bit_position]))
    VAR __String = CONCATENATEX('bitor', [day_of_month_bit_position])
    VAR __Table = 
            ADDCOLUMNS(
                GENERATESERIES(0, __RowCount * (__Length - 1)),
                "__Bit", MID(__String, [Value]+1, 1) + 0,
                "__Mod", MOD([Value], __Length)
            )
    VAR __Table1 = 
        ADDCOLUMNS(
            GENERATESERIES(0, __Length),
            "__BITOR", 
                    VAR __Index = [Value]
                    VAR __Sum = SUMX(FILTER(__Table, [__Mod] = __Index),[__Bit])
                    VAR __Result = IF(__Sum = 0, 0, 1)
                RETURN
                    __Result
        )
RETURN
    COUNTROWS(FILTER(__Table1, [__BITOR] = 1))

[Greg_Deckler]

@GeoffreysS So, if I understand correctly, you want this?

XBITOR_DEC = 
    VAR __RowCount = COUNTROWS('bitor')
    VAR __Length = LEN(MAX('bitor'[day_of_month_bit_position]))
    VAR __String = CONCATENATEX('bitor', [day_of_month_bit_position])
    VAR __Table = 
            ADDCOLUMNS(
                GENERATESERIES(0, __RowCount * (__Length - 1)),
                "__Bit", MID(__String, [Value]+1, 1) + 0,
                "__Mod", MOD([Value], __Length + 1)
            )
    VAR __Table1 = 
        ADDCOLUMNS(
            GENERATESERIES(0, __Length),
            "__BITOR", 
                    VAR __Index = [Value]
                    VAR __Sum = SUMX(FILTER(__Table, [__Mod] = __Index),[__Bit])
                    VAR __Result = IF(__Sum = 0, 0, 1)
                RETURN
                    __Result
        )
RETURN
    COUNTROWS(FILTER(__Table1, [__BITOR] = 1))

[GeoffreyS]

thanks... still have not found the time to try it out.. but will in the upcomign days and let you know.. 

thanks a million again. 

[GeoffreyS]

Sample dataset here: 

day_of_month	month	customer	category	product_group	value_1	day_of_month_bit_position	day_of_month_bit_as_decimal		day_of_month_bit_as_csv
24	2	customer_1	cat a	prod_group_1	62	0000000100000000000000000000000	8388608		0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
27	2	customer_1	cat a	prod_group_2	67	0000100000000000000000000000000	67108864		0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
18	2	customer_1	cat b	prod_group_3	20	0000000000000100000000000000000	131072		0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
29	3	customer_1	cat c	prod_group_4	57	0010000000000000000000000000000	268435456		0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
21	3	customer_1	cat a	prod_group_5	59	0000000000100000000000000000000	1048576		0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
5	3	customer_1	cat b	prod_group_6	78	0000000000000000000000000010000	16		0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
29	1	customer_2	cat b	prod_group_7	20	0010000000000000000000000000000	268435456		0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
17	4	customer_2	cat c	prod_group_8	53	0000000000000010000000000000000	65536		0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
10	5	customer_2	cat b	prod_group_6	46	0000000000000000000001000000000	512		0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
10	1	customer_3	cat a	prod_group_5	81	0000000000000000000001000000000	512		0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
17	1	customer_3	cat b	prod_group_3	22	0000000000000010000000000000000	65536		0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
1	1	customer_3	cat c	prod_group_4	63	0000000000000000000000000000001	1		0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
27	3	customer_3	cat c	prod_group_13	77	0000100000000000000000000000000	67108864		0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
30	3	customer_3	cat a	prod_group_5	41	0100000000000000000000000000000	536870912		0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0