This is a question of floors and logarithms and bases and cabbages and kings and why the sea is boiling hot and whether pigs have wings.

Question

Ok the literary reference is possibly not part of this question. 

Is there a function to make x into the highest multiple of 8 the is lower than or equal to x? For instance, 13 would become 8, because 8 is the largest multiple of 8 less than or equal to 13. 8, 9, 10, 11, 12, 14, and 15 would also go to 8. 16-23 would go to 16, because 16 is the largest multiple of 8 less than or equal to those numbers. the graph is very odd, as you can imagine, but is the some sort of logarithm function or flooring function that you can use to do this? Again that is a function that turns x into the largest multiple of 8 which is less than or equal to x. for numbers less than 8, I consider 0 a multiple of 8. Thank you.

 

-- George

Answer 1

You want 8n ≤ x < 8(n+1), where n = 1, 2, 3, ...

 

I can't think of an elegant function, but I can think of a procedure.  To get n, divide x by 8 and drop the remainder (or truncate the quotient).  Using your example, 13/8 = 1 remainder 5.  n, then, is equal to 1 and 8*1 = 8.  Here are a few other examples: 

 

 x                       n                             8*n

25              25/8 = 3 rem 1          8*3= 24

47              47/8 = 5 rem 7          8*5= 40

259            259/8 = 32 rem 3      8*32= 256

 

Hope that helps.