Booth Martin wrote on 18/08/2007 13:42:48:
I am printing a 13-month graph of values. I can find the highest value,
which might range from tens to millions. The graph's vertical scale
will have 5 values. I plan to reduce the top scale number to be less
than 100,000. But I want it to be an even value that is a larger value
than the highest of the 13 values I am graphing. Since I want to deal
with whole numbers on the graph, my target is to calculate the lowest
number, then multiply it by 2, 3, 4, & 5 to get the other values.
For instance I am thinking that it might be something like this:
Highest value First scale value
123 25
1234 250
12345 2500
123456 25 (x000)
1234567 250 (x000)
12345678 2500 (x000)
This is kind of a long answer, so here's the executive summary:
I think you need three procedures. One will find the number of digits in
a given integer, one will take a number and round it to next highest
multiple of a some other number, and another will determine what number
you should round to in order to have 'nice' values for your scale.
The reasoning:
It looks to me like two separate problems.
1. How to determine the highest number on the scale for numbers less than
100 000?
Essentially, it seems your goal is to round to the next highest X. So, if
X=25, then result values would be 0,25,50,etc. The algorithm is as
follows (with i = input value):
y = i mod X
if ( y = 0 )
return i
else
return i - y + X
So the now the problem is how to determine what X should be for a
particular highest value. What are acceptable values for the scale
markers? Is your goal to have as little "wasted" space at the top of the
graph as possible, or to ensure that the scale values are "pretty" (that
is, multiples of 5 or something like that)?
I expect that you want your scale values to be integers, so X should be a
multiple of 5. So, to minimize wasted space you could choose X = 5 no
matter what the highest value is. If your goal is prettiness, then it
gets more complicated. I think a good way would be to use the formula X
=Y / 4, where Y = (10^(number of digits - 1)). The -1 is because 1000 is
10^3, not 10^4.
2. How to map values greater than 100 000 into the range [0,100 000]?
For the second problem, I guess the simplest solution would be to drop
enough of the least significant digits so that the highest value will fit
in the range. So, (10, 100, 1000, 123456, 12345678, 10000, 50000) => (0,
0, 1, 123, 12345, 10, 50).
In both problems 1 and 2, as well as using Antonio's algorithm, the tricky
bit is how to efficiently find the number of digits in a given number. I
can think of two ways to do this in RPG:
a) Divide by successive powers of 10 until the result is less than 1. The
number of times you need to divide is the number of digits. This is a
good candidate for a recursive procedure:
numberOfDigits (input)
if ( (input / 10) < 1 )
return 1
else
return numberOfDigits(input/10) + 1
endif
endproc
b) numberOfDigits = %len(%trimR(%char( input )))
HTH,
Adam
P.S. - can you tell I'm a math nerd?
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