Making a basic algorithm - the more interesting version

Question

See the edit history of "Making a basic algorithm". There was a palpable sense of disappointment amongst the respondents when OP changed the question, invalidating some interesting answers. So, I figure, why not ask the original question again, to allow those answers to stand.

So basically I want to find a easier way to do this:

if(size == 2)  unit /= 2;
if(size == 2 || size == 6) unit /= 2;
if(size == 2 || size == 6 || size == 10) unit /= 2;

So basically it checking if size is equal to 2 and then every new line it add 4 to the last size check.

I need to go up to 256.

I want to know if there a easy way of doing this.

Answer 1

The fundamental criterion on the numbers checked for equality here is that the remained of size / 4 is 2. This can be detected using the modulo operator, %:

size % 4 == 2

Then there is the question of how many times to divide unit by 2. For the examples above:

• For size == 2, unit /= 8 (matches all 3 conditions);
• For size == 6, unit /= 4 (matches second 2 conditions);
• For size == 10, unit /= 2 (matches last condition).

So the smaller the number, the more times it is divided by 8. If the maximum size checked is 10, unit is divided by 2 ^ (1 + (10 - size) / 4). This can be expressed concisely using the right-shift operator:

unit >>= 1 + (10 - size) / 4

or, more generally:

unit >>= 1 + (max_number - size) / 4

where max_number % 4 == 2.

Setting max_number = 254 (256 is specified in the question, but wouldn't feature in the expression; the last number checked would be 254), and noting that we only apply this if 2 <= size <= 254, we can express the final answer as:

if (size % 4 == 2 && size >= 2 && size <= 254) {
  unit >>= 1 + (254 - size) / 4;
}

Actually, the condition can be expressed more concisely (but undoubtedly less readably) as:

if ((size & 0xffffff03) == 2)

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As noted by @PaulBoddington, care needs to be taken with the size of the right shift: if unit is an int and the number of bits shifted is greater than 31, then unit should simply be set to zero.