Avoid Remainder Operations

Avoid Remainder Operations

One common use of the remainder operator is the use of modulo arithmetic, such as the wraparound array implementation of a queue abstract data type, where the value of a variable is cyclically counted from 0 up to N-1, and then back to 0. The most common idiom for coding this is:

    x = (x + 1) % N;

However, the % operator is expensive, and in this case it is not really needed. The following code sequence performs the same task more efficiently:

    if (x == N - 1)
        x = 0;
    else
        x++;

This can also be written more concisely, but not necessarily more efficiently, as an expression with the “?:” ternary operator:

    (x == N - 1) ? (x = 0) : (x++);

Another example of a clever avoidance of % is when the operand is similar to the usual byte or word size. For example, consider this remainder:

    x % 256

This can be more efficiently coded with bitwise-and using:

    x & 255

But this can be even more efficiently coded as a type cast:

    (unsigned char) x

The conversion to this “unsigned char” type will be efficiently implemented by grabbing a byte out of a word. Unfortunately, this method is not portable to all obscure systems, as it relies on an “overflow” being handled harmlessly, and on “unsigned char” always containing 8 bits.

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