PWR031: Replace call to pow by multiplication, division and/or square root

Issue

The pow mathematical function is computationally expensive and in many cases can be replaced by faster mathematical operations.

Relevance

Function pow is commonly used in scientific computations. In general, it is an expensive function. However, in some cases when the value of exponent is known at compile time, its runtime can be greatly reduced by replacing it with a combination of multiplications, divisions and square roots.

Actions

Replace the pow invocation by the corresponding calculation involving multiplications, divisions and/or square roots.

Notes
Some compilers under some circumstances (e.g. relaxed IEEE 754 semantics) can do this optimization automatically. However, doing it manually will guarantee best performance across all the compilers.

Code example

The following code invokes pow to calculate x^1.5:

void example(float x) {
  float res = pow(x, 1.5);
}

This can also be accomplished by multiplying x by its square root, which is faster:

void example(float x) {
  float res = x * sqrt(x);
}

References

• PWR031 examples at GitHub