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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.

Actions​

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

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.

note

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 to the power of 1.5:

#include <math.h>

void example(float *a, float x) {
  for (int i = 0; i < 10; ++i) {
    a[i] = pow(x, 1.5);
  }
}

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

#include <math.h>

void example(float *a, float x) {
  for (int i = 0; i < 10; ++i) {
    a[i] = x * sqrt(x);
  }
}

References​