Reciprocal, RSqrt, and Sqrt

On the PowerVR Rogue and Volcanic architectures, the reciprocal operation is directly supported by an instruction (RCP):

fragColor.x = 1.0 / t.x;
{rcp}

The same is true with the inversesqrt() function (RSQ):

fragColor.x = 1.0 / t.x;
{rsq}

However, sqrt() is implemented as: 1 / (1/sqrt(x)).

This results in a two cycle cost:

fragColor.x = sqrt(t.x);
{rsq}
{rcp}

A commonly used alternative: x * 1/sqrt(x) gives the same two cycle results.

fragColor.x = t.x * inversesqrt(t.x);
{rsq}
{mul}

The only case when it is better to use the above alternative is if the result is tested. In this case, the test instructions can fit into the second instruction.

fragColor.x = sqrt(t.x) > 0.5 ? 0.5 : 1.0;
{rsq}
{rcp}
p0 = r0 > 0.5f (sc42)
{movc}
-->
fragColor.x = (t.x * inversesqrt(t.x)) > 0.5 ? 0.5 : 1.0;
{rsq}
{mul}
p0 = i0 > 0.5f (sc42)
{movc}