Adrian Lita

Square root approximate calculation function for 32bit embedded C

by Adrian Lita - on 2018-07-23

Keywords: #sqrt #fast-sqrt #c #embedded #32bit #snippet

These days I needed to implement in an embedded algorithm a simple RMS (Root Mean Squre) calculation over an analog-to-digitally converted signal. My most eager and resource consuming problem was, after the efficient accumulation of data (calculating the sum of squares), I needed to extract the square root.

After a couple of Google searches, I found the Newtonian method for calculating the square root pretty effective, and I also found a C-implementation that I'm sharing with you (credits go to Hacker's Delight for their implementation, on which I made small changes):

float fast_sqrt(const float x)
    int32_t ix;
    float x;
  } un;

  un.x = x;                            // x can be viewed as int
  un.ix = 0x1fbb3f80 + (un.ix >> 1);   // Initial guess.
  un.x = 0.5f*(un.x + x/un.x);         // Newton step.
  un.x = 0.5f*(un.x + x/un.x);         // Newton step again.
  return un.x;

Please note and be very careful, as this functions only works properly on 32-bit machines (where sizeof(float) == 4).