Finding min value of an array using SIMD
Correctness

  if( array.Length &lt;= 0 )
    return 0;


This piece of code is suspicious. Maybe you should return sbyte.MaxValue, maybe null, or maybe throw ArgumentException. (I can imagine that there were a Max method, both, together is used to find the range of values, then maybe 0 is a valid return value.) This is one of the rare times I'd appreciate a comment to explain such extrinsic information.

Useless Code

 if( i &lt; length )
      while( i &lt; length )


Lose the if.

Excessive code

When you are operating on fixed size chunks, 
 - pad the input with some appropriate value (sbyte.MaxValue)
 - handle the last fixed size chunk of the input separately.

The last suggestion should read something like this, (which means I don't even guarantee that it will compile):

if (length &lt; stepSize)
    throw new ArgumentException($"this method cannot be used for arrays shorter than {stepSize}") 

Vector128&lt;sbyte&gt; minVector;
SetAllVector128(minVector, sbyte.MaxValue);
for (var i = 0; i &lt; length - stepSize; i += stepSize)
    minVector = Avx.Min(minVector, Avx.LoadVector128(pStep + i));

minVector = Avx.Min(minVector, Avx.LoadVector128(pStep + length - stepSize));


Then you can use the last loop altogether;