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Suppose we have a function which is sampled by a sampling time 10ms. This function comes in to the computer, then this computer should calculate square root (for every sampling time) from that function.

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$ g^*(t) = \sqrt{f^*(t)}$

Here $f^*$ and $g^*$ are sampled signals (discrete)

Only these operations are possible:

Arithmetic shift, inversion, bit wise

Is there any well know square root calculation algorithms appropriate for this situation?

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    You could use this: http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm But I'll be flagging this over to comp sci @ SE.2012-10-31

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