Calculate square root by Newton's method

    x² = N

    x[k+1] = (N ÷ x[k] + x[k]) ÷ 2

    V0  N (Input), x (Output)
    V1  0.5f
    V2  x[k]
    V3  scratch
    V4  0
    V5  x[k-1]
    V6  largest positive number
    V7  10
    V8  5

    Since multiplication is much faster than division, we
    substitute a multiplication by fixed point 0.5 for the
    division by 2.

A set decimal places to +1

    Constants

      123456789012345678901
N001  0.5
N004 0
N006 99999999999999999999999999999999999999999999999999
N007 10
N008 5

    Scale to perform calculation with 1 more decimal places

×
L000
L007
S000

    Calculate initial guess as N ÷ 2

×
L000
L001
>
S002

    Cycle here to perform iterations of Newton's
    method until the result converges to the
    square root.

(?

    Save current term for convergence test

+
L002
L004
S005

    Compute N÷x[k]

÷
L000
<
L002
S003'

    Add x[k] to yield N÷x[k] + x[k]

+
L003
L002
S003

    Divide by two (actually multiply by 0.5) to
    obtain next x[k+1]

×
L003
L001
>
S002

    Subtract x[k] to test for convergence

-
L002
L005
S005

    Cause a run-up if the convergence difference is zero

+
L004
L005
{?
L006
L005
}

    Continue iterating if we haven't yet converged

)

    Round result

+
L002
L008
S000

    Scale result and leave in V0

÷
L000
L007
S000'

A set decimal places to -1