SQRT(P**2 + Q**2)

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PROBLEM

Compute SQRT(P**2+Q**2)

ALGORITHM

Moler and Morrison have described a fast algorithm for computing SQRT(P**2+Q**2). This algorithm has cubic convergence. It means that the result is accurate to 6.5 decimal digits after two iterations, to 20 digits after three iterations, and to 62 digits after four iterations.

IMPLEMENTATION

Unit: internal function, external function without procedure statement
 
Parameters: numbers P, Q, a positive integer IterCount - number of iterations
 
Returns: value SQRT(P**2+Q**2) with IterCount**3 decimal digits

 

SQRTP2AQ2: procedure parse arg P, Q, IterCount numeric digits IterCount ** 3 P = ABS(P); Q = ABS(Q) if P < Q   then do; W = P; P = Q; Q = W; end if P = 0 then return Q do IterCount   R = Q / P; R = R * R; R = R / (4 + R)   P = P + 2 * R * P; Q = Q * R end return P

 

Literature

Bentley J., Programming Pearls

CACM, December 1986, Vol. 29, No. 12, p. 1161

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