Problem Statement

Write a function to compute the arithmetic-geometric mean of two numbers.

The arithmetic-geometric mean of two numbers can be (usefully) denoted as

a g m

( a , g )

{\displaystyle \mathrm {agm} (a,g)}

, and is equal to the limit of the sequence: Since the limit of

a

n

−

g

n

{\displaystyle a_{n}-g_{n}}

tends (rapidly) to zero with iterations, this is an efficient method. Demonstrate the function by calculating:

Let's start with the solution:

USING: kernel math math.functions prettyprint ;
IN: rosetta-code.arithmetic-geometric-mean

: agm ( a g -- a' g' ) 2dup [ + 0.5 * ] 2dip * sqrt ;

1 1 2 sqrt / [ 2dup - 1e-15 > ] [ agm ] while drop .