# gmp  Gauss_Map_Period 
# Input  a floating point number
# Output : n the smallest integer such that x[2*n]=x[n].
# where x[n] is the n'th iterate of the gauss map.
# This n is the smallest n such that gauss map starts to cycle.
# Ref:  Knuth. Vol. 2 Semi-Numerical Algorithms.  exercise 6 page 7.
#  Algorithm due to Floyd.
gmp := proc(a)
 local t,ti,tf,x,y,n;
 t := evalf(a);
 ti := trunc(t);
 tf := t-ti;
 if t<0 then t := t+1; fi;
 x := t;
 if x=0 then y:=0;
 else y := 1/t; ti := trunc(y); y := y-ti; fi;
 for n while x<>y do
  if x<>0 then x := 1/x; ti := trunc(x); x := x-ti; fi;
  if y<>0 then y := 1/y; ti := trunc(y); y := y-ti; fi;
  if y<>0 then y := 1/y; ti := trunc(y); y := y-ti; fi;
 od;
 n;
end:

Digits := 6;
gmp(.3);
Digits := 10;
gmp(.3);
Digits := 19;
gmp(.3);
Digits := 6;
gmp(.787121);
evalhf(gmp(.3));