continued fraction - homographic function

proc cfhomo {a b c d x} {
    while {1} {

	# Egest what terms we can
	
	while {1} {
	    set prod [* $c $d]
	    if {$prod == Inf || $prod <= 0} break
	    set qcoef [/ $a $c]
	    set rcoef [% $a $c]
	    set qconst [/ $b $d]
	    set rconst [% $b $d]
	    if {$qconst != $qcoef} break
	    Yield $qconst [list $x 1]
	    lassign [list $c $d $rcoef $rconst] a b c d
	}

	# Ingest the next term of the input

	set t [$x]
	if {$t == Inf} {
	    tailcall cfint/int $a $c
	}
	lassign [list [expr {$t*$a + $b}] $a [expr {$t*$c + $d}] $c] a b c d
    }
}