new files

Task/Pi/Tcl/pi-1.tcl

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+package require Tcl 8.6
+
+# http://www.cut-the-knot.org/Curriculum/Algorithms/SpigotForPi.shtml
+# http://www.mathpropress.com/stan/bibliography/spigot.pdf
+proc piDigitsBySpigot n {
+    yield [info coroutine]
+    set A [lrepeat [expr {int(floor(10*$n/3.)+1)}] 2]
+    set Alen [llength $A]
+    set predigits {}
+    while 1 {
+	set carry 0
+	for {set i $Alen} {[incr i -1] > 0} {} {
+	    lset A $i [expr {
+		[set val [expr {[lindex $A $i] * 10 + $carry}]]
+		% [set modulo [expr {2*$i + 1}]]
+	    }]
+	    set carry [expr {$val / $modulo * $i}]
+	}
+	lset A 0 [expr {[set val [expr {[lindex $A 0]*10 + $carry}]] % 10}]
+	set predigit [expr {$val / 10}]
+	if {$predigit < 9} {
+	    foreach p $predigits {yield $p}
+	    set predigits [list $predigit]
+	} elseif {$predigit == 9} {
+	    lappend predigits $predigit
+	} else {
+	    foreach p $predigits {yield [incr p]}
+	    set predigits [list 0]
+	}
+    }
+}