-- file B_tree_for_bigs_dbix.stl
package B_tree_for_dbix;		-- B-trees, realized as objects
-- ***************************************************************************************************************
-- ****** B-tree variant for database index, 2 cumulants (cumulated record size, last rec. id) , refcounts  ******
-- ***************************************************************************************************************
	-- Refcounts can be ignored except in the dbix_set_comp, dbix_insert, split_node, share_right, join_left,
	-- and join_left routines.
	-- This code is closely modeled after that of package B_tree_for_wdocstring (file B_tree_for_bigs_wdoc.stl),
	-- which als supports two cumulants, one a cumulating integer, the other a 4-byte field representing a type
	-- of 'record key' which appears in order. The difference is only that in this case the non-compound nodes
	-- have no children, but directly contain the data (record keys and lengths) that the leaves of trees
	-- of this type store. For code compatibility with 'B_tree_for_wdocstring' we represent this data
	-- in cumulated form, so at the non-compound level we store cumulated sums of lengths rather than
	-- raw lengths, recovering the raw lengths by subtraction when they are wanted. This confines most of
	-- the code changes to the bottom-level access routines dbix_get_ch_cum, dbix_set_ch_cum, dbix_dbix_get_cum2,
	-- dbix_get_ch_cum2, dbix_set_ch_cum2, dbix_vect_of_cums, dbix_set_vect_of_cums, and dbix_set_vect_of_cums2.
	-- In non-compound nodes we use the 'number of children' byte to represent the number of data items present;
	-- there are no real children. Since space is not needed for children, these can store up to 14 cumulants.

-- this B-tree represents the record-id-to-length of record index 

const dbix_code_pts := {"dbix_cc_end", "dbix_srch_on2", "dbix_srch_nc1", "dbix_srch_nc2",
	"dbix_set_copy", "dbix_set_last",
	"dbix_set_nodnc", "dbix_set_comp", "dbix_set_final", "dbix_set_notfinal", "dbix_delnc",
	"dbix_delnorem", "dbix_delrem", "dbix_delcomp", "dbix_delcomplast", "dbix_delcomplast",
	"dbix_delnojs", "dbix_canpull", "dbix_canjoin", "dbix_delnonly", "dbix_delonly",
	"dbix_in_copy", "dbix_in_nend", "dbix_in_srch2", "dbix_in_srch1",
	"dbix_in_srch_notend", "dbix_in_srch_end", "dbix_in_srch_ncend",
	"dbix_in_srch_ncend_nos", "dbix_in_srch_ncend_split", "dbix_in_srch_compend_nos",
	"dbix_in_srch_compend_split", "dbix_in_srch_compend_nosrec",
	"dbix_in_srch_compend_splrec", "dbix_inin_nc", "dbix_inin_ncnos",
	"dbix_inin_nctopspl", "dbix_inin_compnos", "dbix_inin_compsplit",
	"dbix_inin_compnosthis", "dbix_inin_compsplitthis", "dbix_halves_nc",
	"dbix_halves_comp", "dbix_canpull_left", "dbix_canpull_right", 
	"dbix_share_nc", "dbix_share_comp", "dbix_share_copy", "dbix_share_copy2",
	"dbix_share_move_left", "dbix_share_move_left_comp", "dbix_share_move_left_nc",
	"dbix_share_move_right_comp", "dbix_share_move_right_nc", "dbix_join_left_comp",
	"dbix_join_left_nc", "dbix_join_left_copy", "dbix_join_right_comp",
	"dbix_join_right_nc", "dbix_join_right_copy"};				-- code points to be traversed

var debug_flag := false;

var prior_debug_c := 0,debug_c := 0;		-- global variables for debugging
	
procedure hdbix_create();				-- create a new B_tree_for_dbix node, as a non_compound node
procedure hdbix_comp(rec,j);			-- fetch of component containing cumulant j
procedure hdbix_comp2(rec,j);			-- fetch of component containing second cumulant j
procedure hdbix_comp_cum(rec,x);		-- fetch of component containing cumulant x, with cumulants
procedure hdbix_comp_cum2(rec,x);		-- fetch of component containing second cumulant x, with cumulants
procedure hdbix_set_comp(rw rec,w,x);	-- assignment of the first component whose cumulant is at least w; w must be in range
procedure hdbix_set_comp2(rw rec,w,x);	-- assignment of the first component whose second cumulant is at least w
procedure hdbix_insert(rw rec,j,x);		-- insertion before j-th component; or at the end if j = OM
procedure hdbix_insert2(rw rec,j,x);	-- insertion before component with second cumulant at least j; or at end (j = OM)
procedure hdbix_get_cum(rec);			-- get the cum value (string length) for this node
procedure hdbix_get_cum2(rec);			-- get the record id string cum value of the final child of this node

procedure dbix_make_from_tuple(t);		-- make B-tree representation from tuple (DEBUGGING ONLY)
procedure dbix_dump(rec);			-- get tuple from B-tree representation (DEBUGGING ONLY)
procedure shexify(stg);			-- put into abbreviated hex (DEBUGGING ONLY)
procedure num_leaves(a_tree); 		--  (DEBUGGING ONLY)
procedure dbix_check_tree_structure(tree);		-- recursive check of tree structure (DEBUGGING ONLY)

end B_tree_for_dbix;

package body B_tree_for_dbix;		-- B-trees, realized as objects
use setldb,byteutil,disk_records_pak,db_records,string_utility_pak;

				-- there are two cumulants, the total length of the records and the recid 

procedure hdbix_create();						-- creation routine
	
	rec := dr_new_rec();			-- create a new record (at this point, the record is loaded
								-- dirty, and holds all zeroes; so it is not compound)
	set_type(rec,db_index_node_ncr);	-- set to non-compound tree
	return rec;
	 
end hdbix_create;

procedure hdbix_get_cum(rec);		-- get the integer cum value of the final child of this node
	if (nc := num_childr(rec)) = 0 then return 0; end if;
	return get_ch_cum(rec,nc);
	
end hdbix_get_cum;

procedure get_ch_cum(rec,j);	-- get the integer cum value for the j-th child of this node

	the_start := if dr_is_compound(rec) then dbix_cum_start else dbnc_cum_start end if;
	return int_of_5(dr_load(rec)(the_start + (j - 1) * 5..the_start + j * 5 - 1));
	
end get_ch_cum;

procedure set_ch_cum(rec,j,cum_int);	-- set the integer cum value for the j-th child of this node

	the_start := if dr_is_compound(rec) then dbix_cum_start else dbnc_cum_start end if;
	stg := dr_load(rec);		-- make sure that this record is loaded
	stg(the_start + (j - 1) * 5..the_start + j * 5 - 1) := stg_of_5(cum_int);
	dr_setrecbuf(rec,stg);
	dr_dirtify(rec);
	
end set_ch_cum;

procedure hdbix_get_cum2(rec);		-- get the record id string cum value of the final child of this node

	if (nc := num_childr(rec)) = 0 then return OM; end if;
	return get_ch_cum2(rec,num_childr(rec));
	
end hdbix_get_cum2;

procedure get_ch_cum2(rec,j);	-- get the record id string cum value for the j-th child of this node
	the_start := if dr_is_compound(rec) then dbix_cum2_start else dbnc_cum2_start end if;
	return dr_load(rec)(the_start + (j - 1) * 4..the_start + j * 4 - 1);
	
end get_ch_cum2;

procedure set_ch_cum2(rec,j,new_rec_id);	-- set the record id string cum value for the j-th child of this node

	the_start := if dr_is_compound(rec) then dbix_cum2_start else dbnc_cum2_start end if;
	stg := dr_load(rec);		-- make sure that this record is loaded
	stg(the_start + (j - 1) * 4..the_start + j * 4 - 1) := new_rec_id;
	dr_setrecbuf(rec,stg);
	dr_dirtify(rec);
	
end set_ch_cum2;

procedure vect_of_children(rec);					-- gets vector of children, as a string of 4-byte record numbers
	
	if not dr_is_compound(rec) then return ""; end if;
	nch := num_childr(rec);		-- number of children
	return dr_load(rec)(dbix_ch_start..dbix_ch_start - 1 + nch * 4);
	
end vect_of_children;

procedure set_vect_of_children(rec,stg);	-- sets vector of children, from a string of 4-byte record numbers
--print("set_vect_of_children: ",hexify(rec)," ",hexify(stg));
	if not dr_is_compound(rec) then print("Illegal effort to set vector of children for non_compound node"); stop; end if;
	set_num_childr(rec,(nstg := #stg)/4);	-- set the number of children (also loads)
	missing := dbix_cum_start - dbix_ch_start - #stg;
--if missing < 0 then print("missing,dbix_cum_start,dbix_ch_start,#stg: ",missing," ",#stg," ",hexify(stg)); stop; end if;
	stg2:=dr_load(rec);
	stg2(dbix_ch_start..dbix_cum_start - 1) := (stg + missing * "\x00");
		-- set the children, remembering not to change the length of the string section containing them

	dr_setrecbuf(rec,stg2);
	dr_dirtify(rec);
	
end set_vect_of_children;

procedure vect_of_cums(rec);					-- gets vector of cums, as a string of 5-byte fields
	
	the_start := if dr_is_compound(rec) then dbix_cum_start else dbnc_cum_start end if;
	nch := num_childr(rec);		-- number of children
	return dr_load(rec)(the_start..the_start - 1 + nch * 5);
	
end vect_of_cums;

procedure set_vect_of_cums(rec,stg);	-- sets vector of cumulants, from a string of 5-byte record numbers

	the_start := if (ic := dr_is_compound(rec)) then dbix_cum_start else dbnc_cum_start end if;
	the_end := if ic then dbix_cum2_start else dbnc_cum2_start end if;
	missing := the_end - the_start - #stg;
	stg2:=dr_load(rec);		-- force load
	stg2(the_start..the_end - 1) := (stg + missing * "\x00");
		-- set the cumulants, remembering not to change the length of the string section containing them
	dr_setrecbuf(rec,stg2);
	dr_dirtify(rec);

end set_vect_of_cums;

procedure vect_of_cums2(rec);					-- gets vector of cums, as a string of 4-byte fields
	
	the_start := if dr_is_compound(rec) then dbix_cum2_start else dbnc_cum2_start end if;
	nch := num_childr(rec);		-- number of children
	return dr_load(rec)(the_start..the_start - 1 + nch * 4);
	
end vect_of_cums2;

procedure set_vect_of_cums2(rec,stg);	-- sets vector of children, from a string of 4-byte record numbers

	the_start := if (ic := dr_is_compound(rec)) then dbix_cum2_start else dbnc_cum2_start end if;
	the_end := if ic then dbix_cum2_end else dbnc_cum2_end end if;
	missing := the_end - the_start + 1 - #stg;
	stg2:=dr_load(rec);		-- force load
	stg2(the_start..the_end) := (stg + missing * "\x00");
		-- set the children, remembering not to change the length of the string section containing them
	dr_setrecbuf(rec,stg2);
	dr_dirtify(rec);
	
end set_vect_of_cums2;

procedure num_leaves(a_tree); 			-- debugging only 
	return if not dr_is_compound(a_tree) then num_childr(a_tree) 
			else 0 +/[num_leaves(voc(a_tree,j)): j in [1..num_childr(a_tree)]] end if;
end num_leaves;

procedure voc(rec,j);					-- n'th member of vector of children

	stg := dr_load(rec);					-- load this string
	if not dr_is_compound(rec) then print("Illegal effort to access vector of children for non_compound node"); stop; end if;
	cjstrt := (j - 1) * 4 + dbix_ch_start; 
	return stg(cjstrt..cjstrt + 3);		-- return child rec
	
end voc;

procedure set_voc(rec,j,chrec);				-- set n'th member of vector of children

	cjstrt := (j - 1) * 4 + dbix_ch_start; 
	stg2:=dr_load(rec);		-- force load; then set the first character of the record
	if not dr_is_compound(rec) then print("Illegal effort to access element of vector of children for non_compound node"); stop; end if;
	stg2(cjstrt..cjstrt + 3) := chrec;
	dr_setrecbuf(rec,stg2);
	dr_dirtify(rec);

end set_voc;

procedure dbix_make_from_tuple(t);	-- make nested representation from tuple
--print("make_from_tuple: ",t);	
	if #t <= dbnc_hi_lim then	-- put into just one section
		stg := dr_load(rec := dbix_create());
		[icums,rids] := convert_tup_sect(t);		-- convert to cumulant string form
		set_vect_of_cums(rec,icums); set_vect_of_cums2(rec,rids);
		set_num_childr(rec,#t);		-- set the nominal number of children
		return rec;
	end if;
	
	last_used := 0;		-- the last component of t already incorporated into a tuple
	tx := [ ];
	for j in [1,dbnc_hi_lim + 1..#t - 2 * dbnc_hi_lim] loop
				-- put the data into a list of non_compound B_tree nodes, saving enough for at least
				-- one full final section
		rec := dbix_create();
		[icums,rids] := convert_tup_sect(t(j..last_used := j + dbnc_hi_lim - 1));
						-- convert one section of input to cumulant string form
		set_vect_of_cums(rec,icums); set_vect_of_cums2(rec,rids);
		set_num_childr(rec,dbnc_hi_lim);		-- set the nominal number of children
		tx with:= rec;

	end loop;
	
	unusedo2 := (#t - last_used)/2;
	t1 := t(last_used + 1..last_used + unusedo2); t2 := t(last_used + unusedo2 + 1..);		
	rec := dbix_create(); [icums,rids] := convert_tup_sect(t1); 
	set_num_childr(rec,unusedo2);		-- set the nominal number of children
	set_vect_of_cums(rec,icums); set_vect_of_cums2(rec,rids); tx with:= rec;

	rec := dbix_create(); [icums,rids] := convert_tup_sect(t2); 
	set_vect_of_cums(rec,icums); set_vect_of_cums2(rec,rids); tx with:= rec;
	set_num_childr(rec,#rids/4);		-- set the nominal number of children

	t := tx;		-- use the converted t
		
	compound_now := false;		-- otherwise we must chop into sections; bottom level sections are not compound

	while (nt := #t) > dbix_hi_lim loop
				-- build tree progressively from bottom, continuing as long as list of nodes obtained is too long
		sections := [t(j..j + dbix_hi_lim - 1): j in [1,dbix_hi_lim + 1..nt - dbix_hi_lim + 1]];	-- these are lists of nodes
	
		if (nt mod dbix_hi_lim) /= 0 then -- may have to rearrange last 2 pieces

			if #(piece := t((nrv := #sections) * dbix_hi_lim + 1..)) >= dbix_low_lim then 
				sections with:= piece; 
			else  -- otherwise rearrange last 2 pieces
				ntp := #(tdbix_pieces := sections(nrv) + piece);
				sections(nrv) := tdbix_pieces(1..ntpo2 := ntp/2);
				sections with:= tdbix_pieces(ntpo2 + 1..);
			end if;

		end if;
	
		t := [ ];		-- recalculate the vector of items to work with
	
		for sec = sections(j) loop		-- convert each section into a tree node

			sec_node := dr_new_rec();		-- make a tree top for this tuple (i.e. this section)
			set_type(sec_node,db_index_node_record);
											-- set the type of the record
			sec_stg := "" +/ sec;	-- convert the list of children to a string
			set_vect_of_children(sec_node,sec_stg);		-- set the list of children
			cumulate(sec_node);						-- initialize the cumulants
			t with:= sec_node;						-- assemble new vector of nodes
--print("sec_node: ",sec_node," ",hexify(dr_load(sec_node)));
		end loop;

		compound_now := true;		-- after first iteration, sections are not compound

	end loop;
	
	rec := dr_new_rec();		-- create a new, top level record
	
	t_stg := "" +/t;	-- convert the list of children to a string
	set_type(rec,db_index_node_record);		-- at this point must be compound
	set_vect_of_children(rec,t_stg); 	-- these become the top-level children
	cumulate(rec);		-- initialize the final cumulants

	return rec; 
	
end dbix_make_from_tuple;

procedure convert_tup_sect(t);		-- converts a tuple of pairs [rid,ridlen] into a pair of strings
	
	cum := 0;		-- integer cumulant, developed below
	rid_stg := "" +/ [stg_of_4(rid): [rid,ridlen] in t];
	len_stg := "" +/ [stg_of_5(cum): [rid,ridlen] in t | (cum := cum + ridlen) >= 0];

	return [len_stg,rid_stg]; 

end convert_tup_sect;

procedure dbix_dump(rec);			-- get tuple from nested representation

var indent := 0;

return dbix_dump_in(rec);			-- call inner workhorse

procedure dbix_dump_in(rec);			-- inner workhorse
				-- is compound representation or direct, depending on whether 'dr_is_compound' flag is set
				-- note that this shows the vector of components, without their cumulants
				-- we ignore the cumulants in the tree nodes
--print("dbix_dump: ",hexify(dr_load(rec)));
	if dr_is_compound(rec) then 		-- compound case
		indent +:= 1; nc := num_childr(rec);
		stg :=  (["\n" + (indent * "   ") + "("] +/ [dbix_dump_in(voc(rec,j)): j in [1..nc]]) 
					+ ["\n" + (indent * "   ")+ "[" + str(nc) + "]"  + shexify(dbix_get_cum2(rec)) + ":" + str(dbix_get_cum(rec)) + ")"]; 
		indent -:= 1;
		return stg;
	end if;						-- done with compound case

	if (ncr := num_childr(rec)) = 0 then return ["(,:0)"]; end if;
	t := [];				-- otherwise we must analyze the non-compound case
	prev := 0;
	for j in [1..ncr] loop
		int := (new := get_ch_cum(rec,j)) - prev; prev := new;
		rid := shexify(get_ch_cum2(rec,j));
		t with := rid + ":" + str(int);
	end loop;
	
	return ["\n" + (indent * "   ") + "("] + t + [shexify(dbix_get_cum2(rec)) + ":" + str(dbix_get_cum(rec)) + ")"];

end dbix_dump_in;

end dbix_dump;

procedure shexify(stg);		-- put into abbreviated hex
	ns := #(stg := hexify(stg)); zers := span(stg,"0"); 
	return if ns = 8 then "." + stg  else "." + stg + "." + str(#zers) end if; 
end shexify;		

procedure hdbix_comp(rec,j);		-- fetch of component containing cumulant j
	oo:=hdbix_comp(rec,j);
	pp:= comp_cum_ix(rec,1,j)(1..2);	
	if (oo/=pp) then 
		print("DBIX_COMP(",int_of_4(rec)," ",j,")");
		print("Exp ",pp," Got ",oo);
		print("# = ",[#pp(1),#oo(1),int_of_4(pp(1)),int_of_4(oo(1))]);
		stop; 
	end if;
	return pp;
end hdbix_comp;

procedure hdbix_comp2(rec,j);		-- fetch of component containing second cumulant j
	oo:=hdbix_comp2(rec,j);
	pp:= comp_cum_ix(rec,2,j)(1..2);	
	if (oo/=pp) then 
		print("DBIX_COMP2(",int_of_4(rec)," ",int_of_4(j),")");
		print("Exp ",pp," Got ",oo);
		stop; 
	end if;
	return pp;
end hdbix_comp2;

procedure hdbix_comp_cum(rec,x);		-- fetch of x-th component, with cumulant
	oo:=hdbix_comp_cum(rec,x);
	pp:= comp_cum_ix(rec,1,x);
	if (oo/=pp) then 
		print("DBIX_COMP_CUM(",int_of_4(rec)," ",x,")");
		print("Exp ",pp," Got ",oo);
		print("# = ",[#pp(1),#oo(1),int_of_4(pp(1)),int_of_4(oo(1))]);
		stop; 
	end if;
	return pp;
end hdbix_comp_cum;

procedure hdbix_comp_cum2(rec,x);		-- fetch of component containing second cumulant x, with cumulant
	oo:=hdbix_comp_cum2(rec,x);
	pp:= comp_cum_ix(rec,2,x);
	if (oo/=pp) then 
		print("DBIX_COMP_CUM2(",int_of_4(rec)," ",int_of_4(x),")");
		print("Exp ",pp," Got ",oo);
		print("# = ",[#pp(1),#oo(1),int_of_4(pp(1)),int_of_4(oo(1))]);
		stop; 
	end if;
	return pp;
end hdbix_comp_cum2;

procedure comp_cum_ix(rec,srch_on,x);		-- fetch of x-th component by search on specified cumulant

--	if (srch_on=1) then
--		print("  1 - comp_cum_ix ",int_of_4(rec)," ",x);
--	else 
--		print("  2 - comp_cum_ix ",int_of_4(rec)," ",int_of_4(x));
--	end if;
									-- returns value in the form [rid,len,cum_len]
					-- component should be found by binary search
					-- search for the first index component with cumulant past
					-- the specified x; Return OM if there is none such.
								-- NOTE: this should be by binary search

							-- find the first node for which a cumulant >= j
	if x = OM then 				-- want last node
pass("dbix_cc_end");
		j := num_childr(rec); 
		the_cum := if srch_on = 1 then get_ch_cum(rec,j) else get_ch_cum2(rec,j) end if;
				-- Note: only needed in non-compound case
	else
		if srch_on = 2 then 
			iofx := int_of_4(x); 
pass("dbix_srch_on2");
		end if;
		if not (exists j in [1..num_childr(rec)] | 
			if srch_on = 1 then (the_cum := get_ch_cum(rec,j)) >= x else 
				int_of_4(the_cum := get_ch_cum2(rec,j)) >= iofx end if) then 
--print("******** return OM: ",x," ",nc := num_childr(rec)," ",dbix_dump(rec)," ",if nc > 0 then get_ch_cum(rec,nc) else "NONE" end if); 
			return OM; 	-- desired node not found
		end if;
	end if;

	prev_cum := if j = 1 then 0 else get_ch_cum(rec,j - 1) end if;	
			-- previous integer cumulant, needed at several points below
	
	if not dr_is_compound(rec) then			 	-- if node is not compound we have what we want
		if srch_on = 1 then 	-- the integer cum was calculated above
pass("dbix_srch_nc1");	
			return [get_ch_cum2(rec,j),the_cum - prev_cum,the_cum];
		else  				-- the rec id was calculated above
pass("dbix_srch_nc2");		
			int_cum := get_ch_cum(rec,j);
			return [the_cum,int_cum - prev_cum,int_cum];
		end if;
	end if;		-- otherwise we deal with the compound case
	
	res := comp_cum_ix(voc(rec,j),srch_on,if x = OM or srch_on = 2 then x else x - prev_cum end if);
			-- continue the search recursively

	[rid,ridl,lencum] := res;	-- decode the result returned recursively
	
	return [rid] + [ridl,prev_cum + lencum];

end comp_cum_ix;

procedure hdbix_set_comp(rw rec,w,x);-- assignment of the first component whose second cumulant is at least w
		return hdbix_set_comp(rec,w,x);
	if (x/=OM) then
		print("DBIX_SET_COMP ",#rec," ",int_of_4(rec)," w=",w," x=",x);
		if (x/=OM) then
			print([int_of_4(x(1)),x(2)]);
		end if;
	end if;
	set_comp_ix(rec,1,w,x);
end hdbix_set_comp;

procedure hdbix_set_comp2(rw rec,w,x);-- assignment of the first component whose second cumulant is at least w
		return hdbix_set_comp2(rec,w,x);
	set_comp_ix(rec,2,w,x);
end hdbix_set_comp2;

procedure set_comp_ix(rw rec,srch_on,w,x);
	-- assignment of the first component whose specified cumulant is at least w; w must be in range
	-- we must first copy rec if its refcount is greater than 1, and transfer one reference
	-- from its old to its copied version

	if refcount(int_of_4(rec)) > 1 then						-- must copy
pass("dbix_set_copy");
		stg := dr_load(rec); new_r := dr_new_rec(); 
	        dr_setrecbuf(new_r,stg);
	        dr_dirtify(new_r);
		increfs(new_r,1); incref(rec,-1); rec := new_r;		-- substitute copy for original
	end if;
	
	ic := dr_is_compound(rec); if srch_on = 2 then wint := int_of_4(w); end if;
	ncr := num_childr(rec);
	
	if w = OM then			-- make change in last node
pass("dbix_set_last");
		w := if srch_on = 1 then get_ch_cum(rec,ix := ncr) else get_ch_cum2(rec,ix := ncr) end if; 
		if ix = 0 then print("Deletion at end of empty tree is not allowed."); stop; end if;
	elseif not (exists ix in [1..ncr] |  
		if srch_on = 1 then get_ch_cum(rec,ix) >= w else int_of_4(get_ch_cum2(rec,ix)) >= wint end if) then 
		print("DBIX - Search index " + str(w) + " out of range in assignment to cumulating vector " + hexify(rec)
		 		+ " " + str(ncr) + " " + str(ic) + " " + hexify(dr_load(rec))); stop;
	end if;
								-- get the local cumulant of the child
	old_cum := get_ch_cum(rec,ix) - (prev_cum := if ix = 1 then 0 else get_ch_cum(rec,ix - 1) end if);
					-- find the last cumulant value of voc(rec,ix), or the length of active part of voc(rec,ix) 
					
	if x /= OM then 			-- we are not dealing with a deletion

		if not ic then 			-- non-compound case; we must add the change in the leaf cumulant
								-- to the cumulant of all following nodes. 
			cum_change := x(2) - old_cum;
			update_cums(rec,ix,cum_change);		-- update the cums,starting with the given child
pass("dbix_set_nodnc");
			set_ch_cum2(rec,ix,x(1));
				-- modify the cum of the changed component. Note that the following 
				-- second cumulants need not be changed. However, if ix references the 
				-- final child of rec, a cum2 entry in the parent of rec may need to be changed below.
			return;				-- done with this case
		end if;						-- otherwise we have the compound case
pass("dbix_set_comp");		
		the_child := voc(rec,ix);				-- the next operation mayy copy the child
		set_comp_ix(the_child,srch_on,if srch_on = 1 then w - prev_cum else w end if,x);		
							-- make the change in the child
		cum_change := dbix_get_cum(the_child) - old_cum;
		
		set_voc(rec,ix,the_child);		-- put the revised, possibly copied child back into position
			-- the 'update_cums' procedure which we call now must then start with the (properly set)
			-- cumulant of the preceding node, and then left_add the change in the the cumulant
			-- to the cumulant of this child to all the subsequent children. This assumes that 
			-- 		(new_d - old_d) + c + old_d + e = c + new_d + e
			-- for all cumulant values. This is obviously true for values using associative-commutative
			-- cumulator functions with an inverse, and also in the (string) case where a + b = b.
	
		update_cums(rec,ix,cum_change);			-- update the cums,starting with the given child
		if ix = ncr then 
		set_ch_cum2(rec,ix,dbix_get_cum2(the_child)); 
pass("dbix_set_final");		
		else
pass("dbix_set_notfinal");		
		end if;
				-- the final cumulant of the_child might have been changed by 
				-- the preceding dbix_set_comp(the_child,..) operation; see preceding comment.
		
--print("compound self,ix: ",dbix_get_cum()," ",ix);
		return;				-- done with the non-deletion case
	
	end if;			-- otherwise we are dealing with a deletion
	
	if not dr_is_compound(rec) then 		-- non-compound case
pass("dbix_delnc");		

		if num_childr(rec) > 0 then		-- need not delete cumulant if no remaining children
pass("dbix_delnorem");		
			stg := vect_of_cums(rec);				-- get the vector of cums
			stg((ix - 1) * 5 + 1..ix * 5) := "";		-- drop one element
			set_vect_of_cums(rec,stg);				-- put back into place
			stg := vect_of_cums2(rec);				-- get the second vector of cums
			stg((ix - 1) * 4 + 1..ix * 4) := "";		-- drop one element
			set_vect_of_cums2(rec,stg);				-- put back into place
		else
pass("dbix_delrem");		
		end if;

				-- delete the child from the string of descendants
		set_num_childr(rec,num_childr(rec) - 1);		-- count down the number of children
		-- note: sets the  'dirty' bit
				-- delete the cumulant of the ix-th node. note that this has already been loaded
		cum_change := -old_cum;
		update_cums(rec,ix,cum_change);			-- update the cums,starting with the appropriate child
		return;				-- done with this case

	end if;				-- otherwise we are dealing with a deletion in a compound case
pass("dbix_delcomp");				
	the_child := voc(rec,ix);		-- get the child

	old_ch_leafsum := dbix_get_cum(old_child := the_child);
	set_comp_ix(the_child,srch_on,if srch_on=1 then w - prev_cum else w end if,OM);		-- make the deletion in the child
	new_ch_leafsum := dbix_get_cum(the_child);
	set_voc(rec,ix,the_child := the_child);		-- re-insert the possibly modified child
	cum_change := new_ch_leafsum - old_ch_leafsum;
	update_cums(rec,ix,cum_change);			-- update the cums,starting with the given child
			-- since the last child may have been deleted, we also need to update the second cum
	if ix = ncr then 
pass("dbix_delcomplast");		
		set_ch_cum2(rec,ix,dbix_get_cum2(the_child)); 
	else
pass("dbix_delcomplast");		
	end if;
	
		-- now it is possible that the child has lost enough children to have fallen below the required dbix_low_lim
		-- if this has happened, we attempt to share or join children with one of the adjacent siblings
	
	if num_childr(the_child) >= dbix_low_lim then 	-- otherwise try to join or share
pass("dbix_delnojs");		
		return; 
	end if;
				
	if pull_from_left(rec,ix) or pull_from_right(rec,ix) then 
pass("dbix_canpull");		
		return; 
	end if;

	if join_with_left(rec,ix) or join_with_right(rec,ix) then 
pass("dbix_canjoin");		
		null; 
	end if;

			-- In the 'join' case, either the left or the right join must work,
			-- since in this compound case we must have at least one sibling.
			-- but we must check to see if the node being processed has fallen to
			-- just one child, and if it has, replace it by its single child.
	
	if num_childr(rec) > 1 then 
pass("dbix_delnonly");		
		return; 
	end if;
pass("dbix_delonly");		
	ch_rec := dr_load(the_ch := voc(rec,1)); dr_load(rec); 
	        dr_setrecbuf(rec,ch_rec);
	        dr_dirtify(rec);
	
	if dr_is_compound(the_ch) then set_vect_of_children(the_ch,""); end if;		-- the children have all moved
	incref(the_ch,-1);		-- child data is inherited from single child, which loses a reference

end set_comp_ix;

procedure update_cums(rec,ix,cum_change);	-- update the cums of this tree,starting with the given child
				-- add cum_change to all subsequent children
	for j in [ix..nvc := num_childr(rec)] loop
		set_ch_cum(rec,j,cum_change + get_ch_cum(rec,j));
	end loop;
		
end update_cums;

procedure cumulate(rec);
	-- initalize the cumulants of a node whose children are either leaves or already initialized
	
	if not dr_is_compound(rec) then return; end if;		-- non-compound nodes are already cumulated

	the_cum := 0;

	for  j in [1..num_childr(rec)] loop
		nd := voc(rec,j);		-- get the j-th child
		nd_cum := dbix_get_cum(nd);
				-- cumulant of the final child of the subnode, or occurence string length
		the_cum := the_cum + nd_cum;
		set_ch_cum(rec,j,the_cum);  		-- update the child's cumulant value
		nd_cum2 := dbix_get_cum2(nd);
				-- cumulant2 of the final child of the subnode, or last element of occurence string
		set_ch_cum2(rec,j,nd_cum2);  		-- update the child's cumulant value
	end loop;

end cumulate;

procedure hdbix_insert(rw rec,j,x);		-- insertion before j-th component; or at the end if j = OM
	insert(rec,1,j,x);
end hdbix_insert;

procedure hdbix_insert2(rw rec,j,x);		-- insertion before component with second cumulant at least j;
	insert(rec,2,j,x);				-- or at the end if j = OM
end hdbix_insert2;

procedure insert(rw rec,srch_on,j,x);	-- insertion before j-th component with at least specified cumulant;
								-- or at the end if j = OM
								-- component should be found by binary search

	if refcount(int_of_4(rec)) > 1 then						-- must copy
pass("dbix_in_copy");		
		stg := dr_load(rec); new_r := dr_new_rec(); 
	        dr_setrecbuf(new_r,stg);
	        dr_dirtify(new_r);
		increfs(new_r,1); incref(rec,-1); rec := new_r;		-- substitute copy for original
	end if;
	
	result := OM; 	-- in case desired element not found
	ic := dr_is_compound(rec); ncr := num_childr(rec);
	the_cum := dbix_get_cum(rec);	-- get final cumulant of this tree
	[x_cum2,x_cum] := x;	-- cumulant values of the leaf x
	
	if j /= OM then 		-- look for target node of insertion, if any
pass("dbix_in_nend");		
		if srch_on = 2 then 
pass("dbix_in_srch2");		
			iofj := int_of_4(j); 
		else
pass("dbix_in_srch1");		
		end if;

		if exists ix in [1..ncr] | 
			if srch_on = 1 then (cum := get_ch_cum(rec,ix)) >= j else 
				int_of_4(cum := get_ch_cum2(rec,ix)) >= iofj end if then 
			result := [ix,if ix = 1 then 0 else get_ch_cum(rec,ix - 1) end if,cum]; 
			if ic then nd := voc(rec,ix); end if;
pass("dbix_in_srch_notend");		
		else 
			result := OM;
pass("dbix_in_srch_end");		
		end if;
	end if;
	
	if result = OM then 		-- we have insertion at the very end
		
		if not ic then -- simply append to vector
pass("dbix_in_srch_ncend");		
			set_num_childr(rec,nvc := ncr + 1);
					-- add the cumulant of x to the present cumulant of this tree
			set_ch_cum(rec,nvc,the_cum := the_cum + x_cum);
			set_ch_cum2(rec,nvc,x_cum2);
--print("num_childr(rec): ",nvc," ",num_childr(rec)," ",ncr," ",dbix_hi_lim + 1); 
			if nvc <= dbnc_hi_lim then 
pass("dbix_in_srch_ncend_nos");		
				return; 
			end if;			-- no need to split
						-- otherwise we must split, and becomes compound
pass("dbix_in_srch_ncend_split");		
								-- note that in this case we are at the very top of the tree
			th := two_halves(rec);		-- get the two halves
			set_is_compound(rec,true);					-- note that it is indeed compound
			set_vect_of_children(rec,th);			-- split into 2 non-compound subtrees
			set_ch_cum(rec,1,dbix_get_cum(voc(rec,1))); set_ch_cum(rec,2,the_cum);				
			set_ch_cum2(rec,1,dbix_get_cum2(voc(rec,1))); set_ch_cum2(rec,2,dbix_get_cum2(voc(rec,2)));				
			return;				-- done with this case

		end if;		-- otherwise we have insertion at the very end of a compound vector 
		
		last_child:= voc(rec,nvc := num_childr(rec));		-- get the last child
		dbix_insert(last_child,OM,x);				-- insert at the end of this last child
		set_voc(rec,ncr,last_child);			-- insert the possibly modified child back into vect_of_children
							-- add the cumulant of x to the present cumulant of this tree
		set_ch_cum(rec,ncr,the_cum := the_cum + x_cum);
		set_ch_cum2(rec,ncr,x_cum2);
		
		if (if dr_is_compound(last_child) then dbix_hi_lim else dbnc_hi_lim end if) > num_childr(last_child) then
pass("dbix_in_srch_compend_nos");		
			return; 	-- no need to split the child
		end if;
						-- otherwise we must split the last child
pass("dbix_in_srch_compend_split");		
		split_node(rec,nvc);	-- split the nvc-th node into two.  we insert an empty node to the right
							-- of node nvc, and then move half the children of the nvc-th node into the new node	

		if (nvc := num_childr(rec)) <= dbix_hi_lim then 		-- no need to split this node
pass("dbix_in_srch_compend_nosrec");		
			return;				-- done with this case
		end if;
		-- otherwise we are at the very top of the tree, so we must split it into two parts and create a new tree level
pass("dbix_in_srch_compend_splrec");		
			
		set_vect_of_children(rec,two_halves(rec));
		set_ch_cum(rec,1,dbix_get_cum(voc(rec,1))); set_ch_cum(rec,2,the_cum);				
		set_ch_cum2(rec,1,dbix_get_cum2(voc(rec,1))); set_ch_cum2(rec,2,dbix_get_cum2(voc(rec,2)));				

		return;				-- done with this case

	end if;		-- end of case of insertion at the very end
				-- in the remaining cases we have an insertion before one of our nodes
	
	 [ix,prev_cum,cum] := result;	-- decode the result returned, geting the insertion result and the preceding cumulant

	if not ic then -- insertion at appropriate position in non-compound vector
pass("dbix_inin_nc");		
		the_cums := vect_of_cums(rec); the_cums2 := vect_of_cums2(rec); 
		the_cums(5 * ix - 4..5 * ix - 5) := 
			if ix = 1 then "\x00\x00\x00\x00\x00" else the_cums(5 * ix - 9..5 * ix - 5) end if;
		the_cums2(4 * ix - 3..4 * ix - 4) := x_cum2;
--print("#the_cums: ",#the_cums); if #the_cums > 70 then stop; end if;
		set_vect_of_cums(rec,the_cums);				-- make insertion into list of cums
		set_vect_of_cums2(rec,the_cums2);				-- make insertion into list of cums
		set_num_childr(rec,nvc := ncr + 1);	-- there is one more child
		update_cums(rec,ix,x_cum);					-- adjust the given and following cumulants

		if nvc <= dbnc_hi_lim then		-- no need to split
pass("dbix_inin_ncnos");		
			return;				-- done with this case
		end if;				-- otherwise we must split, and becomes compound
pass("dbix_inin_nctopspl");		
		-- otherwise we are at the very top of the tree, so we must split it into two parts and create a new tree level
			
		th := two_halves(rec);				-- get the two halves
		set_is_compound(rec,true);			-- note that it is indeed compound
		set_vect_of_children(rec,th);			-- split into 2 non-compound subtrees
		set_ch_cum(rec,1,dbix_get_cum(voc(rec,1))); set_ch_cum(rec,2,the_cum + x_cum);				
		set_ch_cum2(rec,1,dbix_get_cum2(voc(rec,1))); set_ch_cum2(rec,2,dbix_get_cum2(voc(rec,2)));				
--print("just became compound: ",dr_is_compound(rec)," ",dbix_dump(rec)); stop;
		return;									-- done with this case

	end if;		-- otherwise we deal with the compound case
	
	c := voc(rec,ix);		-- get the child into which the insertion will now be made
								-- and get the position in this child at which the insertion will be made
	insert(c,srch_on,if srch_on = 1 then j - prev_cum else j end if,x);		-- insert x into this child
	set_voc(rec,ix,c);				-- put the possibly revised child back into position
	update_cums(rec,ix,x_cum);		-- adjust the given and following cumulants
	set_ch_cum2(rec,ix,dbix_get_cum2(c)); 	-- adjust the second cumulant on record for the child
									-- which may have changed if the insertion was at the end of the child
	
	if (if dr_is_compound(c) then dbix_hi_lim else dbnc_hi_lim end if) > num_childr(c) then
pass("dbix_inin_compnos");		
		return; 	-- no need to split the child
	end if;
pass("dbix_inin_compsplit");		
								-- otherwise we must split the  child
	split_node(rec,ix);				-- split the child into two.  we insert an empty node to the right
								-- of node ix, and then move half the nodes into it	

	if (nvc := num_childr(rec)) <= dbix_hi_lim then 		-- no need to split this node
pass("dbix_inin_compnosthis");		
		return;				-- done with this case
	end if;		-- otherwise we are at the very top of the tree, so we must split it into two parts and create a new tree level
pass("dbix_inin_compsplitthis");		
	set_vect_of_children(rec,two_halves(rec));
	set_ch_cum(rec,1,dbix_get_cum(voc(rec,1))); set_ch_cum(rec,2,the_cum + x_cum);				
	set_ch_cum2(rec,1,dbix_get_cum2(voc(rec,1))); set_ch_cum2(rec,2,dbix_get_cum2(voc(rec,2)));				

end insert;

procedure two_halves(rec);		-- split this tree into two halves
	-- the two nodes created share the children of the original tree, so  that the refcounts of 
	-- these children need no adjustment. The nodes created each have a refcount of 1.
	-- Note that this routine is only called if rec has no parent.

	the_type := if (ic := dr_is_compound(rec)) then db_index_node_record else db_index_node_ncr end if;
	u1 := dr_new_rec(); u2 := dr_new_rec();			-- make and initialize two subtrees
	set_type(u1,the_type); set_type(u2,the_type);	-- the halves are compound iff this tree is compound

	-- we must subtract the cumulant of the last retained child from all the children that move
	-- to get the cumulant of the left node
	hnvc := (nvc := num_childr(rec))/2; cum_last_retained := get_ch_cum(rec,hnvc);
	
	for j in [hnvc + 1..nvc] loop			-- subtract this from the cumulant of each child that will move
		set_ch_cum(rec,j,get_ch_cum(rec,j) - cum_last_retained);
	end loop;
	
	vocums := vect_of_cums(rec);		-- get the vector of cums
	vocums2 := vect_of_cums2(rec);		-- get the vector of cums

	if ic then 
pass("dbix_halves_nc");		
		set_vect_of_children(u1,(voch := vect_of_children(rec))(1..4 * hnvc)); 
	else
pass("dbix_halves_comp");		
		set_num_childr(u1,hnvc);		-- set the number of children of u1
	end if;

	set_vect_of_cums(u1,vocums(1..5 * hnvc));			-- u1 gets half the children and cums
	set_vect_of_cums2(u1,vocums2(1..4 * hnvc));			-- u1 gets half the children and cums
	
	set_vect_of_cums(u2,vocums(5 * hnvc + 1..));	-- the second half inherits adjusted cumulants from the original tree
	set_vect_of_cums2(u2,vocums2(4 * hnvc + 1..));			-- likewise for the second cums
	set_num_childr(u1,hnvc);		-- set the number of children of u1
	if ic then 
		set_vect_of_children(u2,voch(4 * hnvc + 1..));  -- u2 gets the other half of  the children
	else
		set_num_childr(u2,nvc - hnvc);		-- set the number of children of u2
	end if;

--print("two_halves: ",str(dbix_dump(u1)),"\n",str(dbix_dump(u2)),"\n",hexify(voch(4 * hnvc + 1..)),"\n",hexify(dr_load(u2)));
	return u1 + u2;
				-- assemble the two nodes of the new compound tree; return as a string

end two_halves;

procedure pull_from_left(rec,k);		-- split children with left sibling

	if k = 1 or num_childr(voc(rec,k - 1)) <= dbix_low_lim then 
		return false; 
	end if;
--print("pull_from_left before share: ",k," ",dbix_low_lim," ",if k > 1 then num_childr()(k - 1) else OM end if);
pass("dbix_canpull_left");		
	share_right(rec,k - 1);
--print("pull_from_left after share: ",k));
	return true;

end pull_from_left;

procedure pull_from_right(rec,k);	-- split children with right sibling

	if k >= (nrv := num_childr(rec)) or num_childr(voc(rec,k + 1)) <= dbix_low_lim then
		return false;
	end if;
pass("dbix_canpull_right");		
--print("pull_from_right before share: ",k," ",#vect_of_children(k + 1)," ",dbix_low_lim," ",num_cums," ",#vect_of_children(k + 1) <= dbix_low_lim + num_cums);
	share_right(rec,k); 
--print("pull_from_right after share: ",k));
	return true;

end pull_from_right;

procedure ushare_right(rec,k);	-- share children with right-hand sibling
	
		-- we divide the children of the k-th node, together with those of the k+1'st,
		-- into two roughly equal groups, and make these the k-th and k+1'st nodes. The
		-- cumulative totals must be adjusted in the k-th node, in the
		-- children moved between nodes, and in the children of the k+1'st node    
	-- this routine must first copy the nodes among which children will move, if they have more than 1 reference.
	-- but it does not change the number of references to the children, so that their refcounts need no adjustment
--print("share_right: ",k," ",str(dbix_dump(rec)));		
	if (ic := dr_is_compound(ndk := voc(rec,k)))  then 	-- a compound node is involved in the sharing
pass("dbix_share_nc");		
		nchkp1 := #(rkp1 := vect_of_children(ndkp1 := voc(rec,k + 1)))/4;
		nchk := #(rk := vect_of_children(ndk))/4;	-- get the two groups of children, and their lengths
	else 
pass("dbix_share_comp");		
		nchkp1 := num_childr(ndkp1 := voc(rec,k + 1)); nchk := num_childr(ndk);
	end if;
	
	numleft := (nchk + nchkp1)/2;	-- half the children; the left-hand will get this number of children
	
	if refcount(int_of_4(ndkp1)) > 1 then						-- must copy
pass("dbix_share_copy");		
		stg := dr_load(ndkp1); new_r := dr_new_rec(); 
	        dr_setrecbuf(new_r,stg);
	        dr_dirtify(new_r);
		incref(ndkp1,-1); ndkp1 := new_r;		-- substitute copy for original
		increfs(new_r,1); set_voc(rec,k + 1,new_r);
	end if;

	if refcount(int_of_4(ndk)) > 1 then						-- must copy
pass("dbix_share_copy2");		
		stg := dr_load(ndk); new_r := dr_new_rec(); 
	        dr_setrecbuf(new_r,stg);
	        dr_dirtify(new_r);
		incref(ndk,-1); ndk := new_r;		-- substitute copy for original
		increfs(new_r,1); set_voc(rec,k,new_r);
	end if;
	
	if numleft > nchk then		-- children will move left
pass("dbix_share_move_left");				
		num_mov := numleft - nchk;		-- the number that will move left
--print("move left: ",num_mov," ",hexify(dr_load(ndk)),"\n",hexify(dr_load(ndkp1)));		
			-- we must subtract the cumulant of the last child moving left
			-- from the cumulants of all the right-hand children which do not move, 
			-- and must add this to the cumulant of the k-th node. We must also
			-- add the cumulant of the last left-hand child of ndk to the cumulants of all 
			-- the right-hand children which do move. 

		ndk_cum := get_ch_cum(rec,k);			-- get the cumulant of ndk
		right_cum := dbix_get_cum(ndk);			-- cumulant of the last child of ndk

		moved_cum := get_ch_cum(ndkp1,num_mov);		-- cumulant of the last child of ndkp1 that moves 
		set_ch_cum(rec,k,moved_cum + ndk_cum);		-- add moved_cum to the cumulant of the k-th node
		set_ch_cum2(rec,k,get_ch_cum2(ndkp1,num_mov));	-- correct the second cumulant of the k-th node
		
		for j in [1..num_mov] loop
			set_ch_cum(ndkp1,j,right_cum + get_ch_cum(ndkp1,j));
		end loop;
		
		for j in [num_mov + 1..nchkp1] loop
			set_ch_cum(ndkp1,j,get_ch_cum(ndkp1,j) - moved_cum);
		end loop;

											-- and now we must move the corresponding cums
		cumvp1 := vect_of_cums(ndkp1);			-- second vector of cums
--print("ndkp1: ",hexify(ndkp1)," ",hexify(dr_load(ndkp1))); stop;
		set_vect_of_cums(ndk,vect_of_cums(ndk) + cumvp1(1..num_mov * 5));		-- move the cums in
		set_vect_of_cums(ndkp1,cumvp1(num_mov * 5 + 1..));					-- move the cums out
			-- since the number of cums of ndkp1 is defined by its number of children, we need not edit that list 
		cumvp1 := vect_of_cums2(ndkp1);			-- second vector of second cums
--print("ndkp1: ",hexify(ndkp1)," ",hexify(dr_load(ndkp1))); stop;
		set_vect_of_cums2(ndk,vect_of_cums2(ndk) + cumvp1(1..num_mov * 4));		-- move the cums in
		set_vect_of_cums2(ndkp1,cumvp1(num_mov * 4 + 1..));					-- move the cums out
		
		if ic then 		-- if the nodes are compound we must move children in addition to cumulants
pass("dbix_share_move_left_comp");				
			set_vect_of_children(ndk,rk + rkp1(1..4 * num_mov));		-- now actually move the children
			set_vect_of_children(ndkp1,rkp1(4 * num_mov + 1..));
		else 		-- not compound; must adjust the number of children
pass("dbix_share_move_left_nc");				
			set_num_childr(ndk,nchk + num_mov); set_num_childr(ndkp1,nchkp1 - num_mov);
		end if;
--print("move the children: ",rk," ",rkp1," ",num_mov); 

	else						-- children will move right
--print("move right: ",nchk - numleft);		
				--