container/ps_map.fz
# This file is part of the Fuzion language implementation. # # The Fuzion language implementation is free software: you can redistribute it # and/or modify it under the terms of the GNU General Public License as published # by the Free Software Foundation, version 3 of the License. # # The Fuzion language implementation is distributed in the hope that it will be # useful, but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # You should have received a copy of the GNU General Public License along with The # Fuzion language implementation. If not, see <https://www.gnu.org/licenses/>. # ----------------------------------------------------------------------- # # Tokiwa Software GmbH, Germany # # Source code of Fuzion standard library feature ps_map # # Author: Fridtjof Siebert (siebert@tokiwa.software) # # ----------------------------------------------------------------------- # ps_map -- a partially sorted map # # ps_map is a persistent map from an ordered key PK to a value V. This map is # generally well-behaved with respect to cumulative and average performance. # # The keys and values are stored in arrays consisting of sorted sub-arrays, # with sub-arrays corresponding to the 1-bits in the binary representation # of the size. # # This results in cumulative memory usage in O(size log² size), worst-case # lookup time in O(log² size) and average addition time in O(1) and worst-case # addition time in O(size log² size). # # WARNING: Due to the high worst-case time for addition, this structure should # not be used in situations when adding a single element repeatedly to the same # instance of ps_map is performance critical. If the resulting map's size n is a # power of 2, this will trigger the worst-case addition time resulting in # O(m*n log² n) for adding an element m times. # # This constructor is for internal use only, to create instance of ps_map, use # ps_map PK V without arguments. # private:public ps_map ( # key type PK type : property.orderable, # value type V type, # the array containg the sorted arrays, see below for details data fuzion.sys.internal_array (tuple PK V), # the number of key and value pairs in this map. public size i32, # the first index in data that is unused fill i32) : Map PK V is /* The structure of the data array for different values of size and fill is as follows. size fill data.length data array structure 0 0 0 . 1 1 1 A 2 2 3 AA- 3 3 3 AAB 4 4 8 AAAA---- 5 5 8 AAAAB--- 6 7 8 AAAA-BB- 7 8 8 AAAA-BBC 8 8 20 AAAAAAAA------------ 9 9 20 AAAAAAAAB----------- 10 11 20 AAAAAAAA-BB--------- 11 12 20 AAAAAAAA-BBC-------- 12 16 20 AAAAAAAA----BBBB---- 13 17 20 AAAAAAAA----BBBBC--- 14 19 20 AAAAAAAA----BBBB-CC- 15 20 20 AAAAAAAA----BBBB-CCD 16 16 48 AAAAAAAAAAAAAAAA-------------------------------- 17 17 48 AAAAAAAAAAAAAAAAB------------------------------- 18 19 48 AAAAAAAAAAAAAAAA-BB----------------------------- 19 20 48 AAAAAAAAAAAAAAAA-BBC---------------------------- 20 24 48 AAAAAAAAAAAAAAAA----BBBB------------------------ 21 25 48 AAAAAAAAAAAAAAAA----BBBBC----------------------- 22 27 48 AAAAAAAAAAAAAAAA----BBBB-CC--------------------- 23 28 48 AAAAAAAAAAAAAAAA----BBBB-CCD-------------------- 24 36 48 AAAAAAAAAAAAAAAA------------BBBBBBBB------------ 25 37 48 AAAAAAAAAAAAAAAA------------BBBBBBBBC----------- 26 39 48 AAAAAAAAAAAAAAAA------------BBBBBBBB-CC--------- 27 40 48 AAAAAAAAAAAAAAAA------------BBBBBBBB-CCD-------- 28 44 48 AAAAAAAAAAAAAAAA------------BBBBBBBB----CCCC---- 29 45 48 AAAAAAAAAAAAAAAA------------BBBBBBBB----CCCCD--- 30 47 48 AAAAAAAAAAAAAAAA------------BBBBBBBB----CCCC-DD- 31 48 48 AAAAAAAAAAAAAAAA------------BBBBBBBB----CCCC-DDE 32 32 112 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA-------------------------------------------------------------------------------- 33 33 112 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB------------------------------------------------------------------------------- 34 35 112 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA-BB----------------------------------------------------------------------------- 35 36 112 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA-BBC---------------------------------------------------------------------------- etc. Whenever size reaches a power of two, a new data array is allocated. The length of the initial data array is 0, the new length for an allocation when size is a power of two is the old data.length * 2 + ceil(size / 2), i.e, the allocation f for size 0,1,2, 4, 8,16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,... is 0,1,3, 8,20,48,112,256, 576,1280,2816, 6144,13312,28672, 61440,131072,... and the cumulative allocation is is 0,1,4,12,32,80,192,448,1024,2304,5120,11264,24576,53248,114688,245760,... The memory usage for size n as well as the cumulative memory usage are hence in O(n log n). */ # add mapping from k to v # public fixed add (k PK, v V) ps_map PK V => if has k panic "NYI: ps_map currently does not handle updates for existing key" else add (k,v) # add mapping from kv.values.0 to kv.values.1 # # Adding has a cumulative average runtime in O(log size) and a worst-case # runtime of O(size) # public add (kv (tuple PK V)) ps_map PK V => nsize := size + 1 ndata := data nfill := fill # join arrays data[ole..ole+sz-1] and ndata[dest..dest+sz-1] to ndata[dest..dest+2*sz-1] # join (ole i32, dest i32, sz i32) ps_map PK V => if (size & sz) = 0 ps_map ndata nsize dest+sz else tmp := array (tuple PK V) sz (i -> ndata[dest+i]) for i1 := 0, if (use1) i1+1 else i1 i2 := 0, if (use1) i2 else i2+1 use1 := i1 < sz && ((i2 ≥ sz) || data[ole + i1].values.0 < tmp[i2].values.0) e := if use1 then data[ole + i1] else tmp[i2] do ndata[dest + i1 + i2] := e until i1 + i2 = 2*sz-1 join (fill - sz - 2*(fill - ole - sz) - 2*sz) dest 2*sz if (nsize & size) = 0 set ndata := fuzion.sys.internal_array_init (tuple PK V) (data.length * 2 + (nsize+1) / 2) set nfill := 0 ndata[nfill] := kv join fill-1 nfill 1 # find the value k is mapped to or nil if k is not part of this map # public index [] (k PK) option V => binary_search(l, r i32) option V => m := (l + r) / 2 if l > r nil else (mk,mv) := data[m] c := (mk) ⋄ k if c < 0 then binary_search m+1 r else if c > 0 then binary_search l m-1 else mv # find k in sub-arrays starting at data[at] # get (at i32, sz i32, tail i32) option V => if sz = 0 nil else sz0 := sz / 2 nt := (tail - sz0) / 2 at0 := (at + (if (size & sz0) != 0 nt else 0) + (if (size & sz ) != 0 sz else 0)) if (size & sz) != 0 match binary_search at at+sz-1 v V => v nil => get at0 sz0 nt else get at0 sz0 nt sub_sz := size.highest_one_bit get 0 sub_sz (data.length - sub_sz) public show unit => for e in as_key_array sep := "", " " do yak (sep + e) say "" # create sorted array of all keys in this map # public as_key_array array PK => r := fuzion.sys.internal_array_init PK size # join arrays data[ole..ole+sz-1] and r[dest..dest+rsz-1] to r[dest..dest+sz+rsz-1] # join (ole i32, sz i32, rsz i32, skip i32) unit => if sz ≤ size if (size & sz) != 0 tmp := array PK rsz (i -> r[i]) for i1 := 0, if (use1) i1+1 else i1 i2 := 0, if (use1) i2 else i2+1 use1 := i1 < sz && ((i2 ≥ rsz) || (data[ole + i1].values.0 < tmp[i2])) e := if (use1) data[ole + i1].values.0 else tmp[i2] do r[i1 + i2] := e until i1 + i2 = sz+rsz-1 join (ole - skip - 2*sz) 2*sz rsz+sz (skip + sz + skip) else join ole-sz 2*sz rsz (skip + sz + skip) if size != 0 join fill-1 1 0 0 array r unit unit unit # get an array of all key/value pairs in this map # public redef items Sequence (tuple PK V) => as_key_array.map (tuple PK V) (k -> (k, ps_map.this[k].get)) # get the lowest key in this map # public min option PK => if size = 0 nil else min0 (m PK, l i32, r i32) PK => (lk, _) := data[l] if (m ≤ lk) m else lk min (m PK, at i32, sz i32, tail i32) PK => if sz = 0 m else sz0 := sz / 2 nt := (tail - sz0) / 2 at0 := (at + (if (size & sz0) != 0 nt else 0) + (if (size & sz ) != 0 sz else 0)) m0 := if (size & sz) != 0 min0 m at at+sz-1 else m min m0 at0 sz0 nt sub_sz := size.highest_one_bit min data[0].values.0 0 sub_sz (data.length - sub_sz) # get the highest key in this map # public max option PK => if size = 0 nil else max0 (m PK, l i32, r i32) PK => (rk, _) := data[r] if (m ≥ rk) m else rk max (m PK, at i32, sz i32, tail i32) PK => if sz = 0 m else sz0 := sz / 2 nt := (tail - sz0) / 2 at0 := (at + (if (size & sz0) != 0 nt else 0) + (if (size & sz ) != 0 sz else 0)) m0 := if (size & sz) != 0 max0 m at at+sz-1 else m max m0 at0 sz0 nt sub_sz := size.highest_one_bit max data[0].values.0 0 sub_sz (data.length - sub_sz) # union of two ps_maps # # creates a new ps_map that maps all the keys that exist either in ps_map.this # or in other to the values they are mapped to. In case a key k exists in # both ps_map.this and other, it will be mapped to ps_map.this[k] or to other[k], # but it is undefined to which of these two. # public fixed union (other ps_map PK V) ps_map PK V => if other.size < size other ∪ ps_map.this else # helper to add 'ps_map.this.data[l..r]' to 'a' and return the resulting map. # add_all (a ps_map PK V, l i32, r i32) ps_map PK V => if l > r a else kv := data[l] a0 := if (a.has kv.values.0) a else a.add kv add_all a0 l+1 r # helper to add 'sz' elements from 'ps_map.this.data[at..at+sz]' to 'a', with # 'tail' elements at indices larger or equal to 'at+sz' added recursively as # well. # add_all (a ps_map PK V, at i32, sz i32, tail i32) ps_map PK V => if sz = 0 a else sz0 := sz / 2 nt := (tail - sz0) / 2 at0 := (at + (if (size & sz0) != 0 nt else 0) + (if (size & sz ) != 0 sz else 0)) a0 := if (size & sz) != 0 add_all a at at+sz-1 else a add_all a0 at0 sz0 nt add_all other 0 size.highest_one_bit (data.length - size.highest_one_bit) # infix operator synonym for union of two ps_maps # public infix ∪ (other ps_map PK V) => union other # empty -- an empty partially sorted map # # This feature creates an empty instance of ps_map. # public type.empty => container.ps_map (fuzion.sys.internal_array_init (tuple PK V) 0) 0 0 # ps_map -- routine to initialize a partially sorted map from two Sequences # # This feature creates a pre-initialized instance of ps_map. # public type.from_sequence( # list of keys in the map ks Sequence PK, # list of values corresponding to keys in the map vs Sequence V) => for r := (container.ps_map PK V).empty, r.add k v k in ks v in vs else r