I want to define
isGood[___] = False;
isGood[#] = True & /@ list
where list
is a list of several million integers. What's the fastest way of doing this?
Summary: undocumented HashTable
is a bit faster (at least in version 9) both in storage and in retrieval than DownValues
.
list = RandomInteger[{-10^9, 10^9}, 10^6];
ret = RandomInteger[{-10^9, 10^9}, 10^6];
isGood[___] = False;
Scan[(isGood[#] = True) &, list]; // AbsoluteTiming
(* ==> {3.240005, Null} *)
ClearAll[isGood];
isGood[___] = False;
Do[isGood@i = True, {i, list}]; // AbsoluteTiming
(* ==> {2.350003, Null} *)
On my computer, this takes less then 3 seconds for a million integers if Do
is used instead of Scan
. Isn't this fast enough?
Retrieval of the results is also quite quick, and is almost independent whether Table
or Map
is used:
isGood /@ ret; // AbsoluteTiming
(* ==> {1.410002, Null} *)
Table[isGood@i, {i, ret}]; // AbsoluteTiming
(* ==> {1.450002, Null} *)
Out of curiosity, I compared this to the undocumented HashTable
(mentioned here) and got even better results. Note, that the hash table must be checked for existing value (as list
might contain duplicates) otherwise HashTableAdd
returns with error. Or it is even better to prefilter list
by removing duplicates, but that is omitted here not to bias the comparison.
hash = System`Utilities`HashTable[];
Do[If[
Not@System`Utilities`HashTableContainsQ[hash, i],
System`Utilities`HashTableAdd[hash, i, True] (* last argument can be omitted *)
], {i, list}]; // AbsoluteTiming
(* ==> {2.010003, Null} *)
System`Utilities`HashTableContainsQ[hash, #] & /@ ret; // AbsoluteTiming
(* ==> {1.340002, Null} *)
Table[System`Utilities`HashTableContainsQ[hash, i], {i, ret}]; // AbsoluteTiming
(* ==> {1.050001, Null} *)
We see that both storage and retrieval are a bit faster.
HashTable
. I wonder why it was so slow (~27 sec) in your original example. Table
is obviously faster than Scan
& With
, but I also assume that in version 8 HashTable
did not throw an error when encountering a duplicate hash, but silently failed with a slowdown.
$\endgroup$
Jan 11, 2014 at 14:30
HashTable
, but that will need another post.
$\endgroup$
Jan 11, 2014 at 14:32
Are you sure you want to use UpValues
? You can use Dispatch
which is pretty fast when generating the lookup table and is equally fast when accessing values:
n = 6;
list = RandomInteger[{0, 10^(n + 1)}, {10^n}];
AbsoluteTiming[disp = Dispatch@Thread[list -> True];]
{1.6220927, Null}
Remove[isGood];
AbsoluteTiming[isGood[___] = False; Scan[(isGood[#] = True) &, list]]
{3.5982058, Null}
Query values:
test = RandomInteger[{0, 10^(n + 1)}, {10^n}];
AbsoluteTiming[Count[test /. disp, True]]
{1.9151096, 94844}
AbsoluteTiming[Count[isGood /@ test, True]]
{1.7601007, 94844}
This seems to be faster to define downvalues
list = RandomInteger[{-100000000, 100000000}, 1000000];
DownValues[isGood] =
HoldPattern[isGood[#]] :> True & /@ list; // AbsoluteTiming
isGood[___] = False;
Scan[]
would be preferable to using Map[]
in this case...
$\endgroup$
Oct 26, 2012 at 3:46
My solution is ugly, but task-specific. It builds a bitmap out of machine-sized integers in imperative fashion and uses Compile. This works reasonably in memory usage for ranges that have at least couple percent of True values.
A million integers:
n = 6;
list = RandomInteger[{0, 10^(n + 1)}, {10^n}];
Function itself:
<< Developer`
isGood = With[
{bits = Floor[Log[2, $MaxMachineInteger + 1]],
min = Min@list,
max = Max@list},
With[
{bv = Compile[{{list, _Integer, 1}},
Module[
{bitvec = Table[0, {(max - min + bits - 1)~Quotient~bits}]},
Scan[(bitvec[[(# - min)~Quotient~bits + 1]] +=
2^((# - min)~Mod~bits)) &, Union@list];
bitvec
],
CompilationOptions -> {"ExpressionOptimization" -> True,
"InlineExternalDefinitions" -> True}
]@list},
Compile[{{x, _Integer}},
min <= x <= max &&
bv[[(x - min)~Quotient~bits + 1]]~BitAnd~(2^((x - min)~Mod~bits)) != 0,
CompilationOptions -> {"ExpressionOptimization" -> True,
"InlineExternalDefinitions" -> True}
]
]
]; // AbsoluteTiming // First
(* 0.347843 *)
Usage:
isGood /@ list // AbsoluteTiming // First
(* 0.590347 *)
Originally I wanted to solve this problem using bitwise operations of arbitrarily large integers, but the issue with that is that functional programming with bigints has large return value overheads - even when just some individual bits are twiddled.
bits = BitLength[$MaxMachineInteger]
to compute the maximum bit length, and you can use bitvec = ConstantArray[0, Quotient[max - min + bits - 1, bits]]
for initialization.
$\endgroup$
Oct 27, 2012 at 1:13
What you aim at can be done quicker now with Association
. I compare only to the Do
method, which is also reasonably fast:
list = RandomInteger[{-10^9, 10^9}, 10^6];
ret = RandomInteger[{-10^9, 10^9}, 10^6];
ClearAll[isGood];
isGood[___] = False;
Do[isGood@i = True, {i, list}]; // AbsoluteTiming
isAlsoGood = With[{data = Union[list]},
AssociationThread[data -> ConstantArray[True, Length[data]]]
]; // AbsoluteTiming
(* 1.43326 *)
(* 0.673688 *)
And looking up values is even four times faster:
aa = Map[isGood, ret]; // AbsoluteTiming // First
bb = Lookup[isAlsoGood, ret, False]; // AbsoluteTiming // First
aa == bb
(* 0.959888 *)
(* 0.2606 *)
(* True *)
Even deallocation is considerably faster:
ClearAll[isGood]; // AbsoluteTiming // First
ClearAll[isAlsoGood]; // AbsoluteTiming // First
(* 0.656773 *)
(* 0.279496 *)
ToPackedArrayQ
was what remained from may experiments with Boolean
. I removed it.
$\endgroup$
Oct 22, 2017 at 17:07
Scan[]
instead ofMap[]
, for starters... is there no regular pattern to these "several million integers" that can possibly be exploited? $\endgroup$