Finding max clique size and C++ is better than asm.

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bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 21 Apr 2016, 03:11

Usually, in assembly we get what we code, or see in the debugger. JMP is an instruction in many processor families. Razz

One of my professors talked of HLL concepts in terms of the granularity needed to construct and maintain software - if the complexity gets too great it becomes difficult to communicate even in ones own mind what is happening. He called it Containment/Cohesion. I though it was baloney. I've seen many fragments of code that needed much more comments than code. Usually, to explain how it interacts with the external environment.

21 Apr 2016, 03:11

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 20513
Location: In your JS exploiting you and your system

revolution 21 Apr 2016, 04:27

Tyler wrote:

... but they also eliminate the possibility for the compiler to know things it otherwise would have known thus eliminating optimizations the compiler otherwise would have exploited. (Yeah, I do see the irony here that redsock beat the compiler with goto's. He out compiler'ed the compiler.) Generally I would agree with you, but this (compiler optimization) is this professor's thing. I actually argued your point with him and got the concession they can be useful in some cases, but that they should be avoided unless strictly necessary. And that's reasonable. Let the compiler handle the optimization unless you have a really hot codepath. The "gotos are always and absolutely evil" is an overly strict application of a solid general rule with few exceptions.

So even more irony. If your compiler struggles to optimise the non-"hot" code then who cares anyway, and if it can't optimise the "hot" code then use assembly. So where is the compiler optimisation needed then?

Tyler wrote:

Yeah, that Dijkstra guy, he was sssoooooo dumb, amiright?

http://www.u.arizona.edu/~rubinson/copyright_violations/Go_To_Considered_Harmful.html

Oh okay, it was him. Doesn't make it right though. Why are we writing code to suit the compiler anyway? We should be writing code to get the job done in a way that pleases us, not in a way that pleases the compiler. Haha Razz

21 Apr 2016, 04:27

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 20513
Location: In your JS exploiting you and your system

revolution 21 Apr 2016, 04:34

bitRAKE wrote:

I've seen many fragments of code that needed much more comments than code. Usually, to explain how it interacts with the external environment.

Good comments are hard to write. The worst possible comments are the ones that explain the code/instruction operations, i.e. the "how" and the "what". Better comments explain the "why" and most importantly the "goal". IMO of course.

21 Apr 2016, 04:34

redsock

Joined: 09 Oct 2009
Posts: 435
Location: Australia

redsock 21 Apr 2016, 21:27

So over this morning's coffee and as my final post here in the thread, since it is such a trivial mod I removed the goto from my reworked version. Original reworked loop looks like:

Code:

        for (; {
                // Down the tree. Add new nodes to the stack while we can find a neighbor to the
                // top node on the stack that is also adjacent to all nodes in the stack.
        again:
                // Find a neighbor.
                for (unsigned offset = 1; stack[index] + offset < num_nodes; offset++) {
                        if (adj_all(stack[index] + offset, stack, index + 1, adj, num_nodes)) {
                                stack[index + 1] = stack[index] + offset; // Add this node to the stack.
                                index++;
                                goto again;
                        }
                }

And a replacement with no goto statement:

Code:

        for (; {
                // Down the tree. Add new nodes to the stack while we can find a neighbor to the
                // top node on the stack that is also adjacent to all nodes in the stack.
                bool oneoffbool = false;
                // Find a neighbor.
                for (unsigned offset = 1; stack[index] + offset < num_nodes; offset++) {
                        if (adj_all(stack[index] + offset, stack, index + 1, adj, num_nodes)) {
                                stack[index + 1] = stack[index] + offset; // Add this node to the stack.
                                index++;
                                oneoffbool = true;
                                break;
                        }
                }
                if (oneoffbool)
                        continue;

This code also does the same thing, but without goto or a one-off-bool, but lots of programmers I have worked with over the years do not like manipulating for loops directly...

Code:

        for (; {
                // Down the tree. Add new nodes to the stack while we can find a neighbor to the
                // top node on the stack that is also adjacent to all nodes in the stack.
                // Find a neighbor.
                for (unsigned offset = 1; stack[index] + offset < num_nodes; offset++) {
                        if (adj_all(stack[index] + offset, stack, index + 1, adj, num_nodes)) {
                                stack[index + 1] = stack[index] + offset; // Add this node to the stack.
                                index++;
                                offset = 0;
                        }
                }

The interesting part here is that the first two have the same runtime, and the last one is ever-so-slightly slower.

Smile

excellent learning material anyway though. Which version of the exact same functionality is better? hahah. "Don't worry about it, let the compiler work it out" has never really worked out for any of my "hot codepaths." Care is always required, even well away from assembly language. Smile

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21 Apr 2016, 21:27

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 20513
Location: In your JS exploiting you and your system

revolution 21 Apr 2016, 23:37

redsock wrote:

"Don't worry about it, let the compiler work it out" ...

Yeah, I have also heard this a lot. People seem to have so much trust in the compiler. Whereas in reality the compilers aren't good, and can't ever be good because the language limits how one can express the problem solution. Plus the compilers are not sentient or intelligent or smart, they are simple state machine robots, nothing more, regardless of how "clever" they might first appear to the naive that don't understand assembly.

21 Apr 2016, 23:37

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 22 Apr 2016, 02:23

I've worked the kinks out of an original algorithm - seems to bury this one. Need to expand it to work on more than 64 nodes and then I'll time the big one. Fairly hopeful. Very Happy

Although I haven't spent much time with the published papers, the approach seems logical to me - I also know more aggressive pruning of the decision tree is possible(how to do it without storing more data though?). Since I follow the graph, the topology is more important than the number of nodes with regard to it's performance.

22 Apr 2016, 02:23

tthsqe

Joined: 20 May 2009
Posts: 767

tthsqe 22 Apr 2016, 17:23

Guy and Gals!
Would anyone like to help with an asm rewrite of a non-trivial and large project?

I am rewriting the chess engine stockfish https://github.com/official-stockfish/Stockfish

I, as one man/woman, simply do not have the manpower/womanpower to type that much code into x86-64, and there seems to be a lot of ability on this thread.

22 Apr 2016, 17:23

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 22 Apr 2016, 19:52

tthsqe, I respect your gender-less abilities. Very Happy

Yet, why? Is there a shortage of chess engines? Are real life human problems being solved with chess? Is there a monetary bounty of some sort? Bragging rights, even? Maybe, you have passion enough to draw others into your desires/interests?

Quote:

Since 2013, Stockfish is being developed using a distributed testing framework named Fishtest, where volunteers are able to donate CPU time for testing improvements to the program.

Changes to game-playing code are accepted or rejected based on results of playing of tens of thousands of games on the framework against an older version of the program, using sequential probability ratio testing. Tests on the framework are verified using the chi-squared test, and only if the resulting p-value is not statistically significant, the test is deemed reliable.

As of January 2016, the framework has used a total of more than 360 years of CPU time to play more than 240 million chess games. After the inception of Fishtest, Stockfish incurred an explosive growth of 120 Elo points in just 12 months, propelling it to the top of all major rating lists.

Wow.

22 Apr 2016, 19:52

tthsqe

Joined: 20 May 2009
Posts: 767

tthsqe 22 Apr 2016, 22:24

bitRAKE, there is no money involved, only braggin rights. I also have heard a lot of the 'let the compiler optimize the code for you' mantra and want to see to what extent handwritten asm can outperform the compiler. Conforming to language and other standards somewhat limits the compiler.
Also, I don't know of any strong chess engines written entirely in asm, so it would be a first in that department...

22 Apr 2016, 22:24

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 23 Apr 2016, 01:09

There are some out there, for sure!
https://github.com/CrSeth/x86ChessEngine

...and many of the needed parts of the heuristics have been coded in assembly.
https://chessprogramming.wikispaces.com/AVX2

I think I could spend my whole life just trying to understand the problem of chess. Note this honest statement with regard to x86-64:

Quote:

Useful instructions for bitboard-applications are by default not supported by high-level programming languages.

Much respect for the chess engine coders.

23 Apr 2016, 01:09

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 23 Apr 2016, 14:57

Here is the 64 node version of my algorithm:

Code:

; RAX is for temp usage
ADJ   EQU Adj53                         ; address of structure
ADJ.b EQU Adj53.width                   ; static byte width of structure ( 8 )
SET   EQU RDX                           ; bit mask of node filter
I     EQU RCX                           ; [0-63]
I.d   EQU ECX                           ; (needed to load size from structure)
BEST  EQU RBX                           ; [1-64]


AdjMatrixPrep:
; All nodes are self-referential and node count is zero-based!
    sub         DWORD [ADJ-4], 1
    mov         I.d, [ADJ-4]
@@: imul        eax, I.d, ADJ.b
    bts         [ADJ + rax], I.d
    sub         I.d, 1
    jns         @B
    retn


Clique64:
    xor         BEST, BEST
.root:
    ; setup to follow root node
    mov         I.d, [ADJ-4]
.trunk:
    mov         SET, [ADJ+I*8]
    sub         I, 1
    jns         .trunk_new
    retn

.trunk_new:
    push        I 0
    mov         I.d,[ADJ-4]
.node:
    ; filter with active node adjacency?
    bt          SET, I
    jnc         .skip

    ; how does the lack of connections limit set?
    mov         rax, SET
    and         SET, [ADJ+I*8]

    ; did anything change? (optimization)
    cmp         rax, SET
    jz          .skip

    ; change implies a decision needs to be made:
    ;   - follow present SET
    ;   - ignore this node, exclude it from SET
    ;     (on stack to check later)
    btr         rax, I
    push        I rax
.skip:
    sub         I, 1
    jns         .node

    ; is this clique larger than any previous?
    popcnt      rax, SET
    cmp         BEST, rax
    cmovc       BEST, rax

; All branches belong to the same trunk node. Yet, they branch from different
; places along the trunk (different common nodes, different forward branches).
.branch:
    pop         SET I

    popcnt      rax, SET
    jz          .trunk                  ; branch is finished ; NOT TAKEN

    ; (optimization only if least greedy choice on stack?)
    cmp         BEST,rax
    jnc         .branch                 ; not enough bits to bother with

    jmp         .skip


RESTORE ADJ,ADJ.b,SET,I,I.d,BEST

...utilizes the previous macro to create bit matrix; and AdjMatrixPrep needs to called prior to Clique64.

(My extended version has a error in it somewhere - maybe also present in the above. Wink

)

Update: the error was me (trashed the result with timing code, doh!). On the above 129 node graph the extended version takes only 105332ms - this is on a lesser processor. 7x faster Very Happy

23 Apr 2016, 14:57

redsock

Joined: 09 Oct 2009
Posts: 435
Location: Australia

redsock 23 Apr 2016, 21:31

bitRAKE: Awesome! Can you post a complete version w/ the 129 data that compiles/runs?

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23 Apr 2016, 21:31

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 24 Apr 2016, 00:02

The 64-node version is less cluttered if one wants to understand the algorithm. Yet, looking at the below code one can see how to extend it to arBITrary nodes. I'm not going to make it run in the environment specified by the contest - I was more interested in seeing how my idea performed. Still thinking about improvements. AVX didn't seem profitable, but AVX2 should be.

As the name suggests, this should work for 192 nodes.

Code:

MACRO _ALIGN_ base*,delta=0,fill=<db 0> {
  WHILE ((($-$$)+delta) and (base-1)) <> 0
    fill
  END WHILE
}

MACRO import [lib,api] {
        common
                local part0,part1,first
                macro part0 lib0,[api0] \{
                \common         lib0\#_STR db \`lib0
                \forward        rb 2 - RVA $ AND 1
                                label api0\#_STR at $-2
                                db \`api0
                \common         db 0
                \}

                first = 7
                macro part1 lib1,[api1] \{
                \common         rb (8 - RVA $ AND 7) AND first
                                first = 15
                                label lib1\#_TAB
                \forward        api1 dq RVA api1\#_STR
                \}

        forward         part0 lib,api
        forward         part1 lib,api
        common          data import
        forward         dd 0,0,0,RVA lib#_STR,RVA lib#_TAB
        common          rd 5
                        end data
}

;###############################################################################

FORMAT PE64 CONSOLE 5.0 AT $10000
;       Reserve,        Commit
STACK   $100000,        $100000
HEAP    $10000,         $10000

SECTION '' READABLE WRITEABLE EXECUTABLE

MACRO adjacency name,[bit_array*] {
  COMMON
    adjacency@lines = 0
  FORWARD
    adjacency@lines = adjacency@lines + 1
  COMMON
    _ALIGN_ 64,4,<db 0> ; waste of a cacheline
    dd adjacency@lines
    name: ; non sized label
    name#.width = ((adjacency@lines + 63) AND (0-64))/8 ; width in bytes
  FORWARD
    gather@nodes=0
    gather@dq=0
    IRPS bit,bit_array \{
      gather@dq = gather@dq + (bit shl (gather@nodes mod 64))
      gather@nodes = gather@nodes + 1
      IF 0 = (gather@nodes mod 64)
        dq gather@dq
        gather@dq=0
      END IF
    \}
    IF 0 <> (gather@nodes mod 64)
      dq gather@dq
      gather@dq = 0
    END IF
    IF gather@nodes <> adjacency@lines
      ERR "ERROR: Non-square Adjacency Matrix!"
    END IF
}

adjacency Adj129, \
  < 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 >, \
  < 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 >, \
  < 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 >, \
  < 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 >, \
  < 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 >, \
  < 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 >, \
  < 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 >, \
  < 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 >, \
  < 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 >, \
  < 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 >, \
  < 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 >, \
  < 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 >, \
  < 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 >, \
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  < 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 >, \
  < 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 >, \
  < 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 >, \
  < 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 >, \
  < 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 >, \
  < 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 >, \
  < 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 >, \
  < 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 >, \
  < 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 >, \
  < 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 >, \
  < 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 >, \
  < 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 >, \
  < 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 >, \
  < 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 >, \
  < 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 >, \
  < 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 >, \
  < 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 >, \
  < 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 >, \
  < 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 >, \
  < 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 >, \
  < 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 >, \
  < 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 >, \
  < 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 >, \
  < 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 >, \
  < 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 >, \
  < 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 >, \
  < 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 >, \
  < 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 >, \
  < 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 >, \
  < 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 >, \
  < 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 >, \
  < 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 >

ENTRY $ ; $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
    virtual at rbp-.FRAME
        rq 4
      .4 rq 20-4-5-1
      .va_list rq 5
      .lpNumberOfBytesWritten rq 1 ; it makes WriteFile happy

      .FRAME = ($-$$+15)AND-16 ; should be < 160 for byte offsets
    end virtual

        enter .FRAME,0

        mov ecx,-11                     ; STD_OUTPUT_HANDLE
        call [GetStdHandle]
        cmp rax,-1
        jz .INVALID_HANDLE_VALUE
        mov [hStdOut],rax

        xchg rcx,rax                    ; hStdOut
        call [GetFileType]
        cmp eax,2
        jz .FILE_TYPE_CHAR

        bts [FLAGS],NO_INPUT
        jmp .NO_INPUT

.FILE_TYPE_CHAR:
        mov ecx,-10                     ; STD_INPUT_HANDLE
        call [GetStdHandle]
        cmp rax,-1
        jz .INVALID_HANDLE_VALUE
        mov [hStdIn],rax

.NO_INPUT:

        call AdjMatrixPrep

        call [GetTickCount]
        neg rax
        mov [.va_list+8],rax

        call Clique192
        mov [.va_list],rax

        call [GetTickCount]
        add [.va_list+8],rax

        ; output
        lea r8,[.va_list]
        lea rdx,[template.result]
        lea rcx,[_buffer]
        call [wvsprintfA]
        mov byte [_buffer+rax],0

        mov rcx,[hStdOut]
        lea rdx,[_buffer]
        mov r8,rax
        lea r9,[.lpNumberOfBytesWritten]
        and qword [.4],0
        call [WriteFile]

.INVALID_HANDLE_VALUE:
        leave
        retn

template.result db "Clique of size %I64i found.",13,10
                db "It took %I64ims!",13,10,0

; \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/
; RAX is for temp usage
ADJ   EQU Adj129                        ; address of structure
ADJ.b EQU Adj129.width                  ; static byte width of structure (24)

SET0  EQU RBP                           ; bit mask of node filter
SET1  EQU RSI                           ; bit mask of node filter
SET2  EQU RDI                           ; bit mask of node filter

I     EQU RCX                           ; [0-63]
I.d   EQU ECX                           ; (needed to load size from structure)
I24   EQU RDX                           ; 24*[0-63] used to access 2nd array dimension
I24.d EQU EDX
BEST  EQU RBX                           ; [1-64]


AdjMatrixPrep:
; All nodes are self-referential and node count is zero-based!
    sub         DWORD [ADJ-4], 1
    mov         I.d, [ADJ-4]
@@: imul        I24.d, I.d, ADJ.b
    bts         [ADJ + I24], I.d
    sub         I.d, 1
    jns         @B
    retn


Clique192:
    push rbx rbp rsi rdi ; save some registers

@@: push        rsp                     ; very lazy way to align stack
    test        rsp,8*4 - 1
    jnz         @B

    xor         BEST, BEST
.root:
    ; setup to follow root node
    mov         I.d, [ADJ-4]
.trunk:
    imul        I24.d, I.d, ADJ.b
    mov         SET0, [ADJ+I24+8*0]
    mov         SET1, [ADJ+I24+8*1]
    mov         SET2, [ADJ+I24+8*2]

    sub         I, 1
    jns         .trunk_new

@@: pop         rsp                     ; reverse lazy alignment, lol
    lea         rax,[rsp+8]
    cmp         [rsp],rax
    jz          @B

    mov         rax,BEST

    pop rdi rsi rbp rbx ; restore some registers
    retn


.trunk_new:
    push        I 0 0 0
    mov         I.d,[ADJ-4]
.node:
    ; filter with active node adjacency?
    push        I SET2 SET1 SET0
    bt          [rsp],I
    jnc         .skip.32

    ; how does the lack of connections limit set?
    imul        I24.d, I.d, ADJ.b
    and         SET0, [ADJ+I24+8*0]
    and         SET1, [ADJ+I24+8*1]
    and         SET2, [ADJ+I24+8*2]

    ; did anything change? (optimization)
    cmp         [rsp], SET0
    jnz         .delta
    cmp         [rsp+8*1], SET1
    jnz         .delta
    cmp         [rsp+8*2], SET2
    jz          .skip.32
.delta:
    ; change implies a decision needs to be made:
    ;   - follow present SET
    ;   - ignore this node, exclude it from SET
    ;     (on stack to check later)
    btr         [rsp], I ; this requires the above register order
    jmp         .skip

.skip.32:
    add         rsp,8+ADJ.b
.skip:
    sub         I, 1
    jns         .node

    ; is this clique larger than any previous?
    popcnt      I24, SET0
    popcnt      rax, SET1
    add rax,I24
    popcnt      I24, SET2
    add rax,I24

    cmp         BEST, rax
    cmovc       BEST, rax

; All branches belong to the same trunk node. Yet, they branch from different
; places along the trunk (different common nodes, different forward branches).
.branch:
    pop         SET0 SET1 SET2 I

    popcnt      I24, SET0
    popcnt      rax, SET1
    add rax,I24
    popcnt      I24, SET2
    add rax,I24
    jz          .trunk                  ; branch is finished ; NOT TAKEN
    ; (optimization only if least greedy choice on stack?)
    cmp         BEST,rax
    jnc         .branch                 ; not enough nodes to bother with
    jmp         .skip

RESTORE ADJ,ADJ.b,SET0,SET1,SET2,I,I.d,BEST

; /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\

import  kernel32,<\
                GetFileType,\
                GetStdHandle,\
                GetTickCount,\
                ReadFile,\
                SetConsoleTitleA,\
                WriteFile\
                >,\
        user32,<\
                wvsprintfA\
                >

    _ALIGN_ 64

FLAGS           rq 1
        NO_INPUT        = 0

hStdIn          rq 1
hStdOut         rq 1

    _ALIGN_ 64
_buffer:           rb 1024
_buffer.. = $ - _buffer

Edit: left part of some test code in, fixed.

Last edited by bitRAKE on 24 Apr 2016, 13:42; edited 1 time in total

24 Apr 2016, 00:02

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 20513
Location: In your JS exploiting you and your system

revolution 24 Apr 2016, 05:31

I think that bitRAKE's code demonstrates an important fact. A HLL compiler could never figure out how to use an instruction like "popcnt". And even if there is a compiler out there that can, then it would need to see the HLL code presented in precisely the "proper" way to recognise it.

But further to that is the use of AVX and similar SIMD things. Auto-vectorisation is basically terrible at almost everything. And the compilers leave it up to the programmer to do it manually with intrinsics. Intrinsics can be considered assembly code actually except that it looks a whole lot uglier.

24 Apr 2016, 05:31

redsock

Joined: 09 Oct 2009
Posts: 435
Location: Australia

redsock 26 Apr 2016, 02:40

Thanks for putting your code up bitRAKE, it is considerably faster than the original algorithm. On the same machine as I ran Tyler's original C++ and my reworked C++ version, yours completed in 61.826s (versus 1785 for the original version, and 707 for my reworked version).

For a bit more optimising fun, I reworked your assembly version and got it to complete in 24.816s (2.5X faster). I didn't spend a huge amount of time reworking yours, and by no means do I think it is "as optimised as it can get" but a 2.5X improvement is still good educational material anyway for others to learn from.

Case in point, optimising code is fun and this all has been an excellent exercise highlighting how its done.

Note, I modified the code so that it compiles against my HeavyThing library.

Cheers!

Code:

include '../ht_defaults.inc'
include '../ht.inc'

MACRO _ALIGN_ base*,delta=0,fill=<db 0> {
  WHILE ((($-$$)+delta) and (base-1)) <> 0
    fill
  END WHILE
}

MACRO adjacency name,[bit_array*] { 
  COMMON 
    adjacency@lines = 0 
  FORWARD 
    adjacency@lines = adjacency@lines + 1 
  COMMON 
    _ALIGN_ 64,4,<db 0> ; waste of a cacheline 
    dd adjacency@lines 
    name: ; non sized label 
    name#.width = ((adjacency@lines + 63) AND (0-64))/8 ; width in bytes 
  FORWARD 
    gather@nodes=0 
    gather@dq=0 
    IRPS bit,bit_array \{ 
      gather@dq = gather@dq + (bit shl (gather@nodes mod 64)) 
      gather@nodes = gather@nodes + 1 
      IF 0 = (gather@nodes mod 64) 
        dq gather@dq 
        gather@dq=0 
      END IF 
    \} 
    IF 0 <> (gather@nodes mod 64) 
      dq gather@dq 
      gather@dq = 0 
    END IF 
    IF gather@nodes <> adjacency@lines 
      ERR "ERROR: Non-square Adjacency Matrix!" 
    END IF 
} 

globals
{

adjacency Adj129, \ 
  < 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 >, \
  < 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 >, \
  < 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 >, \
  < 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 >, \
  < 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 >, \
  < 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 >, \
  < 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 >, \
  < 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 >, \
  < 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 >, \
  < 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 >, \
  < 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 >, \
  < 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 >, \
  < 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 >, \
  < 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 >, \
  < 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 >, \
  < 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 >, \
  < 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 >, \
  < 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 >, \
  < 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 >, \
  < 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 >, \
  < 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 >, \
  < 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 >, \
  < 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 >, \
  < 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 >, \
  < 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 >, \
  < 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 >, \
  < 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 >, \
  < 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 >, \
  < 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 >, \
  < 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 >, \
  < 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 >, \
  < 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 >, \
  < 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 >, \
  < 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 >, \
  < 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 >, \
  < 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 >, \
  < 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 >, \
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  < 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 >, \
  < 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 >, \
  < 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 >, \
  < 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 >, \
  < 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 >, \
  < 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 >, \
  < 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 >
}

public _start
falign
_start:
        call    ht$init

        call AdjMatrixPrep 

        call    .ts
        neg     rax
        mov     r15, rax

        call Clique192
        mov     r14, rax

        call    .ts
        add     r15, rax

        ; output 
        mov     rdi, .res1
        call    string$to_stdout
        mov     rdi, r14
        mov     esi, 10
        call    string$from_unsigned
        push    rax
        mov     rdi, rax
        call    string$to_stdout
        pop     rdi
        call    heap$free
        mov     rdi, .res2
        call    string$to_stdout
        mov     rdi, r15
        mov     esi, 10
        call    string$from_unsigned
        push    rax
        mov     rdi, rax
        call    string$to_stdout
        pop     rdi
        call    heap$free
        mov     rdi, .res3
        call    string$to_stdoutln
        
        mov     eax, syscall_exit
        xor     edi, edi
        syscall
falign
.ts:
        sub     rsp, 16
        mov     rdi, rsp
        xor     esi, esi
        call    gettimeofday
        mov     ecx, 1000
        pop     rax     ; tv_secs
        mul     rcx
        pop     rdx     ; tv_usecs
        shr     rdx, 10 ; not precise obviously
        add     rax, rdx
        ret

cleartext .res1, 'Clique of size '
cleartext .res2, ' found',10,'It took '
cleartext .res3, 'ms!'

template.result db "Clique of size %I64i found.",13,10 
                db "It took %I64ims!",13,10,0 

; \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ 
; RAX is for temp usage 
ADJ   EQU Adj129                        ; address of structure 
ADJ.b EQU Adj129.width                  ; static byte width of structure (24) 

SET0  EQU RBP                           ; bit mask of node filter 
SET1  EQU RSI                           ; bit mask of node filter 
SET2  EQU RDI                           ; bit mask of node filter 

I     EQU RCX                           ; [0-63] 
I.d   EQU ECX                           ; (needed to load size from structure) 
I24   EQU RDX                           ; 24*[0-63] used to access 2nd array dimension 
I24.d EQU EDX 
BEST  EQU RBX                           ; [1-64] 


AdjMatrixPrep: 
; All nodes are self-referential and node count is zero-based! 
    sub         DWORD [ADJ-4], 1 
    mov         I.d, [ADJ-4] 
@@: imul        I24.d, I.d, ADJ.b 
    bts         [ADJ + I24], I.d 
    sub         I.d, 1 
    jns         @B 
    retn 


Clique192: 
        push rbx rbp rsi rdi ; save some registers 

        @@: push        rsp                     ; very lazy way to align stack 
        test        rsp,8*4 - 1 
        jnz         @B 

        xor         BEST, BEST 
        ; setup to follow root node 
        mov         I.d, [ADJ-4] 
.trunk: 
        imul        I24.d, I.d, ADJ.b 
        mov         SET0, [ADJ+I24+8*0] 
        mov         SET1, [ADJ+I24+8*1] 
        mov         SET2, [ADJ+I24+8*2] 

        sub         I, 1 
        js              .do_return_goods

        push        I 0 0 0 
        ; mov         I.d,[ADJ-4] 

        bitpos = 128

        rept 129 counter
        {
                .scanpos#counter:
                mov     I.d, bitpos
                if bitpos = 128
                        bt      SET2, bitpos
                else if bitpos >= 64
                        bt      SET1, bitpos
                else
                        bt      SET0, bitpos
                end if
                jc      .set
                bitpos = bitpos - 1
        }

.scandone:

        ; is this clique larger than any previous? 
        popcnt      I24, SET0 
        popcnt      rax, SET1 
        add rax,I24 
        popcnt      I24, SET2 
        add rax,I24 

        cmp         BEST, rax 
        cmovc       BEST, rax 

        ; All branches belong to the same trunk node. Yet, they branch from different 
        ; places along the trunk (different common nodes, different forward branches). 
calign
.branch: 
        pop         SET0 SET1 SET2 I 

        popcnt      I24, SET0 
        popcnt      rax, SET1 
        add rax,I24 
        popcnt      I24, SET2 
        add rax,I24 
        jz          .trunk                  ; branch is finished ; NOT TAKEN 
        ; (optimization only if least greedy choice on stack?) 
        cmp         BEST,rax 
        jnc         .branch                 ; not enough nodes to bother with 

        sub     I, 1
        js      .scandone
        jmp     qword [I*8+.scantable]

dalign
.scantable:
        rept 129 counter {
        reverse dq .scanpos#counter
        }

calign
.set:
        PUSH    I SET2 SET1 SET0

        ; how does the lack of connections limit set? 
        imul        I24.d, I.d, ADJ.b 
        and         SET0, [ADJ+I24+8*0] 
        and         SET1, [ADJ+I24+8*1] 
        and         SET2, [ADJ+I24+8*2] 

        ; did anything change? (optimization) 
        cmp         [rsp], SET0 
        jnz         .delta 
        cmp         [rsp+8*1], SET1 
        jnz         .delta 
        cmp         [rsp+8*2], SET2 
        jz          .skip.32 
.delta: 
        ; change implies a decision needs to be made: 
        ;   - follow present SET 
        ;   - ignore this node, exclude it from SET 
        ;     (on stack to check later) 
        btr         [rsp], I ; this requires the above register order 
        sub     I, 1
        js      .scandone
        jmp     qword [I*8+.scantable]
calign
.skip.32:
        add     rsp, 8+ADJ.b
.skip:
        sub     I, 1
        js      .scandone
        jmp     qword [I*8+.scantable]
calign
.do_return_goods:
        pop         rsp                     ; reverse lazy alignment, lol 
        lea         rax,[rsp+8] 
        cmp         [rsp],rax 
        jz          .do_return_goods

        mov         rax,BEST 

        pop rdi rsi rbp rbx ; restore some registers 
        retn 


RESTORE ADJ,ADJ.b,SET0,SET1,SET2,I,I.d,BEST 


include '../ht_data.inc'

_________________
2 Ton Digital - https://2ton.com.au/

26 Apr 2016, 02:40

Furs

Joined: 04 Mar 2016
Posts: 2594

Furs 26 Apr 2016, 12:14

Tyler wrote:

Yeah, that Dijkstra guy, he was sssoooooo dumb, amiright?

No offense but on the subject of the goto, yes he was. Very opinionated, just because he couldn't use them properly.

In some cases, goto can make cleaner code by far (especially with error checking) than functions or switch or bools. Then again I think some people over-use functions, really a shame how people get taught these days to make a function for every little thing. It's also confusing for the reader.

26 Apr 2016, 12:14

bitRAKE

Joined: 21 Jul 2003
Posts: 4153
Location: vpcmpistri

bitRAKE 26 Apr 2016, 21:16

redsock wrote:

For a bit more optimising fun, I reworked your assembly version and got it to complete in 24.816s (2.5X faster). I didn't spend a huge amount of time reworking yours, and by no means do I think it is "as optimised as it can get" but a 2.5X improvement is still good educational material anyway for others to learn from.

Great work, thanks for taking the time. Unrolling to remove the three-way branch was a good choice. For a greater number of nodes the state could remain in memory, or VPTEST could be used with a mask.

One thing I thought might be better is to push the filtered decision because it has a chance to remove more than one bit; and process the single bit removal within the inner loop. Yet, this could have a negative effect of greater stack use - more choices on stack. Could this greedy approach make more stack decisions not taken?

Still trying to think through an optimal way to further truncate some of the redundancy. Yet, this version is quite impressive, IIDSSM.

_________________
¯\(°_o)/¯ “languages are not safe - uses can be” Bjarne Stroustrup

26 Apr 2016, 21:16

redsock

Joined: 09 Oct 2009
Posts: 435
Location: Australia

redsock 26 Apr 2016, 23:22

bitRAKE wrote:

...Yet, this could have a negative effect of greater stack use...

For a 0 bit during the scan unroll, there are no branches and more importantly no 32 byte pushes followed immediately by 32 byte rsp reversals. Aside from the opposite control flow (js versus jns, jc versus jnc, etc) I think those push/pops, especially the one where the 32 byte push was immediately followed by a bt that references the values just pushed is where the real speedup came from... I didn't do an indepth analysis, but agree that for larger node counts a similar technique can certainly be done.

revolution wrote:

I think that bitRAKE's code demonstrates an important fact. A HLL compiler could never figure out how to use an instruction like "popcnt". And even if there is a compiler out there that can, then it would need to see the HLL code presented in precisely the "proper" way to recognise it.

This.

Maybe instead of discussions about "you can't possibly write assembly language to outperform my HLL", maybe we should go the opposite direction and say "I'd love to see your HLL representation of this assembly language."

I consider myself an expert in C/C++, and I know of no way to write C to generate similar machine code as in bitRAKE's approach to this problem. There is no intrinsic for a memory-reference bt instruction that I am aware of, so without dropping to assembly inside the C code, this solution is not possible to even do in HLL. (Though maybe there is some trickery as revo suggests that I could specify it "precisely the proper way" that I am not aware of.) Outside C, this becomes a ridiculous thing to even consider (think Ruby, Java, JS, etc, hahaha).

This entire thread is an absolute beauty! It covers in detail and with reference code a great many arguments/discussions I have witnessed over the years about asm versus arbitrary HLLs, "compilers are better in all but the rarest hot code path cases", hahah, the list goes on and on. Hats off to everyone, awesome stuff!

Cheers

_________________
2 Ton Digital - https://2ton.com.au/

26 Apr 2016, 23:22

rugxulo

Joined: 09 Aug 2005
Posts: 2341
Location: Usono (aka, USA)

rugxulo 08 May 2016, 22:01

(I know I'm late replying here. I'm also probably the worst person to explain this, but ...)

Furs wrote:

Tyler wrote:
Yeah, that Dijkstra guy, he was sssoooooo dumb, amiright?
No offense but on the subject of the goto, yes he was. Very opinionated, just because he couldn't use them properly.

In some cases, goto can make cleaner code by far (especially with error checking) than functions or switch or bools. Then again I think some people over-use functions, really a shame how people get taught these days to make a function for every little thing. It's also confusing for the reader.

Remember that he was against unstructured BASIC, which (over)used GOTO for everything. Also keep in mind that he was heavily involved in ALGOL, which was the first well-designed programming language, meant for expressing algorithms (which are often heavy on theory). He also was one of the pioneers who first taught comp. sci., so he was emphatic on clarity and correctness.

Niklaus Wirth was the one who oversaw the "case against GOTO". IIRC, his opinion was allegedly that "just because it can be misused or is suboptimal isn't enough reason to omit it". Classic Pascal, unlike C/C++ (or even Turbo Pascal), had global goto, which meant unwinding stack when jumping out of (possibly nested) procedures, and you weren't allowed to jump into loops (obviously?).

Of course, in later years even Wirth changed his mind, even lamenting that "it's harder to remove language features than add them". Modula-2 had no goto but did have LOOP..EXIT, multiple RETURNs, coroutines, etc. But his Oberon-07 dialect is even more restricted than earlier versions (no LOOP..EXIT, no multiple RETURNs, WHILE..ELSIF, strictly local or global vars only). But his focus is on simplicity, clarity, correctness, etc. You could even argue that it's easier to write a compiler (or optimize or debug or garbage collect or ...) if there are less loose ends, less loopholes.

There are lots of language features that can make certain specific code easier or (relatively) "faster". To misuse a common saying, "The programming language graveyard is full of features that the world couldn't live without." At some point, you just can't support everything (at least not easily or universally). There is no one-size-fits-all.

08 May 2016, 22:01

revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 20513
Location: In your JS exploiting you and your system

revolution 20 May 2016, 08:55

So who won the awesome life changing prize of $60? I'm so jealous.

20 May 2016, 08:55

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