I implemented a specific filter in C/C++, "encapsulated" in a SystemC-Module. I want to use this filter in my actual verification environment (VE), which is based on SystemVerilog. To transfer data from and to the filter, I want to implement a TLM-connection. For TLM, there is something called a "generic payload", basically defining what can be transmitted via TLM, which is a byte-array.
Because of this, I need to convert the data samples in the VE from datatype real to a byte-array. What I tried to do is create a union-type, such that I can store a real-value and read a byte-array.
typedef union packed {
real value;
byte unsigned array[8];
} real_u;
However, I get the following error message.
real value;
|
ncvlog: *E,SVBPSE (Initiator.sv,7|11): The data type of a packed struct/union member must be a SystemVerilog integral type.
byte unsigned array[8];
|
ncvlog: *E,SVBPSE (Initiator.sv,8|20): The data type of a packed struct/union member must be a SystemVerilog integral type.
How could I resolve that issue? Are there other convenient ways to convert floating-point numbers to byte-arrays in SV/C++?
packed unions and structs might only contain packed members. So, in your case, both, real and byte unsigned array[8] are unpacked. Potentially you can use unpacked unions to do so, but not every vendor implements those.
Moreover, byte size of 'real' is not defined in the standard, therefore, your union most likely will not work at all. However, system verilog provides a set of functions to convert real to certain sized variables. In your case, $realtobits which returns 64 bits, will probably work.
So, i suggest you just pass real value after conversion to bits:
bit[63:0] realBits = $realtobits(value);
Directly represented variables (DRV) in IEC61131-3 languages include in their "addresses" a data-width specifier: X for 1 bit, B for byte, W for word, D for dword, etc.
Furthermore, when a DRV is declared, a IEC data type is specified, as any variable (BYTE, WORD, INT, REAL...).
I'm not sure about how these things are related. Are they orthogonal or not? Can one define a REAL variable with a W (byte) address? What would be the expected result?
A book says:
Assigning a data type to a flag or I/O address enables the programming
system to check whether the variable is being accessed correctly. For
example, a variable declared by AT %QD3 : DINT; cannot be
inadvertently accessed with UINT or REAL.
which does not make things clearer for me. Take for example this fragment (recall that W means Word, i.e., 16 bits - and both DINT and REAL correspond to 32 bits)
X AT %MW3 : DINT;
Y AT %MD4.1 : DINT;
Z AT %MD4.1 : REAL;
The first line maps a 32-bits IEC var to a 16-bits location. Is this legal? would the write/read be equivalent to a "cast" or what?
The other lines declare two 32-bits IEC variables of different type that points to the same address (I guess this should be legal). What is the expected result when reading or writing?
Like everything in PLC world, its all vendor and model specific, unfortunately.
Siemens compiler would not let you declare Real address with bit component like MD4.1, it allowed only MD4 and data length had to be double word, MB4 was not allowed.
Reading would not be equivalent to cast. For example you declare MW2 as integer and copy some value there. PLC stores integer as, lets say in twos complement format. Later in program you read MD2 as real. The PLC does not try to convert integer to real, it just blindly reads the bytes and treats it as real regardless what was saved there or what was declared there. There was no automatic casting.
This is how things worked in Siemens S7 plc-s. But you have to be very careful since each vendor does things its own way.
I'm trying to implement a simple cryptocurrency similar to bitcoin, just to understand it deeply down to the code level.
I understand that a bitcoin block contains a hash of the previous block, many transactions and an reward transaction for the solver.
the miner basically runs SHA256 on this candidate block combined with an random number. As long as the first certain digits of a hash result are zeros, we say this block is solved, and we broadcast the result to the entire network to claim the reward.
but I have never seen anyone proving that a block is solvable at all. I guess this is guaranteed by SHA256? because the solution size is fixed, after trying enough inputs, you are guaranteed to hit every hash result? but how can you prove that the solution distribution of a block is even (uniform), so that you can indeed cover all hash results?
now, suppose a block is indeed always solvable, can I assume that using 64bit for the random integer is enough to solve it? how about 32bit? or I have to use an infinite bit integer?
for example, in the basiccoin project:
the code for proof of work is the following:
def POW(block, hashes):
halfHash = tools.det_hash(block)
block[u'nonce'] = random.randint(0, 10000000000000000000000000000000000000000)
count = 0
while tools.det_hash({u'nonce': block['nonce'],
u'halfHash': halfHash}) > block['target']:
count += 1
block[u'nonce'] += 1
if count > hashes:
return {'error': False}
if restart_signal.is_set():
restart_signal.clear()
return {'solution_found': True}
''' for testing sudden loss in hashpower from miners.
if block[u'length']>150:
else: time.sleep(0.01)
'''
return block
this code randoms a number between [0, 10000000000000000000000000000000000000000] as a start point, and then it just increases the value one by one:
block[u'nonce'] += 1
I'm not a python programmer, I don't know how python handles the type of the integer. there is no handling of integer overflow.
I'm trying to implement similar thing with c++, I don't know what kind of integer can guarantee a solution.
but how can you prove that the solution distribution of a block is even (uniform), so that you can indeed cover all hash results?
SHA256 is deterministic so if you rehash the txns it will always provide the same 256 hash.
The client nodes keep all the txn and the hashes in the merkle tree for the network clients to propagate and verify the longest possible block chain.
The merkle tree is the essential data structure for recording the hashes of previous blocks.
From there the chain of hash confirmations can be tracked from the origin (genesis) block.
I have an array that I would like to initialize to all 1. To do this, I used the following code snippet:
logic [15:0] memory [8];
always_ff #(posedge clk or posedge reset) begin
if(reset) begin
memory <= '{default:'1};
end
else begin
...
end
end
My simulator does what I think is the correct thing and sets the registers to 16'hFFFF on reset. However, my lint tool gives me a warning that bit 0 has an async set while bits 1 through 15 have async resets. This implies that the linter thinks that this code assigns 16'h0001 to the registers.
Since both tools come from the same vendor I file a bug report since they can't both be right.
The question is: Which behavior is correct according to the spec? There is no example that shows this exact situation. Section 5.7.1 mentions that:
An unsized single-bit value can be specified by preceding the single-bit value with an apostrophe ( ' ), but
without the base specifier. All bits of the unsized value shall be set to the value of the specified bit. In a
self-determined context, an unsized single-bit value shall have a width of 1 bit, and the value shall be treated
as unsigned.
'0, '1, 'X, 'x, 'Z, 'z // sets all bits to specified value
I f this is a "self-determined context" then the answer is 1 bit sign extended to 16'h0001, but if it is not, then I guess the example which says it "sets all bits to the specified value" applies. I am not sure if this is a self -determined context.
The simulator is correct: memory <= '{default:'1}; will assign all each bit in memory to 1. The linting tool does have a bug. See IEEE Std 1800-2012 § 10.9.1 Array assignment patterns:
The **default:***value* applies to elements or subarrays that are not matched by either index or type key. If the type of the element or subarray is a simple bit vector type, matches the self-determined type of the value, or is not an array or structure type, then the value is evaluated in the context of each assignment to an element or subarray by the default and shall be castable to the type of the element or subarray; otherwise, an error is generated. ...
The LRM goes beyond what is synthesizable when it comes to assignment patterns. And most of the tools are sill playing catchup with supporting all the SystemVerilog features. Experiment to make sure your tools (simulator,synthesizer, lint tool, logic-equivalency-checker, etc.) all have the necessary support for the features you want.
Consider a lookup function with the following signature, which needs to return an integer for a given string key:
int GetValue(string key) { ... }
Consider furthermore that the key-value mappings, numbering N, are known in advance when the source code for function is being written, e.g.:
// N=3
{ "foo", 1 },
{ "bar", 42 },
{ "bazz", 314159 }
So a valid (but not perfect!) implementation for the function for the input above would be:
int GetValue(string key)
{
switch (key)
{
case "foo": return 1;
case "bar": return 42;
case "bazz": return 314159;
}
// Doesn't matter what we do here, control will never come to this point
throw new Exception();
}
It is also known in advance exactly how many times (C>=1) the function will be called at run-time for every given key. For example:
C["foo"] = 1;
C["bar"] = 1;
C["bazz"] = 2;
The order of such calls is not known, however. E.g. the above could describe the following sequence of calls at run-time:
GetValue("foo");
GetValue("bazz");
GetValue("bar");
GetValue("bazz");
or any other sequence, provided the call counts match.
There is also a restriction M, specified in whatever units is most convenient, defining the upper memory bound of any lookup tables and other helper structures that can be used by the GetValue (the structures are initialized in advance; that initialization is not counted against the complexity of the function). For example, M=100 chars, or M=256 sizeof(object reference).
The question is, how to write the body of GetValue such that it is as fast as possible - in other words, the aggregate time of all GetValue calls (note that we know the total count, per everything above) is minimal, for given N, C and M?
The algorithm may require a reasonable minimal value for M, e.g. M >= char.MaxValue. It may also require that M be aligned to some reasonable boundary - for example, that it may only be a power of two. It may also require that M must be a function of N of a certain kind (for example, it may allow valid M=N, or M=2N, ...; or valid M=N, or M=N^2, ...; etc).
The algorithm can be expressed in any suitable language or other form. For runtime performance constrains for generated code, assume that the generated code for GetValue will be in C#, VB or Java (really, any language will do, so long as strings are treated as immutable arrays of characters - i.e. O(1) length and O(1) indexing, and no other data computed for them in advance). Also, to simplify this a bit, answers which assume that C=1 for all keys are considered valid, though those answers which cover the more general case are preferred.
Some musings on possible approaches
The obvious first answer to the above is using a perfect hash, but generic approaches to finding one seem to be imperfect. For example, one can easily generate a table for a minimal perfect hash using Pearson hashing for the sample data above, but then the input key would have to be hashed for every call to GetValue, and Pearson hash necessarily scans the entire input string. But all sample keys actually differ in their third character, so only that can be used as the input for the hash instead of the entire string. Furthermore, if M is required to be at least char.MaxValue, then the third character itself becomes a perfect hash.
For a different set of keys this may no longer be true, but it may still be possible to reduce the amount of characters considered before the precise answer can be given. Furthermore, in some cases where a minimal perfect hash would require inspecting the entire string, it may be possible to reduce the lookup to a subset, or otherwise make it faster (e.g. a less complex hashing function?) by making the hash non-minimal (i.e. M > N) - effectively sacrificing space for the sake of speed.
It may also be that traditional hashing is not such a good idea to begin with, and it's easier to structure the body of GetValue as a series of conditionals, arranged such that the first checks for the "most variable" character (the one that varies across most keys), with further nested checks as needed to determine the correct answer. Note that "variance" here can be influenced by the number of times each key is going to be looked up (C). Furthermore, it is not always readily obvious what the best structure of branches should be - it may be, for example, that the "most variable" character only lets you distinguish 10 keys out of 100, but for the remaining 90 that one extra check is unnecessary to distinguish between them, and on average (considering C) there are more checks per key than in a different solution which does not start with the "most variable" character. The goal then is to determine the perfect sequence of checks.
You could use the Boyer search, but I think that the Trie would be a much more effiecent method. You can modify the Trie to collapse the words as you make the hit count for a key zero, thus reducing the number of searches you would have to do the farther down the line you get. The biggest benefit you would get is that you are doing array lookups for the indexes, which is much faster than a comparison.
You've talked about a memory limitation when it comes to precomputation - is there also a time limitation?
I would consider a trie, but one where you didn't necessarily start with the first character. Instead, find the index which will cut down the search space most, and consider that first. So in your sample case ("foo", "bar", "bazz") you'd take the third character, which would immediately tell you which string it was. (If we know we'll always be given one of the input words, we can return as soon as we've found a unique potential match.)
Now assuming that there isn't a single index which will get you down to a unique string, you need to determine the character to look at after that. In theory you precompute the trie to work out for each branch what the optimal character to look at next is (e.g. "if the third character was 'a', we need to look at the second character next; if it was 'o' we need to look at the first character next) but that potentially takes a lot more time and space. On the other hand, it could save a lot of time - because having gone down one character, each of the branches may have an index to pick which will uniquely identify the final string, but be a different index each time. The amount of space required by this approach would depend on how similar the strings were, and might be hard to predict in advance. It would be nice to be able to dynamically do this for all the trie nodes you can, but then when you find you're running out of construction space, determine a single order for "everything under this node". (So you don't end up storing a "next character index" on each node underneath that node, just the single sequence.) Let me know if this isn't clear, and I can try to elaborate...
How you represent the trie will depend on the range of input characters. If they're all in the range 'a'-'z' then a simple array would be incredibly fast to navigate, and reasonably efficient for trie nodes where there are possibilities for most of the available options. Later on, when there are only two or three possible branches, that becomes wasteful in memory. I would suggest a polymorphic Trie node class, such that you can build the most appropriate type of node depending on how many sub-branches there are.
None of this performs any culling - it's not clear how much can be achieved by culling quickly. One situation where I can see it helping is when the number of branches from one trie node drops to 1 (because of the removal of a branch which is exhausted), that branch can be eliminated completely. Over time this could make a big difference, and shouldn't be too hard to compute. Basically as you build the trie you can predict how many times each branch will be taken, and as you navigate the trie you can subtract one from that count per branch when you navigate it.
That's all I've come up with so far, and it's not exactly a full implementation - but I hope it helps...
Is a binary search of the table really so awful? I would take the list of potential strings and "minimize" them, the sort them, and finally do a binary search upon the block of them.
By minimize I mean reducing them to the minimum they need to be, kind of a custom stemming.
For example if you had the strings: "alfred", "bob", "bill", "joe", I'd knock them down to "a", "bi", "bo", "j".
Then put those in to a contiguous block of memory, for example:
char *table = "a\0bi\0bo\0j\0"; // last 0 is really redundant..but
char *keys[4];
keys[0] = table;
keys[1] = table + 2;
keys[2] = table + 5;
keys[3] = table + 8;
Ideally the compiler would do all this for you if you simply go:
keys[0] = "a";
keys[1] = "bi";
keys[2] = "bo";
keys[3] = "j";
But I can't say if that's true or not.
Now you can bsearch that table, and the keys are as short as possible. If you hit the end of the key, you match. If not, then follow the standard bsearch algorithm.
The goal is to get all of the data close together and keep the code itty bitty so that it all fits in to the CPU cache. You can process the key from the program directly, no pre-processing or adding anything up.
For a reasonably large number of keys that are reasonably distributed, I think this would be quite fast. It really depends on the number of strings involved. For smaller numbers, the overhead of computing hash values etc is more than search something like this. For larger values, it's worth it. Just what those number are all depends on the algorithms etc.
This, however, is likely the smallest solution in terms of memory, if that's important.
This also has the benefit of simplicity.
Addenda:
You don't have any specifications on the inputs beyond 'strings'. There's also no discussion about how many strings you expect to use, their length, their commonality or their frequency of use. These can perhaps all be derived from the "source", but not planned upon by the algorithm designer. You're asking for an algorithm that creates something like this:
inline int GetValue(char *key) {
return 1234;
}
For a small program that happens to use only one key all the time, all the way up to something that creates a perfect hash algorithm for millions of strings. That's a pretty tall order.
Any design going after "squeezing every single bit of performance possible" needs to know more about the inputs than "any and all strings". That problem space is simply too large if you want it the fastest possible for any condition.
An algorithm that handles strings with extremely long identical prefixes might be quite different than one that works on completely random strings. The algorithm could say "if the key starts with "a", skip the next 100 chars, since they're all a's".
But if these strings are sourced by human beings, and they're using long strings of the same letters, and not going insane trying to maintain that data, then when they complain that the algorithm is performing badly, you reply that "you're doing silly things, don't do that". But we don't know the source of these strings either.
So, you need to pick a problem space to target the algorithm. We have all sorts of algorithms that ostensibly do the same thing because they address different constraints and work better in different situations.
Hashing is expensive, laying out hashmaps is expensive. If there's not enough data involved, there are better techniques than hashing. If you have large memory budget, you could make an enormous state machine, based upon N states per node (N being your character set size -- which you don't specify -- BAUDOT? 7-bit ASCII? UTF-32?). That will run very quickly, unless the amount of memory consumed by the states smashes the CPU cache or squeezes out other things.
You could possibly generate code for all of this, but you may run in to code size limits (you don't say what language either -- Java has a 64K method byte code limit for example).
But you don't specify any of these constraints. So, it's kind of hard to get the most performant solution for your needs.
What you want is a look-up table of look-up tables.
If memory cost is not an issue you can go all out.
const int POSSIBLE_CHARCODES = 256; //256 for ascii //65536 for unicode 16bit
struct LutMap {
int value;
LutMap[POSSIBLE_CHARCODES] next;
}
int GetValue(string key) {
LutMap root = Global.AlreadyCreatedLutMap;
for(int x=0; x<key.length; x++) {
int c = key.charCodeAt(x);
if(root.next[c] == null) {
return root.value;
}
root = root.next[c];
}
}
I reckon that it's all about finding the right hash function. As long as you know what the key-value relationship is in advance, you can do an analysis to try and find a hash function to meet your requrements. Taking the example you've provided, treat the input strings as binary integers:
foo = 0x666F6F (hex value)
bar = 0x626172
bazz = 0x62617A7A
The last column present in all of them is different in each. Analyse further:
foo = 0xF = 1111
bar = 0x2 = 0010
bazz = 0xA = 1010
Bit-shift to the right twice, discarding overflow, you get a distinct value for each of them:
foo = 0011
bar = 0000
bazz = 0010
Bit-shift to the right twice again, adding the overflow to a new buffer:
foo = 0010
bar = 0000
bazz = 0001
You can use those to query a static 3-entry lookup table. I reckon this highly personal hash function would take 9 very basic operations to get the nibble (2), bit-shift (2), bit-shift and add (4) and query (1), and a lot of these operations can be compressed further through clever assembly usage. This might well be faster than taking run-time infomation into account.
Have you looked at TCB . Perhaps the algorithm used there can be used to retrieve your values. It sounds a lot like the problem you are trying to solve. And from experience I can say tcb is one of the fastest key store lookups I have used. It is a constant lookup time, regardless of the number of keys stored.
Consider using Knuth–Morris–Pratt algorithm.
Pre-process given map to a large string like below
String string = "{foo:1}{bar:42}{bazz:314159}";
int length = string.length();
According KMP preprocessing time for the string will take O(length).
For searching with any word/key will take O(w) complexity, where w is length of the word/key.
You will be needed to make 2 modification to KMP algorithm:
key should be appear ordered in the joined string
instead of returning true/false it should parse the number and return it
Wish it can give a good hints.
Here's a feasible approach to determine the smallest subset of chars to target for your hash routine:
let:
k be the amount of distinct chars across all your keywords
c be the max keyword length
n be the number of keywords
in your example (padded shorter keywords w/spaces):
"foo "
"bar "
"bazz"
k = 7 (f,o,b,a,r,z, ), c = 4, n = 3
We can use this to compute a lower bound for our search. We need at least log_k(n) chars to uniquely identify a keyword, if log_k(n) >= c then you'll need to use the whole keyword and there's no reason to proceed.
Next, eliminate one column at a time and check if there are still n distinct values remaining. Use the distinct chars in each column as a heuristic to optimize our search:
2 2 3 2
f o o .
b a r .
b a z z
Eliminate columns with the lowest distinct chars first. If you have <= log_k(n) columns remaining you can stop. Optionally you could randomize a bit and eliminate the 2nd lowest distinct col or try to recover if the eliminated col results in less than n distinct words. This algorithm is roughly O(n!) depending on how much you try to recover. It's not guaranteed to find an optimal solution but it's a good tradeoff.
Once you have your subset of chars, proceed with the usual routines for generating a perfect hash. The result should be an optimal perfect hash.