Does System C support tri-state logic? That is, bits that can get 0, 1 or X, where X means "unknown"?
If it does, does it also support vectors that can contain Xes, including logic and arithmetic operations?
Here is what you need:
http://www.asic-world.com/systemc/data_types2.html
http://en.wikipedia.org/wiki/SystemC#Data_types
It does not have tri-state variables, but quad-state (is that correct? :P) variables (0,1,X,Z). More about it in the above links. It also supports vectors of those variables.
Hope I helped you a little bit :)
Yeah, you're looking for the sc_logic and sc_lv types which are 4 state variables: 0, 1, X, and Z. Pay attention to how they interact when you resolve them together. There's a nice tables on the asic-world.com site taken directly from the SystemC User Manual.
Note though that this doesn't work like in Verilog where X can also act as a wildcard. I had to build my own function to add that functionality.
Related
I am searching some SWI-Prolog function which is able to make some set union with variables as parameters inside. My aim is to make the union first and define the parameters at further on in source code.
Means eg. I have some function union and the call union(A, B, A_UNION_B) makes sense. Means further more the call:
union(A, [1,2], C), A=[3].
would give me as result
C = [3, 1, 2].
(What you call union/3 is most probably just concatenation, so I will use append/3 for keeping this answer short.)
What you expect is impossible without delayed goals or constraints. To see this, consider the following failure-slice
?- append(A, [1,2], C), false, A=[3].
loops, unexpected. % observed, but for us unexpected
false. % expected, but not the case
This query must terminate, in order to make the entire question useful. But there are infinitely many lists of different length for A. So in order to describe all possible solutions, we would need infinitely many answer substitutions, like
?- append(A, [1,2], C).
A = [], C = [1,2]
; A = [_A], C = [_A,1,2]
; A = [_A,_B], C = [_A,_B,1,2]
; A = [_A,_B,_C], C = [_A,_B,_C,1,2]
; ... .
The only way around is to describe that set of solutions with finitely many answers. One possibility could be:
?- when((ground(A);ground(C)), append(A,B,C)).
when((ground(A);ground(C)),append(A,B,C)).
Essentially it reads: Yes, the query is true, provided the query is true.
While this solves your exact problem, it will now delay many otherwise succeeding goals, think of A = [X], B = [].
A more elaborate version could provide more complex tests. But it would require a somehow different definition than append/3 is. Some systems like sicstus-prolog provide block declarations to make this more smoothly (SWI has a coarse emulation for that).
So it is possible to make this even better, but the question remains whether or not this makes much sense. After all, debugging delayed goals becomes more and more difficult with larger programs.
In many situations it is preferable to prevent this and produce an instantiation error in its stead as iwhen/2 does:
?- iwhen((ground(A);ground(C)),append(A,B,C)).
error(instantiation_error,iwhen/2).
That error is not the nicest answer possible, but at least it is not incorrect. It says: You need to provide more instantiations.
If you really want to solve this problem for the general case you have to delve into E-unification. That is an area with most trivial problem statements and extremely evolved answers. Often, just decidability is non-trivial let alone an effective algorithm. For your particular question, either ACI (for sets) or ANlr (for concatenation) are of interest. Where ACI requires solving Diophantine Equations and associative unification alone is even more complex than that. I am unaware of any such implementation for a Prolog system that solves the general problem.
Prolog IV offered an associative infix operator for concatenation but simply delayed more complex cases. So debugging these remains non-trivial.
I am currently interested in billiards. However, I am interested in special billiards with a non-conventional reflection law and specific rules for the trajectories. I, therefore, need to calculate the trajectories using a differential equation solver. Finding one is not a problem at all. However, I still have trouble finding a suitable solution for the reflection. Previously I was working in Mathematica, whose Numerical ODE solver has a WhenEvent option:
Example:
NDSolve[{y''[t] == -9.81, y[0] == 5, y'[0] == 0, WhenEvent[y[t] == 0, y'[t] -> -0.95 y'[t]]}, y, {t, 0, 10}];
The solution that this line of code gives is a bouncing ball.
Basically after each integration step, it checks whether the condition is true and if so, it performs an action. (I suspect it checks if y has switched sign. If, for example, one puts in
WhenEvent[y²[t]==0],
the quantity does not switch sign and this method fails.)
Now, I would like to switch from Mathematica to something that is more openly available (C++ or python based.) but I could not find anything that can has this or a similar options. Does anyone perhaps have an Idea, what I could use instead? Basically I am looking for the option to check for a condition after each integration step and if the condition is met perform an action on the solution.
Does anyone have an idea what I could use?
Any help appreciated
I'm solving an LP in Julia/JuMP using Gurobi as my solver. I want to know which variables in my solution are basic. How do I obtain this information?
Just checking which variables are non-zero is not sufficient, since we might be dealing with a degenerate solution (i.e., basic variables equal to zero).
I found two similar questions online, but the solutions suggested do not seem to apply to the current version of JuMP anymore (or am I missing something?):
https://discourse.julialang.org/t/how-to-obtain-a-basic-solution/1784
https://groups.google.com/g/julia-opt/c/vJ6QuFBfPbw?pli=1
There's a Gurobi attribute called VBasis (https://www.gurobi.com/documentation/9.0/refman/vbasis.html) that seems to be what I'm looking for, but I don't know how to access it.
This is poorly documented, but you can see which constraints are basic:
model = Model(Gurobi.Optimizer)
#variable(model, x >= 0)
#constraint(model, c, 2x >= 1)
#objective(model, Min, x)
optimize!(model)
julia> MOI.get(model, MOI.ConstraintBasisStatus(), c)
NONBASIC::BasisStatusCode = 1
julia> MOI.get(model, MOI.ConstraintBasisStatus(), LowerBoundRef(x))
BASIC::BasisStatusCode = 0
Note that since variables can have lower and upper bounds, we report which constraints are basic, rather than which variables are.
Documentation:
https://jump.dev/MathOptInterface.jl/stable/apireference/#MathOptInterface.ConstraintBasisStatus
https://jump.dev/MathOptInterface.jl/stable/apireference/#MathOptInterface.BasisStatusCode
In[11]:= $Version
Out[11]= 9.0 for Linux x86 (32-bit) (November 20, 2012)
In[12]:= DSolve[{f[0] == d, f'[0] == v0, f''[t] == g*m2/f[t]^2}, f, t]
DSolve::bvimp: General solution contains implicit solutions. In the boundary
value problem these solutions will be ignored, so some of the solutions will
be lost.
Out[12]= {}
The code above pretty much says it all. I get the same error if I replace g*m2 with 1.
This seems like a really simple DFQ to solve. I'd like to tell DSolve to assume all variables are real and that d, g, and m2 are all greater than 0, but there's unfortunately no way to do that.
Thoughts?
You are trying for a symbolic solution. And unfortunately, symbolic integration is hard (while symbolic differentiation is easy).
The way this integration works is to obtain the energy functional by integrating once
E = 1/2*f'[t]^2 + C/f[t]
and then to isolate f'[t]. The resulting integral is not easy to solve and leads to the mentioned implicit solutions.
Did you really want to get the symbolic solution or only some function table to plot the solutions or compute other related quantities?
Since it was clarified that the requested quantity is the maximum of certain solutions: This can be computed by setting v=0 in the energy equation
C/x = E = 1/2*v0^2 + C/x0
or
x = C*x0/(C + 1/2*v0^2*x0 )
One would have to analyze the time aspect to make sure that this extremum is reached before passing again at the initial point x0.
Since many of the Project Euler problems require you to do a divisibility check for quite a number of times, I've been trying to figure out the fastest way to perform this task in ZX81 BASIC.
So far I've compared (N/D) to INT(N/D) to check, whether N is dividable by D or not.
I have been thinking about doing the test in Z80 machine code, I haven't yet figured out how to use the variables in the BASIC in the machine code.
How can it be achieved?
You can do this very fast in machine code by subtracting repeatedly. Basically you have a procedure like:
set accumulator to N
subtract D
if carry flag is set then it is not divisible
if zero flag is set then it is divisible
otherwise repeat subtraction until one of the above occurs
The 8 bit version would be something like:
DIVISIBLE_TEST:
LD B,10
LD A,100
DIVISIBLE_TEST_LOOP:
SUB B
JR C, $END_DIVISIBLE_TEST
JR Z, $END_DIVISIBLE_TEST
JR $DIVISIBLE_TEST_LOOP
END_DIVISIBLE_TEST:
LD B,A
LD C,0
RET
Now, you can call from basic using USR. What USR returns is whatever's in the BC register pair, so you would probably want to do something like:
REM poke the memory addresses with the operands to load the registers
POKE X+1, D
POKE X+3, N
LET r = USR X
IF r = 0 THEN GOTO isdivisible
IF r <> 0 THEN GOTO isnotdivisible
This is an introduction I wrote to Z80 which should help you figure this out. This will explain the flags if you're not familiar with them.
There's a load more links to good Z80 stuff from the main site although it is Spectrum rather than ZX81 focused.
A 16 bit version would be quite similar but using register pair operations. If you need to go beyond 16 bits it would get a bit more convoluted.
How you load this is up to you - but the traditional method is using DATA statements and POKEs. You may prefer to have an assembler figure out the machine code for you though!
Your existing solution may be good enough. Only replace it with something faster if you find it to be a bottleneck in profiling.
(Said with a straight face, of course.)
And anyway, on the ZX81 you can just switch to FAST mode.
Don't know if RANDOMIZE USR is available in ZX81 but I think it can be used to call routines in assembly. To pass arguments you might need to use POKE to set some fixed memory locations before executing RANDOMIZE USR.
I remember to find a list of routines implemented in the ROM to support the ZX Basic. I'm sure there are a few to perform floating operation.
An alternative to floating point is to use fixed point math. It's a lot faster in these kind of situations where there is no math coprocessor.
You also might find more information in Sinclair User issues. They published some articles related to programming in the ZX Spectrum
You should place the values in some pre-known memory locations, first. Then use the same locations from within Z80 assembler. There is no parameter passing between the two.
This is based on what I (still) remember of ZX Spectrum 48. Good luck, but you might consider upgrading your hw. ;/
The problem with Z80 machine code is that it has no floating point ops (and no integer divide or multiply, for that matter). Implementing your own FP library in Z80 assembler is not trivial. Of course, you can use the built-in BASIC routines, but then you may as well just stick with BASIC.