- iterate over all nodes and classify them
- group per level
- book in per level statistics into the Indicator records
- close global averages
...just coded, not yet tested...
The graph will be used to generate a computational load
for testing the Scheduler; thus we need to compute some
statistical indicators to characterise this load.
As starting point sum counts and averages will be aggregated,
accounting for particular characterisation of nodes per level.
It seams indicated to verify the generated connectivity
and the hash calculation and recalculation explicitly
at least for one example topology; choosing a topology
comprised of several sub-graphs, to also verify the
propagation of seed values to further start-nodes.
In order to avoid addressing nodes directly by index number,
those sub-graphs can be processed by ''grouping of nodes'';
all parts are congruent because topology is determined by
the node hashes and thus a regular pattern can be exploited.
To allow for easy processing of groups, I have developed a
simplistic grouping device within the IterExplorer framework.
- with the new pruning option, start-Nodes can now be anywhere
- introduce predicates to detect start-Nodes and exit-Nodes
- ensure each new seed node gets the global seed on graph construction
- provide functionality to re-propagate a seed and clear hashes
- provide functionality to recalculate the hashes over the graph
up to now, random values were completely determined by the
Node's hash, leading to completely symmetrical topology.
This is fine, but sometimes additional randomness is desirable,
while still keeping everything deterministic; the obvious solution
is to make the results optionally dependent on the invocation order,
which is simply to achieve with an additional state field. After some
tinkering, I decided to use the most simplistic solution, which is
just a multiplication with the state.
this is only a minor rearrangement in the Algorithm,
but allows to re-boot computation should node connectivity
go to zero. With current capabilities, this could not happen,
but I'm considering to add a »pruning« parameter to create the
possibility to generate multiple shorter chains instead of one
complete chain -- which more closely emulates reality for
Scheduler load patterns.
...so this was yet another digression, caused by the desire
somehow to salvage this problematic component design. Using a
DSL token fluently, while internally maintaining a complex and
totally open function based configuration is a bit of a stretch.
For context: I've engaged into writing a `LazyInit` helper component,
to resolve the inner contradiction between DSL use of `RandomDraw`
(implying value semantics) and the design of a processing pipeline,
which quite naturally leads to binding by reference into the enclosing
implementation.
In most cases, this change (to lazy on-demand initialisation) should be
transparent for the complete implementation code in `RandomDraw` -- with
one notable exception: when configuring an elaborate pipeline, especially
with dynamic changes of the probability profile during the simulation run,
then then obviously there is the desire to use the existing processing
pipeline from the reconfiguration function (in fact it would be quite
hard to explain why and where this should be avoided). `LazyInit` breaks
this usage scenario, since -- at the time the reconfiguration runs --
now the object is not initialised at all, but holds a »Trojan« functor,
which will trigger initialisation eventually.
After some headaches and grievances (why am I engaging into such an
elaborate solution for such an accidental and marginal topic...),
unfortunately it occurred to me that even this problem can be fixed,
with yet some further "minimal" adjustments to the scheme: the LazyInit
mechanism ''just needs to ensure'' that the init-functor ''sees the
same environment as in eager init'' -- that is, it must clear out the
»Trojan« first, and it ''could apply any previous pending init function''
fist. That is, with just a minimal change, we possibly build a chain
of init functors now, and apply them in given order, so each one
sees the state the previous one created -- as if this was just
direct eager object manipulation...
...this is a more realistic demo example, which mimics
some of the patterns present in RandomDraw. The test also
uses lambdas linking to the actual storage location, so that
the invocation would crash on a copy; LazyInit was invented
to safeguard against this, while still allowing leeway
during the initialisation phase in a DSL.
...oh my.
This is getting messy. I am way into danger territory now....
I've made a nifty cool design with automatically adapted functors;
yet at the end of the day, this does not bode well with a DSL usage,
where objects appear to be simple values from a users point of view.
- Helper function to find out of two objects are located
"close to each other" -- which can be used as heuristics
to distinguish heap vs. stack storage
- further investigation shows that libstdc++ applies the
small-object optimisation for functor up to »two slots«
in size -- but only if the copy-ctor is trivial. Thus
a lambda capturing a shared_ptr by value will *always*
be maintained in heap storage (and LazyInit must be
redesigned accordingly)...
- the verify_inlineStorage() unit test will now trigger
if some implementation does not apply small-object optimisation
under these minimal assumptions
...which is crucial for the solution pursued at the moment;
std::function is known to apply a small-object optimisation,
yet unfortunately there are no guarantees by the C++ standard
(it is only mandated that std::function handles a bare function
pointer without overhead)
Other people have investigated that behaviour already,
indicating that at least one additional »slot« of data
can be handled with embedded storage in all known implementations
(while libstdc++ seemingly imposes the strongest limitations)
https://stackoverflow.com/a/77202545/444796
This experiment in the unit-test shows that for my setup
(libstdc++ and GCC-8) only a lambda capturing a single pointer
is handled entirely embedded into the std::function; already
a lambda capturing a shared-ptr leads to overflow into heap
the RandomDraw rules developed last days are meant to be used
with user-provided λ-adapters; employing these in a context
of a DSL runs danger of producing dangling references.
Attempting to resolve this fundamental problem through
late-initialisation, and then locking the component into
a fixed memory location prior to actual usage. Driven by
the goal of a self-contained component, some advanced
trickery is required -- which again indicates better
to write a library component with adequate test coverage.
RandomDraw as a library component was extracted and (grossly) augmented
to cut down the complexity exposed to the user of TestChainLoad.
To control the generated topology, random-selected parameters
must be configured, defining a probability profile; while
this can be achieved with simple math, getting it correct
turned out surprisingly difficult.
...now using the reworked partial-application helper...
...bind to *this and then recursively re-invoke the adaptation process
...need also to copy-capture the previously existing mapping-function
first test seems to work now
Investigation in test setup reveals that the intended solution
for dynamic configuration of the RandomDraw can not possibly work.
The reason is: the processing function binds back into the object instance.
This implies that RandomDraw must be *non-copyable*.
So we have to go full circle.
We need a way to pass the current instance to the configuration function.
And the most obvious and clear way would be to pass it as function argument.
Which however requires to *partially apply* this function.
So -- again -- we have to resort to one of the functor utilities
written several years ago; and while doing so, we must modernise
these tools further, to support perfect forwarding and binding
of reference arguments.
- strive at complete branch coverage for the mapping function
- decide that the neutral value can deliberately lie outside
the value range, in which case the probability setting
controls the number of _value_ result incidents vs
neutral value result incidents.
- introduce a third path to define this case clearly
- implement the range setting Builder-API functions
- absorb boundrary and illegal cases
For sake of simplicity, since this whole exercise is a byproduct,
the mapping calculations are done in doubles. To get even distribution
of values and a good randomisation, it is thus necessary to break
down the size_t hash value in a first step (size_t can be 64bit
and random numbers would be subject to rounding errors otherwise)
The choice of this quantiser is tricky; it must be a power of two
to guarantee even distribution, and if chosen to close to the grid
of the result values, with lower probabilities we'd fail to cover
some of the possible result values. If chosen to large, then
of course we'd run danger of producing correlated numbers on
consecutive picks.
Attempting to use 4 bits of headroom above the log-2 of the
required value range. For example, 10-step values would use
a quantiser of 128, which looks like a good compromise.
The following tests will show how good this choice holds up.
This highly optimised function was introduced about one year ago
for handling of denomals with rational values (fractions), as
an interim solution until we'll switch to C++20.
Since this function uses an unrolled loop and basically
just does a logarithmic search for the highest set bit,
it can just be declared constexpr. Moreover, it is now
relocated into one of the basic utility headers
Remark: the primary "competitor" is the ilogb(double),
which can exploit hardware acceleration. For 64bit integers,
the ilog2() is only marginally faster according to my own
repeated invocation benchmarks.
The first step was to allow setting a minimum value,
which in theory could also be negative (at no point is the
code actually limited to unsigned values; this is rather
the default in practice).
But reconsidering this extensions, then you'd also want
the "neutral value" to be handled properly. Within context,
this means that the *probability* controls when values other
than the neutral value are produced; especially with p = 1.0
the neutral value shall not be produced at all
...since the Policy class now defines the function signature,
we can no longer assume that "input" is size_t. Rather, all
invocations must rely on the generic adaptaion scheme.
Getting this correct turns out rather tricky again;
best to rely on a generic function-composition.
Indeed I programmed such a helper several years ago,
with the caveat that at that time we used C++03 and
could not perfect-forward arguments. Today this problem
can be solved much more succinct using generic Lambdas.
to define this as a generic library component,
any reference to the actual data source moust be extracted
from the body of the implementation and supplied later
at usage site. In the actual case at hand the source
for randomness would be the node hash, and that is
absolutely an internal implementation detail.
The idea is to use some source of randomness to pick a
limited parameter value with controllable probability.
While the core of the implementation is nothing more
than some simple numeric adjustments, these turn out
to be rather intricate and obscure; the desire to
package these technicalities into a component
however necessitates to make invocations
at usage site self explanatory.
This might seem totally overblown -- but already the development
of this prototype showed me time and again, that it is warranted.
Because it is damn hard to get the probabilities and the mappings
to fixed output values correct.
After in-depth analysis, I decided completely to abandon the
initially chosen approach with the Cap helper, where the user
just specifies an upper and lower bound. While this seems
compellingly simple at start, it directly lures into writing
hard-to-understand code tied to the implementation logic.
With the changed approach, most code should get along rather with
auto myRule = Draw().probabilty(0.6).maxVal(4);
...which is obviously a thousand times more legible than
any kind of tricky modulus expressions with shifted bounds.
While the Cap-Helper introduced yesterday was already a step in the
right direction, I had considerable difficulties picking the correct
parameters for the upper/lower bounds and the divisor for random generation
so as to match an intended probability profile. Since this tool shall be
used for load testing, an easier to handle notation will both help
with focusing on the main tasks and later to document the test cases.
Thus engaging (again) into the DSL building game...
...start with putting the topology generator to work
- turns out it is still challenging to write the ctrl-rules
- and one example tree looked odd in the visualisation
- which (on investigation) indicated unsound behaviour
...this is basically harmless, but involves an integer wrap-around
in a variable not used under this conditions (toReduce), but also
a rather accidental and no very logical round-up of the topology.
With this fix, the code branch here is no longer overloaded with two
distinct concerns, which I consider an improvement
by default, a linear chain without any forking is generated,
and the result hash is computed by hash-chaining from the seed.
Verify proper connections and validate computed hash
..as can be expected, had do chase down some quite hairy problems,
especially since consumption of the fixed amount of nodes is not
directly linked to the ''beat'' of the main loop and thus boundary
conditions and exhausted storage can happen basically anywhere.
Used a simple expansion rule and got a nod graph,
which looks coherent in DOT visualisation.
writing a control-value rule for topology generation typically
involves some modulus and then arthmetic operations to map
only part of the value range to the expected output range.
These calculations are generic, noisy and error-prone.
Thus introduce a helper type, which allows the client just
to mark up the target range of the provided value to map and
transform to the actually expected result range, including some
slight margin to absorb rounding errors. Moreover, all calculations
done in double, to avoid the perils of unsigned-wrap-around.
...these were developed driven by the immediate need
to visualise ''random generated computation patterns''
for ''Scheduler load testing.''
The abstraction level of this DSL is low
and structures closely match some clauses of the DOT language;
this approach may not yet be adequate to generate more complex
graph structures and was extracted as a starting point
for further refinements....
With all the preceding DSL work, this turns out to be surprisingly easy;
the only minor twist is the grouping of nodes into (time)levels,
which can be achieved with a "lagging" update from the loop body
Note: next step will be to extract the DSL helpers into a Library header
...using a pre-established example as starting point
It seems that building up this kind of generator code
from a set of free functions in a secluded namespace
is the way most suitable to the nature of the C++ language
..the idea is to generate a Graphviz-DOT diagram description
by traversing the internal data structures of TestChainLoad.
- refreshed my Graphviz knowledge
- work out a diagram scheme that can be easily generated
- explore ways to structure code generation as a DSL to keep it legible
...introduce statistical control functions (based on hash)
...add processing stage for current set of nodes
...process forking, reduction and injection of new nodes
- use a specialised class, layered on top of std::array
- use additional storage to mark filling degree
- check/fail on link owerflow directly there
We still use fixed size inline storage for the node links,
yet adding this comparatively small overhead in storage helps
getting the code simpler and adding links is now constant-complexity
A »Node« represents one junction point in the dependency graph,
knows his predecessors and successors and carries out one step
of the chained hash calculation.
