This was broken by the previous fix, because I had cast to a numeric value
before invoking `set_defaults`, which needs the empty string retained so
that it knows whether a default ought to be applied.
This also ensures that `set_values` will always return a numeric value when
that default is applied.
DEV-10484
This has been a problem for...ever, but the old classification system (and
calculations) had `||0` for ever variable reference, whereas the new one
does not; NaNs result in undefined behavior in the new classification
system, since those values are not expected to exist.
This ought to have automated tests, but it will be rewritten in TAMER.
DEV-10484
This was originally my plan with the new classification system, but it was
undone because I had hoped to punt on the somewhat controversial
issue. Unfortunately, I see no other way. Here I attempt to summarize the
reasons why, many of which are specific to the design decisions of TAME.
Keep in mind that TAME is a domain-specific language (DSL) for writing
insurance rating systems. It should act intuitively for our use case, while
still being mathematically sound.
If you still aren't convinced, please see the link at the bottom.
Target Language Semantics (ECMAScript)
--------------------------------------
First: let's establish what happens today. TAME compiles into ECMAScript,
which uses IEEE 754-2008 floating-point arithmetic. Here we have:
x/0 = Infinity, x > 0;
x/0 = -Infinity, x < 0;
0/0 = NaN, x = 0.
This is immediately problematic: TAME's calculations must produce concrete
real numbers, always. NaN is not valid in its domain, and Infinity is of no
practical use in our computational model (TAME is build for insurance rating
systems, and one will never have infinite premium). Put plainly: the
behavior is undefined in TAME when any of these values are yielded by an
expression.
Furthermore, we have _three different possible situations_ depending on
whether the numerator is positive, negative, or zero. This makes it more
difficult to reason about the behavior of the system, for values we do not
want in the first place.
We then have these issues in ECMAScript:
Infinity * 0 = NaN.
-Infinity * 0 = NaN.
NaN * 0 = NaN.
These are of particular concern because of how predicates work in TAME,
which will be discussed further below. But it is also problematic because
of how it propagates: once you have NaN, you'll always have NaN, unless you
break out of the situation with some control structure that avoids using it
in an expression at all.
Let's now consider predicates:
NaN > 0 = false.
NaN < 0 = false.
NaN === 0 = false.
NaN === NaN = false.
These will be discussed in terms of classification predicates (matches).
We also have issues of serialization:
JSON.stringify(Infinity) = "null".
JSON.stringify(NaN) = "null".
These means that these values are difficult to transfer between systems,
even if we wanted them.
TAME's Predicates
-----------------
TAME has a classification system based on first-order logic, where ⊥ is
represented by 0 and ⊤ is represented by 1. These classifications are used
as predicates to calculations via the @class attribute of a rate block. For
example:
<rate-each class="property" generates="propValue" index="k">
<c:quotient>
<c:value-of name="buildingTiv" index="k" />
<c:value-of name="tivPropDivisor" index="k" />
</c:quotient>
</rate>
As can be observed via the Summary Page, this calculation compiles into the
following mathematical expression:
∑ₖ(pₖ(tₖ/dₖ)),
that is—the quotient is then multiplied by the value of the `property`
classification, which is a 0 or 1 respectively for that index.
Let's say that tivPropDivisor were defined in this way:
<rate-each class="property" generates="tivPropDivisor" index="k">
<!--- ... logic here ... -->
</rate>
It does not matter what the logic here is. Observe that the predicate here
is `property` as well, which means that, if this risk is not a property
risk, then `tivPropDivisor` will be `0`.
Looking back at `propValue`, let's say that we do have a property risk, and
that `buildingTiv` is `[100_000, 200_000]` and `tivPropDivisor` is 1000. We
then have:
1(100,000 / 1000) + 1(200,000 / 1000)) = 300.
Consider instead what happens if `property` is 0. Since we have no property
locations, we have `[0, 0]` as `buildingTiv` and `tivPropDivisor` is 0.
0(0/0) + 0(0/0)) = 0(NaN + NaN) = NaN.
This is clearly not what was intended. The predicate is expected to be
_strongly_ zero, as if using an Iverson bracket:
((0/0)[0] + (0/0)[0]) = 0.
Of course, one option is to redefine TAME such that we use Iverson's
convention in place of summation, however this is neither necessary nor
desirable given that
(a) NaN is not valid within the domain of any TAME expression, and
(b) Summation is elegantly generalized and efficiently computed using
vector arithmetic and SIMD functions.
That is: there's no use in messing with TAME's computational model for a
valid that should be impossible to represent.
Short-Circuiting Computation
----------------------------
There's another way to look at it, though: that we intended to skip the
computation entirely, and so it doesn't matter what the quotient is. If the
compiler were smart enough (and maybe one day it will be), it would know
that the predicate of `tivPropDivisor` and `propValue` are the same and so
there is no circumstance under which we would compute `propValue` and have
`tivPropDivisor` be 0.
The problem is: that short-circuiting is employed as an _optimization_, and
is an implementation detail. Mathematically, the expression is unchanged,
and is still invalid within TAME's domain. It is unrepresentable, and so
this is not an out.
But let's pretend that it was defined that way, which would yield this:
{ ∑ₖ(pₖ(tₖ/dₖ)), ∀x∈p(x = 1);
propValue = <
{ 0, otherwise.
This is the optimization that is employed, but it's still not mathematically
correct! What happens if p₀ = 1, but p₁ = 0? Then we have:
1(100,000/1000) + 0(0/0) = 100 + NaN = NaN,
but the _intent_ was clearly to have 100 + 0 = 100, and so we return to the
original problem once again.
Classification Predicates and Intent
------------------------------------
Classifications are used as predicates for equations, but classifications
_themselves_ have predicates in the form of _matches_. Consider, for
example, a classification that may be used in an assertion to prevent
negative premium from being generated:
<t:assert failure="premBuilding must not be negative for any index">
<t:match-gte value="premBuilding" value="#0" />
</t:assert>
Simple enough—the system will fail if the premium for a given building is
below $0.
But what happens if premBuilding is calculated as so?
<rate-each class="property" yields="premBuildingTotal"
generates="premBuilding" index="k">
<c:product>
<c:value-of name="propValue" index="k" />
<c:value-of name="propRate" index="k" />
</c:product>
</rate-each>
Alas, if `property` is false for any index, then we know that `propValue` is
NaN, and NaN * x = NaN, and so `premBuilding` is NaN.
The above assertion will compile the match into the first-order sentence
∀x∈b(x > 0).
Unfortunately, NaN is not greater than, less than, equal to, or any other
sort of thing to 0, and so _this assertion will trigger_. This causes
practical problems with the `_premium_` template, which has an
`@allow-zero@` argument to permit zero premium.
Consider this real-world case that I found (variables renamed), to avoid a
strawman:
<t:premium class="loc" round="cent"
yields="locInitialTotal"
generates="locInitial" index="k"
allow-zero="true"
desc="...">
<c:value-of name="premAdditional" />
<c:quotient>
<c:value-of name="premLoc" index="k" />
<c:value-of name="premTotal" />
</c:quotient>
</t:premium>
This appears to be responsible for splitting up `premAdditional` relative to
the total premium contribution of each location. It explicitly states that
it wants to permit a zero value. The intent of this block is clear: a value
of 0 is explicitly permitted and _expected_.
But if `premTotal` is for whatever reason 0—whether it be due to a test
case or some unexpected input—then it'll yield a NaN and make the entire
expression NaN. Or if `premAdditional` or `premLoc` are tainted by a NaN,
the same result will occur. The assertion will trigger. And, indeed, this
is what I'm seeing with test cases against the new classification system.
What about Infinity? Is it intuitive that, should `propValue` in the
previous example be positive and `propRate` be 0, that we would, rather than
producing a very small value, produce an infinitely large one? Does that
match intuition? Remember, this system is a domain-specific language for
_our_ purposes—it is not intended to be used to model infinities.
For example, say we had this submission because the premium exceeds our
authority to write with some carrier:
<t:submit reason="Premium exceeds authority">
<t:match-gt name="premBuilding" value="#100k" />
</t:submit>
If we had
(100,000 / 0) = ∞,
then this submit reason would trigger. Surely that was not intended, since
we have `property` as a predicate and `propRate` with the same predicate,
implying that the answer we _actually_ want is 0! In that case, what we
_probably_ want to trigger is something like
<rate yields="premFinal">
<t:maxreduce>
<c:value-of name="premBuildingTotal" />
<c:value-of name="#500" />
</t:maxreduce>
</rate>,
in order to apply a minimum premium of $500. But if `premBuildingTotal` is
Infinity, then you won't get that—you'll get Infinity, which is of course
nonsense.
And nevermind -Infinity.
Why Wasn't This a Problem Before?
---------------------------------
So why bring this up now? Why have we survived a decade without this?
We haven't, really—these bugs have been hidden. But the old classification
system covered them up; predicates would implicitly treat missing values as
0 by enclosing them in `(x||0)` in the compiled code. Observe this
ECMAScript code:
NaN || 0 = 0.
Consequently, the old classification system absorbed bad values and treated
them implicitly as 0. But that was a bug, and had to be removed; it meant
that missing indexes in classifications would trigger predicates that were
not intended to be triggered, if they matched against 0, or matched against
a value less than some number larger than zero. (See
`core/test/core/class` for examples.)
The new classification system does not perform such defaulting. _But it
also does not expect to receive values outside of its valid domain._
Consequently, _NaN and Infinity lead to undefined behavior_, and the
current implementation causes the predicate to match (NaN < 0) and therefore
fail.
The reason for this is because that this implementation is intended to
convey precisely the computation necessary for the classification system, as
formally defined, so that it can be later optimized even further. Checking
for values outside the domain not only should not be necessary, but it would
prevent such future optimizations.
Furthermore, parameters used to compile into (param||0), to account for
missing values or empty strings. This changed somewhat recently with
5a816a4701, which pre-cast all inputs and
allowed relaxing many of those casts since they were both wasteful and no
longer necessary.
Given that, for all practical purposes, 0/0=0 in the system <1yr ago.
Infinity, of course, is a different story, since (Infinity||0)=Infinity;
this one has always been a problem.
Let's Just Fail
---------------
Okay, so we cannot have a valid expression, so let's just fail.
We could mean that in two different ways:
1. Fail at runtime if we divide by 0; or
2. Fail at compile-time if we _could_ divide by 0.
Both of these have their own challenges.
Let's dismiss #2 right off the bat for now, because until we have TAMER,
that's not really feasible. We need something today. We will discuss that
in the future.
For #1—we cannot just throw an error and halt computation, because if the
`canterm` flag passed into the system is `false`, then _computation must
proceed and return all results_. Terminating classifications are checked
after returning rather than throwing errors.
Since we have to proceed with computation, then the computations have to be
valid, and so we're left with the same problem again—we cannot have
undefined behavior.
One could argue that, okay, we have undefined behavior, but we're going to
fail because of the assertion anyway! That's potentially defensible, but it
is at the moment undesirable, because we get so many failures. And,
relative to the section below, it's not clear to me what benefit we get from
that behavior other than making things more difficult for ourselves.
Furthermore, such an assertion would have to be defined for every
calculation that performs a quotient, and would have to set some
intermediate flag in the calculation which would then have to be checked for
after-the-fact. This muddies the generated calculation, which causes
problems for optimizations, because it requires peering into state of the
calculation that may be hidden or optimized away.
If we decide that calculations must be valid because we cannot fail, and we
have to stick with the domain of calculations, then `x/0` must be
_something_ within that domain.
x/0=0 Makes Sense With the Current System
-----------------------------------------
Let's take a step back. Consider a developer who is unaware that
NaN/Infinity are permitted in the system—they just know that division by
zero is a bad thing to do because that's what they learned, and they want to
avoid it in their code.
Consider that they started with this:
<rate-each class="property" generates="propValue" index="k">
<c:quotient>
<c:value-of name="buildingTiv" index="k" />
<c:value-of name="tivPropDivisor" index="k" />
</c:quotient>
</rate>
They have inspected the output of `tivPropDivisor` and see that it is
sometimes 0. They understand that `property` is a predicate for the
calculation, and so reasonably think that they could do something like this:
<classify as="nonzero-tiv-prop-divisor" ...>
<t:match-ne on="tivPropDivisor" value="#0" />
</classify>
and then change the rate-each to
<rate-each class="property nonzero-tiv-prop-divisor" ...>.
Except that, of course, we know that will have no effect, because a NaN is a
NaN. This is not intuitive.
So they'd have to do this:
<rate-each class="property" generates="propValue" index="k">
<c:cases>
<c:case>
<t:when-ne name="tivPropDivisor" value="#0" />
<c:quotient>
<c:value-of name="buildingTiv" index="k" />
<c:value-of name="tivPropDivisor" index="k" />
</c:quotient>
</c:case>
<c:otherwise>
<c:value-of name="#0" />
</c:otherwise>
</c:cases>
</rate>.
But for what purpose? What have we gained over simply having x/0=0, which
does this for you?
The reason why this is so unintuitive is because 0 is the default case in
every other part of the system. If something doesn't match a predicate, the
value becomes 0. If a value at an index is not defined, it is implicitly
zero. A non-matching predicate is 0.
This is exploited for reducing values using summation. So the behavior of
the system with regards to 0 is always on the mind of the developer. If we
add it in another spot, they would think nothing of it.
It would be nice if it acted as an identity in a monoidic operation,
e.g. as 0 for sums but as 1 for products, but that's not how the system
works at all today. And indeed such a thing could be introduced using a
special template in place of `c:value-of` that copies the predicates of the
referenced value and does the right thing.
The _danger_, of course, is that this is _not_ how the system as worked, and
so changing the behavior has the risk of breaking something that has relied
on undefined behavior for so long. This is indeed a risk, but I have taken
some confident in (a) all the test cases for our system pass despite a
significant number of x/0=0 being triggered due to limited inputs, and (b)
these situations are _not correct today_, resulting in `null` in serialized
result data because `JSON.stringify([NaN, Infinity]) === "[null, null]"`.
Given all of that, predictable incorrect behavior is better than undefined
behavior.
So x/0=0 Isn't Bad?
-------------------
No, and it's mathematically sound. This decision isn't unprecedented—
Coq, Lean, Agda, and other theorem provers define x/0=0. APL originally
defined x/0=1, but later switched to 0. Other languages do their own thing
depending on what is right for their particular situation.
Division is normally derived from
a × a⁻¹ = 1, a ≠ 0.
We're simply not using that definition—when we say "quotient", or use the
`/` symbol, we mean a _different_ function (`div`, in the compiled JS),
where we have an _additional_ axiom that
a / 0 = 0.
And, similarly,
0⁻¹ = 0.
So we've taken a _normally undefined_ case and given it a definition. No
inconsistency arises.
In fact, this makes _sense_ to do, because _this is what we want_. The
alternative, as mentioned above, is a lot of boilerplate—checking for 0 any
time we want to do division. Complicating the compiler to check for those
cases. And so on. It's easier to simple state that, in TAME, quotients
have this extra convenient feature whereby you don't have to worry about
your denominator being zero because it'll act as though you enclosed it in a
case statement, and because of that, all your code continues to operate in
an intuitive way.
I really recommend reading this blog post regarding the Lean theorem prover:
https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/
preproc:symtable-process-symbols is run on each pass (e.g. during initial
processing and after each template expansion) to introduce new symbols into
the symbol table from imports and newly discovered symbols.
This processing was previously optimized a bit using maps to reduce the cost
of symbol table lookups, but the processing was still inefficient, relying
on XSLT1-style processing (as originally written) for deduplication. This
now uses `for-each-group` and `perform-sort` to offload the expensive
computation onto Saxon, which is much more efficient.
Symbol table processing has long been a culprit, but I hadn't attempted to
optimize further in recent months because of TAMER work. Since TAMER has
been on pause for a few months with other things needing my attention, I
needed to provide a short-term performance improvement to keep up with
increasing build times.
DEV-11716
This was incorrect to begin with---it does not make sense that an input
mapping should depend upon the identifier that it maps to, in the sense that
we make use of these dependencies. If we add weak symbol references in the
future, then this can be reintroduced.
By removing this, we free tameld from having to perform the check itself.
.rev-xmlo bumped to force rebuilding of object files since the linker now
expects that no such dependencies will exist within them.
This can occur in generated code (e.g. from proguic if a question-based
predicate inherits a predicate already specified). This commit does not
change anything that's emitted; it merely allows proceeding.
TAMER can be smarter about this; I don't want to invest more time into
generalizing deduplication of predicates.
There was a bug whereby TRUE matches would keep whatever value was being
matched on, even if it was not a boolean. That was an oversight from the
proof-of-concept code, and this fixes it; that's why this is behind a flag!
This also adjusts the class aliasing optimization so that it doesn't check
for a `TRUE` symbol name, which was a bad idea to begin with.
This change also ends up expanding `lv:match[@value="TRUE"]` into the long
form, where it didn't previously; this will result in slightly larger xmlo
files in some cases, but it's nothing significant, and it does not impact
compilation times.
This is a nearly-10-year-old bug that was introduced when the Summary Page
was modified to use the then-new symbol table. The compiler previously
concatenated all packages into a single XML tree and processed that, so no
package resolution was necessary here before.
A long time ago (about a decade), package names were required, but they are
now generated by the compiler relative to the root path. The name here was
incorrect, which was generating an incorrect path for the linked symbols,
which was causing problems with the Summary Page.
This largely reintroduces the legacy classification system, but there are a
number of things that are not affected by the flag. For example:
1. Alias classifications are still optimized when the flag is off;
2. Classifications without predicates emit slightly different code than
before, though their functionality has not changed;
3. There's been a lot of refactoring and minor optimizations that are
unaffected by the flag;
4. lv:match/@pattern will now emit a warning; and
5. Cleaning and casting of input data is not gated.
This allows us to incrementally migrate to the new system where behavior may
be different, but this is admittedly a bit dangerous in that the new system
was aggressively tested and reasoned about, so reintroducing the legacy
system may combine in unexpected ways.
This is another significant milestone.
The next logical step with classification optimization is to inline all of
those intermediate classifications generated from any and all blocks, since
there are so many of them. This means having the parent classification
absorb all dependencies; not output dependencies for the classification; not
compile the assignments for those classifications; and to inline them at the
match site. They’re used only once, since they’re generated for each
individual block.
We need to keep the actual classification generation around (and just inline
them) for now, probably until TAMER, because we depend upon their symbol for
determining their dimensionality, which we need for the optimization work we
just did---we must inline them into the proper group (matrix, vector, or
scalar).
The optimization work done up to this point had inlining in mind---only a
little bit of work was needed to make sure that every classification can
simply be stripped of its assignment and be a valid expression that can be
inlined in place of the original reference.
The result of that was predictably significant for the `ui/package` program
that I've been testing with:
- 4,514 classifications were inlined;
- The file size dropped to 7.5MiB (from 8.2MiB previously---remember that
we started at 16MiB); and
- GC ticks were cut in half, from 67->31.
Unfortunately, this optimization added nearly 1m of time to the compilation
of that program. Speaking from the future: the UI build optimizations in
liza-proguic were introduced to offset this difference (and provide a net
gain in performance).
This convets disjunctive classifications into conjunctive and places an
<any> within it.
This ends up handling all the generated qwhen classifications from proguic,
which were probably converted into <any> by a previous optimization pass.
The UI program I've been using to test these compiler optimizations has
decreased in size down from 8.2MiB since the beginning of this branch; we
started at ~16MiB.
See comments. This is meant to help mitigate the damage done by one of our
code generation systems. The benefit is significant, allowing the code
generator to remain simple. By placing this optimization within the
compiler, hand-written and template-generated code also benefit.
Rather than extracting every any/all into their own classifications,
eliminate them (and replace them with their body) if they contain only one
predicate. This is most likely to happen after template expansion, and
there were an alarming number of them in our system.
Stripping them out of one of our programs saved ~0.2MiB of output, and
removed many intermediate classifications. It removed ~1,075 lines, which
should correspond closely to the actual number of classifications.
Discovering this required stripping the template barriers, which was done in
a previous commit.
Unfortunately, the performance improvement from this wasn't significantly,
largely because of the nondeterminisim of GC, which can easily mask the
gains. But a new line `v8::internal::FixedArray::set(int,
v8::internal::Object)` appeared in the profiler output, making me wonder
whether the JIT is starting to understand more interesting properties of the
system.
`mprotect` and `v8::internal::heap_internals::GenerationalBarrier` also
appeared, which are related to GC.
!!!
(Message from the future: this ends up being reintroduced and the new
classification system being placed behind a feature toggle. But it will be
eliminated eventually.)
This is a major milestone for class optimization---the old anyValue-based
system is no longer in use; the classification system has been wholly
rewritten.
The ticks in the sampling profiler are now where they should be, open to
further optimization with a much more solid foundation.
[JavaScript]:
ticks total nonlib name
5 0.6% 3.0% LazyCompile: *vu [...]/ui/package.strip.js:25191:16
5 0.6% 3.0% LazyCompile: *M [...]/ui/package.strip.js:25267:15
3 0.4% 1.8% LazyCompile: *vmu [...]/ui/package.strip.js:25144:17
3 0.4% 1.8% LazyCompile: *ve [...]/ui/package.strip.js:25204:16
2 0.2% 1.2% LazyCompile: *precision [...]/ui/package.strip.js:25137:23
2 0.2% 1.2% LazyCompile: *me [...]/ui/package.strip.js:25178:16
2 0.2% 1.2% LazyCompile: *cmatch [...]/ui/package.strip.js:25495:20
2 0.2% 1.2% LazyCompile: *ceq [...]/ui/package.strip.js:25273:17
1 0.1% 0.6% LazyCompile: *init_defaults [...]/ui/package.strip.js:25624:27
1 0.1% 0.6% LazyCompile: *MM [...]/ui/package.strip.js:25268:16
1 0.1% 0.6% LazyCompile: *E [...]/ui/package.strip.js:25239:15
1 0.1% 0.6% LazyCompile: *<anonymous> [...]/ui/package.strip.js:25184:13
1 0.1% 0.6% LazyCompile: *<anonymous> [...]/ui/package.strip.js:25171:13
Much better than the 102 ticks that anyValue was taking some time ago!
A lot of time used to be spent compiling functions as well, a lot of which
was removed by previous commits, bringing us to:
[C++]:
ticks total nonlib name
50 5.9% 30.5% node::contextify::ContextifyContext::CompileFunction(v8::FunctionCallbackInfo<v8::Value> const&)
20 2.4% 12.2% write
9 1.1% 5.5% node::native_module::NativeModuleEnv::CompileFunction(v8::FunctionCallbackInfo<v8::Value> const&)
6 0.7% 3.7% __pthread_cond_timedwait
4 0.5% 2.4% mmap
All of this work has simplified the output enough that it's obviated a slew
of other optimizations that can be done in future work, though a lot of that
may wait for TAMER, since performing them in XSLT will be difficult and not
performant; the compiler is slow enough as it is.
This shaves ~1m off of the total build time for our largest system. Output
is impressively slow.
Around this point in time, we have the following profile from V8's sampling
profiler:
[JavaScript]:
ticks total nonlib name
36 2.8% 10.7% LazyCompile: *anyValue [...]/ui/package.strip.new.js:31020:22
3 0.2% 0.9% LazyCompile: *m1v1u [...]/ui/package.strip.new.js:30941:19
2 0.2% 0.6% LazyCompile: *precision [...]/ui/package.strip.new.js:30934:23
1 0.1% 0.3% LazyCompile: *vu [...]/ui/package.strip.new.js:30964:16
1 0.1% 0.3% LazyCompile: *init_defaults [...]/ui/package.strip.new.js:31341:27
Mike Gerwitz