Let's begin from the beginning. Can you define what a 'vector formula' is?
Post by Sascha Bischoff Post by Nilay Vaish Post by Nathan Binkert
This really confuses me. A the idea of the Formula class was that it was a Vector, and we'd simply pretend that Formulas of length 1 were scalars. It seems wrong to me to have two classes here and we need to fix the main class itself.
I second Nate's opinion here. A formula can involve both scalars and vectors. What would you do then?
The basic functionality of the interface to the classes is there
same and therefore does not represent an issue. The issue lies with the
total calculation for the different types of statistic. For example, to
calculate the total of a vector, we sum each of the elements. The same
principle applies for the total for a 2D vector, where we sum each of
the "rows" and then also calculate an overall total. However, in the
case of a formula it becomes more complex. Specifically, if we were to
just sum the value of each element of a vector formula the result would
potentially be incorrect. For example, if we are calculating a rate
using a formula, then we do not want to sum all of the elements as this
will not give the overall rate. Instead we want to calculate the total
of the numerators and the total of the denominators before dividing
them to get the overall total for the formula. This is the reason that
I split the display class into two classes.
The total for a vector is calculated "externally", i.e. we take the
list representing the vector, and sum all of the values to get the
total. This is done as part of the display class. On the other hand,
the total for a formula is calculated "internally", i.e. it is
calculated by the formula class itself (using abstract syntax trees) by
calculating the total for the numerator and denominator separately.
Aside from the calculation of the total these classes are identical,
but are incompatible.
An alternative solution to having separate display classes would be
to add an additional layer of indirection which then provides the same
interface for getting the total of the vectors and formulas, but hides
the mechanics internally. Do you have any better suggestions?
Nilay, regarding your question: the formulas can indeed involve
both scalars and vectors. However the calculation of the formula is
handled using python's eval function. Any formula calculation involving
both vectors and scalars will invariably result in a vector result.
However, based on the length of the vector, it is either processed
directly as a scalar (hence we do not have the issues with the total
calculation), or as a vector formula. Does this clarify things?
Can you tell me how are you expressing the so called vector formula in your example?
The formula, in my opinion, would look like rate = sum(v) / sum(t) where
v and t can be vectors or scalars (does not matter at all). If you are writing rate = v / t
where v and t can be vectors, I would say that this expression is ambiguous.
How do you know I do not intend rate to be a vector, where rate_i = v_i / t_i?
In fact, in my opinion rate = v/t should mean rate_i = v_i / t_i.
system.l2.ReadReq_hits::cpu.dtb.walker 9 # number of ReadReq hits
system.l2.ReadReq_hits::cpu.itb.walker 2 # number of ReadReq hits
system.l2.ReadReq_hits::cpu.inst 49 # number of ReadReq hits
system.l2.ReadReq_hits::cpu.data 1116 # number of ReadReq hits
system.l2.ReadReq_hits::total 1176 # number of ReadReq hits
system.l2.ReadReq_misses::cpu.dtb.walker 5 # number of ReadReq misses
system.l2.ReadReq_misses::cpu.itb.walker 1 # number of ReadReq misses
system.l2.ReadReq_misses::cpu.inst 411 # number of ReadReq misses
system.l2.ReadReq_misses::cpu.data 111 # number of ReadReq misses
system.l2.ReadReq_misses::total 528 # number of ReadReq misses
system.l2.ReadReq_miss_rate::cpu.dtb.walker 0.357143 # miss rate for ReadReq accesses
system.l2.ReadReq_miss_rate::cpu.itb.walker 0.333333 # miss rate for ReadReq accesses
system.l2.ReadReq_miss_rate::cpu.inst 0.893478 # miss rate for ReadReq accesses
system.l2.ReadReq_miss_rate::cpu.data 0.090465 # miss rate for ReadReq accesses
system.l2.ReadReq_miss_rate::total 0.309859 # miss rate for ReadReq accesses
In this case, hits and misses are vectors, where each element in the
vector counts the hits or misses for a particular master. The total for
hits or misses is simply the sum of the elements.
The miss_rate is a formula which is defined as: misses / (hits +
misses). This is calculated for each element of the input vectors, e.g.
miss_rate::cpu.inst = misses::cpu.inst / (hits::cpu.inst +
For the total calculation, we do: total_miss_rate = total(misses) / total(hits + misses)
Therefore, the rate is evaluated on a per-element basis and the total is
not simply the sum of the individual miss rates. This is why we need to
treat formulas slightly different from vectors when calculating the