What 4 layers save, against the size of the machine
At its defaults it draws what 4 layers save, against the size of the machine. The traffic of a flat layout divided by the traffic of a 4-layer one, at four processor counts, on a logarithmic horizontal axis. The upper line is the √4 the asymptotic analysis promises and the lower one is break-even. The measurement runs from 0.88 at 64 processors — a loss — to 1.44 at 576, and it is the same curve at every matrix size, because every word counted here is exactly proportional to n².
replication-crossing is one function in lib/figures/comm.js —
two ways of buying something back — a second pass, and memory spent on messages. Everything below came out of it during this build, at
arguments taken from the essays rather than invented for this page. A figure here is the
figure a reader meets in an essay, and if the generator changes, this page changes with it.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
The traffic of a flat layout divided by the traffic of a 4-layer one, at four processor counts, on a logarithmic horizontal axis. The upper line is the √4 the asymptotic analysis promises and the lower one is break-even. The measurement runs from 0.88 at 64 processors — a loss — to 1.44 at 576, and it is the same curve at every matrix size, because every word counted here is exactly proportional to n².
n: 96
The arguments are the ones Memory bought with messages passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
The traffic of a flat layout divided by the traffic of a 4-layer one, at four processor counts, on a logarithmic horizontal axis. The upper line is the √4 the asymptotic analysis promises and the lower one is break-even. The measurement runs from 0.88 at 64 processors — a loss — to 1.44 at 576, and it is the same curve at every matrix size, because every word counted here is exactly proportional to n².
What it checked while drawing
Every figure above checked its own claims on the way to being drawn, and a claim that failed
would have stopped the picture rather than shipped a wrong one. Those checks used to leave
no trace at all: a passing one returned true and the only evidence the figure had
checked anything was that nothing crashed. The list below is what they actually said, collected
by running this generator with an observer installed — not a description of
what it is believed to check.
17 distinct claims across 2 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.
and saves less than √4 at p = 64 — checked 4 times
the layered layout returns the product at p = 64 — checked 4 times
a matrix that divides into every grid drawn
and costs traffic outright on the smallest machine
enough machine sizes for a trend
matmul shapes agree
the matrix divides into the grid
the processors divide into c layers of a square grid
the replication factor the grids are chosen for
there is at least one summation block per layer
while saving a real factor on the largest
Against the rule
The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.
Across the library: the rule bites on 217
of 397 generators —
199 print a residual and
18 are exempt with a published reason;
180 factorise nothing.
Read from lib/residual-rule.js, which is the same body the gate enforces from,
and the gate's last check fails the build if this page and it disagree about any generator.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.