block-step
At its defaults it draws one block of 32 values at 6-bit significands, spread over 1.94 octaves. Thirty-two bars of differing heights with horizontal rules at the multiples of the shared step. Bars shorter than half a step are drawn in the warning colour.
block-step is one function in lib/figures/lowprec.js —
low precision — eight bits, the format that breaks the rules, and one shared exponent. 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.
Thirty-two bars of differing heights with horizontal rules at the multiples of the shared step. Bars shorter than half a step are drawn in the warning colour.
octaves: 2
The arguments are the ones A norm that overflows before it is a norm passes. A value drawn at the generator's defaults instead would be a picture no essay asked for and no assertion has been run against.
Thirty-two bars of differing heights with horizontal rules at the multiples of the shared step. Bars shorter than half a step are drawn in the warning colour.
octaves: 12
The arguments are the ones One exponent for thirty-two numbers passes. A value drawn at the generator's defaults instead would be a picture no essay asked for and no assertion has been run against.
Thirty-two bars of differing heights with horizontal rules at the multiples of the shared step. Bars shorter than half a step are drawn in the warning colour.
What it checked while drawing
Every figure above asserted its own claims on the way to being drawn, and a claim that failed
would have failed the build rather than drawn a wrong picture. Those assertions 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.
5 distinct claims across 3 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.
a block significand of four to eight bits
a spread inside the range drawn
and the largest entry fits the integer range without clamping
every entry's error is within half a shared step
the block chose a scale
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 52
of 99 generators —
37 print a residual and
15 are exempt with a published reason;
47 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.
A norm that overflows before it is a norm
The vector of sixteen thousands has a Euclidean norm of 4,000, which fp16 represents exactly. Written as the square root of the sum of squares it returns infinity, because squaring doubles the exponent — and the expression costs half the format's range on the one computation every iterative method performs at every step.
The arithmetic underneathOne exponent for thirty-two numbers
Share the exponent across a block and the cost per value drops from eight bits to 6.25, and the accuracy improves — up to about three octaves of spread inside a block. Past that a single outlier deletes the thirty-one values beside it, and the 2-norm barely notices.