map_rows

std.func.map_rows · Level L2

f applied to every row of a matrix: a Scan over the rows whose body, map_rows_step, ignores its carry. A template over f, verified through f = log_softmax, where mapping row by row matters.

Yᵢ = f(Xᵢ)

Signature

map_rows(X: f64[n, m]) → f64[n, m]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference witness f = log_softmax, row by row: x − log Σ eˣ to 80 digits (100-digit arithmetic), on all 40 test cases.
All 480 float64 results inside the running error bound; the closest uses 46% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 73% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 65%
bit-equal to the NumPy formula in float64: 73%
largest error, in units in the last place: 1.3e+4

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

map_rows_step

Called by

—

sha256:b19b7699a590d52f0071531799c138cf11e2e9301d54caa17cbe06616e76f3aa

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.func.map_rows[f=std.nn.log_softmax]
Pins: sha256:51c19d3712dc9b757bed2623033b80cb244bcdf51aca10b95992f98d3bde440cthis graph and the 3 it reaches through calls
Evidence: sha256:9754aeef78696f5ec8bba3afb586bd07854b1892a5e813c0c94842fe67681d24the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.