abs

std.elementwise.abs · Level L0

Absolute value, built from Relu. Exact: one of the two terms is always zero.

|x| = relu(x) + relu(−x)

Signature

abs(x: f64[n]) → f64[n]

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.
Equal to the reference np.abs(x) in exact rational arithmetic, on all 40 test cases.
All 171 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

—

Called by

softplus softsign bce_with_logits huber log_cosh mae mad

sha256:143f8c2ea9ad5f555742d9be560f4b85db177d2c6a6d2d4bdcc8b568cfe449ee

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

Control handle

Symbol: Ω:std.elementwise.abs · Ω:abs
Pins: sha256:ffe96e3e642bdf2fb57d46f1b13483e4c6a2a1dc3d2300367723090f75d13c61this graph alone
Evidence: sha256:ae2b58d34c5742acba05323c1c1d5e334f16fe8b9fc9a8485d79fe503cc52660the 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.