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 a call to another library function; select it to open that function.

xf64[n]ReluposNegatenegxRelunegAddyyf64[n]
  • 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
softsignmae
sha256:143f8c2ea9ad5f555742d9be560f4b85db177d2c6a6d2d4bdcc8b568cfe449ee

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