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TOLERANCES.md

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Differentiation test tolerances

Tolerances and step sizes for finite-difference derivative checks in the BLAS differentiation test generator.

Defaults

rtol/atol by precision family

Family Meaning rtol atol
S S* (single real) 2.0e-3 2.0e-3
C C* (single complex) 1.0e-3 1.0e-3
D D* (double real) 1.0e-5 1.0e-5
Z Z* (double complex) 1.0e-5 1.0e-5

step size h by precision family

Family h
S, C 1.0e-3
D, Z 1.0e-7

Overrides

Mixed-precision D* (single-precision first differentiable input)

Applies when the routine behaves like “double output, but first differentiable input is single precision” (e.g. DSDOT with SX first; the generator also treats SY and SB as single-precision inputs for D*).

  • Scalar forward: override h = 1.0e-3 (rtol/atol remain D* base = 1.0e-5)
  • Scalar reverse / vector forward / vector reverse: override h = 1.0e-3, rtol = atol = 2.0e-3

Relaxed C* tolerance in vector reverse

Only for single-precision complex (C*) vector reverse tests:

Routine family (examples) rtol/atol
DOT (e.g. CDOTC) 2.5e-2
BLAS3 (e.g. CGEMM, CSYMM, CHEMM) 1.0e-2
BLAS2 banded MV (e.g. CGBMV, CTBMV, CHBMV) 1.0e-2

All other C* modes use the base tolerance (1.0e-3). Z* does not use relaxed tolerances.