def _compare_bounds(self, q, sigma, order):
log_a_mp, log_b_mp = self._compute_rdp_mp(q, sigma, order)
log_a = rdp_accountant._compute_log_a(q, sigma, order)
log_bound_b = rdp_accountant._bound_log_b(q, sigma, order)
if log_a_mp < 1000 and log_a_mp > 1e-6:
self._almost_equal(log_a, log_a_mp, rtol=1e-6)
else: # be more tolerant for _very_ large or small logarithms
self._almost_equal(log_a, log_a_mp, rtol=1e-3, atol=1e-14)
if np.isfinite(log_bound_b):
# Ignore divergence between the bound and exact value of B if
# they don't matter anyway (bound on A is larger) or q > .5
if log_bound_b > log_a and q <= .5:
self._almost_equal(log_b_mp, log_bound_b, rtol=1e-6, atol=1e-14)
if np.isfinite(log_a_mp) and np.isfinite(log_b_mp):
# We hypothesize that this assertion is always true; no proof yet.
self.assertLessEqual(log_b_mp, log_a_mp + 1e-6)
def _compare_bounds(self, q, sigma, order):
log_a_mp, log_b_mp = self._compute_rdp_mp(q, sigma, order)
log_a = rdp_accountant._compute_log_a(q, sigma, order)
log_bound_b = rdp_accountant._bound_log_b(q, sigma, order)
if log_a_mp < 1000 and log_a_mp > 1e-6:
self._almost_equal(log_a, log_a_mp, rtol=1e-6)
else: # be more tolerant for _very_ large or small logarithms
self._almost_equal(log_a, log_a_mp, rtol=1e-3, atol=1e-14)
if np.isfinite(log_bound_b):
# Ignore divergence between the bound and exact value of B if
# they don't matter anyway (bound on A is larger) or q > .5
if log_bound_b > log_a and q <= .5:
self._almost_equal(log_b_mp, log_bound_b, rtol=1e-6, atol=1e-14)
if np.isfinite(log_a_mp) and np.isfinite(log_b_mp):
# We hypothesize that this assertion is always true; no proof yet.
self.assertLessEqual(log_b_mp, log_a_mp + 1e-6)
def test_compute_log_a_equals_mp(self, q, sigma, order):
# Compare the cheap computation of log(A) with an expensive, multi-precision
# computation.
log_a = rdp_accountant._compute_log_a(q, sigma, order)
log_a_mp = self._log_float_mp(self._compute_a_mp(sigma, q, order))
np.testing.assert_allclose(log_a, log_a_mp, rtol=1e-4)