There are doctests of the form
sage: x = random_value()
sage: abs(floating_point_computation(x) - exact_value(x)) < tolerance
True
but every floating point computation has SOME values where it is
ill-conditioned. I'm finding a steady trickle of test failures due to the
(now) random seeds for each run. Whats the plan for that?
A) mark them all as # random
B) identify all such tests and pick a fixed seed for those
C) identify all such tests and do the error analysis to find a tolerance(x)
that takes the numerical instabilities into account
D) ignore issue and pick a fixed seed for the buildbot, will still randomly
fail for users
PS: Here is one to illustrate the issue:
sage -t --long --warn-long 50.7
--random-seed=269711721119345330713403621242624346446
src/sage/functions/exp_integral.py
**********************************************************************
File "src/sage/functions/exp_integral.py", line 1493, in
sage.functions.exp_integral.exponential_integral_1
Failed example:
for prec in [20..128]: # long time (15s on sage.math, 2013)
R = RealField(prec)
S = RealField(prec+64)
a = R.random_element(-15,10).exp()
n = 2^ZZ.random_element(14)
x = exponential_integral_1(a, n)
y = exponential_integral_1(S(a), n)
c = RDF(4 * max(1.0, y[0]))
for i in range(n):
e = float(abs(S(x[i]) - y[i]) << prec)
if e >= c:
print("exponential_integral_1(%s, %s)[%s] with precision %s
has error of %s >= %s"%(a, n, i, prec, e, c))
Expected nothing
Got:
exponential_integral_1(57.77854062056109797473161078505723378, 1)[0]
with precision 127 has error of 4.75102130393081 >= 4.0
**********************************************************************
1 item had failures:
1 of 11 in sage.functions.exp_integral.exponential_integral_1
[275 tests, 1 failure, 7.23 s]
----------------------------------------------------------------------
sage -t --long --warn-long 50.7
--random-seed=269711721119345330713403621242624346446
src/sage/functions/exp_integral.py # 1 doctest failed
----------------------------------------------------------------------
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