def evalf_sum(expr, prec, options):
func = expr.function
limits = expr.limits
if len(limits) != 1 or not isinstance(limits[0], tuple) or \
len(limits[0]) != 3:
raise NotImplementedError
prec2 = prec + 10
try:
n, a, b = limits[0]
if b != S.Infinity or a != int(a):
raise NotImplementedError
# Use fast hypergeometric summation if possible
v = hypsum(func, n, int(a), prec2)
delta = prec - fastlog(v)
if fastlog(v) < -10:
v = hypsum(func, n, int(a), delta)
return v, None, min(prec, delta), None
except NotImplementedError:
# Euler-Maclaurin summation for general series
eps = C.Real(2.0)**(-prec)
for i in range(1, 5):
m = n = 2**i * prec
s, err = expr.euler_maclaurin(m=m, n=n, eps=eps, \
eval_integral=False)
err = err.evalf()
if err <= eps:
break
err = fastlog(evalf(abs(err), 20, options)[0])
re, im, re_acc, im_acc = evalf(s, prec2, options)
re_acc = max(re_acc, -err)
im_acc = max(im_acc, -err)
return re, im, re_acc, im_acc
def evalf_piecewise(expr, prec, options):
if 'subs' in options:
expr = expr.subs(options['subs'])
del options['subs']
if hasattr(expr, 'func'):
return evalf(expr, prec, options)
if type(expr) == float:
return evalf(C.Real(expr), prec, options)
if type(expr) == int:
return evalf(C.Integer(expr), prec, options)
# We still have undefined symbols
raise NotImplementedError