def __call__(self, s):
assert len(s) > 0
suffix = 1
if s != "now" and s != "today":
if len(s) > 1 and s[:2] != "0x":
if s[-1] in suffixes_ln:
exponent = suffixes_ln[s[-1]]
if exponent >= 0:
suffix = Zn(10**exponent)
else:
suffix = mpf("1e" + str(exponent))
s = s[:-1]
for func in (self.j, self.i, self.q, self.v, self.r, self.c):
x = func(s)
if x != None:
if suffix == 1:
return x
if isint(x):
if isint(suffix): return Zn(suffix*x)
else: return suffix*mpf(int(x))
elif isinstance(x, Rational):
if isint(suffix): return Rational(suffix*x.n, x.d)
else: return suffix*x.mpf()
elif isinstance(x, mpf) or \
isinstance(x, mpc) or \
isinstance(x, mpi):
if isint(suffix): return mpf(int(suffix))*x
else: return suffix*x
else:
return None
return None
def gcd(a, b):
'''Determine the greatest common divisor of integers u and v.
Euclid's algorithm from Knuth, vol 2, pg 320.
'''
if not isint(a) or not isint(b):
raise ValueError("Arguments must be integers")
a, b = int(a), int(b)
if a == 0: return b
if b == 0: return a
while b != 0:
a, b = b, a % b
return a
def Convert(x, arg_type, digits=0):
'''Converts amongst the numerical types. Some conversions lose
information. The digits argument controls the precision of a conversion
of a real to a rational.
'''
e = SyntaxError("Unknown type")
if arg_type == INT:
if isint(x): return Zn(x)
elif isinstance(x, Rational): return Zn(int(mpf(x.n)/mpf(x.d)))
elif isinstance(x, mpf): return Zn(int(x))
elif isinstance(x, mpc): return Zn(int(abs(x)))
elif isinstance(x, mpi): return Zn(int(x.mid))
elif isinstance(x, Julian): return Zn(int(x))
else: raise e
elif arg_type == RAT:
if isint(x): return Rational(int(x), 1)
elif isinstance(x, Rational): return x
elif isinstance(x, mpf): return Rational().frac(x, digits)
elif isinstance(x, mpc): return Rational().frac(abs(x), digits)
elif isinstance(x, mpi): return Rational(x.mid)
elif isinstance(x, Julian): return Rational().frac(x.to_mpf(), digits)
else: raise e
elif arg_type == MPF:
if isint(x): return mpf(int(x))
elif isinstance(x, Rational): return x.mpf()
elif isinstance(x, mpf): return x
elif isinstance(x, mpc): return abs(x)
elif isinstance(x, mpi): return x.mid
elif isinstance(x, Julian): return x.to_mpf()
else: raise e
elif arg_type == MPC:
if isint(x): return mpc(int(x))
elif isinstance(x, Rational): return x.mpc()
elif isinstance(x, mpf): return mpc(x, 0)
elif isinstance(x, mpc): return x
elif isinstance(x, mpi): return mpc(x.mid, 0)
elif isinstance(x, Julian): return mpc(x.to_mpf(), 0)
else: raise e
elif arg_type == MPI:
if isint(x): return mpi(int(x))
elif isinstance(x, Rational): return x.mpi()
elif isinstance(x, mpf): return mpi(x)
elif isinstance(x, mpc): return mpi(abs(x))
elif isinstance(x, mpi): return x
elif isinstance(x, Julian):
if isinstance(x.value, mpf): return mpi(x.value)
else: return x.value
else: raise e
elif arg_type == JUL:
if isint(x): return Julian(int(x))
elif isinstance(x, Rational): return Julian(mpf(x.n)/mpf(x.d))
elif isinstance(x, mpf): return Julian(x)
elif isinstance(x, mpc): return Julian(abs(x))
elif isinstance(x, mpi): return Julian(x)
elif isinstance(x, Julian): return x
else: raise e
else:
raise SyntaxError("Unknown type")
