def fib2(n):
"""
fib2(n) -> tuple
Return a 2-tuple with the (n-1)-th and n-th Fibonacci numbers.
"""
n = _check_int('fib2', 'n', n)
if n < 0:
raise ValueError('Fibonacci of negative number')
res, res1 = _new_mpz(), _new_mpz()
gmp.mpz_fib2_ui(res, res1, n)
return (mpz._from_c_mpz(res), mpz._from_c_mpz(res1))
def lucas2(n):
"""
lucas2(n) -> tuple
Return a 2-tuple with the (n-1)-th and n-th Lucas numbers.
"""
n = _check_int('lucas2', 'n', n)
if n < 0:
raise ValueError('Lucas of negative number')
res, res1 = _new_mpz(), _new_mpz()
gmp.mpz_lucnum2_ui(res, res1, n)
return (mpz._from_c_mpz(res), mpz._from_c_mpz(res1))
def lucas2(n):
"""
lucas2(n) -> tuple
Return a 2-tuple with the (n-1)-th and n-th Lucas numbers.
"""
n = _check_int('lucas2', 'n', n)
if n < 0:
raise ValueError('Lucas of negative number')
res, res1 = _new_mpz(), _new_mpz()
gmp.mpz_lucnum2_ui(res, res1, n)
return (mpz._from_c_mpz(res), mpz._from_c_mpz(res1))
def fib2(n):
"""
fib2(n) -> tuple
Return a 2-tuple with the (n-1)-th and n-th Fibonacci numbers.
"""
n = _check_int('fib2', 'n', n)
if n < 0:
raise ValueError('Fibonacci of negative number')
res, res1 = _new_mpz(), _new_mpz()
gmp.mpz_fib2_ui(res, res1, n)
return (mpz._from_c_mpz(res), mpz._from_c_mpz(res1))
def __hash__(self):
"""
Agrees with fractions.Fractions
"""
# XXX since this method is expensive, consider caching the result
if self == int(self):
return int(self)
if self == float(self):
return hash(float(self))
else:
num = long(mpz._from_c_mpz(gmp.mpq_numref(self._mpq)))
den = long(mpz._from_c_mpz(gmp.mpq_denref(self._mpq)))
return hash((num, den))
def gcdext(a, b):
"""
gcdext(a, b) - > tuple
Return a 3-element tuple (g,s,t) such that
g == gcd(a,b) and g == a*s + b*t
"""
a = _check_mpz('gcdext', 'a', a)
b = _check_mpz('gcdext', 'b', b)
mpz_g, mpz_s, mpz_t = _new_mpz(), _new_mpz(), _new_mpz()
gmp.mpz_gcdext(mpz_g, mpz_s, mpz_t, a._mpz, b._mpz)
return (mpz._from_c_mpz(mpz_g), mpz._from_c_mpz(mpz_s),
mpz._from_c_mpz(mpz_t))
def gcdext(a, b):
"""
gcdext(a, b) - > tuple
Return a 3-element tuple (g,s,t) such that
g == gcd(a,b) and g == a*s + b*t
"""
a = _check_mpz('gcdext', 'a', a)
b = _check_mpz('gcdext', 'b', b)
mpz_g, mpz_s, mpz_t = _new_mpz(), _new_mpz(), _new_mpz()
gmp.mpz_gcdext(mpz_g, mpz_s, mpz_t, a._mpz, b._mpz)
return (mpz._from_c_mpz(mpz_g),
mpz._from_c_mpz(mpz_s),
mpz._from_c_mpz(mpz_t))
def next_prime(x):
"""
next_prime(x) -> mpz
Return the next _probable_ prime number > x.
"""
x = _check_mpz('next_prime', 'x', x)
res = _new_mpz()
gmp.mpz_nextprime(res, x._mpz)
return mpz._from_c_mpz(res)
def next_prime(x):
"""
next_prime(x) -> mpz
Return the next _probable_ prime number > x.
"""
x = _check_mpz('next_prime', 'x', x)
res = _new_mpz()
gmp.mpz_nextprime(res, x._mpz)
return mpz._from_c_mpz(res)
def lcm(a, b):
"""
lcm(a, b) -> mpz
Return the lowest common multiple of integers a and b.
"""
a = _check_mpz('lcm', 'a', a)
b = _check_mpz('lcm', 'b', b)
res = _new_mpz()
gmp.mpz_lcm(res, a._mpz, b._mpz)
return mpz._from_c_mpz(res)
def gcd(a, b):
"""
gcd(a, b) -> mpz
Return the greatest common denominator of integers a and b.
"""
a = _check_mpz('gcd', 'a', a)
b = _check_mpz('gcd', 'b', b)
res = _new_mpz()
gmp.mpz_gcd(res, a._mpz, b._mpz)
return mpz._from_c_mpz(res)
def gcd(a, b):
"""
gcd(a, b) -> mpz
Return the greatest common denominator of integers a and b.
"""
a = _check_mpz('gcd', 'a', a)
b = _check_mpz('gcd', 'b', b)
res = _new_mpz()
gmp.mpz_gcd(res, a._mpz, b._mpz)
return mpz._from_c_mpz(res)
def lcm(a, b):
"""
lcm(a, b) -> mpz
Return the lowest common multiple of integers a and b.
"""
a = _check_mpz('lcm', 'a', a)
b = _check_mpz('lcm', 'b', b)
res = _new_mpz()
gmp.mpz_lcm(res, a._mpz, b._mpz)
return mpz._from_c_mpz(res)
def lucas(n):
"""
lucas(n) -> mpz
Return the n-th Lucas number.
"""
n = _check_int('lucas', 'n', n)
if n < 0:
raise ValueError('Lucas of negative number')
res = _new_mpz()
gmp.mpz_lucnum_ui(res, n)
return mpz._from_c_mpz(res)
def fib(n):
"""
fib(n) -> mpz
Return the n-th Fibonacci number.
"""
n = _check_int('fib', 'n', n)
if n < 0:
raise ValueError('Fibonacci of negative number')
res = _new_mpz()
gmp.mpz_fib_ui(res, n)
return mpz._from_c_mpz(res)
def fib(n):
"""
fib(n) -> mpz
Return the n-th Fibonacci number.
"""
n = _check_int('fib', 'n', n)
if n < 0:
raise ValueError('Fibonacci of negative number')
res = _new_mpz()
gmp.mpz_fib_ui(res, n)
return mpz._from_c_mpz(res)
def lucas(n):
"""
lucas(n) -> mpz
Return the n-th Lucas number.
"""
n = _check_int('lucas', 'n', n)
if n < 0:
raise ValueError('Lucas of negative number')
res = _new_mpz()
gmp.mpz_lucnum_ui(res, n)
return mpz._from_c_mpz(res)
def invert(x, m):
"""
invert(x, m) -> mpz
Return y such that x*y == 1 (mod m). Raises ZeroDivisionError if no
inverse exists.
"""
x = _check_mpz('invert', 'x', x)
m = _check_mpz('invert', 'm', m)
res = _new_mpz()
if gmp.mpz_invert(res, x._mpz, m._mpz) == 0:
raise ZeroDivisionError
return mpz._from_c_mpz(res)
def invert(x, m):
"""
invert(x, m) -> mpz
Return y such that x*y == 1 (mod m). Raises ZeroDivisionError if no
inverse exists.
"""
x = _check_mpz('invert', 'x', x)
m = _check_mpz('invert', 'm', m)
res = _new_mpz()
if gmp.mpz_invert(res, x._mpz, m._mpz) == 0:
raise ZeroDivisionError
return mpz._from_c_mpz(res)
def fac(n):
"""
fac(n) -> mpz
Return the exact factorial of n.
See factorial(n) to get the floating-point approximation.
"""
n = _check_int('fac', 'n', n)
if n < 0:
raise ValueError('fac() of negative number')
res = _new_mpz()
gmp.mpz_fac_ui(res, n)
return mpz._from_c_mpz(res)
def fac(n):
"""
fac(n) -> mpz
Return the exact factorial of n.
See factorial(n) to get the floating-point approximation.
"""
n = _check_int('fac', 'n', n)
if n < 0:
raise ValueError('fac() of negative number')
res = _new_mpz()
gmp.mpz_fac_ui(res, n)
return mpz._from_c_mpz(res)
def bincoef(x, n):
"""
bincoef(x, n) -> mpz
Return the binomial coefficient ('x over n'). n >= 0.
"""
n = _check_int('bincoef', 'n', n)
if n < 0:
raise ValueError('binomial coefficient with negative k')
res = _new_mpz()
if isinstance(x, mpz):
gmp.mpz_bin_ui(res, x._mpz, n)
elif isinstance(x, (int, long)) and -sys.maxsize - 1 <= x <= sys.maxsize:
gmp.mpz_bin_uiui(res, x, n)
else:
raise TypeError
return mpz._from_c_mpz(res)
def bincoef(x, n):
"""
bincoef(x, n) -> mpz
Return the binomial coefficient ('x over n'). n >= 0.
"""
n = _check_int('bincoef', 'n', n)
if n < 0:
raise ValueError('binomial coefficient with negative k')
res = _new_mpz()
if isinstance(x, mpz):
gmp.mpz_bin_ui(res, x._mpz, n)
elif isinstance(x, (int, long)) and -sys.maxsize - 1 <= x <= sys.maxsize:
gmp.mpz_bin_uiui(res, x, n)
else:
raise TypeError
return mpz._from_c_mpz(res)
def __floor__(self):
res = _new_mpz()
gmp.mpz_fdiv_q(res, gmp.mpq_numref(self._mpq), gmp.mpq_denref(self._mpq))
return mpz._from_c_mpz(res)
def numerator(self):
if self._numerator is None:
num = _new_mpz()
gmp.mpq_get_num(num, self._mpq)
self._numerator = mpz._from_c_mpz(num)
return self._numerator
def __long__(self):
res = _new_mpz()
gmp.mpz_tdiv_q(res, gmp.mpq_numref(self._mpq), gmp.mpq_denref(self._mpq))
return long(mpz._from_c_mpz(res))
def denominator(self):
if self._denominator is None:
den = _new_mpz()
gmp.mpq_get_den(den, self._mpq)
self._denominator = mpz._from_c_mpz(den)
return self._denominator
