def ibincoeff(n, k, integer=True):
"""
Computation of a single binomial coefficient n over k, returning an
integer (possibly long). For integer=True integer arithmetics is used
throughout and there is no risk of overflow. For integer=False a floating-
point gamma function approximation is used and the result converted to
integer at the end (if an overflow occurs ERRCODE is returned).
"""
assert is_posinteger(n), \
"n in n_over_k in ibincoeff must be a positive integer!"
assert is_nonneginteger(k), \
"k in n_over_k in ibincoeff must be a non-negative integer!"
assert n >= k, "n must be >= k in n_over_k in ibincoeff!"
if integer:
ibico = _bicolongint(n, k)
else:
try:
lnbico = lngamma(n + 1) - lngamma(k + 1) - lngamma(n - k + 1)
ibico = safeint(round(exp(lnbico)), 'ibincoeff')
except OverflowError:
ibico = ERRCODE
return ibico
def ibincoeff(n, k, integer=True):
"""
Computation of a single binomial coefficient n over k, returning an
integer (possibly long). For integer=True integer arithmetics is used
throughout and there is no risk of overflow. For integer=False a floating-
point gamma function approximation is used and the result converted to
integer at the end (if an overflow occurs ERRCODE is returned).
"""
assert is_posinteger(n), \
"n in n_over_k in ibincoeff must be a positive integer!"
assert is_nonneginteger(k), \
"k in n_over_k in ibincoeff must be a non-negative integer!"
assert n >= k, "n must be >= k in n_over_k in ibincoeff!"
if integer:
ibico = _bicolongint(n, k)
else:
try:
lnbico = lngamma(n+1) - lngamma(k+1) - lngamma(n-k+1)
ibico = safeint(round(exp(lnbico)), 'ibincoeff')
except OverflowError:
ibico = ERRCODE
return ibico
def ifactorial(n, integer=True):
"""
Computation of a factorial, returning an integer. For integer=True a long,
exact integer is returned. For integer=False an integer obtained from
floating-point arithmetics based on the function lngamma is returned -
it is approximate and may not be exact but faster for large n. ERRCODE
(cf. misclib.numbers) is returned if a floating-point OverflowError occurs
and a warning is sent to stdout (no error can occur when integer=True).
"""
assert is_nonneginteger(n), \
"the argument to ifactorial must be a non-negative integer!"
if integer:
fact = factorial(n)
else:
try:
fact = safeint(round(exp(lngamma(n + 1.0))), 'ifactorial')
except OverflowError:
fact = ERRCODE
warn("OverflowError in ifactorial - ERRCODE is returned")
return fact
def ifactorial(n, integer=True):
"""
Computation of a factorial, returning an integer. For integer=True a long,
exact integer is returned. For integer=False an integer obtained from
floating-point arithmetics based on the function lngamma is returned -
it is approximate and may not be exact but faster for large n. ERRCODE
(cf. misclib.numbers) is returned if a floating-point OverflowError occurs
and a warning is sent to stdout (no error can occur when integer=True).
"""
assert is_nonneginteger(n), \
"the argument to ifactorial must be a non-negative integer!"
if integer:
fact = factorial(n)
else:
try:
fact = safeint(round(exp(lngamma(n+1.0))), 'ifactorial')
except OverflowError:
fact = ERRCODE
warn("OverflowError in ifactorial - ERRCODE is returned")
return fact