def gamma(x):
# type: (float) -> float
t = False
y = 0.0
try:
y = _b.gamma(x) # call c-api
except:
t = True
from amath.DataTypes import Infinity
from amath.testing.types import isinf, isnan, intQ
x = int(x)
if x >= 170 or t: # to not overflow float or if in _basic failure
if intQ(x): # x must be an int
from amath.stats.stats import product
return product(lambda k: k, 1, x) // x
elif isinf(x):
if x > 0:
return Infinity(True)
else:
from amath.Errors import Indeterminate
raise Indeterminate()
else:
raise TypeError("For values over 170, x must be a integer")
else:
if isinf(y) or isnan(y):
return Infinity(None)
elif isinstance(x, int) or int(x) == x:
return int(y)
else:
return y
def gamma(x):
# type: (float) -> float
t = False
y = 0.0
try:
y = _b.gamma(x) # call c-api
except:
t = True
from amath.DataTypes import Infinity, Function
from amath.testing.types import isinf, isnan, intQ
x = int(x)
if x >= 170 or t: # to not overflow float or if in _basic failure
if intQ(x): # x must be an int
from amath.stats.stats import product
return product(lambda k: k, 1, x) // x
elif isinf(x):
if x > 0:
return Infinity(True)
else:
from amath.Errors import Indeterminate
raise Indeterminate()
else:
raise TypeError("For values over 170, x must be a integer")
else:
if isinf(y) or isnan(y):
return Infinity(None)
elif isinstance(x, int) or int(x) == x:
return int(y)
else:
return y
def __rpow__(self, other):
from amath.testing.types import isinf
if not isinf(other):
if other == 0:
if self.n is None:
raise Indeterminate(
"Indeterminate expression 0**ComplexInfinity encountered"
)
elif self.n:
return 0
else:
return Infinity(None)
elif (other == 1) or (other == -1):
raise Indeterminate(
"Indeterminate expression ({0})**{1} encountered".format(
str(other), repr(self)))
elif other < 0:
if self.n is None:
raise Indeterminate(
"Indeterminate expression "
"({0})**ComplexInfinity encountered".format(
str(other)))
elif self.n:
return Infinity(None)
else:
return 0
else:
if self.n is None:
raise Indeterminate(
"Indeterminate expression {0}**ComplexInfinity encountered"
.format(str(other)))
elif self.n:
return Infinity(True)
else:
return 0
def __rpow__(self, other):
from amath.testing.types import isinf
if not isinf(other):
if other == 0:
if self.n is None:
raise Indeterminate("Indeterminate expression 0**ComplexInfinity encountered")
elif self.n:
return 0
else:
return Infinity(None)
elif (other == 1) or (other == -1):
raise Indeterminate("Indeterminate expression ({0})**{1} encountered".format(str(other), repr(self)))
elif other < 0:
if self.n is None:
raise Indeterminate("Indeterminate expression "
"({0})**ComplexInfinity encountered".format(str(other)))
elif self.n:
return Infinity(None)
else:
return 0
else:
if self.n is None:
raise Indeterminate("Indeterminate expression {0}**ComplexInfinity encountered".format(str(other)))
elif self.n:
return Infinity(True)
else:
return 0
def __pow__(self, power, modulo=None):
from amath.testing.types import isinf
if not isinf(power):
if power == 0:
if self.n is None:
raise Indeterminate("Indeterminate expression ComplexInfinity**0 encountered")
elif self.n:
raise Indeterminate("Indeterminate expression inf**0 encountered")
else:
raise Indeterminate("Indeterminate expression (-inf)**0 encountered")
elif power < 0:
return 0
else:
return Infinity(self.n)
else:
if power > 0:
return Infinity(None)
elif power < 0:
return 0
elif isinstance(power, Infinity):
if self.n is None:
raise Indeterminate("Indeterminate expression ComplexInfinity**ComplexInfinity encountered")
elif self.n:
raise Indeterminate("Indeterminate expression inf**ComplexInfinity encountered")
else:
raise Indeterminate("Indeterminate expression (-inf)**ComplexInfinity encountered")
def __mul__(self, other):
from amath.testing.types import isinf
if isinstance(other, Infinity):
if self.n is None:
return Infinity(None)
elif other.n is None:
return Infinity(None)
elif self.n:
if other.n:
return Infinity(True)
else:
return Infinity(False)
elif not self.n:
if other.n:
return Infinity(False)
else:
return Infinity(True)
elif isinf(other):
if self.n is None:
return Infinity(None)
elif self.n:
if other > 0:
return Infinity(True)
else:
return Infinity(False)
else:
if other > 0:
return Infinity(False)
else:
return Infinity(True)
elif isinstance(other, complex):
if other.imag < 0:
return self.__neg__()
elif other.imag > 0:
return Infinity(self.n)
else:
return Infinity(self.n)
else:
if self.n is None:
if other == 0:
raise Indeterminate("Indeterminate expression 0 * ComplexInfinity encountered")
else:
return Infinity(None)
elif self.n:
if other == 0:
raise Indeterminate("Indeterminate expression 0 * inf encountered")
elif other > 0:
return Infinity(True)
else:
return Infinity(False)
else:
if other == 0:
raise Indeterminate("Indeterminate expression 0 * (-inf) encountered")
elif other > 0:
return Infinity(False)
else:
return Infinity(True)
def gamma(x):
# type: (float) -> float
t = False
y = 0.0
try:
y = _b.gamma(x) # call c-api
except:
t = True
from amath.testing.types import isinf, isnan, intQ
if x >= 170 or t: # to not overflow float or if in _basic failure
try:
from amath.constants import e, pi
s = GammaDk[0]
for i in range(1, GammaN + 1):
s += GammaDk[i] / (x + i - 1.0)
return s * 2 * sqrt(e / pi) * pow(
(x - 0.5 + GammaR) / e, x - 0.5)
except OverflowError:
if intQ(x): # x must be an int
from amath.stats.stats import product
return product(lambda k: k, 1, x) // x
elif isinf(x):
if x > 0:
from amath.DataTypes import Infinity
return Infinity(True)
else:
from amath.Errors import Indeterminate
raise Indeterminate()
else:
raise
else:
if isinf(y) or isnan(y):
from amath.DataTypes import Infinity
return Infinity(None)
elif isinstance(x, int) or int(x) == x:
return int(y)
else:
return y
def __cmp__(self, other):
"""
Compares with another value. Used by >, <, ==, and !=
:param other:
:return:
>>> Infinity(True) > 5
True
>>> Infinity(True) < 5
False
>>> Infinity(False) > Infinity(True)
False
>>> Infinity(None) == 0
Traceback (most recent call last):
...
Failure: Cannot be compared
>>> Infinity(True) == float("inf")
True
>>> float("inf") > Infinity(None)
Traceback (most recent call last):
...
Failure: Cannot be compared
>>>
"""
from amath.testing.types import isinf
if isinf(other):
if isinstance(other, Infinity):
if other.n is None:
raise
elif other.n < self.n:
return 1
else:
return -1
if other == float("inf"):
if self.n:
return 0
elif self.n is False:
return -1
elif other == float("-inf"):
if self.n:
return 1
elif self.n is False:
return 0
if self.n:
return 1
elif self.n is False:
return -1
else:
raise Failure("Cannot be compared")
def __cmp__(self, other):
"""
Compares with another value. Used by >, <, ==, and !=
:param other:
:return:
>>> Infinity(True) > 5
True
>>> Infinity(True) < 5
False
>>> Infinity(False) > Infinity(True)
False
>>> Infinity(None) == 0
Traceback (most recent call last):
...
Failure: Cannot be compared
>>> Infinity(True) == float("inf")
True
>>> float("inf") > Infinity(None)
Traceback (most recent call last):
...
Failure: Cannot be compared
>>>
"""
from amath.testing.types import isinf
if isinf(other):
if isinstance(other, Infinity):
if other.n is None:
raise
elif other.n < self.n:
return 1
else:
return -1
if other == float("inf"):
if self.n:
return 0
elif self.n is False:
return -1
elif other == float("-inf"):
if self.n:
return 1
elif self.n is False:
return 0
if self.n:
return 1
elif self.n is False:
return -1
else:
raise Failure("Cannot be compared")
def __pow__(self, power, modulo=None):
from amath.testing.types import isinf
if not isinf(power):
if power == 0:
if self.n is None:
raise Indeterminate(
"Indeterminate expression ComplexInfinity**0 encountered"
)
elif self.n:
raise Indeterminate(
"Indeterminate expression inf**0 encountered")
else:
raise Indeterminate(
"Indeterminate expression (-inf)**0 encountered")
elif power < 0:
return 0
else:
return Infinity(self.n)
else:
if power > 0:
return Infinity(None)
elif power < 0:
return 0
elif isinstance(power, Infinity):
if self.n is None:
raise Indeterminate(
"Indeterminate expression ComplexInfinity**ComplexInfinity encountered"
)
elif self.n:
raise Indeterminate(
"Indeterminate expression inf**ComplexInfinity encountered"
)
else:
raise Indeterminate(
"Indeterminate expression (-inf)**ComplexInfinity encountered"
)
def __mul__(self, other):
from amath.testing.types import isinf
if isinstance(other, Infinity):
if self.n is None:
return Infinity(None)
elif other.n is None:
return Infinity(None)
elif self.n:
if other.n:
return Infinity(True)
else:
return Infinity(False)
elif not self.n:
if other.n:
return Infinity(False)
else:
return Infinity(True)
elif isinf(other):
if self.n is None:
return Infinity(None)
elif self.n:
if other > 0:
return Infinity(True)
else:
return Infinity(False)
else:
if other > 0:
return Infinity(False)
else:
return Infinity(True)
elif isinstance(other, complex):
if other.imag < 0:
return self.__neg__()
elif other.imag > 0:
return Infinity(self.n)
else:
return Infinity(self.n)
else:
if self.n is None:
if other == 0:
raise Indeterminate(
"Indeterminate expression 0 * ComplexInfinity encountered"
)
else:
return Infinity(None)
elif self.n:
if other == 0:
raise Indeterminate(
"Indeterminate expression 0 * inf encountered")
elif other > 0:
return Infinity(True)
else:
return Infinity(False)
else:
if other == 0:
raise Indeterminate(
"Indeterminate expression 0 * (-inf) encountered")
elif other > 0:
return Infinity(False)
else:
return Infinity(True)