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 check(self, *args):
from amath.testing.types import isReal, isComplex, isNatural, isWhole, intQ, isNumber, isValue
if len(args) != len(self.vars):
raise TypeError("check takes exactly {0} arguments ({1} given)".format(len(self.vars), len(args)))
i = 0
for var in self.vars:
tp = self.vars[var]
value = args[i]
if tp == "Value":
if not isValue(value):
raise TypeError("{0} must be a value".format(var))
elif tp == "Number":
if not isNumber(value):
raise TypeError("{0} must be a number".format(var))
elif tp == "Imaginary":
if not isComplex(value):
raise TypeError("{0} must be an Imaginary number".format(var))
elif tp == "Real":
if not isReal(value):
raise TypeError("{0} must be a Real number".format(var))
elif tp == "Integer":
if not intQ(value):
raise TypeError("{0} must be an Integer".format(var))
elif tp == "Whole":
if not isWhole(value):
raise TypeError("{0} must be a Whole number".format(var))
elif tp == "Natural":
if not isNatural(value):
raise TypeError("{0} must be a Natural number".format(var))
else:
raise Exception("Internal Error")
i += 1
def digits(x):
"""
Find the number of digits in x
:param x: Number
:return: Number of digits in x
>>> digits(5)
1
>>> digits(234)
3
>>> digits(3.0)
1
>>> digits(3.4)
2
"""
from amath.testing.types import intQ, isFraction
if isFraction(x): # if x is a Fraction
return x.digits() # run the specified digits function
if intQ(x):
x = int(x)
if int(x) == x:
return len(str(abs(x))) # for int
else:
return len(str(abs(x))) - 1 # for float
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 check(self, *args):
from amath.testing.types import isReal, isComplex, isNatural, isWhole, intQ, isNumber, isValue
if len(args) != len(self.vars):
raise TypeError(
"check takes exactly {0} arguments ({1} given)".format(
len(self.vars), len(args)))
i = 0
for var in self.vars:
tp = self.vars[var]
value = args[i]
if tp == "Value":
if not isValue(value):
raise TypeError("{0} must be a value".format(var))
elif tp == "Number":
if not isNumber(value):
raise TypeError("{0} must be a number".format(var))
elif tp == "Imaginary":
if not isComplex(value):
raise TypeError(
"{0} must be an Imaginary number".format(var))
elif tp == "Real":
if not isReal(value):
raise TypeError("{0} must be a Real number".format(var))
elif tp == "Integer":
if not intQ(value):
raise TypeError("{0} must be an Integer".format(var))
elif tp == "Whole":
if not isWhole(value):
raise TypeError("{0} must be a Whole number".format(var))
elif tp == "Natural":
if not isNatural(value):
raise TypeError("{0} must be a Natural number".format(var))
else:
raise Exception("Internal Error")
i += 1
def digits(x):
# from amath.DataTypes.Fraction import Fraction
from amath.testing.types import intQ
if type(x) is not int:
if type(x) is not float:
if type(x) is not mpq:
try:
x = float(x)
except ValueError:
raise TypeError(str(x) + " is not a number") # x is not a number
if isinstance(x, mpq): # if x is a Fraction
return x.digits() # run the specified digits function
if intQ(x):
x = int(x)
if int(x) == x:
return len(str(abs(x))) # for int
else:
return len(str(abs(x))) - 1 # for float
def digits(x):
from amath.DataTypes.Fraction import Fraction
from amath.testing.types import intQ
if type(x) is not int:
if type(x) is not float:
if type(x) is not Fraction:
try:
x = float(x)
except ValueError:
raise TypeError(str(x) + " is not a number") # x is not a number
if isinstance(x, Fraction): # if x is a Fraction
return x.digits() # run the specified digits function
if intQ(x):
x = int(x)
if int(x) == x:
return len(str(abs(x))) # for int
else:
return len(str(abs(x))) - 1 # for float
def __new__(cls, v, rep=None):
from amath.testing.types import intQ, isReal
self = object.__new__(cls)
if rep is not None:
if not intQ(v):
raise TypeError("If repeating decimal is defined, value must have an integer value")
if not isReal(rep):
raise TypeError("Repeating decimal must be a float or a string")
else:
if not isReal(v):
raise TypeError("value must be a float or a string")
self.value = int(v)
v = str(v)
index = v.find('.')
if index == -1:
raise ValueError("Value must be a float or a string, not an int")
self.rep = v[index + 1:]
return self
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 __new__(cls, v, rep=None):
from amath.testing.types import intQ, isReal
self = object.__new__(cls)
if rep is not None:
if not intQ(v):
raise TypeError(
"If repeating decimal is defined, value must have an integer value"
)
if not isReal(rep):
raise TypeError(
"Repeating decimal must be a float or a string")
else:
if not isReal(v):
raise TypeError("value must be a float or a string")
self.value = int(v)
v = str(v)
index = v.find('.')
if index == -1:
raise ValueError(
"Value must be a float or a string, not an int")
self.rep = v[index + 1:]
return self