def cosh(args):
x = 0
e = get_e()
if len(args) == 1 or (len(args) == 2 and args[1] == 0):
x = args[0]
return (power_function([e, x]) + power_function([e, -x])) / 2
elif len(args) == 2 and args[1] == 1:
x = to_radians(args[0])
return (power_function([e, x]) + power_function([e, -x])) / 2
else:
raise Exception("Invalid input: cosh takes 1 input which is the "
"number in radians, or 2 inputs which is the number "
"and whether the number is in \" radians\" or \" "
"degrees\".")
def get_pi():
global pi
if pi == 0:
series_sum = 0
# We iterate for 2 iterations, as Chudnosvky converges very
# quickly
for i in range(2):
series_sum += (pf.power_function([-1, i]) * af.factorial(6 * i)
* (13591409 + (545140134 * i))) \
/ (af.factorial(3 * i)
* pf.power_function([math.factorial(i), 3])
* pf.power_function([640320, 3 * i + 1.5]))
pi = 1 / (12 * series_sum)
return pi
def standard_deviation(args):
# helper function that returns a list storing each value - mean
def helper(arg_list, length):
# compute mean
mean = total_count(arg_list) / length
# a new list stores the values of each element - mean
args_new = []
for i in range(length):
args_new.append(arg_list[i] - mean)
for i in range(length):
args_new[i] = power_function([args_new[i], 2])
return args_new
count = len(args)
if count > 1:
# Get the last element in the list
flag = args[-1]
# population stdev
if flag == 0.0:
if count == 2:
return 0
else:
args = args[:-1]
count -= 1
args_sqr = helper(args, count)
return power_function([total_count(args_sqr) / count, 0.5])
# sample stdev
if flag == 1.0:
# Sample stdev requires at least 2 numbers
if count == 2:
raise TypeError('Sample Standard Deviation requires at least '
'2 numbers !')
else:
args = args[:-1]
count -= 1
args_sqr = helper(args, count)
return power_function(
[total_count(args_sqr) / (count - 1), 0.5])
else:
raise TypeError('Please specify the type of standard deviation !')
else:
raise TypeError('Invalid Argument !')
def helper(arg_list, length):
# compute mean
mean = total_count(arg_list) / length
# a new list stores the values of each element - mean
args_new = []
for i in range(length):
args_new.append(arg_list[i] - mean)
for i in range(length):
args_new[i] = power_function([args_new[i], 2])
return args_new
def get_ln10():
global ln10
if ln10 == 0:
# if the ln(10) isn't already calculated, then calculate it for
# the first time and store it for the duration of runtime
sum = 0
for i in range(1000):
sum += (1 / (2 * i + 1)) * pf.power_function(
[(10 - 1) / (10 + 1), 2 * i + 1])
ln10 = 2 * sum
return ln10
def sine(args):
if len(args) == 1 or (len(args) == 2 and args[1] == 0):
num = args[0]
elif len(args) == 2 and args[1] == 1:
num = to_radians(args[0])
else:
raise Exception("Invalid input: sine takes 1 input which is the "
"number in degrees, or 2 inputs which is the number "
"and whether the number is in \" radians\" or \" "
"degrees\".")
res = 0
pi = get_pi()
twopi = 2 * pi
# program will crush if num too big, convert to interval 0 -> 2pi
num = num % twopi
# using for loop to create summation i=0 to i=79
for i in range(80):
res += (power_function([-1, i])) \
* (power_function([num, (2 * i + 1)])) \
/ (factorial(2 * i + 1))
return res
def natural_log(x):
a = x
b = 0
# we will rewrite ln(x) where x = a * 10^b, with a < 1
# we can then take the ln(x) = ln(a) + b * ln(10)
while a > 1:
a /= 10
b += 1
# Variable used to store the calculated sum
s = 0
# Number of iterations currently hardcoded at 100, but we can change
# this to an accuracy based metric by calculating the accuracy of
# e^s = x to a certain bound.
for i in range(100):
s += (1 / (2 * i + 1)) * power_function([(a - 1) / (a + 1), 2 * i + 1])
return (2 * s) + b * get_ln10()