# numbers.py


# integers
>>> a = 14
>>> b = 3
>>> a + b  # addition
17
>>> a - b  # subtraction
11
>>> a * b  # multiplication
42
>>> a / b  # true division
4.666666666666667
>>> a // b  # integer division
4
>>> a % b  # modulo operation (reminder of division)
2
>>> a ** b  # power operation
2744

>>> from math import pow

>>> pow(10, 3)
1000
>>> 10 ** 3
1000
>>> pow(10, -3)
0.001
>>> 10 ** -3
0.001


>>> pow(123, 4)
228886641
>>> pow(123, 4, 100)
41  # notice: 228886641 % 100 == 41
>>> pow(37, -1, 43)  # modular inverse of 37 mod 43
7
>>> 7 * 37 % 43  # proof the above is correct
1



# integer and true division
>>> 7 / 4  # true division
1.75
>>> 7 // 4  # integer division, truncation returns 1
1
>>> -7 / 4  # true division again, result is opposite of previous
-1.75
>>> -7 // 4  # integer div., result not the opposite of previous
-2

# modulo operator
>>> 10 % 3  # remainder of the division 10 // 3
1
>>> 10 % 4  # remainder of the division 10 // 4
2


# truncation towards 0
>>> int(1.75)
1
>>> int(-1.75)
-1

# creating ints
>>> int('10110', base=2)
22


# underscored
>>> n = 1_024
>>> n
1024
>>> hex_n = 0x_4_0_0  # 0x400 == 1024
>>> hex_n
1024


# booleans
>>> int(True)  # True behaves like 1
1
>>> int(False)  # False behaves like 0
0
>>> bool(1)  # 1 evaluates to True in a boolean context
True
>>> bool(-42)  # and so does every non-zero number
True
>>> bool(0)  # 0 evaluates to False
False
>>> # quick peak at the operators (and, or, not)
>>> not True
False
>>> not False
True
>>> True and True
True
>>> False or True
True


# int and bool
>>> 1 + True
2
>>> False + 42
42
>>> 7 - True
6


# reals
>>> pi = 3.1415926536  # how many digits of PI can you remember?
>>> radius = 4.5
>>> area = pi * (radius ** 2)
>>> area
63.617251235400005


# sys.float_info
>>> import sys
>>> sys.float_info
sys.float_info(
    max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308,
    min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307,
    dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2,
    rounds=1
)

# approximation issue
>>> 0.3 - 0.1 * 3  # this should be 0!!!
-5.551115123125783e-17


# complex
>>> c = 3.14 + 2.73j
>>> c = complex(3.14, 2.73)  # same as above
>>> c.real  # real part
3.14
>>> c.imag  # imaginary part
2.73
>>> c.conjugate()  # conjugate of A + Bj is A - Bj
(3.14-2.73j)
>>> c * 2  # multiplication is allowed
(6.28+5.46j)
>>> c ** 2  # power operation as well
(2.4067000000000007+17.1444j)
>>> d = 1 + 1j  # addition and subtraction as well
>>> c - d
(2.14+1.73j)


# fractions
>>> from fractions import Fraction
>>> Fraction(10, 6)  # mad hatter?
Fraction(5, 3)  # notice it's been simplified
>>> Fraction(1, 3) + Fraction(2, 3)  # 1/3 + 2/3 == 3/3 == 1/1
Fraction(1, 1)
>>> f = Fraction(10, 6)
>>> f.numerator
5
>>> f.denominator
3
>>> f.as_integer_ratio()
(5, 3)


# decimal
>>> from decimal import Decimal as D  # rename for brevity
>>> D(3.14)  # pi, from float, so approximation issues
Decimal('3.140000000000000124344978758017532527446746826171875')
>>> D('3.14')  # pi, from a string, so no approximation issues
Decimal('3.14')
>>> D(0.1) * D(3) - D(0.3)  # from float, we still have the issue
Decimal('2.775557561565156540423631668E-17')
>>> D('0.1') * D(3) - D('0.3')  # from string, all perfect
Decimal('0.0')
>>> D('1.4').as_integer_ratio()  # 7/5 = 1.4 (isn't this cool?!)
(7, 5)