ch02

ch02/numbers.py

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+# 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)