print(2 ** 100)                               # 1267650600228229401496703205376
print(0b1010, 0o17, 0xFF, 1_000_000)          # 10 15 255 1000000
print(int("1010", 2), int("z", 36), int(" 42 "))   # 10 35 42
n = 37
print(n.bit_length(), n.bit_count(), bin(n))  # 6 3 0b100101
print(7 // 2, -7 // 2, -7 % 3, int(-3.9))     # 3 -4 2 -3
print(divmod(17, 5), divmod(-17, 5))          # (3, 2) (-4, 3)

print(pow(2, 10), pow(2, 10, 1000))    # 1024 24     ← fast modular exponentiation
print(pow(3, -1, 7))                   # 5           ← modular inverse: 3 * 5 % 7 == 1
print(True + True, isinstance(True, int))   # 2 True
print((255).to_bytes(2, "big"), int.from_bytes(b"\x01\x00", "big"))   # b'\x00\xff' 256

print(0.1 + 0.2)                        # 0.30000000000000004
print(0.1 + 0.2 == 0.3)                 # False
import math
print(math.isclose(0.1 + 0.2, 0.3))     # True
print((0.1).as_integer_ratio())         # (3602879701896397, 36028797018963968)
print(f"{0.1:.20f}")                    # 0.10000000000000000555
total = 0.0
for _ in range(10):
    total += 0.1                        # error accumulates step by step
print(total, math.fsum([0.1] * 10))     # 0.9999999999999999 1.0
print(sum([0.1] * 10))                  # 1.0   ← sum() of floats is compensated since 3.12
print(2 ** 53 + 1.0 == 2 ** 53)         # True   ← integers above 2**53 lose precision

import math, sys
inf, nan = float("inf"), float("nan")
print(inf > 10**308, -inf < 0, inf - inf)     # True True nan
print(nan == nan, math.isnan(nan))            # False True
print(1e308 * 10, 2.0 ** -1075)               # inf 0.0
print(sys.float_info.max, sys.float_info.epsilon)   # 1.7976931348623157e+308 2.220446049250313e-16
print(sorted([3, nan, 1]))                    # [3, nan, 1]   ← nan breaks sorting

import math
print(round(2.5), round(3.5), round(-2.5))       # 2 4 -2   ← banker's rounding
print(round(2.675, 2))                           # 2.67     ← 2.675 is really 2.67499999…
print(round(1234.5678, -2))                      # 1200.0
print(math.floor(-2.5), math.ceil(-2.5), math.trunc(-2.5))   # -3 -2 -2
print(int(2.99), math.floor(2.99))               # 2 2

from decimal import Decimal, ROUND_HALF_UP, getcontext, localcontext
print(Decimal("0.1") + Decimal("0.2"))               # 0.3
print(Decimal(0.1))                                  # 0.1000000000000000055511151231257827021181583404541015625
price = Decimal("19.99")
total = price * 3
print(total, total * Decimal("1.18"))                # 59.97 70.7646
tax = (total * Decimal("0.18")).quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)
print(tax)                                           # 10.79
print(Decimal("2.5").quantize(Decimal("1"), rounding=ROUND_HALF_UP))   # 3
print(getcontext().prec)                             # 28
with localcontext() as ctx:
    ctx.prec = 5
    print(Decimal(1) / Decimal(7))                   # 0.14286

from fractions import Fraction
f = Fraction(1, 3) + Fraction(1, 6)
print(f, f.numerator, f.denominator)            # 1/2 1 2
print(Fraction("0.75"), Fraction(0.1).limit_denominator(100))   # 3/4 1/10
print(float(Fraction(22, 7)))                   # 3.142857142857143

z = 3 + 4j
print(z.real, z.imag, abs(z), z.conjugate())    # 3.0 4.0 5.0 (3-4j)
import cmath
print(cmath.sqrt(-1))                           # 1j

import math
print(math.isqrt(10**20), math.sqrt(2))        # 10000000000 1.4142135623730951
print(math.gcd(12, 18, 30), math.lcm(4, 6))    # 6 12
print(math.comb(52, 5), math.perm(5, 2), math.factorial(10))   # 2598960 20 3628800
print(math.prod(range(1, 6)), math.log2(1024), math.log(8, 2))  # 120 10.0 3.0
print(math.hypot(3, 4), math.dist((1, 1), (4, 5)))   # 5.0 5.0
print(math.degrees(math.pi), round(math.sin(math.pi / 6), 3))   # 180.0 0.5