Excellent.
DAY 6 is where we drop below the language surface and inspect number objects at CPython level.

After today, floating-point bugs, big integers, and numeric interview traps will feel obvious instead of confusing.

🧠 DAY 6 — Integers & Floats (CPython Internal Implementation)

🔑 CORE IDEA OF DAY 6

Python numbers are objects, not CPU primitives.
They trade raw speed for correctness, safety, and flexibility.

1️⃣ Numbers in Python ≠ Numbers in C

In C:

int x = 10;   // fixed-size, CPU register

In Python:

x = 10        # object on heap

This single difference explains:

• Arbitrary precision
• Slower arithmetic
• Memory overhead

2️⃣ Python Integer (int) — Arbitrary Precision

What “arbitrary precision” means

Python integers grow as large as memory allows.

x = 10 ** 1000
print(x)

✔ Works
✔ No overflow
✔ No wraparound

3️⃣ CPython Internals of int

In CPython, integers are implemented as variable-length objects.

Conceptually:

PyLongObject
 ├── ob_refcnt
 ├── ob_type
 ├── ob_size     (number of digits)
 └── ob_digit[]  (array of base 2^30 or 2^15 digits)

Important:

• Python stores numbers in base 2ⁿ, not base 10
• Size grows dynamically

This is why:

10 + 1

is much slower than the same operation in C.

4️⃣ Why Python Can’t Overflow Integers

C:

INT_MAX + 1 → undefined / wrap

Python:

(2**63 - 1) + 1

Python allocates more memory instead of overflowing.

✔ Safety
❌ Performance cost

5️⃣ Integer Caching (Small Integer Optimization)

CPython pre-creates and reuses integers in range:

[-5, 256]

a = 100
b = 100
a is b   # True

But:

a = 1000
b = 1000
a is b   # False

⚠️ This is:

• CPython-specific
• An optimization
• Not guaranteed by language spec

Never rely on it.

6️⃣ Boolean Is a Number (Again, but Deeper)

issubclass(bool, int)  # True

Internally:

True  == 1
False == 0

But:

True is 1    # False

Because:

• Same value
• Different objects

7️⃣ Python Float (float) — IEEE 754

Python floats are C doubles (64-bit IEEE 754).

Structure:

1 bit   → sign
11 bits → exponent
52 bits → mantissa

This means:

• Limited precision
• Binary fractions
• Rounding errors

8️⃣ Why 0.1 + 0.2 != 0.3

0.1 + 0.2 == 0.3   # False

Why?

• 0.1 cannot be represented exactly in binary
• Same for 0.2
• Error accumulates

Actual value:

0.1 + 0.2  → 0.30000000000000004

This is NOT a Python bug.
This is math + hardware reality.

9️⃣ Visualizing Float Precision

🔟 Comparing Floats Correctly (INTERVIEW ESSENTIAL)

Never do:

a == b

Instead:

import math
math.isclose(a, b)

Or:

abs(a - b) < 1e-9

11️⃣ Performance Implications

This matters in:

• Cryptography
• Data engineering
• Algorithm design

12️⃣ Memory Footprint Comparison

import sys

sys.getsizeof(1)       # ~28 bytes
sys.getsizeof(10**20)  # larger

Even 1 is not 1 byte or 4 bytes — it’s an object.

🔥 INTERVIEW TRAPS (DAY 6)

Q1

print(1.0 == 1)

✔ True
(Value comparison after coercion)

Q2

print(True + True + False)

✔ 2

Q3

print(0.1 * 3 == 0.3)

✔ False

Q4

Why is decimal.Decimal slower but safer?

✔ Arbitrary precision
✔ Base-10 math
❌ More overhead

🧠 DAY 6 MENTAL MODEL

Before numeric operations, ask:

1. Is this integer or float?
2. Is precision important?
3. Is performance critical?
4. Can overflow happen?

📝 DAY 6 ASSIGNMENT (DO NOT SKIP)

1️⃣ Predict output (no running):

a = 10**20
b = 10**20
print(a is b)

2️⃣ Explain clearly:

• Why Python integers are slower than C integers
• Why floats cannot represent most decimals exactly

3️⃣ Think like a system designer:

Why would Python choose correctness over speed for numbers?

🔜 DAY 7 PREVIEW

DAY 7 — Strings (Immutability, Interning & Unicode Internals)

You’ll learn:

• Why strings are immutable
• Unicode storage
• String interning
• Why string concatenation can kill performance

When ready, say 👉 “START DAY 7”