Numeric Data Types

Hello friend! What is the value scope of int8, int16, int32, int64 data types respectively?

 

ChatGPT said:

Hello my friend! 😃
Let’s break it down. These int8, int16, int32, and int64 are signed integers, meaning they can represent both negative and positive numbers.

The value range is determined by the formula:

where n is the number of bits.

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Value Scopes:

• int8 (8-bit signed integer)
  Range: −128 to 127

• int16 (16-bit signed integer)
  Range: −32,768 to 32,767

• int32 (32-bit signed integer)
  Range: −2,147,483,648 to 2,147,483,647

• int64 (64-bit signed integer)
  Range: −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807

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👉 If you meant unsigned integers (uint8, uint16, etc.), the ranges would instead be from 0 to 2^n − 1.

Do you want me to also list the unsigned ranges for completeness?

 

You said:

What's the difference between float, double and decimal data types?

 

ChatGPT said:

Great question! 🚀 These three—float, double, and decimal—are all used to represent numbers with fractional parts, but they differ in precision, storage size, and use cases. Let’s break it down:

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🔹 1. Float

• Precision: ~7 decimal digits

• Size: Usually 32 bits (4 bytes)

• Storage: IEEE 754 single-precision floating point

• Range: Approximately ±1.5 × 10^−45 to ±3.4 × 10^38

• Use Case: Scientific calculations, graphics, situations where performance matters more than extreme precision.

• ⚠️ Issue: Rounding errors can happen (not exact for decimal fractions).

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🔹 2. Double

• Precision: ~15–16 decimal digits

• Size: Usually 64 bits (8 bytes)

• Storage: IEEE 754 double-precision floating point

• Range: Approximately ±5.0 × 10^−324 to ±1.7 × 10^308

• Use Case: Default for most scientific and engineering calculations where higher precision is needed.

• ⚠️ Still has rounding issues, though much smaller than float.

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🔹 3. Decimal

• Precision: Up to 28–29 significant decimal digits

• Size: Usually 128 bits (16 bytes)

• Storage: Base-10 representation (not binary floating point)

• Range: ±1.0 × 10^−28 to ±7.9 × 10^28 (much smaller range than float/double)

• Use Case: Financial, monetary, or accounting calculations where exact decimal representation is critical (e.g., currency).

• ✅ Advantage: No binary rounding issues (e.g., 0.1 + 0.2 = 0.3 exactly).

• ❌ Slower performance and larger memory use compared to float/double.

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⚖️ Quick Comparison Table

Type	Size	Precision (digits)	Range (approx)	Best For
float	4 bytes	~7	±10^−45 → ±10^38	Fast, scientific/graphics
double	8 bytes	~15–16	±10^−324 → ±10^308	General-purpose high precision
decimal	16 bytes	28–29	±10^−28 → ±10^28	Money, finance, exact decimals

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👉 Rule of thumb:

• Use float/double for scientific/engineering.

• Use decimal for financial/money values.

Would you like me to also show you examples in C# or Python to illustrate how they differ in practice (e.g., 0.1 + 0.2 issue)?

 

You said:

Yes, Python please.

 

ChatGPT said:

Perfect 👍 Let’s test this in Python.

Python’s built-in float is actually a double-precision (64-bit) floating point.
For decimal you can use the decimal module.

Here’s a demo:

 

from decimal import Decimal, getcontext

# set decimal precision high enough
getcontext().prec = 30

# Float (binary floating point)
a = 0.1 + 0.2
print("float 0.1 + 0.2 =", a)        # Not exactly 0.3
print("float equals 0.3 ?", a == 0.3)

# Decimal (exact decimal arithmetic)
b = Decimal("0.1") + Decimal("0.2")
print("decimal 0.1 + 0.2 =", b)      # Exactly 0.3
print("decimal equals 0.3 ?", b == Decimal("0.3"))

 




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🔎 Output:

 

float 0.1 + 0.2 = 0.30000000000000004
float equals 0.3 ? False

decimal 0.1 + 0.2 = 0.3
decimal equals 0.3 ? True

 




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✅ Why this happens:

• float (and double) store numbers in binary fractions, so 0.1 and 0.2 can’t be represented exactly.

• Decimal stores numbers as base-10 fractions, so 0.1 is exact.

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Do you also want me to show how numpy.float32 (float) differs from Python’s built-in float (double) in precision?

 

You said:

Yes, I do.

 

ChatGPT said:

Great! 😃 Let’s dive into numpy.float32 vs Python float (which is float64).

Python’s built-in float is a C double (64-bit).
NumPy gives you float32 (single precision, ~7 digits) and float64 (double precision, ~15–16 digits).

Here’s a demo:

 

import numpy as np

# Float32 (single precision)
a32 = np.float32(0.1) + np.float32(0.2)
print("np.float32 0.1 + 0.2 =", a32)
print("Equals 0.3 ?", a32 == np.float32(0.3))

# Float64 (double precision) - same as Python float
a64 = np.float64(0.1) + np.float64(0.2)
print("np.float64 0.1 + 0.2 =", a64)
print("Equals 0.3 ?", a64 == np.float64(0.3))

# Python built-in float
py_float = 0.1 + 0.2
print("Python float 0.1 + 0.2 =", py_float)
print("Equals 0.3 ?", py_float == 0.3)

 

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🔎 Typical Output:

 

np.float32 0.1 + 0.2 = 0.30000001
Equals 0.3 ? False

np.float64 0.1 + 0.2 = 0.30000000000000004
Equals 0.3 ? False

Python float 0.1 + 0.2 = 0.30000000000000004
Equals 0.3 ? False

 

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✅ Key takeaways:

• np.float32 is less precise → you see 0.30000001.

• np.float64 and Python float are the same (double precision) → 0.30000000000000004.

• Both have binary rounding issues, but float32 is worse because it only keeps ~7 significant digits.

 

 

What's the tata type of numpy.nan?

 

ChatGPT said:

Good question 👍

In NumPy, numpy.nan is a special constant representing “Not a Number” (like IEEE 754 NaN).

🔎 Its data type:

 

import numpy as np

print(type(np.nan))        # Python type
print(np.nan.dtype)        # NumPy dtype (will raise error!)

 

Output:

<class 'float'>
AttributeError: 'float' object has no attribute 'dtype'

 

👉 So np.nan is actually a Python float (specifically, a float('nan')).
That means it has the type:

• Python type: <class 'float'>

• NumPy dtype (when inside arrays): depends on the array’s dtype (e.g., float32, float64).

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Example with arrays:

arr64 = np.array([1.0, np.nan], dtype=np.float64)
print(arr64.dtype)    # float64

arr32 = np.array([1.0, np.nan], dtype=np.float32)
print(arr32.dtype)    # float32

 

✅ So:

• np.nan itself is a Python float (64-bit).

• Inside NumPy arrays, it adapts to the array’s dtype (e.g., float32 nan, float64 nan).

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Would you like me to also explain how np.nan differs from None in NumPy?

 

You said:

Yes, I would.

 

ChatGPT said:

Awesome 👍 Let’s carefully compare np.nan vs None in NumPy, because they behave very differently.

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🔹 1. np.nan

• Meaning: “Not a Number” (IEEE 754 NaN).

• Type: A Python float (<class 'float'>).

• NumPy behavior: Can only live in floating-point dtypes (float32, float64).

• Math operations: Still allowed, but results propagate NaNs.

import numpy as np

x = np.array([1.0, np.nan, 3.0])
print(x.dtype)           # float64
print(np.mean(x))        # nan (NaN propagates)

print(np.isnan(np.nan))  # True

 

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🔹 2. None

• Meaning: Python’s null object (absence of value).

• Type: <class 'NoneType'>.

• NumPy behavior: If you put None in a NumPy array:

  • If all elements are numeric → NumPy upcasts to object dtype.

  • It cannot live in pure numeric dtypes.

y = np.array([1.0, None, 3.0])
print(y.dtype)    # object
print(y)          # [1.0 None 3.0]

 

• Math operations: Fail, because None is not numeric.

print(np.mean(y))   # TypeError: unsupported operand type(s) for +: 'float' and 'NoneType'

 

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🔎 Key Differences

Feature	np.nan	None
Python type	float	NoneType
NumPy dtype	float32/float64	Forces array to object
Math ops	Work but yield nan	Not supported (errors)
Use case	Missing/invalid numeric	General “no value” placeholder

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👉 Rule of thumb:

• Use np.nan for missing numeric data.

• Use None only when working with object arrays or non-numeric data.

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Do you want me to also cover how np.nan interacts with pd.NA and pd.NaT in pandas (since missing values get more nuanced there)?

 

You said:

Yes, I do.

 

ChatGPT said:

Perfect — this is where things get interesting because pandas extends NumPy’s ideas of “missing values.” Let’s break down np.nan, pd.NA, and pd.NaT. 🚀

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🔹 1. np.nan

• From NumPy, a float('nan').

• Type: <class 'float'>.

• Pandas behavior: Used historically to represent missing values in numeric columns.

• Still common, but has quirks:

  • np.nan == np.nan is always False.

  • isna() detects it.

import numpy as np
import pandas as pd

s = pd.Series([1, np.nan, 3])
print(s)
print(s.isna())       # Detects np.nan as missing

 

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🔹 2. pd.NA

• Introduced in pandas 1.0+ as a generic missing value marker.

• Type: <class 'pandas._libs.missing.NAType'>.

• Works across numeric, boolean, string, categorical dtypes (with new “nullable” dtypes like Int64, boolean, string).

• Unlike np.nan, comparisons return pd.NA instead of False (propagates missingness).

s = pd.Series([1, pd.NA, 3], dtype="Int64")
print(s)
print(s.isna())     # Detects pd.NA

print(pd.NA == pd.NA)   # Returns pd.NA (not True/False)

 

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🔹 3. pd.NaT

• Special case of NaT = Not a Time.

• For datetime and timedelta dtypes.

• Type: <class 'pandas._libs.tslibs.nattype.NaTType'>.

s = pd.Series([pd.Timestamp("2023-01-01"), pd.NaT])
print(s)
print(s.isna())     # Detects NaT

 

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🔎 Summary Table

Value	Library	Type	Use case	Comparison behavior
np.nan	NumPy	float	Missing numeric values (legacy in pandas)	np.nan == np.nan → False
pd.NA	pandas	NAType	General missing marker for new dtypes	pd.NA == pd.NA → pd.NA
pd.NaT	pandas	NaTType	Missing datetime/timedelta values	pd.NaT == pd.NaT → False

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👉 Rule of thumb in pandas:

• Use pd.NA for new code (especially with nullable dtypes).

• Use pd.NaT for datetime-like data.

• np.nan is still common in older code and when working directly with NumPy.