Float types (float16, float32, float64) in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of NumPy float type conversion

What is the output of this code snippet that converts a float64 array to float16 and sums it?

NumPy

import numpy as np
arr = np.array([1.123456789, 2.987654321], dtype=np.float64)
arr16 = arr.astype(np.float16)
sum_val = arr16.sum()
print(sum_val)

A 4.11112

B 4.11111

C 4.111114

D 4.11

💡 Hint

Remember that float16 has limited precision and rounds values.

The float16 type rounds the values to fewer decimal places, so the sum is approximately 4.11, not the more precise float64 sum.

❓ data_output

intermediate

Size in bytes of different float types

What are the sizes in bytes of numpy float16, float32, and float64 types?

NumPy

import numpy as np
sizes = (np.dtype(np.float16).itemsize, np.dtype(np.float32).itemsize, np.dtype(np.float64).itemsize)
print(sizes)

A (2, 4, 8)

B (1, 4, 8)

C (2, 8, 16)

D (4, 8, 16)

💡 Hint

Check the number of bytes each float type uses in NumPy.

float16 uses 2 bytes, float32 uses 4 bytes, and float64 uses 8 bytes.

🔧 Debug

advanced

Why does this float32 array sum differ from float64?

Given this code, why does the sum of the float32 array differ from the float64 array sum?

NumPy

import numpy as np
arr64 = np.array([0.1]*1000000, dtype=np.float64)
arr32 = arr64.astype(np.float32)
sum64 = arr64.sum()
sum32 = arr32.sum()
print(sum64, sum32)

A float32 arrays convert values to integers before summing

B float64 arrays are slower so sum is inaccurate

C float32 has less precision causing rounding errors in sum

D float64 arrays use less memory causing overflow

💡 Hint

Think about precision differences between float32 and float64.

float32 has fewer bits for precision, so summing many small values accumulates rounding errors, unlike float64.

🧠 Conceptual

advanced

Choosing float types for large datasets

Which is the best reason to choose float16 over float64 for a large dataset?

A To ensure compatibility with all Python libraries

B To reduce memory usage while accepting lower precision

C To speed up calculations by using 64-bit floats

D To increase precision for scientific calculations

💡 Hint

Think about memory and precision trade-offs.

float16 uses less memory but has lower precision, useful when memory is limited and precision is less critical.

🚀 Application

expert

Detecting precision loss when converting float64 to float32

Which code snippet correctly detects if converting a float64 numpy array to float32 causes any value to change beyond 1e-6 difference?

A

import numpy as np
arr64 = np.array([1.000001, 2.000001], dtype=np.float64)
arr32 = arr64.astype(np.float32)
diff = np.abs(arr64 - arr32)
print(np.any(diff > 1e-6))

B

import numpy as np
arr64 = np.array([1.000001, 2.000001], dtype=np.float64)
arr32 = arr64.astype(np.float32)
diff = np.abs(arr64 - arr32)
print(np.all(diff < 1e-6))

C

import numpy as np
arr64 = np.array([1.000001, 2.000001], dtype=np.float64)
arr32 = arr64.astype(np.float32)
diff = arr64 + arr32
print(np.any(diff > 1e-6))

D

import numpy as np
arr64 = np.array([1.000001, 2.000001], dtype=np.float64)
arr32 = arr64.astype(np.float32)
diff = arr64 - arr32
print(np.all(diff < 1e-6))

💡 Hint

Use absolute difference and check if any value exceeds the threshold.

Option A correctly computes absolute differences and checks if any difference is greater than 1e-6, indicating precision loss.