What are computers good for? Spoiler: it's not (precise) computing

Files from the Unseminar on precise computing on 2025/03/12

• Python test cases
• Julia example: pi approximation (Pluto Notebook)
• R example: banker's rounding (Jupyter Notebook)
• Recommendations (python Jupyter Notebook)

Test cases (python)

1. 10.0 * 0.1 == 1.0
2. 0.1 * 0.1 == 0.01
3. 0.5 * 0.5 == 0.25
4. 0.1 + 0.1 == 0.2
5. 0.1 + 0.1 + 0.1 == 0.3
6. 0.1 + 0.1 + 0.1 + 0.1 == 0.4
7. (0.1 + 0.1) + 1 == 0.1 + (0.1 + 1)
8. 1_00000_00000_00000_00000 + 1 > 1_00000_00000_00000_00000
9. 1e20 + 1 > 1e20
10. 1e20 + 1000 > 1e20
11. 0.1**25 > 0
12. 0.1**5**5 > 0
13. np.all(a>0)
14. np.sum(a) > 0

For 13 and 14:

import numpy as np
large_number = 2**63-1
a = np.array([large_number, large_number])

Further reading

• How Integers and Floats Work by Julia Evans
• Float Exposed
• Integer Exposed
• Python Documentation on Float Issues
• What Every Computer Scientist Should Know About Floating-Point Arithmetic