1.11 · Testing & Debugging

Goal: know the numerical and structural errors the syllabus mentions, and the debugging tools.

Numerical errors (named by the syllabus)

Error	Cause	Example
Rounding	Limited decimal precision	0.1 + 0.2 != 0.3
Truncation	Cutting off extra digits	int(3.9) → 3
Overflow	Result exceeds max representable	Int32 max + 1 wraps
Underflow	Result smaller than min representable	Tiny float becomes 0

Mitigation:

• Use Decimal for money to avoid float rounding.
• Use 64-bit ints (Python's int is arbitrary precision).
• Apply round() deliberately.

Other errors (recap)

Type	When
Syntax	Compile / interpret time
Logical	Runs but wrong output
Run-time	Crash during execution

Debugging tools

Tool	What it does
Stubs	Empty placeholder functions used during top-down development
Flags	Boolean state variables that toggle behaviour
Break points	IDE debugger pauses at a chosen line so you can inspect state
Program trace	Print statements / loggers to show variable values
Test data sets	Normal / boundary / erroneous

A debugging walkthrough

Suppose a function should return the average but returns 0.

1. Reproduce with a small input.
2. Add print(s) at key spots:

   def average(nums):
       print("DEBUG nums:", nums)
       total = sum(nums)
       print("DEBUG total:", total)
       return total / len(nums)

3. Hypothesise — divide by zero? wrong total?
4. Fix and remove debug prints.

Common student mistakes

• Catching exceptions to hide bugs.
• Changing many things at once.
• Forgetting boundary tests.
• Trusting "it worked on my machine".

Exam-style question

Q (5 marks): Identify the type of error and propose a debugging technique for each: (a) Program prints 0 instead of the average. (b) Python raises IndexError: list index out of range. (c) Program won't start: "SyntaxError: invalid syntax". (d) Result is 0.30000000000000004 instead of 0.3.

Sample answer:

(a) Logical error. Use trace tables or print debugging to inspect intermediate values; likely culprits: dividing before accumulating, off-by-one in loop bounds.

(b) Run-time error. Add a breakpoint at the indexing line, inspect the list length vs the index; add a guard like if i < len(arr).

(c) Syntax error. Read the line number in the error message; check for unmatched brackets, missing colons, bad indentation.

(d) Numerical rounding error caused by binary floating-point. Use round(x, 1) for display, or switch to Decimal for precise arithmetic.

Key takeaways

• Numerical errors: rounding, truncation, overflow, underflow.
• Debugging tools: stubs, flags, breakpoints, traces, test data.
• Fix systematically.

Chapter 1 wrap-up

You've finished the meat of 2C. Self-test:

• Can you implement linear & binary search?
• Can you implement bubble, insertion, selection sorts?
• Can you build a stack, queue and linked list in Python?
• Can you debug systematically?

➡️ Next chapter: 2 · Programming in Real Life