Posts: Add AoCO 2025 Day 09 Study Notes

[gapry]

These notes are based on the post Induction variables and loops and the YouTube video [AoCO 9/25] More Loops: Induction Variables which are Day 9 of the Advent of Compiler Optimisations 2025 Series by Matt Godbolt.

[amazon-q-developer]

This PR adds educational content documenting compiler optimization techniques for induction variables. The content is well-structured with clear code examples and assembly analysis. No blocking issues identified - the documentation is ready for merge.

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[gemini-code-assist]

Code Review

This pull request adds study notes on induction variable elimination, featuring C code examples and their corresponding x86 assembly to demonstrate compiler optimizations. The reviewer suggested fixing a Markdown formatting issue that breaks paragraph flow, addressing potential null pointer dereferences in the C code snippets by validating the loop bound before array access, and improving the consistency of the assembly output formatting to facilitate clearer comparison between the two implementations.

[gemini-code-assist]

The sentence explaining the equivalence between the closed-form expression and the recursive definition is split by an empty line. In Markdown, this will cause the text to be rendered as two separate paragraphs, which breaks the logical flow of the introduction.

Suggested change

	The closed-form expression $a_n = a_1 + (n - 1) d$ is mathematically equivalent to the
	recursive definition $a_{n + 1} = a_{n} + d$
	The closed-form expression $a_n = a_1 + (n - 1) d$ is mathematically equivalent to the recursive definition $a_{n + 1} = a_{n} + d$.

[gemini-code-assist]

The code accesses a[0] before checking if n > 0. If n is 0 and a is a NULL pointer or an empty array, this will cause a crash (as seen in the assembly where the movl happens before the testl). It is safer to check the loop bound before accessing the array.

Suggested change

	void sum(int* a, int n, int d) {
	int cache = a[0];
	for (int i = 0; i < n; ++i) {
	void sum(int* a, int n, int d) {
	if (n <= 0) return;
	int cache = a[0];
	for (int i = 0; i < n; ++i) {

[gemini-code-assist]

Similar to Part 01, the code accesses a[0] before checking the loop bound n. Moving the initialization inside a safety check prevents potential null pointer dereferences or out-of-bounds reads when n <= 0.

Suggested change

	void sum(int* a, int n, int d) {
	int cache = a[0];
	for (int i = 0; i < n; ++i) {
	void sum(int* a, int n, int d) {
	if (n <= 0) return;
	int cache = a[0];
	for (int i = 0; i < n; ++i) {

[gemini-code-assist]

The disassembly output for Part 02 includes tool-specific headers and different formatting for jump targets (e.g., <sum+0x18>) compared to Part 01. Since the core argument is that the compiler produces identical code for both implementations, providing consistent output (removing headers and ensuring identical formatting) would make the comparison clearer for the reader.