Posts: Add AoCO 2025 Day 07 Study Notes - #49
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This PR adds study notes for Day 7 of the Advent of Compiler Optimisations 2025 series, focusing on division by a constant optimization. The content is well-structured with clear mathematical explanations and practical examples.
Issues Found:
- Two typos in the markdown content that need correction
- Inconsistent hexadecimal notation (missing "0x" prefixes in some locations)
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| $$ | ||
| \begin{aligned} | ||
| RHS &= \lfloor \frac{N \cdot M}{2^k} \rfloor \\ | ||
| &= \lfloor \frac{100 \cdot 19999999A}{2^36} \rfloor \\ |
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Add "0x" prefix to hexadecimal value for consistency
| &= \lfloor \frac{100 \cdot 19999999A}{2^36} \rfloor \\ | |
| &= \\lfloor \\frac{100 \\cdot 0x19999999A}{2^36} \\rfloor \\\\ |
| \lfloor \frac{N}{D} \rfloor = \lfloor \frac{N \cdot M}{2^k} \rfloor | ||
| $$ | ||
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| The compiler's goal is to find a fixed-point approxmiation such that : |
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Fix typo: "approxmiation" should be "approximation"
| The compiler's goal is to find a fixed-point approxmiation such that : | |
| The compiler's goal is to find a fixed-point approximation such that : |
| &= \lceil \frac{68719476736}{10} \rceil \\ | ||
| &= \lceil 6871947673.6 \rceil \\ | ||
| &= 6871947674 \\ | ||
| &= 19999999A |
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Add "0x" prefix to hexadecimal value for consistency with line 136 where "0xCCCCCCCD" is used
| &= 19999999A | |
| &= 0x19999999A |
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| ## Example : Division by 10 | ||
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| In this example, we analyze how the compile handles unsigned division by 10. |
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Fix typo: "compile" should be "compiler"
| In this example, we analyze how the compile handles unsigned division by 10. | |
| In this example, we analyze how the compiler handles unsigned division by 10. |
| Similarly the magic number $M$ used by the compiler is `0xCCCCCCCD` | ||
| instead of our calculation result `19999999A`. | ||
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| Since we know $35 < 36$ and $0xCCCCCCCD < 19999999A$, |
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Add "0x" prefix to hexadecimal value for consistent notation in the comparison
| Since we know $35 < 36$ and $0xCCCCCCCD < 19999999A$, | |
| Since we know $35 < 36$ and $0xCCCCCCCD < 0x19999999A$, |
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Code Review
This pull request introduces a new blog post containing study notes on compiler optimizations for division by a constant, specifically focusing on the use of magic numbers and bit shifts. Additionally, it updates the CSS for the Markdown renderer to hide vertical overflow in KaTeX display elements. I have no feedback to provide.
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These notes are based on the post Multiplying our way out of division and the YouTube video [AoCO 7/25] Division by a Constant which are Day 7 of the Advent of Compiler Optimisations 2025 Series by Matt Godbolt.