Complex numbers

[PaulRBerg]

Todo

• Basic arithmetic: addition, subtraction, multiplication and division.
  • Note: the multiplication and division functions should both my mulDivSigned function to prevent intermediary overflows. Also, let me know if a mulDivSigned18 function would be useful here.
• Complex conjugate function.
• Complex modulus function (also called complex norm).
• Test the functions you wrote with PRBTest. To generate the expected values, use WolframAlpha and then hardcode them in the tests. Try to be explicit and name the expected values though.
  • Tip: you should read the Foundry Book if you haven’t yet, especially the Writing Tests section.
  • Tip 2: take a look at how I wrote the tests in PRBTest.

Open-ended Questions

1. How do we handle i?
2. How much code can we reuse from SD59x18?
3. Are there any functions which cannot be implemented gas efficiently?

Code Snippets

Enum

enum I {
    ExistPositive,
    ExistNegative,
    NotExist
}

Complex Type

struct C59x18 {
    SD59X18 a;
    SD59x18 b;
}