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Solidity doesn't have fixed-point, floating-point, or double types. What solutions are there to handle the cases where we really have to represent numbers as percentages or fractions?

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Disclaimer: I am the author of PRBMath.

Fixed-Point

  1. PRBMath
    • signed and unsigned denary numbers with 18 decimals of precisions
    • offers advanced math functions (logs, exp, pow, etc.)
    • provides type safety via user defined value types
    • gas efficient, but still user-friendly
    • ergonomic developer experience thanks to using free functions instead of libraries
  2. ABDKMath64x64
    • binary numbers with 2^64 precision
    • offers advanced math functions (logs, exp, pow, etc.)
    • ultra gas efficient (see this praise)
  3. Fixidity
    • denary numbers with arbitrary number of decimals
    • offers advanced math functions (logs, exp, pow, etc.)
    • slower than 64.64, but with a more palatable API
    • used by CementDAO, PoolTogether and Celo
  4. Exponential
    • denary numbers with 18 decimals of precision
    • minimal features, doesn't offer advanced math functions
    • developed by Compound.Finance
  5. DecimalMath
    • denary numbers with 27 decimals of precision
    • minimal features, doesn't offer advanced math functions
    • uses ABIEncoderV2 (experimental in Solidity 0.7 and below)
  6. DSMath
    • denary numbers with 18 (WAD) and 27 decimals of precision (RAY)
    • minimal features, doesn't offer advanced math functions
    • developed by the DappHub team, used by the Maker protocol

Floating-Point

  1. ABDKMathQuad
    • developed by the same company as 64.64
  2. Bankex
    • IEEE-754 octuple precision floating-point

Addenda

  1. There's an open issue in the solidity repo for adding native support for fixed-point types
  2. Mikhail Vladimirov's Math in Solidity blog series is a fantastic resource to learn about how advanced math functions can be implemented in Solidity v0.6 and lower
  3. There are more math libraries mentioned in this OpenZeppelin forum post
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    You forgot the simplest (and most accurate) method: maintain a tuple of numerator and denominator, and in every computation, avoid division for as long as possible (i.e., use it only in order to avoid an overflow).
    – goodvibration
    Commented May 27, 2020 at 20:32
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    That's true, but I'd argue that the simplest approach to fixed-point math in solidity is also the brittlest.
    – Paul Razvan Berg
    Commented May 27, 2020 at 20:39
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    I had to google-translate brittlest, which gave me: having hardness and rigidity but little tensile strength. Now I have to google-translate pretty much every one of the words in that...
    – goodvibration
    Commented May 27, 2020 at 20:52
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    Hah, what I meant is, I wouldn't encourage a simple approach when dealing with fixed-points. There's always something that could go wrong, and I'd rather rely on other more robust contracts (and tests!) that people wrote before me.
    – Paul Razvan Berg
    Commented May 27, 2020 at 20:54

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