Separate DependentCost into LightOperation and HeavyOperation

[xgreenx]

Problem overview

A DependentCost is currently measured by the formula:

$cost(x) = base + \frac{x}{\alpha}$

where:

• $base$ is the minimum cost (y intercept)
• $\alpha$ is units per gas: $\alpha = \frac{U}{g}$. This is the number of units that will fit into 1 gas
• $x$ is the number of units acting as input to the function being measured

This works well when the operation is relatively cheap, and $\alpha$ is a large number: we can fit (process) many units $U$ into a 1 gas. Integer division of $\frac{x}{\alpha}$ will provide sane values.

When the operation is expensive enough that we can fit 1 unit into 1 gas, $\alpha$ is 1. As an operation becomes increasingly expensive, $\alpha$ approaches 0: the number of units $U$ that can fit into 1 gas becomes an increasingly smaller fraction. Because cost is stored as integers, the "resolution" of the function becomes too low: anything more expensive than 1 gas per unit is a fraction $0 < \alpha < 1$ that cannot be accurately represented with integers.

Solution

For expensive operations, we can revaluate the above formula. This formula can also be written as:

$cost(x) = base + \beta * x = \frac{1}{\alpha} * x$

where:

• $base$ is the minimum cost (y intercept)
• $\beta$ is the gas per unit, equivalent to the inverse of the units per gas: $\beta = \frac{1}{\alpha} = \frac{g}{U}$ is the gas per unit.
• $x$ is the number of units acting as input to the function being measured

Instead of representing expensive operations as the number fractional units that can fit into 1 gas, we represent them as the quantity of gas it takes to process a single unit.

To support both cases, we must introduce the concept of light operations (operations that can process many units with 1 gas) and heavy operations (operations that require more than 1 gas to process a single unit).

Implementation details

• Refactor the DependentCost struct into an enum that supports variants LightOperation and HeavyOperation
• LightOperations resolve with the formula for multiple-units-per-gas: $cost(x) = base + \frac{x}{\alpha}$
• HeavyOperations resolve with the formula for multiple-gas-per-unit: $cost(x) = base + \beta * x$
• Update fuel-vm to use new enum for DependentCost
• Update fuel-core to use new enum for DependentCost in GraphQL
• Update benchmarks collection: determine whether an operation is "light" or "heavy" and output the corresponding enum in the output

[xgreenx]

This issue is fixed by #622. We will crate a separate issue to improve our benchmarks to use more mathematical model approach