EL Specifications

##imports

library(plotly)
library(dplyr)

## values for xi and rho
## this is how '<-' assignment works in R

ELASTICITY_MULTIPLIER <- 2
BASE_FEE_MAX_CHANGE_DENOMINATOR <- 8

## Slightly modified function from the spec

calculate_base_fee_per_gas <- function(parent_gas_limit, parent_gas_used, parent_base_fee_per_gas, max_change_denom = BASE_FEE_MAX_CHANGE_DENOMINATOR , elasticity_multiplier = ELASTICITY_MULTIPLIER) {

  #  %/% == // (in python) == floor

  parent_gas_target <- parent_gas_limit %/% elasticity_multiplier
  if (parent_gas_used == parent_gas_target) {
    expected_base_fee_per_gas <- parent_base_fee_per_gas
  } else if (parent_gas_used > parent_gas_target) {
    gas_used_delta <- parent_gas_used - parent_gas_target
    parent_fee_gas_delta <- parent_base_fee_per_gas * gas_used_delta
    target_fee_gas_delta <- parent_fee_gas_delta %/% parent_gas_target
    base_fee_per_gas_delta <- max(target_fee_gas_delta %/% max_change_denom, 1)
    expected_base_fee_per_gas <- parent_base_fee_per_gas + base_fee_per_gas_delta
  } else {
    gas_used_delta <- parent_gas_target - parent_gas_used
    parent_fee_gas_delta <- parent_base_fee_per_gas * gas_used_delta
    target_fee_gas_delta <- parent_fee_gas_delta %/% parent_gas_target
    base_fee_per_gas_delta <- target_fee_gas_delta %/% BASE_FEE_MAX_CHANGE_DENOMINATOR
    expected_base_fee_per_gas <- parent_base_fee_per_gas - base_fee_per_gas_delta
  }
  return(expected_base_fee_per_gas)
}

parent_gas_limit <- 30000  # Fixed for simplification

## lets see the effect on 100 to see the percentage effect this function has on fee
parent_base_fee_per_gas <- 100

## note gas used can not go below the minimum limit of 5k ,
## therefore we can just count from 5k to 30k by ones for complete precision

seq_parent_gas_used <- seq(5000, parent_gas_limit, by = 1) # creates a vector / column

## add the vector / column to the data frame

data <- expand.grid(parent_gas_used = seq_parent_gas_used)

## apply the function we created above and collect it in a new column

dataparent_gas_used, parent_base_fee_per_gas)

fig <- plot_ly(data, x = ~parent_gas_used, y = ~expected_base_fee, type = 'scatter', mode = 'markers')  # scatter plot

## %>% is a pipe operater from dplyr , used extensively in R codebases it's like the pipe | operator used in shell

fig <- fig %>% layout(xaxis = list(title = "Parent Gas Used"),
                      yaxis = list(title = "Expected Base Fee "))

## display the plot
fig

library(forcats)
library(ggplot2)
library(scales)
library(viridis)

## Initial parameters
initial_gas_limit <- 30000000
initial_base_fee <- 100
num_blocks <- 100000

## Sequence of blocks
blocks <- 1:num_blocks

max_natural_number <- 2^256

## Calculate gas limit for each block
gas_limits <- numeric(length = num_blocks)
expected_base_fee <- numeric(length = num_blocks)
gas_limits[1] <- initial_gas_limit
expected_base_fee[1] <- initial_base_fee

for (i in 2:num_blocks) {

   # apply max change to gas_limit at each block
    gas_limits[i] <- gas_limits[i-1] + gas_limits[i-1] %/% 1024

  # Check if the previous expected_base_fee has already reached the threshold
  if (expected_base_fee[i-1] >= max_natural_number) {
    # Once max_natural_number is reached or exceeded, stop increasing expected_base_fee
    expected_base_fee[i] <- expected_base_fee[i-1]
  } else {
    # Calculate expected_base_fee normally until the threshold is reached
    expected_base_fee[i] <- calculate_base_fee_per_gas(gas_limits[i-1], gas_limits[i], expected_base_fee[i-1])
  }
}

## Create data frame for plotting
data <- data.frame(Block = blocks, GasLimit = gas_limits, BaseFee = expected_base_fee)

## Saner labels
label_custom <- function(labels) {
  sapply(labels, function(label) {
    if (is.na(label)) {
      return(NA)
    }
    if (label >= 1e46) {
      paste(format(round(label / 1e46, 2), nsmall = 2), "× 10^46", sep = "")
    } else if (label >= 1e12) {
      paste(format(round(label / 1e12, 2), nsmall = 2), "T", sep = "")  # Trillions
    } else if (label >= 1e9) {
      paste(format(round(label / 1e9, 1), nsmall = 1), "Billion", sep = "")  # Million
    } else if (label >= 1e6) {
      paste(format(round(label / 1e6, 1), nsmall = 1), "Mil", sep = "")  # Million
    } else if (label >= 1e3) {
      paste(format(round(label / 1e3, 1), nsmall = 1), "k", sep = "")  # Thousand
    } else {
      as.character(label)
    }
  })
}

## Bin the ranges we want to observe
data_ranges <- data %>%
  mutate(Range = case_when(
    Block <= 1000 ~ "1-1000",
    Block <= 10000 ~ "1001-10000",
    Block <= 100000 ~ "10001-100000"
  ))

## Rearrange the bins to control where the plots are displayed
data_rangesRange, "1-1000", "1001-10000", "10001-100000")

## Grammar of graphics we can just + the features we want in the plot
plot <- ggplot(data_ranges, aes(x = Block, y = GasLimit, color = BaseFee)) +
  geom_line() +
  facet_wrap(~Range, scales = "free") +  # Using free to allow each facet to have its own x-axis scale
  labs(title = "Gas Limit Over Different Block Ranges",
       x = "Block Number",
       y = "Gas Limit") +
  scale_x_continuous(labels = label_custom) +  # Use custom label function for x-axis
  scale_y_continuous(labels = label_custom) +  # Use custom label function for y-axis
  scale_color_gradientn(colors = viridis(8), trans = "log10",
                        breaks = c(1e3, 1e10, 1e20, 1e40, 1e60, 1e76),
                        labels = c("100", "10^10", "10^20", "10^40", "10^60", "10^76")) +
  theme_bw()

## To view
plot

## Save to file
ggsave("plot_gas_limit.png", plot, width = 7, height = 5)

## we are observing the effects of this parameter
## it's set at 8 but lets see its effect in the range of [2,4, .. ,8, .. ,12]
seq_max_change_denom <- seq(2, 12, by = 2)

parent_gas_limit <- 3 * 10^6
seq_parent_gas_used <- seq(5000, parent_gas_limit, by = 100)

parent_base_fee_per_gas <- 100

data <- expand.grid( parent_gas_used = seq_parent_gas_used, base_fee_max_change_denominator = seq_max_change_denom)

dataparent_gas_used, parent_base_fee_per_gas, data$base_fee_max_change_denominator)

plot <- ggplot(data, aes(x = parent_gas_used, y = expected_base_fee, color = as.factor(base_fee_max_change_denominator))) +
    geom_point() +
    scale_color_brewer(palette = "Spectral") +
    theme_minimal() +
    labs(color = "Base Fee Max Change Denominator") +
    theme_bw()

plot

seq_elasticity_multiplier <- seq(1, 6, by = 1)
seq_max_change_denom <- seq(2, 12, by = 2)

parent_gas_limit <- 3 * 10^6
seq_parent_gas_used <- seq(5000, parent_gas_limit, by = 500)

parent_base_fee_per_gas <- 100

data <- expand.grid( parent_gas_used = seq_parent_gas_used, base_fee_max_change_denominator = seq_max_change_denom, elasticity_multiplier = seq_elasticity_multiplier)

dataparent_gas_used, parent_base_fee_per_gas, dataelasticity_multiplier)

plot <- ggplot(data, aes(x = parent_gas_used, y = expected_base_fee, color = as.factor(base_fee_max_change_denominator))) +
    geom_point() +
    facet_wrap(~elasticity_multiplier) +  #  we break the plots out by the this facet
    scale_color_brewer(palette = "Spectral") +
    theme_minimal() +
    labs(color = "Base Fee Max Change Denominator") +
    theme_bw()

ggsave("rho-xi.png", plot, width = 14, height = 10)

library(ggplot2)
library(tidyr)

## fake exponential or taylor series expansion function
fake_exponential <- function(factor, numerator, denominator) {
    i <- 1
    output <- 0
    numerator_accum <- factor * denominator
    while(numerator_accum > 0){
      output <- output + numerator_accum
      numerator_accum <- (numerator_accum * numerator) %/% (denominator * i)
      i <- i + 1
    }
    output %/% denominator
}

## Blob Gas Target
target_blob_gas_per_block <- 393216

## Blob Gas Max Limit
max_blob_gas_per_block <- 786432

 # Used in header Verificaton
 calc_excess_blob_gas <- function(parent_excess_blob_gas, parent_gas_used) {
   if (parent_gas_used  + parent_excess_blob_gas < target_blob_gas_per_block) {
     return(0)
   } else {
     return(parent_excess_blob_gas + parent_gas_used - target_blob_gas_per_block)
   }
 }

## This is how EL determines the Blob Gas Price
cancun_blob_gas_price <- function(excess_blob_gas) {
  fake_exponential(1, excess_blob_gas, 3338477)
}

## we got from zero to Max each step increasing by 1000
parent_gas_used <- seq(0, max_blob_gas_per_block, by = 1000)
## A column of the same Length
excess_blob_gas <- numeric(length = length(parent_gas_used))
excess_blob_gas[1] <- 0

## We get the T+1(time + 1) excess gas by using values from before
for (i in 2:length(parent_gas_used)) {
  excess_blob_gas[i] <- calc_excess_blob_gas(excess_blob_gas[i - 1],
                                             parent_gas_used[i - 1])
}

data_blob_price <- expand.grid(parent_gas_used = parent_gas_used)
data_blob_price$excess_blob_gas <- excess_blob_gas

## Apply the EL gas price function
data_blob_price$blob_gas_price <- mapply(cancun_blob_gas_price,
                                         data_blob_price$excess_blob_gas)

## Each row represents a block
data_blob_priceparent_gas_used)

## we collapse the 3 columns into 1 Parameter Column
data_long <- pivot_longer(data_blob_price,
                          cols = c(parent_gas_used,
                                   excess_blob_gas,
                                   blob_gas_price),
                          names_to = "Parameter",
                          values_to = "Value")

ggplot(data_long, aes(x = BlockNumber, y = Value)) +
  geom_line() +
  facet_wrap(~ Parameter, scales = "free_y") +   # We break the charts out based on the Parameter Column
  theme_minimal() +
  scale_y_continuous(labels = scales::label_number()) +
  labs(title = "Dynamic Trends in Blob Gas Consumption & Price Over Time",
       x = "Block Number",
       y = "Parameter Value") +
  geom_text(data = subset(data_long, Parameter == "blob_gas_price" &
                            BlockNumber == min(BlockNumber)),
            aes(label = "blobGasPrice = 1", y = 0),
            vjust = -1, hjust = -0.1, size = 3)

normalize <- function(x) {
  return((x - min(x)) / (max(x) - min(x)))
}

data_blob_priceparent_gas_used)
data_blob_priceexcess_blob_gas)
data_blob_priceblob_gas_price)

ggplot(data_blob_price, aes(x = BlockNumber)) +
  geom_line(aes(y = parent_gas_used_normalized, color = "Parent Gas Used")) +
  geom_line(aes(y = excess_blob_gas_normalized, color = "Excess Blob Gas")) +
  geom_line(aes(y = blob_gas_price_normalized, color = "Blob Gas Price")) +
  theme_minimal() +
  labs(title = "Normalized Trends Over Blocks", x = "Block Number", y = "Normalized Value", color = "Parameter")

#!/bin/bash

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