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-# Polariscope
+# Polariscope 🔬
 
-Polariscope is a Ruby gem designed to evaluate the overall health of your Ruby application by analyzing its dependencies. It calculates a health score based on how many dependencies are outdated, meaning there are newer versions available. Keeping dependencies up-to-date is crucial for maintaining application security, performance, and compatibility. This gem provides a quick and easy way to gauge the state of your project's dependencies and take proactive measures to improve its health.
+Polariscope is a Ruby gem to evaluate the overall health of your Ruby application by analyzing its dependencies. It calculates a [health score](#health-score-formula) based on which dependencies are outdated and vulnerable to security issues.
 
-### Health Score Algorithm
+Keeping dependencies up-to-date is crucial for maintaining application security, performance, and compatibility. This gem provides a quick and easy way to gauge the state of your project's dependencies and take measures to improve its health.
 
-The health score calculation is based on the following mathematical formula:
-
-![Health Score Algorithm](docs/algorithm.png)
+Think of it as a way to score outputs of `bundle outdated` and `bundle-audit check`.
 
 ## Installation
 
-Install the gem and add to the application's Gemfile by executing:
+Add it to your Gemfile:
 
     $ bundle add polariscope
 
-If bundler is not being used to manage dependencies, install the gem by executing:
+or install standalone:
 
     $ gem install polariscope
 
-### Known issue
-
-If your default Ruby version is 3.1.2, you might get this error when installing polariscope:
-
-```bash
-.rbenv/versions/3.1.2/lib/ruby/gems/3.1.0/gems/rdoc-6.7.0/lib/rdoc/version.rb:8: warning: already initialized constant RDoc::VERSION
-ERROR:  While executing gem ... (NameError)
-    uninitialized constant RDoc::Markdown
+## Usage
 
-    'markdown' => RDoc::Markdown,
-                      ^^^^^^^^^^
-```
+Polariscope can be used on the CLI and in code.
 
-You can ignore this error. It doesn't occur in other Ruby versions and it doesn't prevent you from using polariscope.
+### CLI
 
-## Usage
+Position yourself at the root of your Ruby application and run:
 
-Polariscope can be used in 2 ways.
+    $ [bundle exec] polariscope scan
 
-### CLI
+The command will read the contents of `Gemfile`, `Gemfile.lock` and [`.bundler-audit.yml`](https://github.com/rubysec/bundler-audit?tab=readme-ov-file#configuration-file) (optional, to ignore advisories) in the current directory and output the health score.
 
-Position yourself in a Ruby application and run:
+### In code
 
-```bash
-polariscope scan
+```ruby
+health_score = Polariscope.scan
 ```
 
-### IRB / Rails
+Without arguments, it will do the same as above. Optionally, you can override various parameters:
 
 ```ruby
-Polariscope.scan
+Polariscope.scan(
+  gemfile_content: '', # e.g. File.read('Gemfile')
+  gemfile_lock_content: '', # e.g. File.read('Gemfile.lock')
+  bundler_audit_config_content: '', # e.g. File.read('.bundler-audit.yml')
+  spec_type: :latest, # see https://docs.ruby-lang.org/en/master/Gem/SpecFetcher.html#method-i-available_specs
+  dependency_priorities: { ruby: 5.0, devise: 10.0 }, # hash of dependency priorities
+  group_priorities: { default: 5.0, test: 2.0 }, # hash of bundler group priorities
+  default_dependency_priority: 2.0,
+  advisory_severity: 1.09, # number >= 1
+  advisory_penalties: { medium: 2.0, critical: 5.0 }, # hash of advisory penalties by criticality
+  fallback_advisory_penalty: 2.0, # used if value not found in previous hash
+  major_version_penalty: 0.5, # number in range [0, 1]
+  new_versions_severity: 1.09, # number >= 1
+  segment_severities: [1.7, 1.15, 1.01], # ordered by segments: [major, minor, patch]
+  fallback_segment_severity: 1.01, # in case dependency versions have more segments than in segment_severities
+)
 ```
 
-The return value will indicate how healthy your project is on a scale from 0 to 100.
+For details on what these parameters mean, consult [this section](#health-score-formula).
 
 #### Additional features
 
-##### Gem versions
-
 Get the released or latest version of gems with:
 
 ```ruby
 # released versions
-gem_specs = Polariscope.gem_versions(['gem_name_1', 'gem_name_2'])
-gem_specs.versions_for('gem_name_1') # => returns potentially many versions
+gem_specs = Polariscope.gem_versions(['devise', 'pundit'])
+gem_specs.versions_for('devise')
+# => returns potentially many versions
 
 # latest version
-gem_specs = Polariscope.gem_versions(['gem_name_1', 'gem_name_2'], spec_type: :latest)
-gem_specs.versions_for('gem_name_1') # => returns latest version
+gem_specs = Polariscope.gem_versions(['devise', 'punt'], spec_type: :latest)
+gem_specs.versions_for('pundit')
+# => returns only the latest version
+```
+
+## Health Score Formula
+
+The formula takes the contents of `Gemfile` and `Gemfile.lock` and produces a decimal number in range $[0,100]$ representing the health score based on which dependencies (gems and Ruby) are outdated and vulnerable to known security issues. $100$ means everything is up-to-date and there are no security issues, and it lowers as newer versions are released or security issues are discovered.
+
+By design, health score is most useful as a relative measure of application health: if your health score suddenly drops one day from 100 to 90, it signals a serious issue (e.g. a new vulnerability in your Ruby version). If it drops from 100 to 95, it may signal that a new minor version of Rails has been released, for example. If it drops from 100 to 99.5, it may mean a gem like Pundit has a new patch version with a bug fix.
+
+How much the score changes depends on various factors:
+- dependency priority (by default, [Ruby and Rails have a higher priority](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L6) than other dependencies)
+- [bundler group](https://bundler.io/guides/groups.html) priority (by default, [`:default` and `:production` groups have a higher priority](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L7))
+- number of new versions between the current and the latest version of a dependency
+- the kind of outdatedness according to [SemVer](https://semver.org/); if there's a new major version, that will cause a sharper drop in the score than a new minor version
+- the number of active security advisories
+- [advisory severity](https://nvd.nist.gov/vuln-metrics/cvss) (e.g. a High severity advisory will cause a sharper drop in score than one that is Low)
+
+### Formula
+
+[This is the complete formula](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gemfile_health_score.rb#L22) (it's simpler than it may seem):
+```math
+\mathrm{HS} =
+100
+\cdot
+\underbrace{\left(1-\frac{\sum_{d \in G_{dd}}w_d \cdot mp_d}{\sum_{d \in G_{dd}}w_d}\right)}_{\text{major versions score}}
+\cdot
+\underbrace{\left(\frac{\sum_{d \in G_{dd}}w_d \cdot {dhs}_d}{\sum_{d \in G_{dd}}w_d}\right)}_{\text{versions score}}
+\cdot
+\underbrace{\left(1 +\sum_{d \in G} \sum_{a \in d} p_a\right)^{-\ln{S_A}}}_{\text{advisories score}}
+```
+
+```math
+\begin{array}{ll}
+G & \text{Gemfile} \\
+G_{dd} & \text{subset of Gemfile with direct dependencies only} \\
+d & \text{dependency} \\
+\dotso & \text{see below for other symbols}
+\end{array}
+```
+
+It's comprised of several scores in range $[0,1]$ multiplied together and then finally by $100$ to produce the health score in range $[0,100]$. Score formulas are described in the following sections.
+
+Note that, by design, health score can never be higher than the lowest of its scores. For example, if your major versions score is $0.75$, then health score can never be higher than $75$, regardless of other scores being $1$.
+
+### Major versions score
+
+Score which signals how many dependencies have outdated major versions (it doesn't care about minor or patch versions). $1$ means no dependency has an outdated major, $0$ means all have an outdated major. All other combinations fall in between those extremes.
+
+[The formula](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gemfile_health_score.rb#L30-L36) $1-\frac{\sum_{d \in G_{dd}}w_d \cdot mp_d}{\sum_{d \in G_{dd}}w_d}$ starts with score $1$ and is subtracted by the [weighted arithmetic mean](https://en.wikipedia.org/wiki/Weighted_arithmetic_mean) of major version penalties for all direct dependencies (only dependencies specified in the `Gemfile` and not dependencies of dependencies present in `Gemfile.lock`).
+
+[Dependency priority (weight)](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L40-L44) $w_d$ is either a custom dependency priority, bundler group priority if dependency doesn't have a custom priority, or default priority if dependency's group doesn't have a defined priority ([default value](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L6-L8)).
+
+[Major version penalty](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L21-L23) ${mp}_d$ equals $1$ ([by default](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L20)) when major of $d$ is outdated, otherwise $0$.
+
+### Versions score
+
+Score which represents how outdated direct dependencies are based on the number of new versions and the kind of outdatedness. Score $1$ means all dependencies are up-to-date. As dependencies get outdated, it starts to lower. Unlike major versions score, this score can never reach $0$, it only gravitates towards it.
+
+[The formula](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gemfile_health_score.rb#L38-L40) $`\frac{\sum_{d \in G_{dd}}w_d \cdot {dhs}_d}{\sum_{d \in G_{dd}}w_d}`$ is a weighted arithmetic mean of dependency health scores. Same dependency priority $w_d$ is used as for major versions score.
+
+[Dependency health score](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L15-L18) ${dhs}_d$ is calculated with the following formula:
+```math
+{dhs}_d=
+\underbrace{(1+{sp}_d)^{-\ln{{ss}_d}}}_{\text{segment subscore}}
+\cdot
+\underbrace{(1+{vp}_d)^{-\ln{S_{V}}}}_{\text{versions subscore}}
 ```
 
+#### Segment subscore
+
+[Score](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L16) in range $(0,1]$ which represents how outdated is the **first** outdated segment (major, minor or patch) of a dependency.
+
+[Segment penalty](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L43-L45) ${sp}_d$ is defined as the number of new versions for the first outdated segment. Take this example: your dependency is on `v1.0.0`, but `v1.1.0`, `v2.0.0` and `v3.0.0` have been released in the meantime. The first outdated segment is major (minor is also outdated, but it comes after major, so it's not the first). ${sp}_d$ is then the number of new majors, in this case $2$.
+
+[Segment severity](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L35-L37) ${ss}_d$ is a number selected based on the first outdated segment. Default list of severities can be found [here](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L22) (ordered major, minor, patch). For example, if major is outdated, first value is used.
+
+#### Versions subscore
+
+[Score](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/gem_health_score.rb#L17) in range $(0,1]$ which represents how many new versions have been released for the dependency since the current version. Penalty $`{vp}_d`$ is defined as the total number of versions between the current and the latest version (inclusive). Severity $`S_{V}`$ is a constant ([default value](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L21)).
+
+(For more context on the function used for both subscores, see [this section](#penalty-and-severity-function).)
+
+### Advisories score
+
+Score which represents how many security advisories impact your dependencies. Unlike previous scores, this score takes into account all dependencies, direct or indirect (basically, everything in `Gemfile.lock`). Score $1$ means no dependency has an active advisory, and it starts gravitating towards $0$ when new advisories are found.
+
+[The formula](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/advisories_health_score.rb#L12) $\left(1 +\sum_{d \in G} \sum_{a \in d} p_a\right)^{-\ln{S_A}}$ in essence sums advisory penalties $p_a$ for all advisories of all dependencies, adds $1$, and raises it to a power. See the next section for a detailed explanation.
+
+[Advisory penalty](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L46-L48) $p_a$ is a number selected based on the criticality of the advisory ([default mapping](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L11-L17)). If criticality is unknown, fallback penalty is used ([default value](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L18)). Severity $S_A$ is a constant ([default value](https://github.com/infinum/polariscope/blob/master/lib/polariscope/scanner/calculation_context.rb#L10)).
+
+### Penalty and severity function
+
+Function used for several scores is of type $f(x)=(1+x)^{-S}$, where $S$ is some positive constant.$`^*`$
+
+See this graph for various values $S$ (we'll focus on case $x\ge0$):
+![graph plots f(x) for three values of S: 0.05, 0.17, 0.5](./docs/severity_function_graph.png)
+and notice several interesting properties:
+1. $f(0)=1$
+2. $f(x+1) \lt f(x)$
+3. $\lim_{x \to \infty} f(x)=0$
+4. bigger $S$ -> more severe "drop"
+
+Function returns values in range $(0,1]$ (properties 1, 2, 3). It starts from value $1$ (prop 1) which drops the further away we move (prop 2). Property 4 allows us to control how quickly the value drops with a higher $x$.
+
+This can be used a simple but an okay way to model certain scores. For scoring purposes we will refer to $x$ as penalty and $S$ as severity. Take for example the [versions subscore](#versions-subscore), which uses this function: penalty is the number of new versions for a dependency, so the more new versions there are, the lower the score.
+
+$^*$ In all formulas, severity is a natural logarithm $ln$ of some constant greater than $1$. This is purely because actual constants $S$ need to be small enough (smaller than $0.1$) to not cause too sharp a drop in the score too fast. It's easier to work with bigger numbers, so instead of $(1+x)^{-S}$ we work with $(1+x)^{-\ln(S)}$.
+
 ## Development
 
 After checking out the repo, run `bin/setup` to install dependencies. Then, run `rake spec` to run the tests. You can also run `bin/console` for an interactive prompt that will allow you to experiment.
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