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//! The [`Graph`](./struct.Graph.html) type constructs a directed, acyclic graph of DSP `Node` //! types. //! //! It supports multiple input and multiple output nodes per node. //! //! `Graph` uses the daggy crate. See more [here](https://crates.io/crates/daggy). //! //! The `Graph` type requires that its nodes implement the [`Node`](../node/trait.Node.html) trait. use daggy::{self, Walker}; use node::Node; use sample::{self, Frame, Sample}; /// An alias for our Graph's Node Index. pub type NodeIndex = daggy::NodeIndex<usize>; /// An alias for our Graph's Edge Index. pub type EdgeIndex = daggy::EdgeIndex<usize>; /// An alias for the iterator yielding mutable access to all node weights. pub type NodesMut<'a, N> = daggy::NodeWeightsMut<'a, N, usize>; /// Read only access to a **Graph**'s internal node array. pub type RawNodes<'a, N> = daggy::RawNodes<'a, N, usize>; /// Read only access to a **Graph**'s internal edge array. pub type RawEdges<'a, F> = daggy::RawEdges<'a, Connection<F>, usize>; /// An iterator yielding indices to recently added connections. pub type EdgeIndices = daggy::EdgeIndices<usize>; /// An alias for the **Dag** used within our **Graph**. pub type Dag<F, N> = daggy::Dag<N, Connection<F>, usize>; /// An alias for the **PetGraph** used by our **Graph**'s internal **Dag**. pub type PetGraph<F, N> = daggy::PetGraph<N, Connection<F>, usize>; /// A directed, acyclic DSP graph. /// /// Designed for easily and safely setting up high performance audio signal generating, processing /// and mixing. Useful for both simple and highly complex signal graphs. /// /// There are a variety of use cases for `Graph`: /// /// - Designing effects. /// - Creating an audio mixer. /// - Making a sampler. /// - Writing a DSP backend for a DAW. /// - Any kind of modular audio synthesis or processing. /// /// `Graph` is a wrapper around [daggy](http://mitchmindtree.github.io/daggy/daggy/)'s /// [`Dag`](http://mitchmindtree.github.io/daggy/daggy/struct.Dag.html) type - an abstraction for /// working with directed acyclic graph's where high performance node adding and accessing is /// required. /// /// An input -> output connection in this `Graph` is represented as a parent -> child connection /// within the internal `Dag`. The following terms are all equivalent: /// /// - *input -> output* /// - *src -> dest* /// - *parent -> child* /// /// Audio can be requested from any node in the **Graph** using the /// [`audio_requested_from`](./struct.Graph.html#method.audio_requested_from) method. /// /// When [`audio_requested`](../node/trait.Node.html#method.audio_requested) is called on the /// **Graph**, audio will be requested from the node specified by the index at `maybe_master`. If /// `maybe_master` is `None`, audio will be requested from the first, input-only node found - that /// is, the first node that is found with only input connections and no outputs. /// /// **NodeIndex** is a type that acts as a reference to a node, while **EdgeIndex** is a type that /// acts as a reference to an edge (which in this case describes a *src -> dest* **Connection** /// between two nodes). It should be noted that these are only stable across certain operations. /// **Removing indices may shift other indices of the same type!** Adding nodes or edges to the /// **Graph** keeps all indices stable, but removing a node or edge will force the last node/edge /// to shift its index to take its place. /// /// **Graph** also offers methods for accessing its underlying **Dag** or **PetGraph**. #[derive(Clone, Debug)] pub struct Graph<F, N> { dag: Dag<F, N>, /// The order in which audio will be requested from each node. visit_order: Vec<NodeIndex>, /// The node from which audio will be requested upon a call to `Node::audio_requested`. maybe_master: Option<NodeIndex>, /// A buffer to re-use when mixing the dry and wet signals when audio is requested. dry_buffer: Vec<F>, } /// Describes a connection between two Nodes within the Graph: *input -> connection -> output*. /// /// **Graph**'s API only allows for read-only access to **Connection**s, so you can be sure that /// their buffers always represent the last frames rendered by their input node. #[derive(Clone, Debug)] pub struct Connection<F> { /// The buffer used to pass audio between nodes. /// /// After `Graph::audio_requested_from` is called, this buffer will contain the audio rendered /// by the **Connection**'s input node. pub buffer: Vec<F>, } /// The error returned when adding an edge that would create a cycle. #[derive(Copy, Clone, Debug)] pub struct WouldCycle; /// A walker object for walking over nodes that are inputs to some node. pub struct Inputs<F, N> { parents: daggy::Parents<N, Connection<F>, usize>, } /// A walker object for walking over nodes that are outputs to some node. pub struct Outputs<F, N> { children: daggy::Children<N, Connection<F>, usize>, } /// A walker type for walking over a **Graph**'s nodes in the order in which they will visited when /// audio is requested from the **Graph**. pub struct VisitOrder { current_visit_order_idx: usize, } /// A walker type for walking over a **Graph**'s nodes in the order in which they will visited when /// audio is requested from the **Graph**. pub struct VisitOrderReverse { current_visit_order_idx: usize, } impl<F, N> Graph<F, N> where F: Frame, N: Node<F> { /// Constructor for a new dsp Graph. /// /// [`with_capacity`](./struct.Graph.html#method.with_capacity) is recommended if you have a /// rough idea of the number of nodes, connections and frames per buffer upon the **Graph**'s /// instantiation. pub fn new() -> Self { let dag = daggy::Dag::new(); Graph { dag: dag, visit_order: Vec::new(), dry_buffer: Vec::new(), maybe_master: None, } } /// Constructor for a new dsp Graph with some minimum capacity. /// /// - **nodes** is the capacity for the underlying **Dag**'s node `Vec`. /// - **connections** is the capacity for the underlying **Dag**'s edge `Vec`. /// - **frames_per_buffer** is the capacity for the **Graph**'s `dry_buffer`, which is used /// for mixing the dry and wet signals when `Node::audio_requested` is called. pub fn with_capacity(nodes: usize, connections: usize, frames_per_buffer: usize) -> Self { Graph { dag: daggy::Dag::with_capacity(nodes, connections), visit_order: Vec::with_capacity(nodes), dry_buffer: Vec::with_capacity(frames_per_buffer), maybe_master: None, } } /// A reference to the underlying **Dag**. pub fn dag(&self) -> &Dag<F, N> { &self.dag } /// Takes ownership of the **Graph** and returns the underlying **Dag**. pub fn into_dag(self) -> Dag<F, N> { let Graph { dag, .. } = self; dag } /// A reference to the internal **Dag**'s underlying **PetGraph**. pub fn pet_graph(&self) -> &PetGraph<F, N> { self.dag.graph() } /// Takes ownership of the **Graph** and returns the internal **Dag**'s underlying **PetGraph**. pub fn into_pet_graph(self) -> PetGraph<F, N> { self.into_dag().into_graph() } /// The total number of nodes in the **Graph**. pub fn node_count(&self) -> usize { self.dag.node_count() } /// The total number of connections in the **Graph**. pub fn connection_count(&self) -> usize { self.dag.edge_count() } /// Return the **Graph**'s master index if there is one. /// /// **Graph**'s **Node** implementation will request audio from the node at `maybe_master` /// when the `Node::audio_requested` method is called. pub fn master_index(&self) -> Option<NodeIndex> { self.maybe_master } /// Set the master node for the **Graph**. /// /// **Graph** will check to see if a node exists for the given index before assigning. /// /// **Graph**'s **Node** implementation will request audio from the node at `maybe_master` /// when the `Node::audio_requested` method is called. pub fn set_master(&mut self, maybe_index: Option<NodeIndex>) { let maybe_index = maybe_index.and_then(|index| { if self.dag.node_weight(index).is_some() { Some(index) } else { None } }); self.maybe_master = maybe_index; self.prepare_visit_order(); } /// Add a node to the dsp graph. /// /// This computes in **O(1)** time. pub fn add_node(&mut self, node: N) -> NodeIndex { let idx = self.dag.add_node(node); idx } /// A reference to the node at the given index (or `None` if it doesn't exist). pub fn node(&self, node: NodeIndex) -> Option<&N> { self.dag.node_weight(node) } /// A mutable reference to the node at the given index (or `None` if it doesn't exist). pub fn node_mut(&mut self, node: NodeIndex) -> Option<&mut N> { self.dag.node_weight_mut(node) } /// Read only access to the internal node array. pub fn raw_nodes(&self) -> RawNodes<N> { self.dag.raw_nodes() } /// An iterator yielding mutable access to all nodes. /// /// The order in which nodes are yielded matches the order of their indices. pub fn nodes_mut(&mut self) -> NodesMut<N> { self.dag.node_weights_mut() } /// A reference to the connection at the given index (or `None` if it doesn't exist). pub fn connection(&self, edge: EdgeIndex) -> Option<&Connection<F>> { self.dag.edge_weight(edge) } /// Read only access to the internal edge array. pub fn raw_edges(&self) -> RawEdges<F> { self.dag.raw_edges() } /// Index the **Graph** by two `NodeIndex`s at once. /// /// **Panics** if the indices are equal or if they are out of bounds. pub fn index_twice_mut(&mut self, a: NodeIndex, b: NodeIndex) -> (&mut N, &mut N) { self.dag.index_twice_mut(a, b) } /// Remove a node from the dsp graph. /// /// Resets the master to None if the index matches the current master index. /// /// **Note:** This method may shift (and in turn invalidate) previously returned node indices! /// /// **Graph** will re-prepare its visit order if some node was removed. pub fn remove_node(&mut self, idx: NodeIndex) -> Option<N> { if self.maybe_master == Some(idx) { self.maybe_master = None; } self.dag.remove_node(idx).map(|node| { self.prepare_visit_order(); node }) } /// Adds an edge from `src` to `dest`. That is, `src` is now an input to `dest`. /// /// Returns an error instead if the input would create a cycle in the graph. /// /// **Graph** will re-prepare its visit order if some connection was successfully added. /// /// If you're using `add_node` followed by this method, consider using /// [`add_input`](./struct.Graph.html#method.add_input) or /// [`add_output`](./struct.Graph.html#method.add_output) instead for greater performance. /// This is because when adding a new node and edge simultaneously, we don't have to check /// whether adding the edge would create a cycle. /// /// **Panics** if there is no node for either `src` or `dest`. /// /// **Panics** if the Graph is at the maximum number of edges for its index. pub fn add_connection(&mut self, src: NodeIndex, dest: NodeIndex) -> Result<EdgeIndex, WouldCycle> { self.dag.add_edge(src, dest, Connection { buffer: Vec::new() }) .map(|edge| { self.prepare_visit_order(); edge }) .map_err(|_| WouldCycle) } /// The same as [`add_connection`](./struct.Graph.html#method.add_connection) but adds /// multiple connections to the **Graph**. Rather than checking for introduced cycles and /// re-preparing the visit order after adding each edge, we only do so after **all** edges are /// added. Thus, this is a far more efficient alternative to repeatedly calling the /// `add_connection` method. /// /// Returns an error instead if any of the connections would create a cycle in the graph. /// /// **Graph** will re-prepare its visit order if the connections were successfully added. /// /// If you're using `add_node` followed by this method, consider using /// [`add_input`](./struct.Graph.html#method.add_input) or /// [`add_output`](./struct.Graph.html#method.add_output) instead for greater performance. /// This is because when adding a new node and edge simultaneously, we don't have to check /// whether adding the edge would create a cycle. /// /// **Panics** if there is no node for either `src` or `dest`. /// /// **Panics** if the Graph is at the maximum number of edges for its index. pub fn add_connections<I>(&mut self, connections: I) -> Result<EdgeIndices, WouldCycle> where I: ::std::iter::IntoIterator<Item=(NodeIndex, NodeIndex)>, { fn new_connection<F>() -> Connection<F> { Connection { buffer: Vec::new() } } self.dag.add_edges(connections.into_iter().map(|(src, dest)| (src, dest, new_connection()))) .map(|edges| { self.prepare_visit_order(); edges }) .map_err(|_| WouldCycle) } /// Find and return the index to the edge that describes the connection where `src` is an input /// to `dest`. /// /// Computes in **O(e')** time, where **e'** is the number of edges connected to the nodes `a` /// and `b`. pub fn find_connection(&self, src: NodeIndex, dest: NodeIndex) -> Option<EdgeIndex> { self.dag.find_edge(src, dest) } /// Remove the connection described by the edge at the given index. /// /// Returns true if an edge was removed, returns false if there was no edge at the given index. /// /// Re-prepares the visit order if some edge was removed. pub fn remove_edge(&mut self, edge: EdgeIndex) -> bool { if self.dag.remove_edge(edge).is_some() { self.prepare_visit_order(); true } else { false } } /// Find and remove any connection between a and b if there is one, whether it is *a -> b* or /// *b -> a*. We know that their may only be one edge as our API does not allow for creating a /// cyclic graph. /// /// Returns true if an edge was removed, returns false if there was no edge at the given index. /// /// Graph will re-prepare its visit order if some edge was removed. /// /// Note: If you have an index to the edge you want to remove, /// [`remove_edge`](./struct.Graph.html#method.remove_edge) is a more performant option. pub fn remove_connection(&mut self, a: NodeIndex, b: NodeIndex) -> bool { match self.dag.find_edge(a, b).or_else(|| self.dag.find_edge(b, a)) { Some(edge) => self.remove_edge(edge), None => false, } } /// Add a new node weight to the graph as an input to the wait at the given `dest` node index. /// /// *src -> new edge -> dest* /// /// Returns an index to both the new `src` node and the edge that represents the new connection /// between it and the node at `dest`. /// /// Computes in **O(n)** time where n is the number of nodes. This is because must update the /// visit order after adding the new connection. /// /// **Panics** if there is no node for the given `dest` index. /// /// **Panics** if the Graph is at the maximum number of edges for its index. pub fn add_input(&mut self, src: N, dest: NodeIndex) -> (EdgeIndex, NodeIndex) { let indices = self.dag.add_parent(dest, Connection { buffer: Vec::new() }, src); self.prepare_visit_order(); indices } /// Add a new node weight to the graph as an output to the wait at the given `src` node index. /// /// *src -> new edge -> dest* /// /// Returns an index to both the new `dest` node and the edge that represents the new connection /// between it and the node at `src`. /// /// Computes in **O(n)** time where n is the number of nodes. This is because must update the /// visit order after adding the new connection. /// /// **Panics** if there is no node for the given `dest` index. /// /// **Panics** if the Graph is at the maximum number of edges for its index. pub fn add_output(&mut self, src: NodeIndex, dest: N) -> (EdgeIndex, NodeIndex) { let indices = self.dag.add_child(src, Connection { buffer: Vec::new() }, dest); self.prepare_visit_order(); indices } /// A "walker" object that may be used to step through the inputs of the given node. /// /// Unlike the `Inputs` type, `WalkInputs` does not borrow the `Graph`. /// /// Can be converted to an iterator using `.iter()`. pub fn inputs(&self, idx: NodeIndex) -> Inputs<F, N> { Inputs { parents: self.dag.parents(idx) } } /// A "walker" object that may be used to step through the outputs of the given node. /// /// Unlike the `Outputs` type, `WalkOutputs` does not borrow the **Graph**. /// /// Can be converted to an iterator using `.iter()`. pub fn outputs(&self, idx: NodeIndex) -> Outputs<F, N> { Outputs { children: self.dag.children(idx) } } /// A "walker" type that may be used to step through all node indices in the order in which /// they will be visited when audio is requested from the **Graph**. pub fn visit_order(&self) -> VisitOrder { VisitOrder { current_visit_order_idx: 0 } } /// A "walker" type that may be used to step through all node indices in the order in which /// they will be visited when audio is requested from the **Graph**. /// /// Unlike the VisitOrder type, VisitOrder does not borrow the **Graph**. pub fn visit_order_rev(&self) -> VisitOrderReverse { VisitOrderReverse { current_visit_order_idx: self.visit_order.len() } } /// Remove all incoming connections to the node at the given index. /// /// Return the number of connections removed. pub fn remove_all_input_connections(&mut self, idx: NodeIndex) -> usize { let mut inputs = self.inputs(idx); let mut num = 0; while let Some(connection) = inputs.next_edge(&self) { self.remove_edge(connection); num += 1; } num } /// Remove all outgoing connections from the node at the given index. /// /// Return the number of connections removed. pub fn remove_all_output_connections(&mut self, idx: NodeIndex) -> usize { let mut outputs = self.outputs(idx); let mut num = 0; while let Some(connection) = outputs.next_edge(&self) { self.remove_edge(connection); num += 1; } num } /// Clear all dsp nodes that have no inputs or outputs. /// /// Returns the number of nodes removed. /// /// Note: this may shift (and in turn invalidate) previously returned node and edge indices! pub fn clear_disconnected(&mut self) -> usize { let mut num_removed = 0; for i in 0..self.dag.node_count() { let idx = NodeIndex::new(i); let num_inputs = self.inputs(idx).count(self); let num_outputs = self.outputs(idx).count(self); if num_inputs == 0 && num_outputs == 0 { if self.maybe_master == Some(idx) { self.maybe_master = None; } self.dag.remove_node(idx); num_removed += 1; } } num_removed } /// Clear all dsp nodes. pub fn clear(&mut self) { self.dag.clear(); self.visit_order.clear(); self.maybe_master = None; } /// Prepare the buffers for all nodes within the Graph. pub fn prepare_buffers(&mut self, buffer_size: usize) { // Initialise the dry signal buffer. resize_buffer_to(&mut self.dry_buffer, buffer_size); // Initialise all connection buffers. for connection in self.dag.edge_weights_mut() { resize_buffer_to(&mut connection.buffer, buffer_size); } } /// Request audio from the node at the given index. /// /// **Panics** if there is no node for the given index. pub fn audio_requested_from(&mut self, out_node: NodeIndex, output: &mut [F], sample_hz: f64) { // We can only go on if a node actually exists for the given index. if self.node(out_node).is_none() { panic!("No node for the given index"); } let buffer_size = output.len(); // Ensure the dry_buffer is the same length as the output buffer. if self.dry_buffer.len() != buffer_size { resize_buffer_to(&mut self.dry_buffer, buffer_size); } let mut visit_order = self.visit_order(); while let Some(node_idx) = visit_order.next(self) { // Set the buffers to equilibrium, ready to sum the inputs of the current node. for i in 0..buffer_size { output[i] = F::equilibrium(); self.dry_buffer[i] = F::equilibrium(); } // Walk over each of the input connections to sum their buffers to the output. let mut inputs = self.inputs(node_idx); while let Some(connection_idx) = inputs.next_edge(self) { let connection = &self[connection_idx]; // Sum the connection's buffer onto the output. // // We can be certain that `connection`'s buffer is the same size as the // `output` buffer as all connections are visited from their input nodes // (towards the end of the visit_order while loop) before being visited here // by their output nodes. sample::slice::zip_map_in_place(output, &connection.buffer, |out_frame, con_frame| { out_frame.zip_map(con_frame, |out_sample, con_sample| { let out_signed = out_sample.to_sample::<<F::Sample as Sample>::Signed>(); let con_signed = con_sample.to_sample::<<F::Sample as Sample>::Signed>(); (out_signed + con_signed).to_sample::<F::Sample>() }) }); } // Store the dry signal in the dry buffer for later summing. sample::slice::write(&mut self.dry_buffer, output); // Render the audio with the current node and sum the dry and wet signals. let (dry, wet) = { let node = &mut self[node_idx]; // Render our `output` buffer with the current node. // The `output` buffer is now representative of a fully wet signal. node.audio_requested(output, sample_hz); let dry = node.dry(); let wet = node.wet(); (dry, wet) }; // Combine the dry and wet signals. sample::slice::zip_map_in_place(output, &self.dry_buffer, |f_wet, f_dry| f_wet.zip_map(f_dry, |s_wet, s_dry| { let wet = s_wet.mul_amp(wet); let dry = s_dry.mul_amp(dry); wet.add_amp(dry.to_sample()) }) ); // If we've reached our output node, we're done! if node_idx == out_node { return; } // Walk over each of the outgoing connections and write the rendered output to them. let mut outputs = self.outputs(node_idx); while let Some(connection_idx) = outputs.next_edge(self) { let connection = &mut self.dag[connection_idx]; // Ensure the buffer matches the target length. if connection.buffer.len() != output.len() { resize_buffer_to(&mut connection.buffer, output.len()); } // Write the rendered audio to the outgoing connection buffers. sample::slice::write(&mut connection.buffer, output); } } } /// Prepare the visit order for the graph in its current state. /// /// This is called whenever the **Graph** is mutated in some way that may change the flow of /// its edges. /// /// When audio is requested from the graph, we need to iterate through all nodes so that all /// child nodes are visited before their parents. To do this, we can use petgraph's toposort /// algorithm to return the topological order of our graph. /// /// The user should never have to worry about this, thus the method is private. fn prepare_visit_order(&mut self) { self.visit_order = daggy::petgraph::algo::toposort(self.dag.graph()); } } impl<F, N> ::std::ops::Index<NodeIndex> for Graph<F, N> { type Output = N; #[inline] fn index<'a>(&'a self, index: NodeIndex) -> &'a N { &self.dag[index] } } impl<F, N> ::std::ops::IndexMut<NodeIndex> for Graph<F, N> { #[inline] fn index_mut(&mut self, index: NodeIndex) -> &mut N { &mut self.dag[index] } } impl<F, N> ::std::ops::Index<EdgeIndex> for Graph<F, N> { type Output = Connection<F>; #[inline] fn index<'a>(&'a self, index: EdgeIndex) -> &'a Connection<F> { &self.dag[index] } } impl<F, N> Node<F> for Graph<F, N> where F: Frame, N: Node<F>, { fn audio_requested(&mut self, output: &mut [F], sample_hz: f64) { match self.maybe_master { Some(master) => self.audio_requested_from(master, output, sample_hz), None => { // If there is no set master node, we'll start from the back of the visit_order and // use the first node that has no output connections. let mut visit_order_rev = self.visit_order_rev(); while let Some(node) = visit_order_rev.next(self) { if self.inputs(node).count(self) == 0 { self.audio_requested_from(node, output, sample_hz); return; } } }, } } } impl<F, N> Walker<Graph<F, N>> for Inputs<F, N> { type Index = usize; /// The next (connection, node) input pair to some node in our walk for the given **Graph**. #[inline] fn next(&mut self, graph: &Graph<F, N>) -> Option<(EdgeIndex, NodeIndex)> { self.parents.next(&graph.dag) } /// The next input connection to some node in our walk for the given **Graph**. #[inline] fn next_edge(&mut self, graph: &Graph<F, N>) -> Option<EdgeIndex> { self.parents.next_edge(&graph.dag) } /// The next input node to some node in our walk for the given **Graph**. #[inline] fn next_node(&mut self, graph: &Graph<F, N>) -> Option<NodeIndex> { self.parents.next_node(&graph.dag) } } impl<F, N> Walker<Graph<F, N>> for Outputs<F, N> { type Index = usize; /// The next (connection, node) output pair from some node in our walk for the given **Graph**. #[inline] fn next(&mut self, graph: &Graph<F, N>) -> Option<(EdgeIndex, NodeIndex)> { self.children.next(&graph.dag) } /// The next output connection from some node in our walk for the given **Graph**. #[inline] fn next_edge(&mut self, graph: &Graph<F, N>) -> Option<EdgeIndex> { self.children.next_edge(&graph.dag) } /// The next output node from some node in our walk for the given **Graph**. #[inline] fn next_node(&mut self, graph: &Graph<F, N>) -> Option<NodeIndex> { self.children.next_node(&graph.dag) } } impl VisitOrder { /// The index of the next node that would be visited during audio requested in our walk of the /// given **Graph**'s visit order. #[inline] pub fn next<F, N>(&mut self, graph: &Graph<F, N>) -> Option<NodeIndex> { graph.visit_order.get(self.current_visit_order_idx).map(|&idx| { self.current_visit_order_idx += 1; idx }) } } impl VisitOrderReverse { /// The index of the next node that would be visited during audio requested in our walk of the /// given **Graph**'s visit order. #[inline] pub fn next<F, N>(&mut self, graph: &Graph<F, N>) -> Option<NodeIndex> { if self.current_visit_order_idx > 0 { self.current_visit_order_idx -= 1; graph.visit_order.get(self.current_visit_order_idx).map(|&idx| idx) } else { None } } } /// Resize the given buffer to the given target length. fn resize_buffer_to<F>(buffer: &mut Vec<F>, target_len: usize) where F: Frame, { let len = buffer.len(); if len < target_len { buffer.extend((len..target_len).map(|_| F::equilibrium())) } else if len > target_len { buffer.truncate(target_len); } } impl ::std::fmt::Display for WouldCycle { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> Result<(), ::std::fmt::Error> { writeln!(f, "{:?}", self) } } impl ::std::error::Error for WouldCycle { fn description(&self) -> &str { "Adding this input would have caused the graph to cycle!" } }