xDy crate

The xdy crate is the core library of the xDy project. It compiles dice expressions into reusable functions, optimizes them, and evaluates them against client-supplied pseudorandom number generators. For a high-level overview of the project, language features, and usage examples, see the project README.

This document covers the internal architecture for contributors and curious power users.

• Architecture
  • Compilation pipeline
  • Intermediate representation
  • Evaluator
  • Optimizer
  • Histogram engine
  • Diagnostics
• Instruction set reference
  • Addressing modes
  • Roll instructions
  • Drop instructions
  • Reduce instructions
  • Arithmetic instructions
  • Control instructions
• Cargo features
• Safety

Architecture

Compilation pipeline

Source code flows through a six-stage pipeline. The compile() convenience function drives the full pipeline; compile_unoptimized() skips the optimizer.

graph LR
    A["Source Code<br/><code>&str</code>"] --> B["Parser<br/><code>parser::parse</code>"]
    B --> C["AST<br/><code>ast::Function</code>"]
    C --> D["Compiler<br/><code>Compiler::compile</code>"]
    D --> E["Unoptimized IR<br/><code>Function</code>"]
    E --> F["Optimizer<br/><code>StandardOptimizer</code>"]
    F --> G["Optimized IR<br/><code>Function</code>"]
    style A fill:#f9f,stroke:#333,color:#000
    style G fill:#9f9,stroke:#333,color:#000

Parser. A nom-based combinator parser recognizes the xDy grammar and produces an abstract syntax tree (ast::Function). The grammar supports operator precedence via recursive descent: add_sub → mul_div_mod → unary → exponent → primary. See parser::combinators for the full set of production rules; the Rustdoc includes a railroad diagram generated from the EBNF grammar.

Compiler. The Compiler implements the ASTVisitor trait and walks the AST in a single pass to emit IR instructions. It uses static single assignment (SSA) form — every instruction writes to a fresh register or rolling record. Parameters are allocated first (in declaration order), then external variables (depth-first, left-to-right), ensuring deterministic register layout.

Optimizer. The StandardOptimizer applies five transformation passes in a fixed-point loop, then a final register coalescing pass. See Optimizer below.

Intermediate representation

The IR is a simple register transfer language (RTL) with no control flow — all instructions reside in a single basic block. The machine model provides two register files:

• Register bank (@0, @1, …): holds i32 values for parameters, external variables, and computed intermediates.
• Rolling record bank (⚅0, ⚅1, …): holds the individual results of dice rolls and range selections, along with drop counters.

Each operand uses one of three addressing modes:

See Instruction set reference for the complete ISA.

Evaluator

The evaluator is a linear instruction interpreter. For each evaluation it:

1. Allocates a register bank (sized at compile time) and a rolling record bank.
2. Loads arguments into parameter registers and environment bindings into external variable registers.
3. Walks the instruction stream sequentially — there is no branching, so the program counter simply increments.
4. Returns the final Evaluation, which includes both the i32 result and the complete Vec<RollingRecord> for display.

graph TD
    subgraph VM["Evaluator VM"]
        direction TB
        PC["Program Counter"]
        subgraph RF["Register Bank (i32)"]
            R0["@0: param"]
            R1["@1: extern"]
            RN["@N: computed"]
        end
        subgraph RR["Rolling Record Bank"]
            RR0["⚅0: dice results"]
            RR1["⚅1: range results"]
        end
    end
    F["Function (IR)"] --> PC
    RNG["pRNG"] --> RR
    ARGS["Arguments"] --> RF
    ENV["Environment"] --> RF
    VM --> OUT["Evaluation<br/>result + records"]
    style VM fill:#e8f4fd,stroke:#333,color:#000
    style RF fill:#d4edda,stroke:#333,color:#000
    style RR fill:#fff3cd,stroke:#333,color:#000

All arithmetic saturates to i32::MIN/i32::MAX. Division by zero yields zero. 0^0 = 1. Negative exponents yield zero.

The evaluator also provides bounds(), which computes static min/max bounds and (when possible) the total outcome count — without requiring an RNG.

Optimizer

The StandardOptimizer applies six passes. The first five run in a fixed-point loop; the sixth runs once at the end:

graph TD
    A["Input Function (SSA)"] --> B["Common Subexpression Elimination"]
    B --> C["Constant Commuting"]
    C --> D["Constant Folding"]
    D --> E["Strength Reduction"]
    E --> F["Dead Code Elimination"]
    F --> G{"Changed?"}
    G -- Yes --> B
    G -- No --> H["Register Coalescing"]
    H --> I["Optimized Function"]
    style A fill:#f9f,stroke:#333,color:#000
    style I fill:#9f9,stroke:#333,color:#000
    style G fill:#ff9,stroke:#333,color:#000

Histogram engine

The histogram engine computes the complete probability distribution of a dice expression by exhaustive enumeration. It uses a state-machine approach:

1. Each EvaluationState suspends at roll/range instructions.
2. For each possible outcome of the suspended instruction, a successor state is generated.
3. States that reach Return contribute their result to the histogram.
4. A configurable gas tank (MAX_SUCCESSORS = 30) bounds the branching factor per instruction.

Two builders are provided: SerialHistogramBuilder and ParallelHistogramBuilder (the latter requires the parallel-histogram feature and uses rayon).

Diagnostics

The diagnostics module provides structured error reporting with a fix-and-retry strategy. When parsing fails, the diagnostics engine:

1. Analyzes the parse error to identify the failure kind (unclosed delimiter, missing operand, etc.).
2. Applies a minimal fix to the source text.
3. Re-parses the fixed source to discover additional errors.
4. Maps error spans back to the original source using an offset map.

This produces rich Diagnostic values with error kinds, source spans, messages, and suggested fixes — designed to power IDE-style error reporting on every keystroke.

Instruction set reference

Addressing modes

Roll instructions

Drop instructions

Reduce instructions

Arithmetic instructions

All arithmetic instructions saturate on overflow/underflow.

Control instructions

Cargo features

Safety

xDy is designed to be well-behaved for all inputs. Dice expression values are i32 and all arithmetic operations saturate on overflow or underflow. Neither the compiler nor evaluator should panic or cause undefined behavior, even for invalid dice expressions and inputs, though client misuse of vector results can lead to panics. The main crate contains no unsafe code.