[SPARK-56940][SQL] Extend OptimizeRand optimizer to support arithmetic expressions

[xuzifu666]

What changes were proposed in this pull request?

1. Support for Arithmetic Expression Optimization

• Previously: Only direct comparisons like rand() < 1 were optimized
• Now: Supports arithmetic operations like rand() * 2 < 1, rand() + 1 < 2, rand() - 1 < 0, rand() / 2 < 1
• Also supports nested expressions: 2 * rand() + 1 < 3

2. Support for Equality Comparisons

• Added optimization for == (EqualTo) operator
• Example: rand() == 2 optimizes to false (since rand() range is [0,1))

3. Implementation Details

   Added 3 key helper functions:

• extractDouble(): Safely extracts Double values from various Literal types
  case DoubleLiteral(v) => Some(v)
  case Literal(v: Double, _) => Some(v)
  case Literal(v: java.lang.Number, _) => Some(v.doubleValue())
• extractRandCoeffOffset(): Recursively extracts coefficients and offsets, normalizing any arithmetic expression into canonical form coeff * rand() + offset
  • Supports: Rand, Multiply, Add, Subtract, Divide
• optimizeWithCoeffOffset(): Performs mathematical transformation and constant folding
  • Handles zero coefficient: direct comparison
  • Handles positive coefficient: computes threshold t = (value - offset) / coeff
  • Handles negative coefficient: correctly reverses inequality direction

Why are the changes needed?
Before optimization (without this change):

  Query: SELECT * FROM large_table WHERE 2 * rand() < 1
  ├─ Parser: Creates expression tree
  ├─ Analyzer: Type checking
  ├─ Optimizer: Cannot simplify (no arithmetic support)
  └─ Executor: Evaluates 2 * rand() for every row (millions of times!)
      ├─ Generates random seed
      ├─ Computes rand() value
      ├─ Multiplies by 2 
      └─ Compares with 1
  Result: INEFFICIENT - unnecessary computation on every row

After optimization (with this change):

  Query: SELECT * FROM large_table WHERE 2 * rand() < 1
  ├─ Parser: Creates expression tree
  ├─ Analyzer: Type checking
  ├─ Optimizer: Recognizes pattern, applies mathematical transformation
  │   └─ Calculates: t = (1 - 0) / 2 = 0.5
  │   └─ Since 0 ≤ 0.5 < 1, result is always TRUE
  └─ Executor: Skips rand() completely, evaluates to TRUE for all rows
  Result: EFFICIENT - compile-time constant folding

Does this PR introduce any user-facing change?
No

Was this patch authored or co-authored using generative AI tooling?
No.