Add AllocatedNum::from_parts for zero-cost variable reuse (#487)

* Initial plan

* Add AllocatedNum::from_parts for zero-cost variable reuse

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Co-authored-by: srinathsetty <14947526+srinathsetty@users.noreply.github.com>

* Bump crate version to 0.70.0

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Co-authored-by: srinathsetty <14947526+srinathsetty@users.noreply.github.com>

* fix build

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: srinathsetty <14947526+srinathsetty@users.noreply.github.com>
Co-authored-by: Srinath Setty <srinath@microsoft.com>

Author: Copilot

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "nova-snark"
-version = "0.69.0"
+version = "0.70.0"
 authors = ["Srinath Setty <srinath@microsoft.com>"]
 edition = "2021"
 description = "High-speed recursive arguments from folding schemes"

src/frontend/gadgets/num.rs

@@ -24,6 +24,20 @@ impl<Scalar: PrimeField> Clone for AllocatedNum<Scalar> {
 }
 
 impl<Scalar: PrimeField> AllocatedNum<Scalar> {
+  /// Construct an [`AllocatedNum`] from a variable and value without adding constraints.
+  ///
+  /// # Safety (Logical)
+  /// The caller MUST ensure that:
+  /// 1. The variable already exists in the constraint system
+  /// 2. The value correctly reflects the variable's assignment
+  ///
+  /// This is useful when a variable is known to hold a valid field element
+  /// due to constraints added separately, enabling zero-cost reinterpretation
+  /// (e.g., wrapping an [`AllocatedBit`](super::boolean::AllocatedBit)'s variable as a number).
+  pub fn from_parts(variable: Variable, value: Option<Scalar>) -> Self {
+    AllocatedNum { value, variable }
+  }
+
   /// Returns an `AllocatedNum` wrapping the built-in `CS::one()` variable.
   /// Costs zero constraints since it uses the input-0 wire directly.
   pub fn one<CS: ConstraintSystem<Scalar>>() -> Self {