attempt at compatible compare gadget

src/lib/provable/gadgets/comparison.ts

@@ -0,0 +1,51 @@
+import type { Field } from '../field.js';
+import { createBool, createField } from '../core/field-constructor.js';
+import { Fp } from '../../../bindings/crypto/finite-field.js';
+import { assert } from '../../../lib/util/assert.js';
+import { exists } from '../core/exists.js';
+import { assertMul } from './compatible.js';
+
+export { compareCompatible };
+
+/**
+ * Compare x and y assuming both have at most `n` bits.
+ */
+function compareCompatible(x: Field, y: Field, n = Fp.sizeInBits - 2) {
+  // compatible with snarky's `compare`
+
+  let maxLength = Fp.sizeInBits - 2;
+  assert(n <= maxLength, `bitLength must be at most ${maxLength}`);
+
+  // 2^n + x - y
+  let z = createField(1n << BigInt(n))
+    .add(y)
+    .sub(x);
+
+  let zBits = unpack(z, n + 1);
+
+  // n-th bit tells us if x <= y
+  let lessOrEqual = zBits[n];
+
+  // other bits tell us if x = y
+  let prefix = zBits.slice(0, n);
+  let notAllZeros = prefix.reduce((a, b) => a.or(b));
+  let less = lessOrEqual.and(notAllZeros);
+
+  return { lessOrEqual, less };
+}
+
+// custom version of toBits to be compatible
+
+function unpack(x: Field, length: number) {
+  let bits = exists(length, () => {
+    let x0 = x.toBigInt();
+    return Array.from({ length }, (_, k) => (x0 >> BigInt(k)) & 1n);
+  });
+  bits.forEach((b) => b.assertBool());
+  let lc = bits.reduce(
+    (acc, b, i) => acc.add(b.mul(1n << BigInt(i))),
+    createField(0)
+  );
+  assertMul(lc, createField(1), x);
+  return bits.map((b) => createBool(b.value));
+}