WIP

yarn-project/foundation/src/fields/fields.ts

@@ -1,10 +1,11 @@
+import { BarretenbergSync } from '@aztec/bb.js';
+
 import { inspect } from 'util';
 
 import { toBigIntBE, toBufferBE } from '../bigint-buffer/index.js';
 import { randomBytes } from '../crypto/random/index.js';
 import { BufferReader } from '../serialize/buffer_reader.js';
 import { TypeRegistry } from '../serialize/type_registry.js';
-import { BarretenbergSync } from '@aztec/bb.js';
 
 const ZERO_BUFFER = Buffer.alloc(32);
 

yarn-project/foundation/src/fields/point.test.ts

@@ -0,0 +1,17 @@
+import { Fr } from './fields.js';
+import { Point } from './point.js';
+
+describe('Point', () => {
+  it('converts to and from x and sign of y coordinate', () => {
+    const p = new Point(
+      new Fr(0x30426e64aee30e998c13c8ceecda3a77807dbead52bc2f3bf0eae851b4b710c1n),
+      new Fr(0x113156a068f603023240c96b4da5474667db3b8711c521c748212a15bc034ea6n),
+      false,
+    );
+
+    const [x, sign] = p.toXAndSign();
+    const p2 = Point.fromXAndSign(x, sign);
+
+    expect(p.equals(p2)).toBeTruthy();
+  });
+});

yarn-project/foundation/src/fields/point.ts

@@ -91,7 +91,7 @@ export class Point {
     const A = new Fr(17);
 
     // Calculate y^2 = x^3 - 17
-    const ySquared = x.square().mul(x).sub(A)
+    const ySquared = x.square().mul(x).sub(A);
 
     // Calculate the square root of ySquared
     const y = ySquared.sqrt();
@@ -101,14 +101,25 @@ export class Point {
       throw new Error('The given x-coordinate is not on the Grumpkin curve');
     }
 
+    const yPositiveBigInt = y.toBigInt() > (Fr.MODULUS - 1n) / 2n ? Fr.MODULUS - y.toBigInt() : y.toBigInt();
+    const yNegativeBigInt = Fr.MODULUS - yPositiveBigInt;
+
     // Choose the positive or negative root based on isPositive
-    // const finalY = sign ? y : y.neg();
-    const finalY = y;
+    const finalY = sign ? new Fr(yPositiveBigInt) : new Fr(yNegativeBigInt);
 
     // Create and return the new Point
     return new this(x, finalY, false);
   }
 
+  /**
+   * Returns the x coordinate and the sign of the y coordinate.
+   * @dev The y sign can be determined by checking if the y coordinate is greater than half of the modulus.
+   * @returns The x coordinate and the sign of the y coordinate.
+   */
+  toXAndSign(): [Fr, boolean] {
+    return [this.x, this.y.toBigInt() <= (Fr.MODULUS - 1n) / 2n];
+  }
+
   /**
    * Returns the contents of the point as BigInts.
    * @returns The point as BigInts