Implement FieldSqrt hint (#179)

* added UpdatePc tests and fixed a bug in UpdatePc

* Fixed accessing field value without Read()

* fixed failing tests

* small refactor for TestUpdatePcJump

* randomEcPoint done

* move comment

* move randomizers into utils.go

* address PR comments

* FieldSqrt hint done

* added test

* added testcase

pkg/hintrunner/hint.go

@@ -1388,6 +1388,7 @@ func (hint *RandomEcPoint) Execute(vm *VM.VirtualMachine) error {
 		// Legendre == 1 -> Quadratic residue
 		// Legendre == -1 -> Quadratic non-residue
 		// Legendre == 0 -> Zero
+		// https://en.wikipedia.org/wiki/Legendre_symbol
 		if randomYSquared.Legendre() == 1 {
 			break
 		}
@@ -1418,3 +1419,49 @@ func (hint *RandomEcPoint) Execute(vm *VM.VirtualMachine) error {
 
 	return nil
 }
+
+type FieldSqrt struct {
+	val  ResOperander
+	sqrt CellRefer
+}
+
+func (hint *FieldSqrt) String() string {
+	return "FieldSqrt"
+}
+
+func (hint *FieldSqrt) Execute(vm *VM.VirtualMachine) error {
+	val, err := hint.val.Resolve(vm)
+	if err != nil {
+		return fmt.Errorf("resolve val operand %s: %v", hint.val, err)
+	}
+
+	valFelt, err := val.FieldElement()
+	if err != nil {
+		return err
+	}
+
+	threeFelt := f.Element{}
+	threeFelt.SetUint64(3)
+
+	var res f.Element
+	// Legendre == 1 -> Quadratic residue
+	// Legendre == -1 -> Quadratic non-residue
+	// Legendre == 0 -> Zero
+	// https://en.wikipedia.org/wiki/Legendre_symbol
+	if valFelt.Legendre() == 1 {
+		res = *valFelt
+	} else {
+		res = *valFelt.Mul(valFelt, &threeFelt)
+	}
+
+	res.Sqrt(&res)
+
+	sqrtVal := mem.MemoryValueFromFieldElement(&res)
+
+	sqrtAddr, err := hint.sqrt.Get(vm)
+	if err != nil {
+		return fmt.Errorf("get sqrt address: %v", err)
+	}
+
+	return vm.Memory.WriteToAddress(&sqrtAddr, &sqrtVal)
+}

pkg/hintrunner/hint_bechmark_test.go

@@ -298,7 +298,6 @@ func BenchmarkAssertLeIsFirstArcExcluded(b *testing.B) {
 
 		vm.Context.Ap += 1
 	}
-
 }
 
 func BenchmarkAssertLeIsSecondArcExcluded(b *testing.B) {
@@ -327,7 +326,6 @@ func BenchmarkAssertLeIsSecondArcExcluded(b *testing.B) {
 
 		vm.Context.Ap += 1
 	}
-
 }
 
 func BenchmarkAssertLeFindSmallArc(b *testing.B) {
@@ -388,5 +386,27 @@ func BenchmarkRandomEcPoint(b *testing.B) {
 
 		vm.Context.Ap += 2
 	}
+}
+
+func BenchmarkFieldSqrt(b *testing.B) {
+	vm := defaultVirtualMachine()
+
+	rand := defaultRandGenerator()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
 
+		hint := FieldSqrt{
+			val:  Immediate(randomFeltElement(rand)),
+			sqrt: ApCellRef(0),
+		}
+
+		err := hint.Execute(vm)
+		if err != nil {
+			b.Error(err)
+			break
+		}
+
+		vm.Context.Ap += 1
+	}
 }

pkg/hintrunner/hint_test.go

@@ -916,3 +916,46 @@ func TestRandomEcPoint(t *testing.T) {
 	require.Equal(t, expectedX, actualX)
 	require.Equal(t, expectedY, actualY)
 }
+
+func TestFieldSqrt(t *testing.T) {
+	testCases := []struct {
+		name     string
+		value    uint64
+		expected int
+	}{
+		{
+			name:     "TestFieldSqrt",
+			value:    49,
+			expected: 7,
+		},
+		{
+			name:     "TestFieldSqrtNonResidue",
+			value:    27,
+			expected: -9,
+		},
+	}
+
+	for _, tc := range testCases {
+		t.Run(tc.name, func(t *testing.T) {
+			vm := defaultVirtualMachine()
+			vm.Context.Ap = 0
+			vm.Context.Fp = 0
+
+			value := Immediate(f.NewElement(tc.value))
+			hint := FieldSqrt{
+				val:  value,
+				sqrt: ApCellRef(0),
+			}
+
+			err := hint.Execute(vm)
+
+			require.NoError(t, err)
+			require.Equal(
+				t,
+				mem.MemoryValueFromInt(tc.expected),
+				readFrom(vm, VM.ExecutionSegment, 0),
+			)
+		})
+	}
+}
+