feat(std): add LessThan() and IsEqual()

std/math/math.go

@@ -0,0 +1,52 @@
+package math
+
+import "github.com/consensys/gnark/frontend"
+
+type Math struct {
+	api frontend.API // underlying constraint system
+}
+
+func NewMath(api frontend.API) (Math, error) {
+	return Math{api}, nil
+}
+
+// Returns 1 if a < b
+func (m *Math) LessThan(a, b frontend.Variable) frontend.Variable {
+	aBits := m.api.ToBinary(a)
+	bBits := m.api.ToBinary(b)
+
+	var output frontend.Variable
+	output = 0
+
+	// This section performs Compare()
+	// Output is 1 if a > b
+	// Output is 0 if a == b
+	// Output is -1 if a < b
+
+	// Backwards due to little endian
+	for i := len(aBits) - 1; i >= 0; i-- {
+		m.api.AssertIsBoolean(aBits[i])
+		m.api.AssertIsBoolean(bBits[i])
+
+		aIsOne := aBits[i]
+		bIsOne := bBits[i]
+
+		aIsNotOne := m.api.IsZero(aBits[i])
+		bIsNotOne := m.api.IsZero(bBits[i])
+
+		aBeatsB := m.api.And(aIsOne, bIsNotOne)
+		bBeatsA := m.api.And(bIsOne, aIsNotOne)
+
+		newOutput := m.api.Select(aBeatsB, 1, 0)
+		newOutput = m.api.Select(bBeatsA, -1, newOutput)
+
+		output = m.api.Select(m.api.IsZero(output), newOutput, output)
+	}
+
+	// Now, convert output of Convert() into LessThan()
+	return m.IsEqual(output, -1)
+}
+
+func (m *Math) IsEqual(a, b frontend.Variable) frontend.Variable {
+	return m.api.IsZero(m.api.Sub(a, b))
+}

std/math/math_test.go

@@ -0,0 +1,80 @@
+package math
+
+import (
+	"testing"
+
+	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/gnark/test"
+)
+
+type LessThanCircuit struct {
+	A              frontend.Variable `gnark:",public"`
+	B              frontend.Variable `gnark:",public"`
+	ExpectedOutput frontend.Variable `gnark:",public"`
+}
+
+func (c *LessThanCircuit) Define(api frontend.API) error {
+	math, _ := NewMath(api)
+	output := math.LessThan(c.A, c.B)
+
+	api.AssertIsEqual(output, c.ExpectedOutput)
+
+	return nil
+}
+
+func TestLessThan(t *testing.T) {
+	assert := test.NewAssert(t)
+
+	var lessThanCircuit LessThanCircuit
+
+	assert.ProverSucceeded(&lessThanCircuit, &LessThanCircuit{
+		A:              9,
+		B:              10,
+		ExpectedOutput: 1,
+	})
+
+	assert.ProverSucceeded(&lessThanCircuit, &LessThanCircuit{
+		A:              10,
+		B:              10,
+		ExpectedOutput: 0,
+	})
+
+	assert.ProverSucceeded(&lessThanCircuit, &LessThanCircuit{
+		A:              11,
+		B:              10,
+		ExpectedOutput: 0,
+	})
+}
+
+type IsEqualCircuit struct {
+	A              frontend.Variable `gnark:",public"`
+	B              frontend.Variable `gnark:",public"`
+	ExpectedOutput frontend.Variable `gnark:",public"`
+}
+
+func (c *IsEqualCircuit) Define(api frontend.API) error {
+	math, _ := NewMath(api)
+	output := math.IsEqual(c.A, c.B)
+
+	api.AssertIsEqual(output, c.ExpectedOutput)
+
+	return nil
+}
+
+func TestIsEqual(t *testing.T) {
+	assert := test.NewAssert(t)
+
+	var isEqualCircuit IsEqualCircuit
+
+	assert.ProverSucceeded(&isEqualCircuit, &IsEqualCircuit{
+		A:              10,
+		B:              10,
+		ExpectedOutput: 1,
+	})
+
+	assert.ProverSucceeded(&isEqualCircuit, &IsEqualCircuit{
+		A:              9,
+		B:              10,
+		ExpectedOutput: 0,
+	})
+}