fix(inclusion): fix integer overflow+inefficient Round*PowerOfTwo

This code fixes an integer flow using finer bit twiddling
and even makes it much more efficient to always run
deterministically in O(1) time essentially and not O(k) where
k=log2(input) due to the prior k iterations that then caused
the overflow when result became > maxInt.

While here also added some benchmarks and more test cases.

Fixes celestiaorg#117

inclusion/blob_share_commitment_rules.go

@@ -3,6 +3,7 @@ package inclusion
 import (
 	"fmt"
 	"math"
+	"math/bits"
 
 	"golang.org/x/exp/constraints"
 )
@@ -50,23 +51,32 @@ func RoundUpByMultipleOf(cursor, v int) int {
 
 // RoundUpPowerOfTwo returns the next power of two greater than or equal to input.
 func RoundUpPowerOfTwo[I constraints.Integer](input I) I {
-	var result I = 1
-	for result < input {
-		result <<= 1
+	if input <= 1 {
+		return 1
 	}
-	return result
+	if input&(input-1) == 0 { // It is already a power of 2
+		return input
+	}
+	var powUp I = 1 << bits.Len64(uint64(input))
+	if powUp < input {
+		// An overflow occured due to a very large size
+		// of input and we should return a positive power of 2.
+		powUp = 1
+	}
+	return powUp
 }
 
 // RoundDownPowerOfTwo returns the next power of two less than or equal to input.
 func RoundDownPowerOfTwo[I constraints.Integer](input I) (I, error) {
 	if input <= 0 {
 		return 0, fmt.Errorf("input %v must be positive", input)
 	}
-	roundedUp := RoundUpPowerOfTwo(input)
-	if roundedUp == input {
-		return roundedUp, nil
+	if input&(input-1) == 0 { // It is already a power of 2
+		return input, nil
 	}
-	return roundedUp / 2, nil
+
+	// Return 1 << (numberOfBits-1)
+	return 1 << (bits.Len64(uint64(input)) - 1), nil
 }
 
 // BlobMinSquareSize returns the minimum square size that can contain shareCount
@@ -79,6 +89,9 @@ func BlobMinSquareSize(shareCount int) int {
 // commitment over a given blob. The input should be the total number of shares
 // used by that blob. See ADR-013.
 func SubTreeWidth(shareCount, subtreeRootThreshold int) int {
+	if subtreeRootThreshold <= 0 {
+		return 1
+	}
 	// Per ADR-013, we use a predetermined threshold to determine width of sub
 	// trees used to create share commitments
 	s := (shareCount / subtreeRootThreshold)

inclusion/blob_share_commitment_rules_test.go

@@ -2,6 +2,7 @@ package inclusion_test
 
 import (
 	"fmt"
+	"math"
 	"testing"
 
 	"github.com/celestiaorg/go-square/v2/inclusion"
@@ -257,25 +258,35 @@ func TestRoundUpByMultipleOf(t *testing.T) {
 	}
 }
 
+type roundUpTestCase struct {
+	input int
+	want  int
+}
+
+var roundUpTestCases = []roundUpTestCase{
+	{input: -1, want: 1},
+	{input: 0, want: 1},
+	{input: 1, want: 1},
+	{input: 2, want: 2},
+	{input: 4, want: 4},
+	{input: 5, want: 8},
+	{input: 8, want: 8},
+	{input: 11, want: 16},
+	{input: 511, want: 512},
+	{input: math.MaxInt32 - 1, want: 1<<31},
+	{input: math.MaxInt32 + 1, want: 1<<31},
+	{input: math.MaxInt32, want: 1<<31},
+	{input: math.MaxInt>>1, want: 1<<62},
+	{input: math.MaxInt, want: 1},
+}
+
 func TestRoundUpPowerOfTwo(t *testing.T) {
-	type testCase struct {
-		input int
-		want  int
-	}
-	testCases := []testCase{
-		{input: -1, want: 1},
-		{input: 0, want: 1},
-		{input: 1, want: 1},
-		{input: 2, want: 2},
-		{input: 4, want: 4},
-		{input: 5, want: 8},
-		{input: 8, want: 8},
-		{input: 11, want: 16},
-		{input: 511, want: 512},
-	}
-	for _, tc := range testCases {
-		got := inclusion.RoundUpPowerOfTwo(tc.input)
-		assert.Equal(t, tc.want, got)
+	for _, tc := range roundUpTestCases {
+		testName := fmt.Sprintf("%d=%x", tc.input, tc.input)
+		t.Run(testName, func(t *testing.T) {
+			got := inclusion.RoundUpPowerOfTwo(tc.input)
+			assert.Equal(t, tc.want, got)
+		})
 	}
 }
 
@@ -326,86 +337,150 @@ func TestBlobMinSquareSize(t *testing.T) {
 	}
 }
 
+type subtreeWidthTestCase struct {
+	shareCount int
+	want       int
+}
+
+var subtreeWidthTestCases = []subtreeWidthTestCase{
+	{
+		shareCount: 0,
+		want:       1,
+	},
+	{
+		shareCount: 1,
+		want:       1,
+	},
+	{
+		shareCount: 2,
+		want:       1,
+	},
+	{
+		shareCount: defaultSubtreeRootThreshold,
+		want:       1,
+	},
+	{
+		shareCount: defaultSubtreeRootThreshold + 1,
+		want:       2,
+	},
+	{
+		shareCount: defaultSubtreeRootThreshold - 1,
+		want:       1,
+	},
+	{
+		shareCount: defaultSubtreeRootThreshold * 2,
+		want:       2,
+	},
+	{
+		shareCount: (defaultSubtreeRootThreshold * 2) + 1,
+		want:       4,
+	},
+	{
+		shareCount: (defaultSubtreeRootThreshold * 3) - 1,
+		want:       4,
+	},
+	{
+		shareCount: (defaultSubtreeRootThreshold * 4),
+		want:       4,
+	},
+	{
+		shareCount: (defaultSubtreeRootThreshold * 5),
+		want:       8,
+	},
+	{
+		shareCount: (defaultSubtreeRootThreshold * defaultMaxSquareSize) - 1,
+		want:       128,
+	},
+}
+
 func TestSubTreeWidth(t *testing.T) {
-	type testCase struct {
-		shareCount int
-		want       int
-	}
-	testCases := []testCase{
-		{
-			shareCount: 0,
-			want:       1,
-		},
-		{
-			shareCount: 1,
-			want:       1,
-		},
-		{
-			shareCount: 2,
-			want:       1,
-		},
-		{
-			shareCount: defaultSubtreeRootThreshold,
-			want:       1,
-		},
-		{
-			shareCount: defaultSubtreeRootThreshold + 1,
-			want:       2,
-		},
-		{
-			shareCount: defaultSubtreeRootThreshold - 1,
-			want:       1,
-		},
-		{
-			shareCount: defaultSubtreeRootThreshold * 2,
-			want:       2,
-		},
-		{
-			shareCount: (defaultSubtreeRootThreshold * 2) + 1,
-			want:       4,
-		},
-		{
-			shareCount: (defaultSubtreeRootThreshold * 3) - 1,
-			want:       4,
-		},
-		{
-			shareCount: (defaultSubtreeRootThreshold * 4),
-			want:       4,
-		},
-		{
-			shareCount: (defaultSubtreeRootThreshold * 5),
-			want:       8,
-		},
-		{
-			shareCount: (defaultSubtreeRootThreshold * defaultMaxSquareSize) - 1,
-			want:       128,
-		},
-	}
-	for i, tc := range testCases {
+	for i, tc := range subtreeWidthTestCases {
 		t.Run(fmt.Sprintf("shareCount %d", tc.shareCount), func(t *testing.T) {
 			got := inclusion.SubTreeWidth(tc.shareCount, defaultSubtreeRootThreshold)
 			assert.Equal(t, tc.want, got, i)
 		})
 	}
 }
 
-func TestRoundDownPowerOfTwo(t *testing.T) {
-	type testCase struct {
-		input int
-		want  int
+var sink any
+
+func BenchmarkSubTreeWidth(b *testing.B) {
+	b.ReportAllocs()
+
+	for i := 0; i < b.N; i++ {
+		for _, tc := range subtreeWidthTestCases {
+			got := inclusion.SubTreeWidth(tc.shareCount, defaultSubtreeRootThreshold)
+			assert.Equal(b, tc.want, got)
+			sink = got
+		}
 	}
-	testCases := []testCase{
-		{input: 1, want: 1},
-		{input: 2, want: 2},
-		{input: 4, want: 4},
-		{input: 5, want: 4},
-		{input: 8, want: 8},
-		{input: 11, want: 8},
-		{input: 511, want: 256},
+
+	if sink == nil {
+		b.Fatal("Benchmark did not run!")
 	}
-	for _, tc := range testCases {
-		got, err := inclusion.RoundDownPowerOfTwo(tc.input)
-		require.NoError(t, err)
-		assert.Equal(t, tc.want, got)
+	sink = nil
+}
+
+func BenchmarkRoundDownPowerOfTwo(b *testing.B) {
+	b.ReportAllocs()
+
+	for i := 0; i < b.N; i++ {
+		for _, tc := range roundDownTestCases {
+			got, _ := inclusion.RoundDownPowerOfTwo(tc.input)
+			assert.Equal(b, tc.want, got)
+			sink = got
+		}
+	}
+
+	if sink == nil {
+		b.Fatal("Benchmark did not run!")
+	}
+	sink = nil
+}
+
+func BenchmarkRoundUpPowerOfTwo(b *testing.B) {
+	b.ReportAllocs()
+
+	for i := 0; i < b.N; i++ {
+		for _, tc := range roundUpTestCases {
+			got := inclusion.RoundUpPowerOfTwo(tc.input)
+			assert.Equal(b, tc.want, got)
+			sink = got
+		}
+	}
+
+	if sink == nil {
+		b.Fatal("Benchmark did not run!")
+	}
+	sink = nil
+}
+
+type roundDownTestCase struct {
+	input int
+	want  int
+}
+
+var roundDownTestCases = []roundDownTestCase{
+	{input: 1, want: 1},
+	{input: 2, want: 2},
+	{input: 4, want: 4},
+	{input: 5, want: 4},
+	{input: 8, want: 8},
+	{input: 11, want: 8},
+	{input: 511, want: 256},
+	{input: math.MaxInt32 - 1, want: 1 << 30},
+	{input: math.MaxInt32, want: 1 << 30},
+	{input: math.MaxInt32 + 1, want: 1 << 31},
+	{input: math.MaxInt, want: 1 << 62},
+}
+
+func TestRoundDownPowerOfTwo(t *testing.T) {
+	for _, tc := range roundDownTestCases {
+		testName := fmt.Sprintf("%d=%x", tc.input, tc.input)
+		t.Run(testName, func(t *testing.T) {
+			got, err := inclusion.RoundDownPowerOfTwo(tc.input)
+			require.NoError(t, err)
+			assert.Equal(t, tc.want, got)
+		})
 	}
 }