Fix signed saturating math functions

util/arbmath/math.go

@@ -74,14 +74,6 @@ func MaxInt[T Number](values ...T) T {
 	return max
 }
 
-// AbsValue the absolute value of a number
-func AbsValue[T Number](value T) T {
-	if value < 0 {
-		return -value // never happens for unsigned types
-	}
-	return value
-}
-
 // Checks if two ints are sufficiently close to one another
 func Within[T Unsigned](a, b, bound T) bool {
 	min := MinInt(a, b)
@@ -267,14 +259,32 @@ func BigFloatMulByUint(multiplicand *big.Float, multiplier uint64) *big.Float {
 	return new(big.Float).Mul(multiplicand, UintToBigFloat(multiplier))
 }
 
+func MaxIntValue[T Integer]() T {
+	allBits := ^T(0)
+	if allBits < 0 {
+		// This is a signed integer
+		return T((uint64(1) << (8*unsafe.Sizeof(allBits) - 1)) - 1)
+	}
+	return allBits
+}
+
+func MinIntValue[T Integer]() T {
+	allBits := ^T(0)
+	if allBits < 0 {
+		// This is a signed integer
+		return T(uint64(1) << ((8 * unsafe.Sizeof(allBits)) - 1))
+	}
+	return 0
+}
+
 // SaturatingAdd add two integers without overflow
 func SaturatingAdd[T Signed](a, b T) T {
 	sum := a + b
 	if b > 0 && sum < a {
-		sum = ^T(0) >> 1
+		sum = MaxIntValue[T]()
 	}
 	if b < 0 && sum > a {
-		sum = (^T(0) >> 1) + 1
+		sum = MinIntValue[T]()
 	}
 	return sum
 }
@@ -290,7 +300,11 @@ func SaturatingUAdd[T Unsigned](a, b T) T {
 
 // SaturatingSub subtract an int64 from another without overflow
 func SaturatingSub(minuend, subtrahend int64) int64 {
-	return SaturatingAdd(minuend, -subtrahend)
+	if subtrahend == math.MinInt64 {
+		// The absolute value of MinInt64 is one greater than MaxInt64
+		return SaturatingAdd(SaturatingAdd(minuend, math.MaxInt64), 1)
+	}
+	return SaturatingAdd(minuend, SaturatingNeg(subtrahend))
 }
 
 // SaturatingUSub subtract an integer from another without underflow
@@ -315,9 +329,9 @@ func SaturatingMul[T Signed](a, b T) T {
 	product := a * b
 	if b != 0 && product/b != a {
 		if (a > 0 && b > 0) || (a < 0 && b < 0) {
-			product = ^T(0) >> 1
+			product = MaxIntValue[T]()
 		} else {
-			product = (^T(0) >> 1) + 1
+			product = MinIntValue[T]()
 		}
 	}
 	return product
@@ -367,8 +381,8 @@ func SaturatingCastToUint(value *big.Int) uint64 {
 
 // Negates an int without underflow
 func SaturatingNeg[T Signed](value T) T {
-	if value == ^T(0) {
-		return (^T(0)) >> 1
+	if value < 0 && value == MinIntValue[T]() {
+		return MaxIntValue[T]()
 	}
 	return -value
 }

util/arbmath/math_fuzz_test.go

@@ -0,0 +1,112 @@
+// Copyright 2024, Offchain Labs, Inc.
+// For license information, see https://github.com/nitro/blob/master/LICENSE
+
+package arbmath
+
+import (
+	"math/big"
+	"testing"
+)
+
+func toBig[T Signed](a T) *big.Int {
+	return big.NewInt(int64(a))
+}
+
+func saturatingBigToInt[T Signed](a *big.Int) T {
+	// MinIntValue and MaxIntValue are already separately tested
+	if a.Cmp(toBig(MaxIntValue[T]())) > 0 {
+		return MaxIntValue[T]()
+	}
+	if a.Cmp(toBig(MinIntValue[T]())) < 0 {
+		return MinIntValue[T]()
+	}
+	return T(a.Int64())
+}
+
+func fuzzSaturatingAdd[T Signed](f *testing.F) {
+	f.Fuzz(func(t *testing.T, a, b T) {
+		got := SaturatingAdd(a, b)
+		expected := saturatingBigToInt[T](new(big.Int).Add(toBig(a), toBig(b)))
+		if got != expected {
+			t.Errorf("SaturatingAdd(%v, %v) = %v, expected %v", a, b, got, expected)
+		}
+	})
+}
+
+func fuzzSaturatingMul[T Signed](f *testing.F) {
+	f.Fuzz(func(t *testing.T, a, b T) {
+		got := SaturatingMul(a, b)
+		expected := saturatingBigToInt[T](new(big.Int).Mul(toBig(a), toBig(b)))
+		if got != expected {
+			t.Errorf("SaturatingMul(%v, %v) = %v, expected %v", a, b, got, expected)
+		}
+	})
+}
+
+func fuzzSaturatingNeg[T Signed](f *testing.F) {
+	f.Fuzz(func(t *testing.T, a T) {
+		got := SaturatingNeg(a)
+		expected := saturatingBigToInt[T](new(big.Int).Neg(toBig(a)))
+		if got != expected {
+			t.Errorf("SaturatingNeg(%v) = %v, expected %v", a, got, expected)
+		}
+	})
+}
+
+func FuzzSaturatingAddInt8(f *testing.F) {
+	fuzzSaturatingAdd[int8](f)
+}
+
+func FuzzSaturatingAddInt16(f *testing.F) {
+	fuzzSaturatingAdd[int16](f)
+}
+
+func FuzzSaturatingAddInt32(f *testing.F) {
+	fuzzSaturatingAdd[int32](f)
+}
+
+func FuzzSaturatingAddInt64(f *testing.F) {
+	fuzzSaturatingAdd[int64](f)
+}
+
+func FuzzSaturatingSub(f *testing.F) {
+	f.Fuzz(func(t *testing.T, a, b int64) {
+		got := SaturatingSub(a, b)
+		expected := saturatingBigToInt[int64](new(big.Int).Sub(toBig(a), toBig(b)))
+		if got != expected {
+			t.Errorf("SaturatingSub(%v, %v) = %v, expected %v", a, b, got, expected)
+		}
+	})
+}
+
+func FuzzSaturatingMulInt8(f *testing.F) {
+	fuzzSaturatingMul[int8](f)
+}
+
+func FuzzSaturatingMulInt16(f *testing.F) {
+	fuzzSaturatingMul[int16](f)
+}
+
+func FuzzSaturatingMulInt32(f *testing.F) {
+	fuzzSaturatingMul[int32](f)
+}
+
+func FuzzSaturatingMulInt64(f *testing.F) {
+	fuzzSaturatingMul[int64](f)
+}
+
+func FuzzSaturatingNegInt8(f *testing.F) {
+	fuzzSaturatingNeg[int8](f)
+}
+
+func FuzzSaturatingNegInt16(f *testing.F) {
+	fuzzSaturatingNeg[int16](f)
+}
+
+func FuzzSaturatingNegInt32(f *testing.F) {
+	fuzzSaturatingNeg[int32](f)
+}
+
+func FuzzSaturatingNegInt64(f *testing.F) {
+	fuzzSaturatingNeg[int64](f)
+}

util/arbmath/math_test.go

@@ -5,6 +5,7 @@ package arbmath
 
 import (
 	"bytes"
+	"fmt"
 	"math"
 	"math/rand"
 	"testing"
@@ -120,6 +121,114 @@ func TestSlices(t *testing.T) {
 	assert_eq(SliceWithRunoff(data, 7, 8), []uint8{})
 }
 
+func testMinMaxValues[T Integer](t *testing.T, min T, max T) {
+	gotMin := MinIntValue[T]()
+	if gotMin != min {
+		Fail(t, "expected min", min, "but got", gotMin)
+	}
+	gotMax := MaxIntValue[T]()
+	if gotMax != max {
+		Fail(t, "expected max", max, "but got", gotMax)
+	}
+}
+
+func TestMinMaxValues(t *testing.T) {
+	testMinMaxValues[uint8](t, 0, math.MaxUint8)
+	testMinMaxValues[uint16](t, 0, math.MaxUint16)
+	testMinMaxValues[uint32](t, 0, math.MaxUint32)
+	testMinMaxValues[uint64](t, 0, math.MaxUint64)
+	testMinMaxValues[int8](t, math.MinInt8, math.MaxInt8)
+	testMinMaxValues[int16](t, math.MinInt16, math.MaxInt16)
+	testMinMaxValues[int32](t, math.MinInt32, math.MaxInt32)
+	testMinMaxValues[int64](t, math.MinInt64, math.MaxInt64)
+}
+
+func TestSaturatingAdd(t *testing.T) {
+	tests := []struct {
+		a, b, expected int64
+	}{
+		{2, 3, 5},
+		{-1, -2, -3},
+		{math.MaxInt64, 1, math.MaxInt64},
+		{math.MaxInt64, math.MaxInt64, math.MaxInt64},
+		{math.MinInt64, -1, math.MinInt64},
+		{math.MinInt64, math.MinInt64, math.MinInt64},
+	}
+
+	for _, tc := range tests {
+		t.Run(fmt.Sprintf("%v + %v = %v", tc.a, tc.b, tc.expected), func(t *testing.T) {
+			sum := SaturatingAdd(int64(tc.a), int64(tc.b))
+			if sum != tc.expected {
+				t.Errorf("SaturatingAdd(%v, %v) = %v; want %v", tc.a, tc.b, sum, tc.expected)
+			}
+		})
+	}
+}
+
+func TestSaturatingSub(t *testing.T) {
+	tests := []struct {
+		a, b, expected int64
+	}{
+		{5, 3, 2},
+		{-3, -2, -1},
+		{math.MinInt64, 1, math.MinInt64},
+		{math.MinInt64, -1, math.MinInt64 + 1},
+		{math.MinInt64, math.MinInt64, 0},
+		{0, math.MinInt64, math.MaxInt64},
+	}
+
+	for _, tc := range tests {
+		t.Run("", func(t *testing.T) {
+			sum := SaturatingSub(int64(tc.a), int64(tc.b))
+			if sum != tc.expected {
+				t.Errorf("SaturatingSub(%v, %v) = %v; want %v", tc.a, tc.b, sum, tc.expected)
+			}
+		})
+	}
+}
+
+func TestSaturatingMul(t *testing.T) {
+	tests := []struct {
+		a, b, expected int64
+	}{
+		{5, 3, 15},
+		{-3, -2, 6},
+		{math.MaxInt64, 2, math.MaxInt64},
+		{math.MinInt64, 2, math.MinInt64},
+	}
+
+	for _, tc := range tests {
+		t.Run(fmt.Sprintf("%v - %v = %v", tc.a, tc.b, tc.expected), func(t *testing.T) {
+			sum := SaturatingMul(int64(tc.a), int64(tc.b))
+			if sum != tc.expected {
+				t.Errorf("SaturatingMul(%v, %v) = %v; want %v", tc.a, tc.b, sum, tc.expected)
+			}
+		})
+	}
+}
+
+func TestSaturatingNeg(t *testing.T) {
+	tests := []struct {
+		value    int64
+		expected int64
+	}{
+		{0, 0},
+		{5, -5},
+		{-5, 5},
+		{math.MinInt64, math.MaxInt64},
+		{math.MaxInt64, math.MinInt64 + 1},
+	}
+
+	for _, tc := range tests {
+		t.Run(fmt.Sprintf("-%v = %v", tc.value, tc.expected), func(t *testing.T) {
+			result := SaturatingNeg(tc.value)
+			if result != tc.expected {
+				t.Errorf("SaturatingNeg(%v) = %v: expected %v", tc.value, result, tc.expected)
+			}
+		})
+	}
+}
+
 func Fail(t *testing.T, printables ...interface{}) {
 	t.Helper()
 	testhelpers.FailImpl(t, printables...)