tests: verify rounding parameter effects for Add/Mul/Div in IEEE mode across rounding modes

Author: dndungu

arithmetic_rounding_test.go

@@ -0,0 +1,110 @@
+package float16
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+func modes() []RoundingMode {
+	return []RoundingMode{
+		RoundNearestEven,
+		RoundNearestAway,
+		RoundTowardZero,
+		RoundTowardPositive,
+		RoundTowardNegative,
+	}
+}
+
+func TestAddWithMode_RoundingMatchesConverter(t *testing.T) {
+	cases := [][2]float32{
+		{1.0, float32(math.Pow(2, -11))},     // halfway between 1.0 and next
+		{1.0, 1e-3},                          // general positive
+		{-1.0, float32(math.Pow(2, -11))},    // negative with halfway increment
+		{-0.75, 0.125},                       // mixed signs, exact binary fractions
+	}
+
+	for _, c := range cases {
+		for _, m := range modes() {
+			name := func(a, b float32, mode RoundingMode) string {
+				return fmt.Sprintf("a=%g b=%g mode=%v", a, b, mode)
+			}(c[0], c[1], m)
+			t.Run(name, func(t *testing.T) {
+				a16 := FromFloat32(c[0])
+				b16 := FromFloat32(c[1])
+				expected := FromFloat32WithRounding(a16.ToFloat32()+b16.ToFloat32(), m)
+				got, err := AddWithMode(a16, b16, ModeIEEEArithmetic, m)
+				if err != nil {
+					t.Fatalf("unexpected error: %v", err)
+				}
+				if got != expected {
+					t.Fatalf("AddWithMode mismatch: got=%v want=%v (a=%g b=%g mode=%v)", got, expected, c[0], c[1], m)
+				}
+			})
+		}
+	}
+}
+
+func TestMulWithMode_RoundingMatchesConverter(t *testing.T) {
+	cases := [][2]float32{
+		{1.25, 0.2},          // positive * positive
+		{-1.25, 0.2},         // negative * positive
+		{1.5, -0.75},         // positive * negative
+		{-0.5, -0.125},       // negative * negative
+		{float32(math.Pow(2, -3)), float32(math.Pow(2, -8))}, // exact powers of two
+	}
+
+	for _, c := range cases {
+		for _, m := range modes() {
+			name := func(a, b float32, mode RoundingMode) string {
+				return fmt.Sprintf("a=%g b=%g mode=%v", a, b, mode)
+			}(c[0], c[1], m)
+			t.Run(name, func(t *testing.T) {
+				a16 := FromFloat32(c[0])
+				b16 := FromFloat32(c[1])
+				expected := FromFloat32WithRounding(a16.ToFloat32()*b16.ToFloat32(), m)
+				got, err := MulWithMode(a16, b16, ModeIEEEArithmetic, m)
+				if err != nil {
+					t.Fatalf("unexpected error: %v", err)
+				}
+				if got != expected {
+					t.Fatalf("MulWithMode mismatch: got=%v want=%v (a=%g b=%g mode=%v)", got, expected, c[0], c[1], m)
+				}
+			})
+		}
+	}
+}
+
+func TestDivWithMode_RoundingMatchesConverter(t *testing.T) {
+	cases := [][2]float32{
+		{1.25, 0.2},          // positive / positive
+		{-1.25, 0.2},         // negative / positive
+		{1.5, -0.75},         // positive / negative
+		{-0.5, -0.125},       // negative / negative
+		{7.0, 3.0},           // non-terminating in binary
+	}
+
+	for _, c := range cases {
+		// avoid division by zero
+		if c[1] == 0 {
+			continue
+		}
+		for _, m := range modes() {
+			name := func(a, b float32, mode RoundingMode) string {
+				return fmt.Sprintf("a=%g b=%g mode=%v", a, b, mode)
+			}(c[0], c[1], m)
+			t.Run(name, func(t *testing.T) {
+				a16 := FromFloat32(c[0])
+				b16 := FromFloat32(c[1])
+				expected := FromFloat32WithRounding(a16.ToFloat32()/b16.ToFloat32(), m)
+				got, err := DivWithMode(a16, b16, ModeIEEEArithmetic, m)
+				if err != nil {
+					t.Fatalf("unexpected error: %v", err)
+				}
+				if got != expected {
+					t.Fatalf("DivWithMode mismatch: got=%v want=%v (a=%g b=%g mode=%v)", got, expected, c[0], c[1], m)
+				}
+			})
+		}
+	}
+}