init

fixed/fixed_test.go

@@ -0,0 +1,78 @@
+package fixed
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+func near(t *testing.T, name string, got F, want, tol float64) {
+	t.Helper()
+	if d := math.Abs(got.Float64() - want); d > tol {
+		t.Errorf("%s: got %v want %v (diff %g)", name, got.Float64(), want, d)
+	}
+}
+
+func TestMulDiv(t *testing.T) {
+	near(t, "mul", FromInt(3).Mul(FromRatio(1, 2)), 1.5, 1e-9)
+	near(t, "mulneg", FromInt(-3).Mul(FromRatio(1, 2)), -1.5, 1e-9)
+	near(t, "div", FromInt(1).Div(FromInt(3)), 1.0/3, 1e-9)
+	near(t, "divneg", FromInt(-7).Div(FromInt(2)), -3.5, 1e-9)
+	if FromInt(1<<30).Mul(FromInt(1<<30)) != Max {
+		t.Error("expected saturation")
+	}
+	if FromInt(1).Div(0) != Max || FromInt(-1).Div(0) != Min {
+		t.Error("div by zero should saturate")
+	}
+}
+
+func TestSqrt(t *testing.T) {
+	for _, v := range []float64{0.25, 1, 2, 3, 100, 1e6, 2e9} {
+		f := F(v * float64(One))
+		near(t, "sqrt", f.Sqrt(), math.Sqrt(v), 1e-8)
+	}
+	if IntSqrt(1<<62) != 1<<31 || IntSqrt(99) != 9 {
+		t.Error("IntSqrt")
+	}
+}
+
+func TestSinCos(t *testing.T) {
+	r := rand.New(rand.NewSource(1))
+	for i := 0; i < 2000; i++ {
+		a := (r.Float64() - 0.5) * 40
+		f := F(a * float64(One))
+		s, c := SinCos(f)
+		af := f.Float64()
+		near(t, "sin", s, math.Sin(af), 2e-9)
+		near(t, "cos", c, math.Cos(af), 2e-9)
+	}
+}
+
+func TestAtan2(t *testing.T) {
+	r := rand.New(rand.NewSource(2))
+	for i := 0; i < 2000; i++ {
+		x, y := (r.Float64()-0.5)*1e6, (r.Float64()-0.5)*1e6
+		got := Atan2(F(y*float64(One)), F(x*float64(One)))
+		near(t, "atan2", got, math.Atan2(y, x), 2e-8)
+	}
+	near(t, "atan2(0,-1)", Atan2(0, -One), math.Pi, 1e-8)
+}
+
+func TestVec3(t *testing.T) {
+	// A 3-4-12 vector has length 13; scale it far past what a naive x*x would allow.
+	v := Vec{FromInt(3_000_000), FromInt(4_000_000), FromInt(12_000_000)}
+	near(t, "norm3", v.Len(), 13_000_000, 1e-6)
+	u := Vec{FromInt(3), FromInt(4), FromInt(12)}.Unit()
+	near(t, "unit", u.Len(), 1, 1e-8)
+
+	d := FromSpherical(FromRatio(1, 2), FromRatio(3, 10))
+	near(t, "spherical len", d.Len(), 1, 1e-8)
+	near(t, "spherical z", d.Z, math.Sin(0.3), 1e-8)
+	near(t, "spherical x", d.X, math.Cos(0.3)*math.Cos(0.5), 1e-8)
+
+	r := Vec{One, 0, 0}.RotateX(HalfPi).RotateZ(HalfPi)
+	near(t, "rot x", r.X, 0, 1e-8)
+	near(t, "rot y", r.Y, 1, 1e-8)
+	r = Vec{0, One, 0}.RotateX(HalfPi)
+	near(t, "rotx z", r.Z, 1, 1e-8)
+}