// checkIsBestApprox32 checks that f is the best possible float32
// approximation of r.
// Returns true on success.
func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
if math.Abs(float64(f)) >= math.MaxFloat32 {
// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
// But we have tests for these special cases.
return true
}
// r must be strictly between f0 and f1, the floats bracketing f.
f0 := math.Nextafter32(f, float32(math.Inf(-1)))
f1 := math.Nextafter32(f, float32(math.Inf(+1)))
// For f to be correct, r must be closer to f than to f0 or f1.
df := delta(r, float64(f))
df0 := delta(r, float64(f0))
df1 := delta(r, float64(f1))
if df.Cmp(df0) > 0 {
t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
return false
}
if df.Cmp(df1) > 0 {
t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
return false
}
if df.Cmp(df0) == 0 && !isEven32(f) {
t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
return false
}
if df.Cmp(df1) == 0 && !isEven32(f) {
t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
return false
}
return true
}
func TestRound(t *testing.T) {
ival := []float32{0}
x := float32(1)
for !math.IsInf(float64(x), 1) {
ival = append(ival, x)
x *= 2
}
fval := []float32{}
x = 0.5
for x != 0 {
fval = append(fval, x, math.Nextafter32(x, 1), math.Nextafter32(x, -1))
x /= 2
}
for _, i := range ival {
for _, f := range fval {
x := i + f
y := Round(x)
d := Abs(y - x)
assert(d <= 0.5, "Round/Abs", t)
assert(d < 0.5 || int(y)&1 == 0, "Round/Abs", t)
assert(Round(-x) == -Round(x), "Round", t)
assert(Signbit(Round(-x)) == !Signbit(y), "Signbit/Round", t)
}
}
}
func TestRasterizeAlmostAxisAligned(t *testing.T) {
z := NewRasterizer(8, 8)
z.MoveTo(2, 2)
z.LineTo(6, math.Nextafter32(2, 0))
z.LineTo(6, 6)
z.LineTo(math.Nextafter32(2, 0), 6)
z.ClosePath()
dst := image.NewAlpha(z.Bounds())
z.Draw(dst, dst.Bounds(), image.Opaque, image.Point{})
if err := checkCornersCenter(dst); err != nil {
t.Error(err)
}
}
func TestTrunc(t *testing.T) {
ival := []float32{}
x := float32(1)
for !math.IsInf(float64(x), 1) {
ival = append(ival, x)
x *= 2
}
fval := []float32{}
x = math.Nextafter32(1, -1)
for x != 0 {
fval = append(fval, x)
x = 1 - (1-x)*2
}
for _, i := range ival {
for _, f := range fval {
x := i + f
y := Trunc(x)
assert(y == i || x-i == 1, "Trunc", t)
z := Trunc(-x)
assert(z == -y, "Trunc", t)
assert(Signbit(Trunc(-x)) == !Signbit(y), "Signbit/Trunc", t)
}
}
}
func init() {
epsilon32 = math.Nextafter32(1, 2) - 1
}
func TestMarshalFloat(t *testing.T) {
t.Parallel()
nfail := 0
test := func(f float64, bits int) {
vf := interface{}(f)
if bits == 32 {
f = float64(float32(f)) // round
vf = float32(f)
}
bout, err := Marshal(vf)
if err != nil {
t.Errorf("Marshal(%T(%g)): %v", vf, vf, err)
nfail++
return
}
out := string(bout)
// result must convert back to the same float
g, err := strconv.ParseFloat(out, bits)
if err != nil {
t.Errorf("Marshal(%T(%g)) = %q, cannot parse back: %v", vf, vf, out, err)
nfail++
return
}
if f != g || fmt.Sprint(f) != fmt.Sprint(g) { // fmt.Sprint handles ±0
t.Errorf("Marshal(%T(%g)) = %q (is %g, not %g)", vf, vf, out, float32(g), vf)
nfail++
return
}
bad := badFloatREs
if bits == 64 {
bad = bad[:len(bad)-2]
}
for _, re := range bad {
if re.MatchString(out) {
t.Errorf("Marshal(%T(%g)) = %q, must not match /%s/", vf, vf, out, re)
nfail++
return
}
}
}
var (
bigger = math.Inf(+1)
smaller = math.Inf(-1)
)
var digits = "1.2345678901234567890123"
for i := len(digits); i >= 2; i-- {
for exp := -30; exp <= 30; exp++ {
for _, sign := range "+-" {
for bits := 32; bits <= 64; bits += 32 {
s := fmt.Sprintf("%c%se%d", sign, digits[:i], exp)
f, err := strconv.ParseFloat(s, bits)
if err != nil {
log.Fatal(err)
}
next := math.Nextafter
if bits == 32 {
next = func(g, h float64) float64 {
return float64(math.Nextafter32(float32(g), float32(h)))
}
}
test(f, bits)
test(next(f, bigger), bits)
test(next(f, smaller), bits)
if nfail > 50 {
t.Fatalf("stopping test early")
}
}
}
}
}
test(0, 64)
test(math.Copysign(0, -1), 64)
test(0, 32)
test(math.Copysign(0, -1), 32)
}
func Nextafter32(x, y float32) float32 { return math.Nextafter32(x, y) }