math/big: implemented Float.Rat

Change-Id: If516e12d4b5dfb6f9288437d270569f7e4e2a1cd
Reviewed-on: https://go-review.googlesource.com/5871
Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/float.go

@@ -789,6 +789,7 @@ func (x *Float) Float64() (float64, Accuracy) {
 // if x is an infinity. The result is Exact if x.IsInt();
 // otherwise it is Below for x > 0, and Above for x < 0.
 func (x *Float) Int() (res *Int, acc Accuracy) {
+	// TODO(gri) accept z argument for result storage (see Float.Rat below)
 	if debugFloat {
 		validate(x)
 	}
@@ -830,9 +831,45 @@ func (x *Float) Int() (res *Int, acc Accuracy) {
 	return
 }
 
-// BUG(gri) Rat is not yet implemented
-func (x *Float) Rat() *Rat {
-	panic("unimplemented")
+// Rat returns x converted into an exact fraction; or nil if x is an infinity.
+// If a non-nil *Rat argument z is provided, it is used to store the result;
+// otherwise a new Rat is allocated.
+func (x *Float) Rat(z *Rat) *Rat {
+	if debugFloat {
+		validate(x)
+	}
+	// pick off easy cases
+	switch x.ord() {
+	case -2, +2:
+		return nil // ±Inf
+	case 0:
+		if z == nil {
+			return new(Rat)
+		}
+		return z.SetInt64(0)
+	}
+	// x != 0 && x != ±Inf
+	allBits := int32(len(x.mant)) * _W
+	// build up numerator and denominator
+	if z == nil {
+		z = new(Rat)
+	}
+	z.a.neg = x.neg
+	switch {
+	case x.exp > allBits:
+		z.a.abs = z.a.abs.shl(x.mant, uint(x.exp-allBits))
+		z.b.abs = z.b.abs[:0] // == 1 (see Rat)
+		return z              // already in normal form
+	default:
+		z.a.abs = z.a.abs.set(x.mant)
+		z.b.abs = z.b.abs[:0] // == 1 (see Rat)
+		return z              // already in normal form
+	case x.exp < allBits:
+		z.a.abs = z.a.abs.set(x.mant)
+		t := z.b.abs.setUint64(1)
+		z.b.abs = t.shl(t, uint(allBits-x.exp))
+		return z.norm()
+	}
 }
 
 // Abs sets z to the (possibly rounded) value |x| (the absolute value of x)

src/math/big/float_test.go

@@ -149,7 +149,7 @@ func TestFloatMantExp(t *testing.T) {
 		frac := makeFloat(test.frac)
 		f, e := x.MantExp(nil)
 		if !feq(f, frac) || e != test.exp {
-			t.Errorf("%s.MantExp() = %s, %d; want %s, %d", test.x, f.Format('g', 10), e, test.frac, test.exp)
+			t.Errorf("%s.MantExp(nil) = %s, %d; want %s, %d", test.x, f.Format('g', 10), e, test.frac, test.exp)
 		}
 	}
 }
@@ -158,10 +158,10 @@ func TestFloatMantExpAliasing(t *testing.T) {
 	x := makeFloat("0.5p10")
 	z := new(Float)
 	if m, _ := x.MantExp(z); m != z {
-		t.Fatalf("MantExp didn't use supplied *Float")
+		t.Fatalf("Float.MantExp didn't use supplied *Float")
 	}
 	if _, e := x.MantExp(x); e != 10 {
-		t.Fatalf("MantExp aliasing error: got %d; want 10", e)
+		t.Fatalf("Float.MantExp aliasing error: got %d; want 10", e)
 	}
 }
 
@@ -692,7 +692,7 @@ func TestFloatInt64(t *testing.T) {
 func TestFloatInt(t *testing.T) {
 	for _, test := range []struct {
 		x    string
-		out string
+		want string
 		acc  Accuracy
 	}{
 		{"0", "0", Exact},
@@ -714,19 +714,64 @@ func TestFloatInt(t *testing.T) {
 		{"1e+100", "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", Exact},
 	} {
 		x := makeFloat(test.x)
-		out, acc := x.Int()
+		res, acc := x.Int()
 		got := "nil"
-		if out != nil {
-			got = out.String()
+		if res != nil {
+			got = res.String()
 		}
-		if got != test.out || acc != test.acc {
-			t.Errorf("%s: got %s (%s); want %s (%s)", test.x, got, acc, test.out, test.acc)
+		if got != test.want || acc != test.acc {
+			t.Errorf("%s: got %s (%s); want %s (%s)", test.x, got, acc, test.want, test.acc)
 		}
 	}
 }
 
 func TestFloatRat(t *testing.T) {
-	// TODO(gri) implement this
+	for _, test := range []struct {
+		x, want string
+	}{
+		{"0", "0/1"},
+		{"+0", "0/1"},
+		{"-0", "0/1"},
+		{"Inf", "nil"},
+		{"+Inf", "nil"},
+		{"-Inf", "nil"},
+		{"1", "1/1"},
+		{"-1", "-1/1"},
+		{"1.25", "5/4"},
+		{"-1.25", "-5/4"},
+		{"1e10", "10000000000/1"},
+		{"1p10", "1024/1"},
+		{"-1p-10", "-1/1024"},
+		{"3.14159265", "7244019449799623199/2305843009213693952"},
+	} {
+		x := makeFloat(test.x).SetPrec(64)
+		res := x.Rat(nil)
+		got := "nil"
+		if res != nil {
+			got = res.String()
+		}
+		if got != test.want {
+			t.Errorf("%s: got %s; want %s", test.x, got, test.want)
+			continue
+		}
+
+		// inverse conversion
+		if res != nil {
+			got := new(Float).SetPrec(64).SetRat(res)
+			if got.Cmp(x) != 0 {
+				t.Errorf("%s: got %s; want %s", test.x, got, x)
+			}
+		}
+	}
+
+	// check that supplied *Rat is used
+	for _, f := range []string{"0", "1"} {
+		x := makeFloat(f)
+		r := new(Rat)
+		if res := x.Rat(r); res != r {
+			t.Errorf("(%s).Rat is not using supplied *Rat", f)
+		}
+	}
 }
 
 func TestFloatAbs(t *testing.T) {