big: implemented Rat.Inv

Also:
- changed semantics of return values for [Int|Rat].SetString
  if an error occured (returned value is nil); will expose
  hidden errors where return values are not checked
- added more tests
- various cleanups throughout

Fixes #2384.

R=r
CC=golang-dev
https://golang.org/cl/5312044

src/pkg/big/int.go

@@ -58,22 +58,24 @@ func NewInt(x int64) *Int {
 
 // Set sets z to x and returns z.
 func (z *Int) Set(x *Int) *Int {
+	if z != x {
 		z.abs = z.abs.set(x.abs)
 		z.neg = x.neg
+	}
 	return z
 }
 
 // Abs sets z to |x| (the absolute value of x) and returns z.
 func (z *Int) Abs(x *Int) *Int {
-	z.abs = z.abs.set(x.abs)
+	z.Set(x)
 	z.neg = false
 	return z
 }
 
 // Neg sets z to -x and returns z.
 func (z *Int) Neg(x *Int) *Int {
-	z.abs = z.abs.set(x.abs)
-	z.neg = len(z.abs) > 0 && !x.neg // 0 has no sign
+	z.Set(x)
+	z.neg = len(z.abs) > 0 && !z.neg // 0 has no sign
 	return z
 }
 
@@ -422,8 +424,8 @@ func (x *Int) Format(s fmt.State, ch int) {
 // scan sets z to the integer value corresponding to the longest possible prefix
 // read from r representing a signed integer number in a given conversion base.
 // It returns z, the actual conversion base used, and an error, if any. In the
-// error case, the value of z is undefined. The syntax follows the syntax of
-// integer literals in Go.
+// error case, the value of z is undefined but the returned value is nil. The
+// syntax follows the syntax of integer literals in Go.
 //
 // The base argument must be 0 or a value from 2 through MaxBase. If the base
 // is 0, the string prefix determines the actual conversion base. A prefix of
@@ -434,7 +436,7 @@ func (z *Int) scan(r io.RuneScanner, base int) (*Int, int, os.Error) {
 	// determine sign
 	ch, _, err := r.ReadRune()
 	if err != nil {
-		return z, 0, err
+		return nil, 0, err
 	}
 	neg := false
 	switch ch {
@@ -448,7 +450,7 @@ func (z *Int) scan(r io.RuneScanner, base int) (*Int, int, os.Error) {
 	// determine mantissa
 	z.abs, base, err = z.abs.scan(r, base)
 	if err != nil {
-		return z, base, err
+		return nil, base, err
 	}
 	z.neg = len(z.abs) > 0 && neg // 0 has no sign
 
@@ -497,7 +499,7 @@ func (x *Int) Int64() int64 {
 
 // SetString sets z to the value of s, interpreted in the given base,
 // and returns z and a boolean indicating success. If SetString fails,
-// the value of z is undefined.
+// the value of z is undefined but the returned value is nil.
 //
 // The base argument must be 0 or a value from 2 through MaxBase. If the base
 // is 0, the string prefix determines the actual conversion base. A prefix of
@@ -508,10 +510,13 @@ func (z *Int) SetString(s string, base int) (*Int, bool) {
 	r := strings.NewReader(s)
 	_, _, err := z.scan(r, base)
 	if err != nil {
-		return z, false
+		return nil, false
 	}
 	_, _, err = r.ReadRune()
-	return z, err == os.EOF // err == os.EOF => scan consumed all of s
+	if err != os.EOF {
+		return nil, false
+	}
+	return z, true // err == os.EOF => scan consumed all of s
 }
 
 // SetBytes interprets buf as the bytes of a big-endian unsigned

src/pkg/big/int_test.go

@@ -311,7 +311,16 @@ func TestSetString(t *testing.T) {
 			t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok)
 			continue
 		}
-		if !ok1 || !ok2 {
+		if !ok1 {
+			if n1 != nil {
+				t.Errorf("#%d (input '%s') n1 != nil", i, test.in)
+			}
+			continue
+		}
+		if !ok2 {
+			if n2 != nil {
+				t.Errorf("#%d (input '%s') n2 != nil", i, test.in)
+			}
 			continue
 		}
 

src/pkg/big/rat.go

@@ -13,8 +13,8 @@ import (
 	"strings"
 )
 
-// A Rat represents a quotient a/b of arbitrary precision. The zero value for
-// a Rat, 0/0, is not a legal Rat.
+// A Rat represents a quotient a/b of arbitrary precision.
+// The zero value for a Rat, 0/0, is not a legal Rat.
 type Rat struct {
 	a Int
 	b nat
@@ -62,6 +62,39 @@ func (z *Rat) SetInt64(x int64) *Rat {
 	return z
 }
 
+// Set sets z to x (by making a copy of x) and returns z.
+func (z *Rat) Set(x *Rat) *Rat {
+	if z != x {
+		z.a.Set(&x.a)
+		z.b = z.b.set(x.b)
+	}
+	return z
+}
+
+// Abs sets z to |x| (the absolute value of x) and returns z.
+func (z *Rat) Abs(x *Rat) *Rat {
+	z.Set(x)
+	z.a.neg = false
+	return z
+}
+
+// Neg sets z to -x and returns z.
+func (z *Rat) Neg(x *Rat) *Rat {
+	z.Set(x)
+	z.a.neg = len(z.a.abs) > 0 && !z.a.neg // 0 has no sign
+	return z
+}
+
+// Inv sets z to 1/x and returns z.
+func (z *Rat) Inv(x *Rat) *Rat {
+	if len(x.a.abs) == 0 {
+		panic("division by zero")
+	}
+	z.Set(x)
+	z.a.abs, z.b = z.b, z.a.abs // sign doesn't change
+	return z
+}
+
 // Sign returns:
 //
 //	-1 if x <  0
@@ -133,17 +166,10 @@ func mulNat(x *Int, y nat) *Int {
 //    0 if x == y
 //   +1 if x >  y
 //
-func (x *Rat) Cmp(y *Rat) (r int) {
+func (x *Rat) Cmp(y *Rat) int {
 	return mulNat(&x.a, y.b).Cmp(mulNat(&y.a, x.b))
 }
 
-// Abs sets z to |x| (the absolute value of x) and returns z.
-func (z *Rat) Abs(x *Rat) *Rat {
-	z.a.Abs(&x.a)
-	z.b = z.b.set(x.b)
-	return z
-}
-
 // Add sets z to the sum x+y and returns z.
 func (z *Rat) Add(x, y *Rat) *Rat {
 	a1 := mulNat(&x.a, y.b)
@@ -183,20 +209,6 @@ func (z *Rat) Quo(x, y *Rat) *Rat {
 	return z.norm()
 }
 
-// Neg sets z to -x (by making a copy of x if necessary) and returns z.
-func (z *Rat) Neg(x *Rat) *Rat {
-	z.a.Neg(&x.a)
-	z.b = z.b.set(x.b)
-	return z
-}
-
-// Set sets z to x (by making a copy of x if necessary) and returns z.
-func (z *Rat) Set(x *Rat) *Rat {
-	z.a.Set(&x.a)
-	z.b = z.b.set(x.b)
-	return z
-}
-
 func ratTok(ch int) bool {
 	return strings.IndexRune("+-/0123456789.eE", ch) >= 0
 }
@@ -219,23 +231,23 @@ func (z *Rat) Scan(s fmt.ScanState, ch int) os.Error {
 
 // SetString sets z to the value of s and returns z and a boolean indicating
 // success. s can be given as a fraction "a/b" or as a floating-point number
-// optionally followed by an exponent. If the operation failed, the value of z
-// is undefined.
+// optionally followed by an exponent. If the operation failed, the value of
+// z is undefined but the returned value is nil.
 func (z *Rat) SetString(s string) (*Rat, bool) {
 	if len(s) == 0 {
-		return z, false
+		return nil, false
 	}
 
 	// check for a quotient
 	sep := strings.Index(s, "/")
 	if sep >= 0 {
 		if _, ok := z.a.SetString(s[0:sep], 10); !ok {
-			return z, false
+			return nil, false
 		}
 		s = s[sep+1:]
 		var err os.Error
 		if z.b, _, err = z.b.scan(strings.NewReader(s), 10); err != nil {
-			return z, false
+			return nil, false
 		}
 		return z.norm(), true
 	}
@@ -248,10 +260,10 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
 	if e >= 0 {
 		if e < sep {
 			// The E must come after the decimal point.
-			return z, false
+			return nil, false
 		}
 		if _, ok := exp.SetString(s[e+1:], 10); !ok {
-			return z, false
+			return nil, false
 		}
 		s = s[0:e]
 	}
@@ -261,7 +273,7 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
 	}
 
 	if _, ok := z.a.SetString(s, 10); !ok {
-		return z, false
+		return nil, false
 	}
 	powTen := nat{}.expNN(natTen, exp.abs, nil)
 	if exp.neg {

src/pkg/big/rat_test.go

@@ -50,8 +50,14 @@ func TestRatSetString(t *testing.T) {
 	for i, test := range setStringTests {
 		x, ok := new(Rat).SetString(test.in)
 
-		if ok != test.ok || ok && x.RatString() != test.out {
-			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
+		if ok {
+			if !test.ok {
+				t.Errorf("#%d SetString(%q) expected failure", i, test.in)
+			} else if x.RatString() != test.out {
+				t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
+			}
+		} else if x != nil {
+			t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
 		}
 	}
 }
@@ -113,8 +119,10 @@ func TestFloatString(t *testing.T) {
 func TestRatSign(t *testing.T) {
 	zero := NewRat(0, 1)
 	for _, a := range setStringTests {
-		var x Rat
-		x.SetString(a.in)
+		x, ok := new(Rat).SetString(a.in)
+		if !ok {
+			continue
+		}
 		s := x.Sign()
 		e := x.Cmp(zero)
 		if s != e {
@@ -153,12 +161,14 @@ func TestRatCmp(t *testing.T) {
 func TestIsInt(t *testing.T) {
 	one := NewInt(1)
 	for _, a := range setStringTests {
-		var x Rat
-		x.SetString(a.in)
+		x, ok := new(Rat).SetString(a.in)
+		if !ok {
+			continue
+		}
 		i := x.IsInt()
 		e := x.Denom().Cmp(one) == 0
 		if i != e {
-			t.Errorf("got %v; want %v for z = %v", i, e, &x)
+			t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
 		}
 	}
 }
@@ -166,16 +176,50 @@ func TestIsInt(t *testing.T) {
 func TestRatAbs(t *testing.T) {
 	zero := NewRat(0, 1)
 	for _, a := range setStringTests {
-		var z Rat
-		z.SetString(a.in)
-		var e Rat
-		e.Set(&z)
-		if e.Cmp(zero) < 0 {
-			e.Sub(zero, &e)
+		x, ok := new(Rat).SetString(a.in)
+		if !ok {
+			continue
 		}
-		z.Abs(&z)
-		if z.Cmp(&e) != 0 {
-			t.Errorf("got z = %v; want %v", &z, &e)
+		e := new(Rat).Set(x)
+		if e.Cmp(zero) < 0 {
+			e.Sub(zero, e)
+		}
+		z := new(Rat).Abs(x)
+		if z.Cmp(e) != 0 {
+			t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
+		}
+	}
+}
+
+func TestRatNeg(t *testing.T) {
+	zero := NewRat(0, 1)
+	for _, a := range setStringTests {
+		x, ok := new(Rat).SetString(a.in)
+		if !ok {
+			continue
+		}
+		e := new(Rat).Sub(zero, x)
+		z := new(Rat).Neg(x)
+		if z.Cmp(e) != 0 {
+			t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
+		}
+	}
+}
+
+func TestRatInv(t *testing.T) {
+	zero := NewRat(0, 1)
+	for _, a := range setStringTests {
+		x, ok := new(Rat).SetString(a.in)
+		if !ok {
+			continue
+		}
+		if x.Cmp(zero) == 0 {
+			continue // avoid division by zero
+		}
+		e := new(Rat).SetFrac(x.Denom(), x.Num())
+		z := new(Rat).Inv(x)
+		if z.Cmp(e) != 0 {
+			t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
 		}
 	}
 }
@@ -186,10 +230,10 @@ type ratBinArg struct {
 }
 
 func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
-	x, _ := NewRat(0, 1).SetString(a.x)
-	y, _ := NewRat(0, 1).SetString(a.y)
-	z, _ := NewRat(0, 1).SetString(a.z)
-	out := f(NewRat(0, 1), x, y)
+	x, _ := new(Rat).SetString(a.x)
+	y, _ := new(Rat).SetString(a.y)
+	z, _ := new(Rat).SetString(a.z)
+	out := f(new(Rat), x, y)
 
 	if out.Cmp(z) != 0 {
 		t.Errorf("%s #%d got %s want %s", name, i, out, z)