big: Improvements to Rat.SetString

* Allow an exponent part. This is necessary for exp/eval.
* Fix a bug for input that had no numbers after the decimal.
* In Int.SetString, allow a leading + sign.
* In Int.SetString, error if the input is "-" with no number.
* In nat.scan, normalize the resulting nat.

R=gri
CC=golang-dev
https://golang.org/cl/1733045

5 files changed, 61 insertions, 27 deletions

diff --git a/src/pkg/big/int.go b/src/pkg/big/int.go
index 873d5b50cf..f16c0d93a7 100755
--- a/src/pkg/big/int.go
+++ b/src/pkg/big/int.go
@@ -347,10 +347,12 @@ func (z *Int) SetString(s string, base int) (*Int, bool) {
 		return z, false
 	}
 
-	neg := false
-	if s[0] == '-' {
-		neg = true
+	neg := s[0] == '-'
+	if neg || s[0] == '+' {
 		s = s[1:]
+		if len(s) == 0 {
+			return z, false
+		}
 	}
 
 	var scanned int
diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go
index 269c814d46..82b5417dae 100755
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -219,6 +219,7 @@ var stringTests = []stringTest{
 	stringTest{in: "a", ok: false},
 	stringTest{in: "z", ok: false},
 	stringTest{in: "+", ok: false},
+	stringTest{in: "-", ok: false},
 	stringTest{in: "0b", ok: false},
 	stringTest{in: "0x", ok: false},
 	stringTest{in: "2", base: 2, ok: false},
@@ -230,13 +231,17 @@ var stringTests = []stringTest{
 	stringTest{"0", "0", 0, 0, true},
 	stringTest{"0", "0", 10, 0, true},
 	stringTest{"0", "0", 16, 0, true},
+	stringTest{"+0", "0", 0, 0, true},
+	stringTest{"-0", "0", 0, 0, true},
 	stringTest{"10", "10", 0, 10, true},
 	stringTest{"10", "10", 10, 10, true},
 	stringTest{"10", "10", 16, 16, true},
 	stringTest{"-10", "-10", 16, -16, true},
+	stringTest{"+10", "10", 16, 16, true},
 	stringTest{"0x10", "16", 0, 16, true},
 	stringTest{in: "0x10", base: 16, ok: false},
 	stringTest{"-0x10", "-16", 0, -16, true},
+	stringTest{"+0x10", "16", 0, 16, true},
 	stringTest{"00", "0", 0, 0, true},
 	stringTest{"0", "0", 8, 0, true},
 	stringTest{"07", "7", 0, 7, true},
diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go
index dc2e6be288..72d9f05ee2 100755
--- a/src/pkg/big/nat.go
+++ b/src/pkg/big/nat.go
@@ -103,9 +103,7 @@ func (z nat) setUint64(x uint64) nat {
 
 func (z nat) set(x nat) nat {
 	z = z.make(len(x))
-	for i, d := range x {
-		z[i] = d
-	}
+	copy(z, x)
 	return z
 }
 
@@ -666,7 +664,7 @@ func (z nat) scan(s string, base int) (nat, int, int) {
 		}
 	}
 
-	return z, base, i
+	return z.norm(), base, i
 }
 
 
diff --git a/src/pkg/big/rat.go b/src/pkg/big/rat.go
index ddd858d5ce..c465ab86bf 100644
--- a/src/pkg/big/rat.go
+++ b/src/pkg/big/rat.go
@@ -186,26 +186,17 @@ func (z *Rat) Set(x *Rat) *Rat {
 
 
 // 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 decimal number "a.b".
-// If the operation failed, the value of z is undefined.
+// 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.
 func (z *Rat) SetString(s string) (*Rat, bool) {
 	if len(s) == 0 {
 		return z, false
 	}
 
-	// Check for a decimal point
-	sep := strings.Index(s, ".")
-	if sep < 0 {
-		// Check for a quotient
-		sep = strings.Index(s, "/")
-		if sep < 0 {
-			// Just read in the string as an integer
-			if _, ok := z.a.SetString(s, 10); !ok {
-				return z, false
-			}
-			z.b = z.b.setWord(1)
-			return z, true
-		}
+	// check for a quotient
+	sep := strings.Index(s, "/")
+	if sep >= 0 {
 		if _, ok := z.a.SetString(s[0:sep], 10); !ok {
 			return z, false
 		}
@@ -214,17 +205,42 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
 		if z.b, _, n = z.b.scan(s, 10); n != len(s) {
 			return z, false
 		}
-
 		return z.norm(), true
 	}
 
-	s = s[0:sep] + s[sep+1:]
+	// check for a decimal point
+	sep = strings.Index(s, ".")
+	// check for an exponent
+	e := strings.IndexAny(s, "eE")
+	var exp Int
+	if e >= 0 {
+		if e < sep {
+			// The E must come after the decimal point.
+			return z, false
+		}
+		if _, ok := exp.SetString(s[e+1:], 10); !ok {
+			return z, false
+		}
+		s = s[0:e]
+	}
+	if sep >= 0 {
+		s = s[0:sep] + s[sep+1:]
+		exp.Sub(&exp, NewInt(int64(len(s)-sep)))
+	}
+
 	if _, ok := z.a.SetString(s, 10); !ok {
 		return z, false
 	}
-	z.b = z.b.expNN(natTen, nat{Word(len(s) - sep)}, nil)
+	powTen := nat{}.expNN(natTen, exp.abs, nil)
+	if exp.neg {
+		z.b = powTen
+		z.norm()
+	} else {
+		z.a.abs = z.a.abs.mul(z.a.abs, powTen)
+		z.b = z.b.setWord(1)
+	}
 
-	return z.norm(), true
+	return z, true
 }
 
 
@@ -257,7 +273,7 @@ func (z *Rat) FloatString(prec int) string {
 	r = r.mul(r, p)
 	r, r2 := r.div(nat{}, r, z.b)
 
-	// See if we need to round up
+	// see if we need to round up
 	r2 = r2.mul(r2, natTwo)
 	if z.b.cmp(r2) <= 0 {
 		r = r.add(r, natOne)
diff --git a/src/pkg/big/rat_test.go b/src/pkg/big/rat_test.go
index 2379cc0d56..c74ec857f3 100644
--- a/src/pkg/big/rat_test.go
+++ b/src/pkg/big/rat_test.go
@@ -17,6 +17,13 @@ var setStringTests = []setStringTest{
 	setStringTest{"-0", "0", true},
 	setStringTest{"1", "1", true},
 	setStringTest{"-1", "-1", true},
+	setStringTest{"1.", "1", true},
+	setStringTest{"1e0", "1", true},
+	setStringTest{"1.e1", "10", true},
+	setStringTest{in: "1e", ok: false},
+	setStringTest{in: "1.e", ok: false},
+	setStringTest{in: "1e+14e-5", ok: false},
+	setStringTest{in: "1e4.5", ok: false},
 	setStringTest{in: "r", ok: false},
 	setStringTest{in: "a/b", ok: false},
 	setStringTest{in: "a.b", ok: false},
@@ -25,6 +32,12 @@ var setStringTests = []setStringTest{
 	setStringTest{"2/4", "1/2", true},
 	setStringTest{".25", "1/4", true},
 	setStringTest{"-1/5", "-1/5", true},
+	setStringTest{"8129567.7690E14", "812956776900000000000", true},
+	setStringTest{"78189e+4", "781890000", true},
+	setStringTest{"553019.8935e+8", "55301989350000", true},
+	setStringTest{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
+	setStringTest{"9877861857500000E-7", "3951144743/4", true},
+	setStringTest{"2169378.417e-3", "2169378417/1000000", true},
 	setStringTest{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
 	setStringTest{"53/70893980658822810696", "53/70893980658822810696", true},
 	setStringTest{"106/141787961317645621392", "53/70893980658822810696", true},