math/big: compute 10**exp efficiently when converting Floats

Change-Id: Ic2d9fdae43d18255c198ae62376212bdc89b75da
Reviewed-on: https://go-review.googlesource.com/8464
Reviewed-by: Alan Donovan <adonovan@google.com>

src/math/big/floatconv.go

@@ -163,24 +163,54 @@ func (z *Float) Scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
 	}
 	// exp10 != 0
 
-	// compute decimal exponent power
-	expabs := exp10
-	if expabs < 0 {
-		expabs = -expabs
-	}
-	powTen := nat(nil).expNN(natTen, nat(nil).setUint64(uint64(expabs)), nil)
-	fpowTen := new(Float).SetInt(new(Int).SetBits(powTen))
-
 	// apply 10**exp10
+	p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
 	if exp10 < 0 {
-		z.uquo(z, fpowTen)
+		z.uquo(z, p.pow10(-exp10))
 	} else {
-		z.umul(z, fpowTen)
+		z.umul(z, p.pow10(exp10))
 	}
 
 	return
 }
 
+// These powers of 10 can be represented exactly as a float64.
+var pow10tab = [...]float64{
+	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+}
+
+// pow10 sets z to 10**n and returns z.
+// n must not be negative.
+func (z *Float) pow10(n int64) *Float {
+	if n < 0 {
+		panic("pow10 called with negative argument")
+	}
+
+	const m = int64(len(pow10tab) - 1)
+	if n <= m {
+		return z.SetFloat64(pow10tab[n])
+	}
+	// n > m
+
+	z.SetFloat64(pow10tab[m])
+	n -= m
+
+	// use more bits for f than for z
+	// TODO(gri) what is the right number?
+	f := new(Float).SetPrec(z.Prec() + 64).SetInt64(10)
+
+	for n > 0 {
+		if n&1 != 0 {
+			z.Mul(z, f)
+		}
+		f.Mul(f, f)
+		n >>= 1
+	}
+
+	return z
+}
+
 // Parse is like z.Scan(r, base), but instead of reading from an
 // io.ByteScanner, it parses the string s. An error is also returned
 // if the string contains invalid or trailing bytes not belonging to

src/math/big/floatconv_test.go

@@ -330,6 +330,12 @@ func TestFloatFormat(t *testing.T) {
 		{"3e40", 100, 'f', 4, "30000000000000000000000000000000000000000.0000"},
 		{"3e40", 100, 'g', 40, "3e+40"},
 
+		// make sure "stupid" exponents don't stall the machine
+		{"1e1000000", 64, 'p', 0, "0x.88b3a28a05eade3ap3321929"},
+		{"1e1000000000", 64, 'p', 0, "0x.ecc5f45aa573d3p1538481529"},
+		{"1e-1000000", 64, 'p', 0, "0x.efb4542cc8ca418ap-3321928"},
+		{"1e-1000000000", 64, 'p', 0, "0x.8a64dd983a4c7dabp-1538481528"},
+
 		// TODO(gri) need tests for actual large Floats
 
 		{"0", 53, 'b', 0, "0"},