math/big: avoid allocation in float.{Add, Sub} when there's no aliasing

name               old time/op    new time/op    delta
FloatAdd/10-4         116ns ± 1%      82ns ± 0%   -28.74%  (p=0.008 n=5+5)
FloatAdd/100-4        124ns ± 0%      86ns ± 1%   -30.34%  (p=0.016 n=4+5)
FloatAdd/1000-4       192ns ± 1%     123ns ± 0%   -35.94%  (p=0.008 n=5+5)
FloatAdd/10000-4      826ns ± 0%     438ns ± 0%   -46.99%  (p=0.000 n=4+5)
FloatAdd/100000-4    6.82µs ± 1%    3.36µs ± 0%   -50.74%  (p=0.008 n=5+5)
FloatSub/10-4         108ns ± 1%      77ns ± 1%   -29.06%  (p=0.008 n=5+5)
FloatSub/100-4        115ns ± 0%      79ns ± 0%   -31.48%  (p=0.029 n=4+4)
FloatSub/1000-4       168ns ± 0%      99ns ± 0%   -41.09%  (p=0.029 n=4+4)
FloatSub/10000-4      690ns ± 2%     288ns ± 1%   -58.24%  (p=0.008 n=5+5)
FloatSub/100000-4    5.37µs ± 1%    2.10µs ± 1%   -60.89%  (p=0.008 n=5+5)

name               old alloc/op   new alloc/op   delta
FloatAdd/10-4         48.0B ± 0%     0.0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatAdd/100-4        64.0B ± 0%     0.0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatAdd/1000-4        176B ± 0%       0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatAdd/10000-4     1.41kB ± 0%   0.00kB ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatAdd/100000-4    13.6kB ± 0%    0.0kB ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatSub/10-4         48.0B ± 0%     0.0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatSub/100-4        64.0B ± 0%     0.0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatSub/1000-4        176B ± 0%       0B ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatSub/10000-4     1.41kB ± 0%   0.00kB ±NaN%  -100.00%  (p=0.008 n=5+5)
FloatSub/100000-4    13.6kB ± 0%    0.0kB ±NaN%  -100.00%  (p=0.008 n=5+5)

Fixes #14868

Change-Id: Ia2b8b1a8ef0868288ecb25f812b17bd03ff40d1c
Reviewed-on: https://go-review.googlesource.com/23568Reviewed-by: Robert Griesemer <gri@golang.org>

src/math/big/float.go

@@ -1210,20 +1210,30 @@ func (z *Float) uadd(x, y *Float) {
 	ex := int64(x.exp) - int64(len(x.mant))*_W
 	ey := int64(y.exp) - int64(len(y.mant))*_W
 
+	al := alias(z.mant, x.mant) || alias(z.mant, y.mant)
+
 	// TODO(gri) having a combined add-and-shift primitive
 	//           could make this code significantly faster
 	switch {
 	case ex < ey:
-		// cannot re-use z.mant w/o testing for aliasing
-		t := nat(nil).shl(y.mant, uint(ey-ex))
-		z.mant = z.mant.add(x.mant, t)
+		if al {
+			t := nat(nil).shl(y.mant, uint(ey-ex))
+			z.mant = z.mant.add(x.mant, t)
+		} else {
+			z.mant = z.mant.shl(y.mant, uint(ey-ex))
+			z.mant = z.mant.add(x.mant, z.mant)
+		}
 	default:
 		// ex == ey, no shift needed
 		z.mant = z.mant.add(x.mant, y.mant)
 	case ex > ey:
-		// cannot re-use z.mant w/o testing for aliasing
-		t := nat(nil).shl(x.mant, uint(ex-ey))
-		z.mant = z.mant.add(t, y.mant)
+		if al {
+			t := nat(nil).shl(x.mant, uint(ex-ey))
+			z.mant = z.mant.add(t, y.mant)
+		} else {
+			z.mant = z.mant.shl(x.mant, uint(ex-ey))
+			z.mant = z.mant.add(z.mant, y.mant)
+		}
 		ex = ey
 	}
 	// len(z.mant) > 0
@@ -1247,18 +1257,28 @@ func (z *Float) usub(x, y *Float) {
 	ex := int64(x.exp) - int64(len(x.mant))*_W
 	ey := int64(y.exp) - int64(len(y.mant))*_W
 
+	al := alias(z.mant, x.mant) || alias(z.mant, y.mant)
+
 	switch {
 	case ex < ey:
-		// cannot re-use z.mant w/o testing for aliasing
-		t := nat(nil).shl(y.mant, uint(ey-ex))
-		z.mant = t.sub(x.mant, t)
+		if al {
+			t := nat(nil).shl(y.mant, uint(ey-ex))
+			z.mant = t.sub(x.mant, t)
+		} else {
+			z.mant = z.mant.shl(y.mant, uint(ey-ex))
+			z.mant = z.mant.sub(x.mant, z.mant)
+		}
 	default:
 		// ex == ey, no shift needed
 		z.mant = z.mant.sub(x.mant, y.mant)
 	case ex > ey:
-		// cannot re-use z.mant w/o testing for aliasing
-		t := nat(nil).shl(x.mant, uint(ex-ey))
-		z.mant = t.sub(t, y.mant)
+		if al {
+			t := nat(nil).shl(x.mant, uint(ex-ey))
+			z.mant = t.sub(t, y.mant)
+		} else {
+			z.mant = z.mant.shl(x.mant, uint(ex-ey))
+			z.mant = z.mant.sub(z.mant, y.mant)
+		}
 		ex = ey
 	}
 

src/math/big/float_test.go

@@ -1762,3 +1762,41 @@ func TestFloatCmpSpecialValues(t *testing.T) {
 		}
 	}
 }
+
+func BenchmarkFloatAdd(b *testing.B) {
+	x := new(Float)
+	y := new(Float)
+	z := new(Float)
+
+	for _, prec := range []uint{10, 1e2, 1e3, 1e4, 1e5} {
+		x.SetPrec(prec).SetRat(NewRat(1, 3))
+		y.SetPrec(prec).SetRat(NewRat(1, 6))
+		z.SetPrec(prec)
+
+		b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
+			b.ReportAllocs()
+			for i := 0; i < b.N; i++ {
+				z.Add(x, y)
+			}
+		})
+	}
+}
+
+func BenchmarkFloatSub(b *testing.B) {
+	x := new(Float)
+	y := new(Float)
+	z := new(Float)
+
+	for _, prec := range []uint{10, 1e2, 1e3, 1e4, 1e5} {
+		x.SetPrec(prec).SetRat(NewRat(1, 3))
+		y.SetPrec(prec).SetRat(NewRat(1, 6))
+		z.SetPrec(prec)
+
+		b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
+			b.ReportAllocs()
+			for i := 0; i < b.N; i++ {
+				z.Sub(x, y)
+			}
+		})
+	}
+}