interp: increase speed of findSegment

Using slices.BinarySearch instead of sort.Search increases the speed of
findSegment by a factor of two and overall performance by about 30%.

goos: linux
goarch: amd64
pkg: gonum.org/v1/gonum/interp
cpu: AMD Ryzen 7 5800 8-Core Processor
                            │  old.bench   │              new.bench              │
                            │    sec/op    │   sec/op     vs base                │
FindSegment-16                104.60n ± 1%   50.78n ± 1%  -51.45% (p=0.000 n=10)
NewPiecewiseLinear-16          114.5n ± 5%   112.2n ± 2%        ~ (p=0.109 n=10)
PiecewiseLinearPredict-16     116.00n ± 1%   84.44n ± 2%  -27.21% (p=0.000 n=10)
PiecewiseConstantPredict-16    87.95n ± 2%   63.93n ± 1%  -27.31% (p=0.000 n=10)
geomean                        105.2n        74.47n       -29.18%

interp/interp.go

@@ -4,7 +4,7 @@
 
 package interp
 
-import "sort"
+import "slices"
 
 const (
 	differentLengths        = "interp: input slices have different lengths"
@@ -156,10 +156,13 @@ func (pc PiecewiseConstant) Predict(x float64) float64 {
 }
 
 // findSegment returns 0 <= i < len(xs) such that xs[i] <= x < xs[i + 1], where xs[len(xs)]
-// is assumed to be +Inf. If no such i is found, it returns -1. It assumes that len(xs) >= 2
+// is assumed to be +Inf. If no such i is found, it returns -1.
-// without checking.
 func findSegment(xs []float64, x float64) int {
-	return sort.Search(len(xs), func(i int) bool { return xs[i] > x }) - 1
+	i, found := slices.BinarySearch(xs, x)
+	if !found {
+		return i - 1
+	}
+	return i
 }
 
 // calculateSlopes calculates slopes (ys[i+1] - ys[i]) / (xs[i+1] - xs[i]).

interp/interp_test.go

@@ -50,6 +50,28 @@ func TestFindSegment(t *testing.T) {
 	}
 }
 
+func TestFindSegmentEdgeCases(t *testing.T) {
+	t.Parallel()
+
+	cases := []struct {
+		xs   []float64
+		x    float64
+		want int
+	}{
+		{xs: nil, x: 0, want: -1},
+		{xs: []float64{0}, x: -1, want: -1},
+		{xs: []float64{0}, x: 0, want: 0},
+		{xs: []float64{0}, x: 1, want: 0},
+	}
+
+	for _, test := range cases {
+		if got := findSegment(test.xs, test.x); got != test.want {
+			t.Errorf("unexpected value of findSegment(%v, %f): got %d want: %d",
+				test.xs, test.x, got, test.want)
+		}
+	}
+}
+
 func BenchmarkFindSegment(b *testing.B) {
 	xs := []float64{0, 1.5, 3, 4.5, 6, 7.5, 9, 12, 13.5, 16.5}
 	for i := 0; i < b.N; i++ {