step one

internal/numerics/search.go

@@ -0,0 +1,19 @@
+package numerics
+
+// Bisect returns the largest index i in [imin, imax] such that f(i) < target,
+// assuming f is monotonically nondecreasing on that range.
+//
+// If target <= f(imin), returns imin. If target > f(imax), returns imax.
+// Performs O(log(imax-imin)) evaluations of f.
+func Bisect(imin, imax int, target float64, f func(i int) float64) int {
+	lo, hi := imin, imax
+	for lo < hi {
+		mid := (lo + hi + 1) / 2
+		if target <= f(mid) {
+			hi = mid - 1
+		} else {
+			lo = mid
+		}
+	}
+	return lo
+}