sched_ext: Maintain an online cid mask in the scheduler arenagrafted

Schedulers on the default cid mapping treat [0, nr_online_cids) as the
online set and restart on hotplug. Schedulers that install their own mapping
with scx_bpf_cid_override() have no way to learn which cids are online: the
count no longer identifies members and the CPU-form cpumask is unusable from
cid programs. This is an obvious hole in the cid API.

Add scx_bpf_online_cmask(), a kernel-maintained cmask in the scheduler's
arena, allocated alongside the per-CPU scratch masks and populated after the
cid mapping is finalized and before ops.init(), for child schedulers too.
The pointer stays valid through ops.exit() with no reference to take. It is
the arena offset as a void pointer, the same form struct_ops arena arguments
arrive in. The verifier types the void return as a scalar for the program's
arena cast.

The mask follows the SCX hotplug notifications: seeded from cpu_active_mask
and updated before ops.cid_online/offline() runs, so it lags cpu_online_mask
only inside a hotplug transition. Updates walk the scheduler list under the
lock that also serializes unlinking. Reads are live, not atomic snapshots.
Root initialization excludes hotplug.

v2: Reworded the getter kerneldoc (Andrea Righi).

Signed-off-by: Tejun Heo <tj@kernel.org>
Reviewed-by: Andrea Righi <arighi@nvidia.com>

1 files changed, 112 insertions, 0 deletions

diff --git a/lib/math/rational.c b/lib/math/rational.c
new file mode 100644
index 000000000..d2c34e629
--- /dev/null
+++ b/lib/math/rational.c
@@ -0,0 +1,112 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
+ * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
+ *
+ * helper functions when coping with rational numbers
+ */
+
+#include <linux/rational.h>
+#include <linux/compiler.h>
+#include <linux/export.h>
+#include <linux/minmax.h>
+#include <linux/limits.h>
+#include <linux/module.h>
+
+/*
+ * calculate best rational approximation for a given fraction
+ * taking into account restricted register size, e.g. to find
+ * appropriate values for a pll with 5 bit denominator and
+ * 8 bit numerator register fields, trying to set up with a
+ * frequency ratio of 3.1415, one would say:
+ *
+ * rational_best_approximation(31415, 10000,
+ *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
+ *
+ * you may look at given_numerator as a fixed point number,
+ * with the fractional part size described in given_denominator.
+ *
+ * for theoretical background, see:
+ * https://en.wikipedia.org/wiki/Continued_fraction
+ */
+
+void rational_best_approximation(
+	unsigned long given_numerator, unsigned long given_denominator,
+	unsigned long max_numerator, unsigned long max_denominator,
+	unsigned long *best_numerator, unsigned long *best_denominator)
+{
+	/* n/d is the starting rational, which is continually
+	 * decreased each iteration using the Euclidean algorithm.
+	 *
+	 * dp is the value of d from the prior iteration.
+	 *
+	 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
+	 * approximations of the rational.  They are, respectively,
+	 * the current, previous, and two prior iterations of it.
+	 *
+	 * a is current term of the continued fraction.
+	 */
+	unsigned long n, d, n0, d0, n1, d1, n2, d2;
+	n = given_numerator;
+	d = given_denominator;
+	n0 = d1 = 0;
+	n1 = d0 = 1;
+
+	for (;;) {
+		unsigned long dp, a;
+
+		if (d == 0)
+			break;
+		/* Find next term in continued fraction, 'a', via
+		 * Euclidean algorithm.
+		 */
+		dp = d;
+		a = n / d;
+		d = n % d;
+		n = dp;
+
+		/* Calculate the current rational approximation (aka
+		 * convergent), n2/d2, using the term just found and
+		 * the two prior approximations.
+		 */
+		n2 = n0 + a * n1;
+		d2 = d0 + a * d1;
+
+		/* If the current convergent exceeds the maxes, then
+		 * return either the previous convergent or the
+		 * largest semi-convergent, the final term of which is
+		 * found below as 't'.
+		 */
+		if ((n2 > max_numerator) || (d2 > max_denominator)) {
+			unsigned long t = ULONG_MAX;
+
+			if (d1)
+				t = (max_denominator - d0) / d1;
+			if (n1)
+				t = min(t, (max_numerator - n0) / n1);
+
+			/* This tests if the semi-convergent is closer than the previous
+			 * convergent.  If d1 is zero there is no previous convergent as this
+			 * is the 1st iteration, so always choose the semi-convergent.
+			 */
+			if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
+				n1 = n0 + t * n1;
+				d1 = d0 + t * d1;
+			}
+			break;
+		}
+		n0 = n1;
+		n1 = n2;
+		d0 = d1;
+		d1 = d2;
+	}
+	*best_numerator = n1;
+	*best_denominator = d1;
+}
+
+EXPORT_SYMBOL(rational_best_approximation);
+
+MODULE_DESCRIPTION("Rational fraction support library");
+MODULE_LICENSE("GPL v2");