Merge branch 'akpm' (patches from Andrew)

Merge more updates from Andrew Morton:
 "Most of the rest of MM and various other things. Some Kconfig rework
  still awaits merges of dependent trees from linux-next.

  Subsystems affected by this patch series: mm/hotfixes, mm/memcg,
  mm/vmstat, mm/thp, procfs, sysctl, misc, notifiers, core-kernel,
  bitops, lib, checkpatch, epoll, binfmt, init, rapidio, uaccess, kcov,
  ubsan, ipc, bitmap, mm/pagemap"

* akpm: (86 commits)
  mm: remove __ARCH_HAS_4LEVEL_HACK and include/asm-generic/4level-fixup.h
  um: add support for folded p4d page tables
  um: remove unused pxx_offset_proc() and addr_pte() functions
  sparc32: use pgtable-nopud instead of 4level-fixup
  parisc/hugetlb: use pgtable-nopXd instead of 4level-fixup
  parisc: use pgtable-nopXd instead of 4level-fixup
  nds32: use pgtable-nopmd instead of 4level-fixup
  microblaze: use pgtable-nopmd instead of 4level-fixup
  m68k: mm: use pgtable-nopXd instead of 4level-fixup
  m68k: nommu: use pgtable-nopud instead of 4level-fixup
  c6x: use pgtable-nopud instead of 4level-fixup
  arm: nommu: use pgtable-nopud instead of 4level-fixup
  alpha: use pgtable-nopud instead of 4level-fixup
  gpio: pca953x: tighten up indentation
  gpio: pca953x: convert to use bitmap API
  gpio: pca953x: use input from regs structure in pca953x_irq_pending()
  gpio: pca953x: remove redundant variable and check in IRQ handler
  lib/bitmap: introduce bitmap_replace() helper
  lib/test_bitmap: fix comment about this file
  lib/test_bitmap: move exp1 and exp2 upper for others to use
  ...

1 files changed, 50 insertions, 13 deletions

diff --git a/lib/math/rational.c b/lib/math/rational.c
index ba7443677c90..31fb27db2deb 100644
--- a/lib/math/rational.c
+++ b/lib/math/rational.c
@@ -3,6 +3,7 @@
  * 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
  */
@@ -10,6 +11,7 @@
 #include <linux/rational.h>
 #include <linux/compiler.h>
 #include <linux/export.h>
+#include <linux/kernel.h>
 
 /*
  * calculate best rational approximation for a given fraction
@@ -33,30 +35,65 @@ void rational_best_approximation(
 	unsigned long max_numerator, unsigned long max_denominator,
 	unsigned long *best_numerator, unsigned long *best_denominator)
 {
-	unsigned long n, d, n0, d0, n1, d1;
+	/* 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 t, a;
-		if ((n1 > max_numerator) || (d1 > max_denominator)) {
-			n1 = n0;
-			d1 = d0;
-			break;
-		}
+		unsigned long dp, a;
+
 		if (d == 0)
 			break;
-		t = d;
+		/* Find next term in continued fraction, 'a', via
+		 * Euclidean algorithm.
+		 */
+		dp = d;
 		a = n / d;
 		d = n % d;
-		n = t;
-		t = n0 + a * n1;
+		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 = min((max_numerator - n0) / n1,
+					      (max_denominator - d0) / d1);
+
+			/* This tests if the semi-convergent is closer
+			 * than the previous convergent.
+			 */
+			if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
+				n1 = n0 + t * n1;
+				d1 = d0 + t * d1;
+			}
+			break;
+		}
 		n0 = n1;
-		n1 = t;
-		t = d0 + a * d1;
+		n1 = n2;
 		d0 = d1;
-		d1 = t;
+		d1 = d2;
 	}
 	*best_numerator = n1;
 	*best_denominator = d1;