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authorLinus Torvalds <torvalds@linux-foundation.org>2026-08-24 08:46:03 -0700
committerLinus Torvalds <torvalds@linux-foundation.org>2026-08-24 08:46:03 -0700
commitcf9610f9116d55c5a66ef9f1faecacabd93a9322 (patch)
tree757a3d280760c654767631cab5ad8af2d86d1848 /lib/math/rational.c
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Merge tag 'pinctrl-v7.3-1' of git://git.kernel.org/pub/scm/linux/kernel/git/linusw/linux-pinctrlgrafted
Pull pin control updates from Linus Walleij: "Core changes: - Use the non-blocking mux_state_try_select() in the generic MUX pin control back-end - Free pin maps on pinctrl_generic_to_map() failure in the core helpers New hardware pin control: - Qualcomm Maili TLMM SoC, PMG1110 PMIC, and Eliza LPASS LPI TLMM SoC (this is for the low power audio, LPASS = Low Power Audio SubSystem portions) - Upboard support on top of the Intel pin controller - Apple T6030 and T6031 support (just compatible strings) - Samsung Exynos 8855 SoC - Mediatek MT6858 SoC - Rockchip RK3308B and RV1106 SoCs - Airoha EN7523 and AN7563 SoCs Improvements: - Qualcomm TLMM GPIOs are unconditionally marked as wakeup capable - Qualcomm improvements on top of the Qualcomm PDC (power domain controller) irqchip improvements from tglx:s tree - Qualcomm IPQ806x and IPQ9650 non-urgent pin grop fixups - The NPCM8xx driver has been put into shape fixing many pin and group definitions - Some non-urgent Tegra 264 pin assignments are fixed up - Some non-urgent fixups to Airoha AN7581 and AN7583 registers and pin assignments, missing features etc" * tag 'pinctrl-v7.3-1' of git://git.kernel.org/pub/scm/linux/kernel/git/linusw/linux-pinctrl: (130 commits) dt-bindings: pinctrl: Convert TI DA850 pupd to DT schema pinctrl: meson: sync some modify from A4 pinctrl: meson: a4: Add input enable pin configuration pinctrl: realtek: rtd1625: remove unused group name spdif_sel pinctrl: realtek: rtd1625: fix base_bit for VE4 GPIO 13 dt-bindings: pinctrl: microchip,pic32mzda-pinctrl: Convert to DT schema Revert "Merge branch 'ib-rsk7204' into devel" pinctrl: rockchip: Add RV1106 pinctrl support dt-bindings: pinctrl: rockchip: Add RV1106 compatible pinctrl: rockchip: Decode drive strength in the get function pinctrl: fix PINCTRL_GENERIC_MUX not always being selectable pinctrl: airoha: add support of an7563 SoC dt-bindings: pinctrl: airoha: add support of an7563 pin controller pinctrl: airoha: try to find chip scu node by phandle first pinctrl: airoha: add support of en7523 SoC dt-bindings: pinctrl: airoha: add support of en7523 pin controller pinctrl: airoha: an7583: add support for olt pinmux pinctrl: airoha: an7583: add support for pon_alt pinmux pinctrl: airoha: an7583: add support for npu_uart pinmux dt-bindings: pinctrl: airoha: an7583: add missed features ...
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diff --git a/lib/math/rational.c b/lib/math/rational.c
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+// 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");