commonlib: Add support for rational number approximation

This patch adds a function to calculate best rational approximation
for a given fraction and unit tests for it.

Change-Id: I2272d9bb31cde54e65721f95662b80754eee50c2
Signed-off-by: Vinod Polimera <quic_vpolimer@quicinc.com>
Reviewed-on: https://review.coreboot.org/c/coreboot/+/66010
Reviewed-by: Yu-Ping Wu <yupingso@google.com>
Tested-by: build bot (Jenkins) <no-reply@coreboot.org>

src/commonlib/Makefile.inc

@@ -21,6 +21,9 @@ ramstage-y += region.c
 smm-y += region.c
 postcar-y += region.c
 
+romstage-y += rational.c
+ramstage-y += rational.c
+
 ramstage-$(CONFIG_PLATFORM_USES_FSP1_1) += fsp_relocate.c
 ifeq ($(CONFIG_FSP_M_XIP),)
 romstage-$(CONFIG_PLATFORM_USES_FSP2_0) += fsp_relocate.c

src/commonlib/include/commonlib/rational.h

@@ -0,0 +1,22 @@
+/* SPDX-License-Identifier: GPL-2.0-only */
+
+#ifndef _COMMONLIB_RATIONAL_H_
+#define _COMMONLIB_RATIONAL_H_
+
+#include <stddef.h>
+
+/*
+ * Calculate the best rational approximation for a given fraction,
+ * with the restriction of maximum numerator and denominator.
+ * For example, to find the approximation of 3.1415 with 5 bit denominator
+ * and 8 bit numerator fields:
+ *
+ * rational_best_approximation(31415, 10000,
+ *			       (1 << 8) - 1, (1 << 5) - 1, &n, &d);
+ */
+void rational_best_approximation(
+	unsigned long numerator, unsigned long denominator,
+	unsigned long max_numerator, unsigned long max_denominator,
+	unsigned long *best_numerator, unsigned long *best_denominator);
+
+#endif /* _COMMONLIB_RATIONAL_H_ */

src/commonlib/rational.c

@@ -0,0 +1,95 @@
+/* SPDX-License-Identifier: GPL-2.0-only */
+/*
+ * Helper functions for rational numbers.
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
+ * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
+ */
+
+#include <commonlib/helpers.h>
+#include <commonlib/rational.h>
+#include <limits.h>
+
+/*
+ * For theoretical background, see:
+ * https://en.wikipedia.org/wiki/Continued_fraction
+ */
+void rational_best_approximation(
+	unsigned long numerator, unsigned long denominator,
+	unsigned long max_numerator, unsigned long max_denominator,
+	unsigned long *best_numerator, unsigned long *best_denominator)
+{
+	/*
+	 * n/d is the starting rational, where both n and d will
+	 * decrease in 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 = numerator;
+	d = 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 maximum, 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;
+}