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>
diff --git a/src/commonlib/Makefile.inc b/src/commonlib/Makefile.inc
index 2477e07..e90ed4f 100644
--- a/src/commonlib/Makefile.inc
+++ b/src/commonlib/Makefile.inc
@@ -21,6 +21,9 @@
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
diff --git a/src/commonlib/include/commonlib/rational.h b/src/commonlib/include/commonlib/rational.h
new file mode 100644
index 0000000..f172e0b
--- /dev/null
+++ b/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_ */
diff --git a/src/commonlib/rational.c b/src/commonlib/rational.c
new file mode 100644
index 0000000..2e5f329
--- /dev/null
+++ b/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;
+}