lib: isolate rational fractions helper function

Provide a helper function to determine optimum numerator
denominator value pairs taking into account restricted
register size. Useful especially with PLL and other clock
configurations.

Signed-off-by: Oskar Schirmer <[e-mail]>
Signed-off-by: Alan Cox <[e-mail]>
Signed-off-by: Linus Torvalds <[e-mail]>

include/linux/rational.h

···
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[e-mail]>
+ *
+ * helper functions when coping with rational numbers,
+ * e.g. when calculating optimum numerator/denominator pairs for
+ * pll configuration taking into account restricted register size
+ */
+
+#ifndef _LINUX_RATIONAL_H
+#define _LINUX_RATIONAL_H
+
+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);
+
+#endif /* _LINUX_RATIONAL_H */

lib/Kconfig

···
 config BITREVERSE
 	tristate
 
+config RATIONAL
+	boolean
+
 config GENERIC_FIND_FIRST_BIT
 	bool
 

lib/Makefile

···
 endif
 
 obj-$(CONFIG_BITREVERSE) += bitrev.o
+obj-$(CONFIG_RATIONAL)	+= rational.o
 obj-$(CONFIG_CRC_CCITT)	+= crc-ccitt.o
 obj-$(CONFIG_CRC16)	+= crc16.o
 obj-$(CONFIG_CRC_T10DIF)+= crc-t10dif.o

lib/rational.c

···
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[e-mail]>
+ *
+ * helper functions when coping with rational numbers
+ */
+
+#include <linux/rational.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:
+ * http://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)
+{
+	unsigned long n, d, n0, d0, n1, d1;
+	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;
+		}
+		if (d == 0)
+			break;
+		t = d;
+		a = n / d;
+		d = n % d;
+		n = t;
+		t = n0 + a * n1;
+		n0 = n1;
+		n1 = t;
+		t = d0 + a * d1;
+		d0 = d1;
+		d1 = t;
+	}
+	*best_numerator = n1;
+	*best_denominator = d1;
+}
+
+EXPORT_SYMBOL(rational_best_approximation);