diff options
| -rw-r--r-- | lib/math/rational.c | 63 |
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; |