| /* 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; |
| } |