| Tero Kristo | 7d0f3fb | 2021-06-11 11:45:02 +0300 | [diff] [blame] | 1 | // SPDX-License-Identifier: GPL-2.0 |
| 2 | /* |
| 3 | * rational fractions |
| 4 | * |
| 5 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com> |
| 6 | * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com> |
| 7 | * |
| 8 | * helper functions when coping with rational numbers |
| 9 | */ |
| 10 | |
| 11 | #include <linux/rational.h> |
| 12 | #include <linux/compiler.h> |
| 13 | #include <linux/kernel.h> |
| 14 | |
| 15 | /* |
| 16 | * calculate best rational approximation for a given fraction |
| 17 | * taking into account restricted register size, e.g. to find |
| 18 | * appropriate values for a pll with 5 bit denominator and |
| 19 | * 8 bit numerator register fields, trying to set up with a |
| 20 | * frequency ratio of 3.1415, one would say: |
| 21 | * |
| 22 | * rational_best_approximation(31415, 10000, |
| 23 | * (1 << 8) - 1, (1 << 5) - 1, &n, &d); |
| 24 | * |
| 25 | * you may look at given_numerator as a fixed point number, |
| 26 | * with the fractional part size described in given_denominator. |
| 27 | * |
| 28 | * for theoretical background, see: |
| 29 | * http://en.wikipedia.org/wiki/Continued_fraction |
| 30 | */ |
| 31 | |
| 32 | void rational_best_approximation( |
| 33 | unsigned long given_numerator, unsigned long given_denominator, |
| 34 | unsigned long max_numerator, unsigned long max_denominator, |
| 35 | unsigned long *best_numerator, unsigned long *best_denominator) |
| 36 | { |
| 37 | /* n/d is the starting rational, which is continually |
| 38 | * decreased each iteration using the Euclidean algorithm. |
| 39 | * |
| 40 | * dp is the value of d from the prior iteration. |
| 41 | * |
| 42 | * n2/d2, n1/d1, and n0/d0 are our successively more accurate |
| 43 | * approximations of the rational. They are, respectively, |
| 44 | * the current, previous, and two prior iterations of it. |
| 45 | * |
| 46 | * a is current term of the continued fraction. |
| 47 | */ |
| 48 | unsigned long n, d, n0, d0, n1, d1, n2, d2; |
| 49 | n = given_numerator; |
| 50 | d = given_denominator; |
| 51 | n0 = d1 = 0; |
| 52 | n1 = d0 = 1; |
| 53 | |
| 54 | for (;;) { |
| 55 | unsigned long dp, a; |
| 56 | |
| 57 | if (d == 0) |
| 58 | break; |
| 59 | /* Find next term in continued fraction, 'a', via |
| 60 | * Euclidean algorithm. |
| 61 | */ |
| 62 | dp = d; |
| 63 | a = n / d; |
| 64 | d = n % d; |
| 65 | n = dp; |
| 66 | |
| 67 | /* Calculate the current rational approximation (aka |
| 68 | * convergent), n2/d2, using the term just found and |
| 69 | * the two prior approximations. |
| 70 | */ |
| 71 | n2 = n0 + a * n1; |
| 72 | d2 = d0 + a * d1; |
| 73 | |
| 74 | /* If the current convergent exceeds the maxes, then |
| 75 | * return either the previous convergent or the |
| 76 | * largest semi-convergent, the final term of which is |
| 77 | * found below as 't'. |
| 78 | */ |
| 79 | if ((n2 > max_numerator) || (d2 > max_denominator)) { |
| 80 | unsigned long t = min((max_numerator - n0) / n1, |
| 81 | (max_denominator - d0) / d1); |
| 82 | |
| 83 | /* This tests if the semi-convergent is closer |
| 84 | * than the previous convergent. |
| 85 | */ |
| 86 | if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) { |
| 87 | n1 = n0 + t * n1; |
| 88 | d1 = d0 + t * d1; |
| 89 | } |
| 90 | break; |
| 91 | } |
| 92 | n0 = n1; |
| 93 | n1 = n2; |
| 94 | d0 = d1; |
| 95 | d1 = d2; |
| 96 | } |
| 97 | *best_numerator = n1; |
| 98 | *best_denominator = d1; |
| 99 | } |