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/export.h> 14 #include <linux/minmax.h> 15 #include <linux/limits.h> 16 17 /* 18 * calculate best rational approximation for a given fraction 19 * taking into account restricted register size, e.g. to find 20 * appropriate values for a pll with 5 bit denominator and 21 * 8 bit numerator register fields, trying to set up with a 22 * frequency ratio of 3.1415, one would say: 23 * 24 * rational_best_approximation(31415, 10000, 25 * (1 << 8) - 1, (1 << 5) - 1, &n, &d); 26 * 27 * you may look at given_numerator as a fixed point number, 28 * with the fractional part size described in given_denominator. 29 * 30 * for theoretical background, see: 31 * https://en.wikipedia.org/wiki/Continued_fraction 32 */ 33 34 void rational_best_approximation( 35 unsigned long given_numerator, unsigned long given_denominator, 36 unsigned long max_numerator, unsigned long max_denominator, 37 unsigned long *best_numerator, unsigned long *best_denominator) 38 { 39 /* n/d is the starting rational, which is continually 40 * decreased each iteration using the Euclidean algorithm. 41 * 42 * dp is the value of d from the prior iteration. 43 * 44 * n2/d2, n1/d1, and n0/d0 are our successively more accurate 45 * approximations of the rational. They are, respectively, 46 * the current, previous, and two prior iterations of it. 47 * 48 * a is current term of the continued fraction. 49 */ 50 unsigned long n, d, n0, d0, n1, d1, n2, d2; 51 n = given_numerator; 52 d = given_denominator; 53 n0 = d1 = 0; 54 n1 = d0 = 1; 55 56 for (;;) { 57 unsigned long dp, a; 58 59 if (d == 0) 60 break; 61 /* Find next term in continued fraction, 'a', via 62 * Euclidean algorithm. 63 */ 64 dp = d; 65 a = n / d; 66 d = n % d; 67 n = dp; 68 69 /* Calculate the current rational approximation (aka 70 * convergent), n2/d2, using the term just found and 71 * the two prior approximations. 72 */ 73 n2 = n0 + a * n1; 74 d2 = d0 + a * d1; 75 76 /* If the current convergent exceeds the maxes, then 77 * return either the previous convergent or the 78 * largest semi-convergent, the final term of which is 79 * found below as 't'. 80 */ 81 if ((n2 > max_numerator) || (d2 > max_denominator)) { 82 unsigned long t = ULONG_MAX; 83 84 if (d1) 85 t = (max_denominator - d0) / d1; 86 if (n1) 87 t = min(t, (max_numerator - n0) / n1); 88 89 /* This tests if the semi-convergent is closer than the previous 90 * convergent. If d1 is zero there is no previous convergent as this 91 * is the 1st iteration, so always choose the semi-convergent. 92 */ 93 if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) { 94 n1 = n0 + t * n1; 95 d1 = d0 + t * d1; 96 } 97 break; 98 } 99 n0 = n1; 100 n1 = n2; 101 d0 = d1; 102 d1 = d2; 103 } 104 *best_numerator = n1; 105 *best_denominator = d1; 106 } 107 108 EXPORT_SYMBOL(rational_best_approximation); 109