projects / J-u-boot.git / blame
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| 7d0f3fbb TK |
1 | // SPDX-License-Identifier: GPL-2.0 |
| 2 | /* | |
| 3 | * rational fractions | |
| 4 | * | |
| 5 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[email protected]> | |
| 6 | * Copyright (C) 2019 Trent Piepho <[email protected]> | |
| 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 | } |