^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 1) // SPDX-License-Identifier: GPL-2.0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 2) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 3) * rational fractions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 4) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 5) * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 6) * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 7) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 8) * helper functions when coping with rational numbers
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 9) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 10)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 11) #include <linux/rational.h>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 12) #include <linux/compiler.h>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 13) #include <linux/export.h>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 14) #include <linux/minmax.h>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 15) #include <linux/limits.h>
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 16)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 17) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 18) * calculate best rational approximation for a given fraction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 19) * taking into account restricted register size, e.g. to find
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 20) * appropriate values for a pll with 5 bit denominator and
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 21) * 8 bit numerator register fields, trying to set up with a
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 22) * frequency ratio of 3.1415, one would say:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 23) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 24) * rational_best_approximation(31415, 10000,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 25) * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 26) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 27) * you may look at given_numerator as a fixed point number,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 28) * with the fractional part size described in given_denominator.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 29) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 30) * for theoretical background, see:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 31) * https://en.wikipedia.org/wiki/Continued_fraction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 32) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 33)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 34) void rational_best_approximation(
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 35) unsigned long given_numerator, unsigned long given_denominator,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 36) unsigned long max_numerator, unsigned long max_denominator,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 37) unsigned long *best_numerator, unsigned long *best_denominator)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 38) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 39) /* n/d is the starting rational, which is continually
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 40) * decreased each iteration using the Euclidean algorithm.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 41) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 42) * dp is the value of d from the prior iteration.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 43) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 44) * n2/d2, n1/d1, and n0/d0 are our successively more accurate
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 45) * approximations of the rational. They are, respectively,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 46) * the current, previous, and two prior iterations of it.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 47) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 48) * a is current term of the continued fraction.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 49) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 50) unsigned long n, d, n0, d0, n1, d1, n2, d2;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 51) n = given_numerator;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 52) d = given_denominator;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 53) n0 = d1 = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 54) n1 = d0 = 1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 55)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 56) for (;;) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 57) unsigned long dp, a;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 58)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 59) if (d == 0)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 60) break;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 61) /* Find next term in continued fraction, 'a', via
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 62) * Euclidean algorithm.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 63) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 64) dp = d;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 65) a = n / d;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 66) d = n % d;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 67) n = dp;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 68)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 69) /* Calculate the current rational approximation (aka
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 70) * convergent), n2/d2, using the term just found and
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 71) * the two prior approximations.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 72) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 73) n2 = n0 + a * n1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 74) d2 = d0 + a * d1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 75)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 76) /* If the current convergent exceeds the maxes, then
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 77) * return either the previous convergent or the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 78) * largest semi-convergent, the final term of which is
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 79) * found below as 't'.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 80) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 81) if ((n2 > max_numerator) || (d2 > max_denominator)) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 82) unsigned long t = ULONG_MAX;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 83)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 84) if (d1)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 85) t = (max_denominator - d0) / d1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 86) if (n1)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 87) t = min(t, (max_numerator - n0) / n1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 88)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 89) /* This tests if the semi-convergent is closer than the previous
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 90) * convergent. If d1 is zero there is no previous convergent as this
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 91) * is the 1st iteration, so always choose the semi-convergent.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 92) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 93) if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 94) n1 = n0 + t * n1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 95) d1 = d0 + t * d1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 96) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 97) break;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 98) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 99) n0 = n1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 100) n1 = n2;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 101) d0 = d1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 102) d1 = d2;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 103) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 104) *best_numerator = n1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 105) *best_denominator = d1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 106) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 107)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 108) EXPORT_SYMBOL(rational_best_approximation);
Orange Pi5 kernel
Deprecated Linux kernel 5.10.110 for OrangePi 5/5B/5+ boards
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