| 1 | |
| 2 | |
| 3 | * rational fractions
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| 4 | *
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| 5 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[email protected]>
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| 6 | * Copyright (C) 2019 Trent Piepho <[email protected]>
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| 7 | *
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| 8 | * helper functions when coping with rational numbers
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| 9 |
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| 10 |
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| 11 | #include <linux/rational.h>
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| 12 | #include <linux/compiler.h>
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| 13 | #include <linux/export.h>
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| 14 | #include <linux/minmax.h>
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| 15 |
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| 16 | |
| 17 | * calculate best rational approximation for a given fraction
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| 18 | * taking into account restricted register size, e.g. to find
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| 19 | * appropriate values for a pll with 5 bit denominator and
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| 20 | * 8 bit numerator register fields, trying to set up with a
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| 21 | * frequency ratio of 3.1415, one would say:
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| 22 | *
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| 23 | * rational_best_approximation(31415, 10000,
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| 24 | * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
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| 25 | *
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| 26 | * you may look at given_numerator as a fixed point number,
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| 27 | * with the fractional part size described in given_denominator.
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| 28 | *
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| 29 | * for theoretical background, see:
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| 30 | * https://en.wikipedia.org/wiki/Continued_fraction
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| 31 |
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| 32 |
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| 33 | void rational_best_approximation(
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| 34 | unsigned long given_numerator, unsigned long given_denominator,
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| 35 | unsigned long max_numerator, unsigned long max_denominator,
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| 36 | unsigned long *best_numerator, unsigned long *best_denominator)
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| 37 | {
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| 38 | |
| 39 | * decreased each iteration using the Euclidean algorithm.
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| 40 | *
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| 41 | * dp is the value of d from the prior iteration.
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| 42 | *
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| 43 | * n2/d2, n1/d1, and n0/d0 are our successively more accurate
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| 44 | * approximations of the rational. They are, respectively,
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| 45 | * the current, previous, and two prior iterations of it.
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| 46 | *
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| 47 | * a is current term of the continued fraction.
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| 48 |
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| 49 | unsigned long n, d, n0, d0, n1, d1, n2, d2;
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| 50 | n = given_numerator;
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| 51 | d = given_denominator;
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| 52 | n0 = d1 = 0;
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| 53 | n1 = d0 = 1;
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| 54 |
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| 55 | for (;;) {
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| 56 | unsigned long dp, a;
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| 57 |
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| 58 | if (d == 0)
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| 59 | break;
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| 60 | |
| 61 | * Euclidean algorithm.
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| 62 |
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| 63 | dp = d;
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| 64 | a = n / d;
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| 65 | d = n % d;
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| 66 | n = dp;
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| 67 |
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| 68 | |
| 69 | * convergent), n2/d2, using the term just found and
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| 70 | * the two prior approximations.
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| 71 |
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| 72 | n2 = n0 + a * n1;
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| 73 | d2 = d0 + a * d1;
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| 74 |
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| 75 | |
| 76 | * return either the previous convergent or the
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| 77 | * largest semi-convergent, the final term of which is
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| 78 | * found below as 't'.
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| 79 |
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| 80 | if ((n2 > max_numerator) || (d2 > max_denominator)) {
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| 81 | unsigned long t = min((max_numerator - n0) / n1,
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| 82 | (max_denominator - d0) / d1);
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| 83 |
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| 84 | |
| 85 | * than the previous convergent.
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| 86 |
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| 87 | if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
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| 88 | n1 = n0 + t * n1;
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| 89 | d1 = d0 + t * d1;
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| 90 | }
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| 91 | break;
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| 92 | }
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| 93 | n0 = n1;
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| 94 | n1 = n2;
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| 95 | d0 = d1;
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| 96 | d1 = d2;
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| 97 | }
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| 98 | *best_numerator = n1;
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| 99 | *best_denominator = d1;
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| 100 | }
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| 101 |
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| 102 | EXPORT_SYMBOL(rational_best_approximation);
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