| 1 | |
| 2 | * rational fractions
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| 3 | *
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| 4 | * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[email protected]>
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| 5 | *
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| 6 | * helper functions when coping with rational numbers
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| 7 |
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| 8 |
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| 9 | #include <linux/rational.h>
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| 10 | #include <linux/compiler.h>
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| 11 | #include <linux/export.h>
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| 12 |
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| 13 | |
| 14 | * calculate best rational approximation for a given fraction
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| 15 | * taking into account restricted register size, e.g. to find
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| 16 | * appropriate values for a pll with 5 bit denominator and
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| 17 | * 8 bit numerator register fields, trying to set up with a
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| 18 | * frequency ratio of 3.1415, one would say:
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| 19 | *
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| 20 | * rational_best_approximation(31415, 10000,
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| 21 | * (1 << 8) - 1, (1 << 5) - 1, &n, &d);
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| 22 | *
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| 23 | * you may look at given_numerator as a fixed point number,
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| 24 | * with the fractional part size described in given_denominator.
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| 25 | *
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| 26 | * for theoretical background, see:
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| 27 | * http://en.wikipedia.org/wiki/Continued_fraction
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| 28 |
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| 29 |
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| 30 | void rational_best_approximation(
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| 31 | unsigned long given_numerator, unsigned long given_denominator,
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| 32 | unsigned long max_numerator, unsigned long max_denominator,
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| 33 | unsigned long *best_numerator, unsigned long *best_denominator)
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| 34 | {
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| 35 | unsigned long n, d, n0, d0, n1, d1;
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| 36 | n = given_numerator;
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| 37 | d = given_denominator;
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| 38 | n0 = d1 = 0;
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| 39 | n1 = d0 = 1;
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| 40 | for (;;) {
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| 41 | unsigned long t, a;
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| 42 | if ((n1 > max_numerator) || (d1 > max_denominator)) {
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| 43 | n1 = n0;
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| 44 | d1 = d0;
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| 45 | break;
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| 46 | }
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| 47 | if (d == 0)
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| 48 | break;
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| 49 | t = d;
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| 50 | a = n / d;
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| 51 | d = n % d;
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| 52 | n = t;
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| 53 | t = n0 + a * n1;
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| 54 | n0 = n1;
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| 55 | n1 = t;
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| 56 | t = d0 + a * d1;
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| 57 | d0 = d1;
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| 58 | d1 = t;
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| 59 | }
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| 60 | *best_numerator = n1;
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| 61 | *best_denominator = d1;
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| 62 | }
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| 63 |
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| 64 | EXPORT_SYMBOL(rational_best_approximation);
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