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gerrit.devboardsforandroid.linaro.org / platform / external / u-boot / e5baf2873aa69de186cc8c39bf7d86c10679b0f3 / . / lib / rational.c

Tero Kristo | 7d0f3fb | 2021-06-11 11:45:02 +0300 | [diff] [blame] | 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/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 | } |