1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156

//! Find "simple" numbers is some range. Used by sliders.

const NUM_DECIMALS: usize = 15;

/// Find the "simplest" number in a closed range [min, max], i.e. the one with the fewest decimal digits.
///
/// So in the range `[0.83, 1.354]` you will get `1.0`, and for `[0.37, 0.48]` you will get `0.4`.
/// This is used when dragging sliders etc to get the values that users are most likely to desire.
/// This assumes a decimal centric user.
pub fn best_in_range_f64(min: f64, max: f64) -> f64 {
    // Avoid NaN if we can:
    if min.is_nan() {
        return max;
    }
    if max.is_nan() {
        return min;
    }

    if max < min {
        return best_in_range_f64(max, min);
    }
    if min == max {
        return min;
    }
    if min <= 0.0 && 0.0 <= max {
        return 0.0; // always prefer zero
    }
    if min < 0.0 {
        return -best_in_range_f64(-max, -min);
    }

    // Prefer finite numbers:
    if !max.is_finite() {
        return min;
    }
    debug_assert!(min.is_finite() && max.is_finite());

    let min_exponent = min.log10();
    let max_exponent = max.log10();

    if min_exponent.floor() != max_exponent.floor() {
        // pick the geometric center of the two:
        let exponent = (min_exponent + max_exponent) / 2.0;
        return 10.0_f64.powi(exponent.round() as i32);
    }

    if is_integer(min_exponent) {
        return 10.0_f64.powf(min_exponent);
    }
    if is_integer(max_exponent) {
        return 10.0_f64.powf(max_exponent);
    }

    let exp_factor = 10.0_f64.powi(max_exponent.floor() as i32);

    let min_str = to_decimal_string(min / exp_factor);
    let max_str = to_decimal_string(max / exp_factor);

    let mut ret_str = [0; NUM_DECIMALS];

    // Select the common prefix:
    let mut i = 0;
    while i < NUM_DECIMALS && max_str[i] == min_str[i] {
        ret_str[i] = max_str[i];
        i += 1;
    }

    if i < NUM_DECIMALS {
        // Pick the deciding digit.
        // Note that "to_decimal_string" rounds down, so we that's why we add 1 here
        ret_str[i] = simplest_digit_closed_range(min_str[i] + 1, max_str[i]);
    }

    from_decimal_string(&ret_str) * exp_factor
}

fn is_integer(f: f64) -> bool {
    f.round() == f
}

fn to_decimal_string(v: f64) -> [i32; NUM_DECIMALS] {
    debug_assert!(v < 10.0, "{v:?}");
    let mut digits = [0; NUM_DECIMALS];
    let mut v = v.abs();
    for r in &mut digits {
        let digit = v.floor();
        *r = digit as i32;
        v -= digit;
        v *= 10.0;
    }
    digits
}

fn from_decimal_string(s: &[i32]) -> f64 {
    let mut ret: f64 = 0.0;
    for (i, &digit) in s.iter().enumerate() {
        ret += (digit as f64) * 10.0_f64.powi(-(i as i32));
    }
    ret
}

/// Find the simplest integer in the range [min, max]
fn simplest_digit_closed_range(min: i32, max: i32) -> i32 {
    debug_assert!(1 <= min && min <= max && max <= 9);
    if min <= 5 && 5 <= max {
        5
    } else {
        (min + max) / 2
    }
}

#[allow(clippy::approx_constant)]
#[test]
fn test_aim() {
    assert_eq!(best_in_range_f64(-0.2, 0.0), 0.0, "Prefer zero");
    assert_eq!(best_in_range_f64(-10_004.23, 3.14), 0.0, "Prefer zero");
    assert_eq!(best_in_range_f64(-0.2, 100.0), 0.0, "Prefer zero");
    assert_eq!(best_in_range_f64(0.2, 0.0), 0.0, "Prefer zero");
    assert_eq!(best_in_range_f64(7.8, 17.8), 10.0);
    assert_eq!(best_in_range_f64(99.0, 300.0), 100.0);
    assert_eq!(best_in_range_f64(-99.0, -300.0), -100.0);
    assert_eq!(best_in_range_f64(0.4, 0.9), 0.5, "Prefer ending on 5");
    assert_eq!(best_in_range_f64(14.1, 19.99), 15.0, "Prefer ending on 5");
    assert_eq!(best_in_range_f64(12.3, 65.9), 50.0, "Prefer leading 5");
    assert_eq!(best_in_range_f64(493.0, 879.0), 500.0, "Prefer leading 5");
    assert_eq!(best_in_range_f64(0.37, 0.48), 0.40);
    // assert_eq!(best_in_range_f64(123.71, 123.76), 123.75); // TODO(emilk): we get 123.74999999999999 here
    // assert_eq!(best_in_range_f32(123.71, 123.76), 123.75);
    assert_eq!(best_in_range_f64(7.5, 16.3), 10.0);
    assert_eq!(best_in_range_f64(7.5, 76.3), 10.0);
    assert_eq!(best_in_range_f64(7.5, 763.3), 100.0);
    assert_eq!(best_in_range_f64(7.5, 1_345.0), 100.0);
    assert_eq!(best_in_range_f64(7.5, 123_456.0), 1000.0, "Geometric mean");
    assert_eq!(best_in_range_f64(9.9999, 99.999), 10.0);
    assert_eq!(best_in_range_f64(10.000, 99.999), 10.0);
    assert_eq!(best_in_range_f64(10.001, 99.999), 50.0);
    assert_eq!(best_in_range_f64(10.001, 100.000), 100.0);
    assert_eq!(best_in_range_f64(99.999, 100.000), 100.0);
    assert_eq!(best_in_range_f64(10.001, 100.001), 100.0);

    const NAN: f64 = f64::NAN;
    const INFINITY: f64 = f64::INFINITY;
    const NEG_INFINITY: f64 = f64::NEG_INFINITY;
    assert!(best_in_range_f64(NAN, NAN).is_nan());
    assert_eq!(best_in_range_f64(NAN, 1.2), 1.2);
    assert_eq!(best_in_range_f64(NAN, INFINITY), INFINITY);
    assert_eq!(best_in_range_f64(1.2, NAN), 1.2);
    assert_eq!(best_in_range_f64(1.2, INFINITY), 1.2);
    assert_eq!(best_in_range_f64(INFINITY, 1.2), 1.2);
    assert_eq!(best_in_range_f64(NEG_INFINITY, 1.2), 0.0);
    assert_eq!(best_in_range_f64(NEG_INFINITY, -2.7), -2.7);
    assert_eq!(best_in_range_f64(INFINITY, INFINITY), INFINITY);
    assert_eq!(best_in_range_f64(NEG_INFINITY, NEG_INFINITY), NEG_INFINITY);
    assert_eq!(best_in_range_f64(NEG_INFINITY, INFINITY), 0.0);
    assert_eq!(best_in_range_f64(INFINITY, NEG_INFINITY), 0.0);
}