enum base = 10;
auto testValues = [
0: 0,
1: 1,
2: 2,
9: 9,
10: 10,
11: 10,
19: 10,
20: 11,
21: 11,
29: 11,
99: 18,
100: 19,
101: 19,
199: 19,
200: 20,
1000: 28,
];
foreach (value, result; testValues)
assert(
logIndex(value, base) == result,
format!"%d != %d"(logIndex(value, base), result),
);enum base = 16;
auto testValues = [
0x0000: 0,
0x0001: 0x1,
0x0002: 0x2,
0x000f: 0xf,
0x0010: 0x10,
0x0011: 0x10,
0x001f: 0x10,
0x0020: 0x11,
0x0021: 0x11,
0x002f: 0x11,
0x00ff: 0x1e,
0x0100: 0x1f,
0x0101: 0x1f,
0x01ff: 0x1f,
0x0200: 0x20,
0x1000: 0x2e
];
foreach (value, result; testValues)
assert(
logIndex(value, base) == result,
format!"0x%x != 0x%x"(logIndex(value, base), result),
);enum base = 10;
auto testValues = [
0: 0,
1: 1,
2: 2,
9: 9,
10: 10,
10: 10,
11: 20,
11: 20,
18: 90,
19: 100,
20: 200,
28: 1000,
];
foreach (value, result; testValues)
assert(
inverseLogIndex(value, base) == result,
format!"%d != %d"(inverseLogIndex(value, base), result),
);enum base = 16;
auto testValues = [
0x00: 0x0,
0x01: 0x1,
0x02: 0x2,
0x0f: 0xf,
0x10: 0x10,
0x10: 0x10,
0x10: 0x10,
0x11: 0x20,
0x1e: 0xf0,
0x1f: 0x100,
0x20: 0x200,
0x2e: 0x1000
];
foreach (value, result; testValues)
assert(
inverseLogIndex(value, base) == result,
format!"0x%x != 0x%x"(inverseLogIndex(value, base), result),
);
Compute a logarithmic index to base of value and vice versa. The function is piecewise linear for each interval of base indices. For interger values, the functions are mathematically equivalent to:
logIndex(x, b) = (b - 1) ⌊log_b(x)⌋ + x / b^^⌊log_b(x)⌋
inverseLogIndex(y, b) = (m + 1) * b^^d where m = (y - 1) mod (b - 1) d = ⌊(y - 1) / (b - 1)⌋