inverseLogIndex

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)⌋

size_t logIndex(size_t value, size_t base)
size_t inverseLogIndex(size_t value, size_t base)
pure nothrow @safe
size_t
inverseLogIndex
(
size_t value
,
size_t base
)

Examples

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),
    );

inverseLogIndex

Examples

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