approx_log10_int.c

#include <stdint.h>
#include <stdio.h>
#include <math.h>
#include <time.h>

int fast_approx_log10(float x, uint32_t C_offset, uint32_t C_mult) {
    uint32_t X = *(uint32_t*)&x;
    uint64_t diff = (uint64_t)X - C_offset;
    uint32_t shift = (uint32_t)((diff * C_mult) >> 32);

    int D = (int)shift + 1;

    return D;
}


float log10_standard(float x) {
    return floor(log10((double)x)) + 1;
}

int main() {
    // --- マジックナンバーの導出 ---
    const double L = pow(2, 23);
    const double B = 127.0;
    const double sigma = 0.043035666028;

    const double C_offset_double = L * (B - sigma);
    const uint32_t C_offset = (uint32_t)C_offset_double;
    const double C_divider_double = L * log2(10.0);
    const double C_mult_double = pow(2, 32) / C_divider_double;
    const uint32_t C_mult = (uint32_t)ceil(C_mult_double);

    printf("  C_offset_int : %u\n", C_offset);
    printf("  C_mult_int   : %u\n", C_mult);
    printf("---------------------------------------------------------\n");

    float test_cases[] = {1.0f, 9.9f, 10.0f, 99.9f, 100.0f, 12345.0f, 99999.0f, 100000.0f, 1234567.0f, 9999999.0f, 10000000.0f,8e13};

    printf("Approx log10 (Test Cases):\n");
    printf("| %-17s | %-15s | %-15s |\n", "Input (x)", "True Digits", "Approx.");
    printf("|-------------------|-----------------|-----------------|\n");

    for (int i = 0; i < sizeof(test_cases) / sizeof(float); ++i) {
        float x = test_cases[i];
        float true_digits = log10_standard(x);
        int approx_digits = fast_approx_log10(x, C_offset, C_mult);
        printf("| %-17.1f | %-15.1f | %-15d |\n", x, true_digits, approx_digits);
    }
    printf("---------------------------------------------------------\n");

    return 0;
}

result:

  C_offset_int : 1064992206
  C_mult_int   : 155
---------------------------------------------------------
Approx log10 (Test Cases):
| Input (x)         | True Digits     | Approx.         |
|-------------------|-----------------|-----------------|
| 1.0               | 1.0             | 1               |
| 9.9               | 1.0             | 1               |
| 10.0              | 2.0             | 1               |
| 99.9              | 2.0             | 2               |
| 100.0             | 3.0             | 2               |
| 12345.0           | 5.0             | 5               |
| 99999.0           | 5.0             | 6               |
| 100000.0          | 6.0             | 6               |
| 1234567.0         | 7.0             | 7               |
| 9999999.0         | 7.0             | 8               |
| 10000000.0        | 8.0             | 8               |
| 79999998623744.0  | 14.0            | 14              |
---------------------------------------------------------