Program to attempt to figure out the multiplication by a power of 10 that gives a particular float.

scale_floats.c

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

#define ARRAY_COUNT(arr) (sizeof(arr) / sizeof(arr[0]))

// Test values for 0.05f
// float test_mult[] = {
//     5.0e-06f * 10000.0f, 5.0e-05f * 1000.0f, 0.0005f * 100.0f, 0.005f * 10.0f,   0.05f * 1.0f,
//     0.5f * 0.1f,     5.0f * 0.01f,     50.0f * 0.001f,   500.0f * 0.0001f,
// };
// float test_div[] = {
//     5.0e-06f / 0.0001f, 5.0e-05f / 0.001f, 0.0005f / 0.01f,
//     0.005f / 0.1f,      0.05f / 1.0f,        0.5f / 10.0f,
//     5.0f / 100.0f,        50.0f / 1000.0f,     500.0f / 10000.0f,
// };

typedef union {
    float f;
    uint32_t x;
} HexFloat;

uint32_t hex_of_float(float f) {
    HexFloat xf;

    xf.f = f;
    return xf.x;
}

double multipliers_double[] = { 10000.0, 1000.0, 100.0, 10.0, 1.0, 0.1, 0.01, 0.001, 0.0001 };
double divisors_double[] = { 0.0001, 0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0, 10000.0 };

float multipliers[] = { 10000.0f, 1000.0f, 100.0f, 10.0f, 1.0f, 0.1f, 0.01f, 0.001f, 0.0001f };
float divisors[] = { 0.0001f, 0.001f, 0.01f, 0.1f, 1.0f, 10.0f, 100.0f, 1000.0f, 10000.0f };

int main(int argc, char** argv) {
    double input;
    size_t i;

    if (argc < 2) {
        fprintf(stderr, "Not enough inputs: need float");
        return 1;
    }

    if (sscanf(argv[1], "%lf", &input) == 0) {
        fprintf(stderr, "Could not read float from argument %s", argv[1]);
        return 1;
    }

    for (i = 0; i < ARRAY_COUNT(multipliers); i++) {
        float temp = input * divisors_double[i];
        float output = temp * multipliers[i];

        printf("%10g * %-10g = %.10f, %08X  ", temp, multipliers[i], output, hex_of_float(output));
        // printf("%08X", hex_of_float(test_mult[i]));
        putchar('\n');
    }

    putchar('\n');

    for (i = 0; i < ARRAY_COUNT(multipliers); i++) {
        float temp = input / multipliers_double[i];
        float output = temp / divisors[i];

        printf("%10g / %-10g = %.10f, %08X  ", temp, divisors[i], output, hex_of_float(output));
        // printf("%08X", hex_of_float(test_div[i]));
        putchar('\n');
    }

    return 0;
}