Decimal number format that makes some sense

decimalsense.c

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

char * numberAsString(uint64_t num) {
    static char result[] = "+1.234567890123456e-123";

    char sign = (num & 0x8000000000000000L) ? '-' : '+';
    uint16_t scale = (num  >> 50) & 0x1fff;
    if (scale << 2 == 0x7ff0)
    {
        static char inf[] = "+Infinity";
        inf[0] = sign;
        return inf;
    }
    uint32_t units = (scale != 0) * (1 + (scale - 1) % 9);
    int exp = -455 + (scale != 0) * (scale - 1) / 9;
    
    uint32_t s[5];
    uint32_t shift = 50;
    for (int i = 0; i < 5; ++i)
    {
        shift -= 10;
        s[i] = (num >> shift) & 0x3ff;

        if (s[i] >= 1000)
        {
            return "NaN";
        }
    }
    
    sprintf(result, "%c%u.%.3u%.3u%.3u%.3u%.3ue%+d", sign, units, s[0], s[1], s[2], s[3], s[4], exp);
    return result;
}

uint64_t makeNumber(int units, uint32_t s1, uint32_t s2, uint32_t s3, uint32_t s4, uint32_t s5, int exp) {
    uint64_t sign = (units < 0);
    uint64_t scale = (units != 0) * (abs(units) + 9 * (455 + exp));
    return (sign << 63) | (scale << 50) | ((uint64_t)s1 << 40) | ((uint64_t)s2 << 30) | (s3 << 20) | (s4 << 10) | s5;
}

uint64_t shiftDecimals(uint64_t decimals, int amount) {
    const int small = (amount + 810) % 3;
    const int final_shift = (amount - small) * 10 / 3;
    const uint16_t m[] = {1, 10, 100};
    const uint32_t limit[] = {1000, 100, 10};
    uint64_t raw = decimals * m[small];
    uint64_t compens = 0;

    for (uint32_t shift = 50; shift > 0;)
    {
        shift -= 10;
        uint16_t s = ((decimals >> shift) & 0x3ff);
        if (s >= limit[small])
        {
            compens |= (s * m[small] / 1000 * 24L) << shift;    // | okay because 24 = 0x18 and 99 * 24 < (0x8 << 10)
        }
    }
    raw += compens;
    return (amount >= 0) ? (raw << final_shift) : (raw >> -final_shift);
}

int main(int n, char * args[]) {
    puts(numberAsString(0x7fefe7f9fe7f9fe7L));  // Largest number 6.99...e+454
    puts(numberAsString(0x0004000000000000L));  // Smallest normal number 1.0e-455
    puts(numberAsString(0x0003e7f9fe7f9fe7L));  // Largest subnormal number 0.99...e-455
    puts(numberAsString(0x0000000000000001L));  // Smallest number 1.0e-470
    puts(numberAsString(makeNumber(+4, 698, 543, 100, 238, 333, +10)));
    puts(numberAsString(0xfff));                // Not a number (invalid 3-decimal block)
    puts(numberAsString(0x7ff0000000000000L));  // +∞
    puts(numberAsString(makeNumber(-7, 0, 0, 0, 0, 0, +454)));              // -∞
    printf("Zero: 0x%.16llx \n", makeNumber(0, 0, 0, 0, 0, 0, 0));           // 0
    printf("One: 0x%.16llx \n", makeNumber(+1, 0, 0, 0, 0, 0, 0));           // 0x4000000000000000
    printf("Ten: 0x%.16llx \n", makeNumber(+1, 0, 0, 0, 0, 0, +1));          // 0x4024000000000000
    printf("Minus five: 0x%.16llx \n", makeNumber(-5, 0, 0, 0, 0, 0, 0));    // 0xc010000000000000
    uint64_t v = 0x001236f9c0cf9fddL;
    uint64_t res = shiftDecimals(v, -5);
    char converse[100] = {0};
    strncpy(converse, numberAsString(v), 99); //shiftDecimals(res, +4)), 99);
    printf("0x%.16llx (%s) * 1e-5 = 0x%.16llx (%s) \n", v, converse, res, numberAsString(res));
}