Representing rationals as rounded decimal fractions

Question

Using the gmp library and rationals (mpq_t), I am trying to print out the rational I have as a decimal fraction up to a given precision (digits after the decimal separator).

My current approach is to write to a char buffer, do the rounding on the digits in the buffer, then print this out. It works, but I have the feeling that I am doint it waaaay too complicated, namely:

• calculate the integer part by division
• calculate the fractional part by multiplying the remainder by 10^(prec+1) and dividing
• put both in a char buffer
• go back from the end of the buffer doing the rounding on the digits
• print out the number with all the little extra information collected along the way
  • optional minus sign
  • overflow (so 0.9999 with precision 3 would actually be 1, for example)
  • taking care of extra zeroes (0.00001, for example)

The question:

Is there a way of doing this better? More simple? Something I am missing completely?

Note that the numerator and denominator of the rational can be "arbitrarily" big.

Here is the relevant code, mpz1, mpz2 are of type mpz_t and are already initialized, the rational I am converting is in mpq1:

edit: there is at least one error somewhere in this code, but I don't feel like finding it as I re-wrote it anyway.

/* We might need to insert a digit between the sign
 * and the rest of the number:
 * deal with the sign explicitly
 */
int negative = 0;
if (mpz_sgn(mpq_numref(mpq1)) == -1) /* negative number */
    negative = 1;

/* Calculate the integer part and the remainder */
mpz_tdiv_qr(mpz1, mpz2, mpq_numref(mpq1), mpq_denref(mpq1));
if (mpz_cmp_ui(mpz2, 0) == 0) { /* remainder is 0 */
    gmp_printf("%Zd", mpz1);
    return;
}

/* What is the maximum possible length of the decimal fraction? */
size_t max_len =
      mpz_sizeinbase(mpz1, 10) /* length of the string in digits */
    + 1 /* '\0' terminator */
    /* + 1  possible minus sign: dealing with it explicitly */
    /* + 1  decimal point: dealing with it explicitly */
    + real_precision + 1; /* precision and the extra digit */

/* Prepare the buffer for the string */
/* ... */
/* block of sufficient size at char *str */
char *end = str;
end += gmp_sprintf(end, "%Zd", mpz1);
char *dec_point = end;

/* Calculate the fractional part and write it to the buffer:
 * to round correctly, we need to know one more digit than
 * the precision we are aiming at
 */
mpz_abs(mpz2, mpz2);
mpz_ui_pow_ui(mpz1, 10, real_precision + 1);
mpz_mul(mpz2, mpz2, mpz1);
mpz_tdiv_q(mpz2, mpz2, mpq_denref(mpq1));
end += gmp_sprintf(end, "%Zd", mpz2);
size_t extra_zeros = real_precision + 1 - (end - dec_point);

char *p = end - 1; /* position of the extra digit */
/* Do we need to round up or not? */
int roundup = 0;
if (*p > '4')
    roundup = 1;

/* Propagate the round up back the string of digits */
while (roundup && p != str) {
    --p;
    ++*p;
    if (*p > '9')
        *p = '0';
    else
        roundup = 0;
}

/* Move end back to the first non-zero of the fractional part */
p = end - 2; /* position of the last significant digit */
while (*p == '0' && p != dec_point - 1)
    --p;
end = p + 1; /* the new end */

/* Output the number */
if (negative) /* minus sign */
    putc('-', stdout);

if (roundup) /* overflow */
    putc('1', stdout);

/* Integer part */
p = str;
while (p != dec_point) {
    putc(*p, stdout);
    ++p;
}
if (p == end) /* There is no fractional part after rounding */
    return;

/* Fractional part */
putc('.', stdout);
while (extra_zeros-- != 0)
    putc('0', stdout);
while (p != end) {
    putc(*p, stdout);
    ++p;
}

Answer 1

If you wanted to round an unsigned rational value to the nearest integer you'd add 0.5 and then only display the integer part.

For 1 digit after the decimal point you'd add 0.05.

For 2 digits after the decimal point you'd add 0.005.

For n digits after the decimal point you'd add 5 / ( 10**(n+1) ).

Answer 2

Just for posterity, what I ended up doing is indeed along the lines of Brendan's answer. As I have signed rationals, I do the following (without going in detail):

• Add 1/(2*10^precision) to the positive, or -1/(2*10^precision) to the negative rational
• Divide, print out leaving out the last digit and trailing zeroes.