/*

  Name:     imrat.c

  Purpose:  Arbitrary precision rational arithmetic routines.

  Author:   M. J. Fromberger <http://spinning-yarns.org/michael/>

  Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved.

  Permission is hereby granted, free of charge, to any person obtaining a copy

  of this software and associated documentation files (the "Software"), to deal

  in the Software without restriction, including without limitation the rights

  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

  copies of the Software, and to permit persons to whom the Software is

  furnished to do so, subject to the following conditions:

  The above copyright notice and this permission notice shall be included in

  all copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE

  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

  SOFTWARE.

 */

#include "imrat.h"

#include <stdlib.h>

#include <string.h>

#include <ctype.h>

#include <assert.h>

/* {{{ Useful macros */

#define TEMP(K) (temp + (K))

#define SETUP(E, C) \

do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0)

/* Argument checking:

   Use CHECK() where a return value is required; NRCHECK() elsewhere */

#define CHECK(TEST)   assert(TEST)

#define NRCHECK(TEST) assert(TEST)

/* }}} */

/* Reduce the given rational, in place, to lowest terms and canonical form.

   Zero is represented as 0/1, one as 1/1.  Signs are adjusted so that the sign

   of the numerator is definitive. */

static mp_result s_rat_reduce(mp_rat r);

/* Common code for addition and subtraction operations on rationals. */

static mp_result s_rat_combine(mp_rat a, mp_rat b, mp_rat c,

			       mp_result (*comb_f)(mp_int, mp_int, mp_int));

/* {{{ mp_rat_init(r) */

mp_result mp_rat_init(mp_rat r)

{

  mp_result res;

  if ((res = mp_int_init(MP_NUMER_P(r))) != MP_OK)

    return res;

  if ((res = mp_int_init(MP_DENOM_P(r))) != MP_OK) {

    mp_int_clear(MP_NUMER_P(r));

    return res;

  }

  return mp_int_set_value(MP_DENOM_P(r), 1);

}

/* }}} */

/* {{{ mp_rat_alloc() */

mp_rat mp_rat_alloc(void)

{

  mp_rat out = malloc(sizeof(*out));

  if (out != NULL) {

    if (mp_rat_init(out) != MP_OK) {

      free(out);

      return NULL;

    }

  }

  return out;

}

/* }}} */

/* {{{ mp_rat_reduce(r) */

mp_result mp_rat_reduce(mp_rat r) {

  return s_rat_reduce(r);

}

/* }}} */

/* {{{ mp_rat_init_size(r, n_prec, d_prec) */

mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec)

{

  mp_result res;

  if ((res = mp_int_init_size(MP_NUMER_P(r), n_prec)) != MP_OK)

    return res;

  if ((res = mp_int_init_size(MP_DENOM_P(r), d_prec)) != MP_OK) {

    mp_int_clear(MP_NUMER_P(r));

    return res;

  }

  return mp_int_set_value(MP_DENOM_P(r), 1);

}

/* }}} */

/* {{{ mp_rat_init_copy(r, old) */

mp_result mp_rat_init_copy(mp_rat r, mp_rat old)

{

  mp_result res;

  if ((res = mp_int_init_copy(MP_NUMER_P(r), MP_NUMER_P(old))) != MP_OK)

    return res;

  if ((res = mp_int_init_copy(MP_DENOM_P(r), MP_DENOM_P(old))) != MP_OK) 

    mp_int_clear(MP_NUMER_P(r));

  return res;

}

/* }}} */

/* {{{ mp_rat_set_value(r, numer, denom) */

mp_result mp_rat_set_value(mp_rat r, mp_small numer, mp_small denom)

{

  mp_result res;

  if (denom == 0)

    return MP_UNDEF;

  if ((res = mp_int_set_value(MP_NUMER_P(r), numer)) != MP_OK)

    return res;

  if ((res = mp_int_set_value(MP_DENOM_P(r), denom)) != MP_OK)

    return res;

  return s_rat_reduce(r);

}

/* }}} */

/* {{{ mp_rat_set_uvalue(r, numer, denom) */

mp_result mp_rat_set_uvalue(mp_rat r, mp_usmall numer, mp_usmall denom)

{

  mp_result res;

  if (denom == 0)

    return MP_UNDEF;

  if ((res = mp_int_set_uvalue(MP_NUMER_P(r), numer)) != MP_OK)

    return res;

  if ((res = mp_int_set_uvalue(MP_DENOM_P(r), denom)) != MP_OK)

    return res;

  return s_rat_reduce(r);

}

/* }}} */

/* {{{ mp_rat_clear(r) */

void      mp_rat_clear(mp_rat r)

{

  mp_int_clear(MP_NUMER_P(r));

  mp_int_clear(MP_DENOM_P(r));

}

/* }}} */

/* {{{ mp_rat_free(r) */

void      mp_rat_free(mp_rat r)

{

  NRCHECK(r != NULL);

  if (r->num.digits != NULL)

    mp_rat_clear(r);

  free(r);

}

/* }}} */

/* {{{ mp_rat_numer(r, z) */

mp_result mp_rat_numer(mp_rat r, mp_int z)

{

  return mp_int_copy(MP_NUMER_P(r), z);

}

/* }}} */

/* {{{ mp_rat_numer_ref(r) */

mp_int mp_rat_numer_ref(mp_rat r)

{

  return MP_NUMER_P(r);

}

/* }}} */

/* {{{ mp_rat_denom(r, z) */

mp_result mp_rat_denom(mp_rat r, mp_int z)

{

  return mp_int_copy(MP_DENOM_P(r), z);

}

/* }}} */

/* {{{ mp_rat_denom_ref(r) */

mp_int    mp_rat_denom_ref(mp_rat r)

{

  return MP_DENOM_P(r);

}

/* }}} */

/* {{{ mp_rat_sign(r) */

mp_sign   mp_rat_sign(mp_rat r)

{

  return MP_SIGN(MP_NUMER_P(r));

}

/* }}} */

/* {{{ mp_rat_copy(a, c) */

mp_result mp_rat_copy(mp_rat a, mp_rat c)

{

  mp_result res;

  if ((res = mp_int_copy(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK)

    return res;

  res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c));

  return res;

}

/* }}} */

/* {{{ mp_rat_zero(r) */

void      mp_rat_zero(mp_rat r)

{

  mp_int_zero(MP_NUMER_P(r));

  mp_int_set_value(MP_DENOM_P(r), 1);

}

/* }}} */

/* {{{ mp_rat_abs(a, c) */

mp_result mp_rat_abs(mp_rat a, mp_rat c)

{

  mp_result res;

  if ((res = mp_int_abs(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK)

    return res;

  res = mp_int_abs(MP_DENOM_P(a), MP_DENOM_P(c));

  return res;

}

/* }}} */

/* {{{ mp_rat_neg(a, c) */

mp_result mp_rat_neg(mp_rat a, mp_rat c)

{

  mp_result res;

  if ((res = mp_int_neg(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK)

    return res;

  res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c));

  return res;

}

/* }}} */

/* {{{ mp_rat_recip(a, c) */

mp_result mp_rat_recip(mp_rat a, mp_rat c)

{

  mp_result res;

  if (mp_rat_compare_zero(a) == 0)

    return MP_UNDEF;

  if ((res = mp_rat_copy(a, c)) != MP_OK)

    return res;

  mp_int_swap(MP_NUMER_P(c), MP_DENOM_P(c));

  /* Restore the signs of the swapped elements */

  {

    mp_sign tmp = MP_SIGN(MP_NUMER_P(c));

    MP_SIGN(MP_NUMER_P(c)) = MP_SIGN(MP_DENOM_P(c));

    MP_SIGN(MP_DENOM_P(c)) = tmp;

  }

  return MP_OK;

}

/* }}} */

/* {{{ mp_rat_add(a, b, c) */

mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c)

{

  return s_rat_combine(a, b, c, mp_int_add);

}

/* }}} */

/* {{{ mp_rat_sub(a, b, c) */

mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c)

{

  return s_rat_combine(a, b, c, mp_int_sub);

}

/* }}} */

/* {{{ mp_rat_mul(a, b, c) */

mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c)

{

  mp_result res;

  if ((res = mp_int_mul(MP_NUMER_P(a), MP_NUMER_P(b), MP_NUMER_P(c))) != MP_OK)

    return res;

  if (mp_int_compare_zero(MP_NUMER_P(c)) != 0) {

    if ((res = mp_int_mul(MP_DENOM_P(a), MP_DENOM_P(b), MP_DENOM_P(c))) != MP_OK)

      return res;

  }

  return s_rat_reduce(c);

}

/* }}} */

/* {{{ mp_int_div(a, b, c) */

mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c)

{

  mp_result res = MP_OK;

  if (mp_rat_compare_zero(b) == 0)

    return MP_UNDEF;

  if (c == a || c == b) {

    mpz_t tmp;

    if ((res = mp_int_init(&tmp)) != MP_OK) return res;

    if ((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), &tmp)) != MP_OK) 

      goto CLEANUP;

    if ((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK)

      goto CLEANUP;

    res = mp_int_copy(&tmp, MP_NUMER_P(c));

  CLEANUP:

    mp_int_clear(&tmp);

  }

  else {

    if ((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), MP_NUMER_P(c))) != MP_OK)

      return res;

    if ((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK)

      return res;

  }

  if (res != MP_OK)

    return res;

  else

    return s_rat_reduce(c);

}

/* }}} */

/* {{{ mp_rat_add_int(a, b, c) */

mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c)

{

  mpz_t tmp;

  mp_result res;

  if ((res = mp_int_init_copy(&tmp, b)) != MP_OK)

    return res;

  if ((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK)

    goto CLEANUP;

  if ((res = mp_rat_copy(a, c)) != MP_OK)

    goto CLEANUP;

  if ((res = mp_int_add(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK)

    goto CLEANUP;

  res = s_rat_reduce(c);

 CLEANUP:

  mp_int_clear(&tmp);

  return res;

}

/* }}} */

/* {{{ mp_rat_sub_int(a, b, c) */

mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c)

{

  mpz_t tmp;

  mp_result res;

  if ((res = mp_int_init_copy(&tmp, b)) != MP_OK)

    return res;

  if ((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK)

    goto CLEANUP;

  if ((res = mp_rat_copy(a, c)) != MP_OK)

    goto CLEANUP;

  if ((res = mp_int_sub(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK)

    goto CLEANUP;

  res = s_rat_reduce(c);

 CLEANUP:

  mp_int_clear(&tmp);

  return res;

}

/* }}} */

/* {{{ mp_rat_mul_int(a, b, c) */

mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c)

{

  mp_result res;

  if ((res = mp_rat_copy(a, c)) != MP_OK)

    return res;

  if ((res = mp_int_mul(MP_NUMER_P(c), b, MP_NUMER_P(c))) != MP_OK)

    return res;

  return s_rat_reduce(c);

}

/* }}} */

/* {{{ mp_rat_div_int(a, b, c) */

mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c)

{

  mp_result res;

  if (mp_int_compare_zero(b) == 0)

    return MP_UNDEF;

  if ((res = mp_rat_copy(a, c)) != MP_OK)

    return res;

  if ((res = mp_int_mul(MP_DENOM_P(c), b, MP_DENOM_P(c))) != MP_OK)

    return res;

  return s_rat_reduce(c);

}

/* }}} */

/* {{{ mp_rat_expt(a, b, c) */

mp_result mp_rat_expt(mp_rat a, mp_small b, mp_rat c)

{

  mp_result  res;

  /* Special cases for easy powers. */

  if (b == 0)

    return mp_rat_set_value(c, 1, 1);

  else if(b == 1)

    return mp_rat_copy(a, c);

  /* Since rationals are always stored in lowest terms, it is not necessary to

     reduce again when raising to an integer power. */

  if ((res = mp_int_expt(MP_NUMER_P(a), b, MP_NUMER_P(c))) != MP_OK)

    return res;

  return mp_int_expt(MP_DENOM_P(a), b, MP_DENOM_P(c));

}

/* }}} */

/* {{{ mp_rat_compare(a, b) */

int       mp_rat_compare(mp_rat a, mp_rat b)

{

  /* Quick check for opposite signs.  Works because the sign of the numerator

     is always definitive. */

  if (MP_SIGN(MP_NUMER_P(a)) != MP_SIGN(MP_NUMER_P(b))) {

    if (MP_SIGN(MP_NUMER_P(a)) == MP_ZPOS)

      return 1;

    else

      return -1;

  }

  else {

    /* Compare absolute magnitudes; if both are positive, the answer stands,

       otherwise it needs to be reflected about zero. */

    int cmp = mp_rat_compare_unsigned(a, b);

    if (MP_SIGN(MP_NUMER_P(a)) == MP_ZPOS)

      return cmp;

    else

      return -cmp;

  }

}

/* }}} */

/* {{{ mp_rat_compare_unsigned(a, b) */

int       mp_rat_compare_unsigned(mp_rat a, mp_rat b)

{

  /* If the denominators are equal, we can quickly compare numerators without

     multiplying.  Otherwise, we actually have to do some work. */

  if (mp_int_compare_unsigned(MP_DENOM_P(a), MP_DENOM_P(b)) == 0)

    return mp_int_compare_unsigned(MP_NUMER_P(a), MP_NUMER_P(b));

  else {

    mpz_t  temp[2];

    mp_result res;

    int  cmp = INT_MAX, last = 0;

    /* t0 = num(a) * den(b), t1 = num(b) * den(a) */

    SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(a)), last);

    SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(b)), last);

    if ((res = mp_int_mul(TEMP(0), MP_DENOM_P(b), TEMP(0))) != MP_OK ||

	(res = mp_int_mul(TEMP(1), MP_DENOM_P(a), TEMP(1))) != MP_OK)

      goto CLEANUP;

    cmp = mp_int_compare_unsigned(TEMP(0), TEMP(1));

  CLEANUP:

    while (--last >= 0)

      mp_int_clear(TEMP(last));

    return cmp;

  }

}

/* }}} */

/* {{{ mp_rat_compare_zero(r) */

int       mp_rat_compare_zero(mp_rat r)

{

  return mp_int_compare_zero(MP_NUMER_P(r));

}

/* }}} */

/* {{{ mp_rat_compare_value(r, n, d) */

int       mp_rat_compare_value(mp_rat r, mp_small n, mp_small d)

{

  mpq_t tmp;

  mp_result res;

  int  out = INT_MAX;

  if ((res = mp_rat_init(&tmp)) != MP_OK)

    return out;

  if ((res = mp_rat_set_value(&tmp, n, d)) != MP_OK)

    goto CLEANUP;

  out = mp_rat_compare(r, &tmp);

 CLEANUP:

  mp_rat_clear(&tmp);

  return out;

}

/* }}} */

/* {{{ mp_rat_is_integer(r) */

int       mp_rat_is_integer(mp_rat r)

{

  return (mp_int_compare_value(MP_DENOM_P(r), 1) == 0);

}

/* }}} */

/* {{{ mp_rat_to_ints(r, *num, *den) */

mp_result mp_rat_to_ints(mp_rat r, mp_small *num, mp_small *den)

{

  mp_result res;

  if ((res = mp_int_to_int(MP_NUMER_P(r), num)) != MP_OK)

    return res;

  res = mp_int_to_int(MP_DENOM_P(r), den);

  return res;

}

/* }}} */

/* {{{ mp_rat_to_string(r, radix, *str, limit) */

mp_result mp_rat_to_string(mp_rat r, mp_size radix, char *str, int limit)

{

  char *start;

  int   len;

  mp_result res;

  /* Write the numerator.  The sign of the rational number is written by the

     underlying integer implementation. */

  if ((res = mp_int_to_string(MP_NUMER_P(r), radix, str, limit)) != MP_OK)

    return res;

  /* If the value is zero, don't bother writing any denominator */

  if (mp_int_compare_zero(MP_NUMER_P(r)) == 0)

    return MP_OK;

  /* Locate the end of the numerator, and make sure we are not going to exceed

     the limit by writing a slash. */

  len = strlen(str);

  start = str + len;

  limit -= len;

  if(limit == 0)

    return MP_TRUNC;

  *start++ = '/';

  limit -= 1;

  res = mp_int_to_string(MP_DENOM_P(r), radix, start, limit);

  return res;

}

/* }}} */

/* {{{ mp_rat_to_decimal(r, radix, prec, *str, limit) */

mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec,

                            mp_round_mode round, char *str, int limit)

{

  mpz_t temp[3];

  mp_result res;

  char *start = str;

  int len, lead_0, left = limit, last = 0;

  SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(r)), last);

  SETUP(mp_int_init(TEMP(last)), last);

  SETUP(mp_int_init(TEMP(last)), last);

  /* Get the unsigned integer part by dividing denominator into the absolute

     value of the numerator. */

  mp_int_abs(TEMP(0), TEMP(0));

  if ((res = mp_int_div(TEMP(0), MP_DENOM_P(r), TEMP(0), TEMP(1))) != MP_OK)

    goto CLEANUP;

  /* Now:  T0 = integer portion, unsigned;

           T1 = remainder, from which fractional part is computed. */

  /* Count up leading zeroes after the radix point. */

  for (lead_0 = 0; lead_0 < prec && mp_int_compare(TEMP(1), MP_DENOM_P(r)) < 0; 

      ++lead_0) {

    if ((res = mp_int_mul_value(TEMP(1), radix, TEMP(1))) != MP_OK)

      goto CLEANUP;

  }

  /* Multiply remainder by a power of the radix sufficient to get the right

     number of significant figures. */

  if (prec > lead_0) {

    if ((res = mp_int_expt_value(radix, prec - lead_0, TEMP(2))) != MP_OK)

      goto CLEANUP;

    if ((res = mp_int_mul(TEMP(1), TEMP(2), TEMP(1))) != MP_OK)

      goto CLEANUP;

  }

  if ((res = mp_int_div(TEMP(1), MP_DENOM_P(r), TEMP(1), TEMP(2))) != MP_OK)

    goto CLEANUP;

  /* Now:  T1 = significant digits of fractional part;

           T2 = leftovers, to use for rounding. 

     At this point, what we do depends on the rounding mode.  The default is

     MP_ROUND_DOWN, for which everything is as it should be already.

  */

  switch (round) {

    int cmp;

  case MP_ROUND_UP:

    if (mp_int_compare_zero(TEMP(2)) != 0) {

      if (prec == 0)

	res = mp_int_add_value(TEMP(0), 1, TEMP(0));

      else

	res = mp_int_add_value(TEMP(1), 1, TEMP(1));

    }

    break;

  case MP_ROUND_HALF_UP:

  case MP_ROUND_HALF_DOWN:

    if ((res = mp_int_mul_pow2(TEMP(2), 1, TEMP(2))) != MP_OK)

      goto CLEANUP;

    cmp = mp_int_compare(TEMP(2), MP_DENOM_P(r));    

    if (round == MP_ROUND_HALF_UP)

      cmp += 1;

    if (cmp > 0) {

      if (prec == 0)

	res = mp_int_add_value(TEMP(0), 1, TEMP(0));

      else

	res = mp_int_add_value(TEMP(1), 1, TEMP(1));

    }

    break;

  case MP_ROUND_DOWN:

    break;  /* No action required */

  default: 

    return MP_BADARG; /* Invalid rounding specifier */

  }

  /* The sign of the output should be the sign of the numerator, but if all the

     displayed digits will be zero due to the precision, a negative shouldn't

     be shown. */

  if (MP_SIGN(MP_NUMER_P(r)) == MP_NEG &&

      (mp_int_compare_zero(TEMP(0)) != 0 ||

       mp_int_compare_zero(TEMP(1)) != 0)) {

    *start++ = '-';

    left -= 1;

  }

  if ((res = mp_int_to_string(TEMP(0), radix, start, left)) != MP_OK)

    goto CLEANUP;

  len = strlen(start);

  start += len;

  left -= len;

  if (prec == 0) 

    goto CLEANUP;

  *start++ = '.';

  left -= 1;

  if (left < prec + 1) {

    res = MP_TRUNC;

    goto CLEANUP;

  }

  memset(start, '0', lead_0 - 1);

  left -= lead_0;

  start += lead_0 - 1;

  res = mp_int_to_string(TEMP(1), radix, start, left);

 CLEANUP:

  while (--last >= 0)

    mp_int_clear(TEMP(last));

  return res;

}

/* }}} */

/* {{{ mp_rat_string_len(r, radix) */

mp_result mp_rat_string_len(mp_rat r, mp_size radix)

{

  mp_result n_len, d_len = 0;

  n_len = mp_int_string_len(MP_NUMER_P(r), radix);

  if (mp_int_compare_zero(MP_NUMER_P(r)) != 0)

    d_len = mp_int_string_len(MP_DENOM_P(r), radix);

  /* Though simplistic, this formula is correct.  Space for the sign flag is

     included in n_len, and the space for the NUL that is counted in n_len

     counts for the separator here.  The space for the NUL counted in d_len

     counts for the final terminator here. */

  return n_len + d_len;

}

/* }}} */

/* {{{ mp_rat_decimal_len(r, radix, prec) */

mp_result mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec)

{

  int  z_len, f_len;

  z_len = mp_int_string_len(MP_NUMER_P(r), radix);

  if (prec == 0)

    f_len = 1; /* terminator only */

  else

    f_len = 1 + prec + 1; /* decimal point, digits, terminator */

  return z_len + f_len;

}

/* }}} */

/* {{{ mp_rat_read_string(r, radix, *str) */

mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char *str)

{

  return mp_rat_read_cstring(r, radix, str, NULL);

}

/* }}} */

/* {{{ mp_rat_read_cstring(r, radix, *str, **end) */

mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char *str, 

			      char **end)

{

  mp_result res;

  char *endp;

  if ((res = mp_int_read_cstring(MP_NUMER_P(r), radix, str, &endp)) != MP_OK &&

      (res != MP_TRUNC))

    return res;

  /* Skip whitespace between numerator and (possible) separator */

  while (isspace((unsigned char) *endp))

    ++endp;

  /* If there is no separator, we will stop reading at this point. */

  if (*endp != '/') {

    mp_int_set_value(MP_DENOM_P(r), 1);

    if (end != NULL)

      *end = endp;

    return res;

  }

  ++endp; /* skip separator */

  if ((res = mp_int_read_cstring(MP_DENOM_P(r), radix, endp, end)) != MP_OK)

    return res;

  /* Make sure the value is well-defined */

  if (mp_int_compare_zero(MP_DENOM_P(r)) == 0)

    return MP_UNDEF;

  /* Reduce to lowest terms */

  return s_rat_reduce(r);

}

/* }}} */

/* {{{ mp_rat_read_ustring(r, radix, *str, **end) */

/* Read a string and figure out what format it's in.  The radix may be supplied