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/* mpfr_set_str -- set a floating-point number from a string
Copyright 2000, 2001, 2002, 2003 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
#include "log_b2.h"
static double __gmpfr_ceil _PROTO((double));
static int digit_value_in_base _PROTO ((int, int));
static double
__gmpfr_ceil (double x)
{
double y = (double) (long int) x;
return ((y < x) ? y + 1.0 : y);
}
/* Compatible with any locale, but one still assumes that 'a', 'b', 'c',
..., 'z', and 'A', 'B', 'C', ..., 'Z' are consecutive values (like
in any ASCII-based character set). */
static int
digit_value_in_base (int c, int base)
{
int digit;
if (isdigit (c))
digit = c - '0';
else if (c >= 'a' && c <= 'z')
digit = c - 'a' + 10;
else if (c >= 'A' && c <= 'Z')
digit = c - 'A' + 10;
else
return -1;
if (digit < base)
return digit;
return -1;
}
/* Set x to the value of str, in base base, rounded in direction rnd.
return value is: 0 if the entire string up to the final required '\0'
is a valid number, otherwise -1 (compatibility with
mpf_set_str)
*/
int
mpfr_set_str (mpfr_t x, const char *str, int base, mp_rnd_t rnd)
{
mp_limb_t *y; /* current value of x */
mp_exp_t exp_y; /* such as x = y*base^exp_y */
mp_limb_t *z, *result; /* temporary variables */
mp_exp_t exp_z; /* exponent of z */
size_t n; /* working precision in limbs */
size_t prec_s; /* precision of str */
mp_exp_t pr; /* needed precision requise for str */
mp_exp_t exp_s = 0; /* exponent in base 'base', normalized for a
mantissa 0.xxx...xxx */
mp_exp_t binexp = 0; /* binary exponent (for base 16) */
mp_exp_t prec_x; /* working precision for x */
char *str1; /* copy of str */
size_t size_str1; /* number of characters in str1 */
char *mant_s; /* pointer in str1 */
int negative; /* 1 if str<=0, 0 otherwise */
size_t i, j;
long err = 0;
int exact; /* is the computation exact */
int point = 0; /* position in str */
int cboucle = 1;
int c, res = 0;
TMP_DECL(marker);
if (base < 2 || base > 36)
return -1;
if (strncasecmp (str, "@NaN@", 5) == 0 ||
(base <= 16 && strcasecmp (str, "NaN") == 0))
{
MPFR_SET_NAN(x);
/* MPFR_RET_NAN not used as the return value isn't a ternary value */
__gmpfr_flags |= MPFR_FLAGS_NAN;
return 0;
}
/* deals with the sign */
negative = (str[0] == '-');
if ((str[0] == '-') || (str[0] == '+'))
str ++;
/* be careful that 'inf' is a valid number in base >= 24,
since i=18, n=23, f=15 */
if (strncasecmp (str, "@Inf@", 5) == 0 ||
(base <= 16 && strcasecmp (str, "Inf") == 0))
{
MPFR_CLEAR_NAN (x);
MPFR_SET_INF (x);
(negative) ? MPFR_SET_NEG (x) : MPFR_SET_POS (x);
return 0;
}
/* string "", "+" and "-" are invalid */
if (str[0] == '\0')
return -1;
/* allocate str1 to store value of characters in str.
FIXME: we could use str directly here if mpn_set_str would deal
with real characters. */
size_str1 = strlen (str);
str1 = (*__gmp_allocate_func) (size_str1 * sizeof (char));
/* the str1 pointer should not be modified */
/* checks if the input string is valid, and converts characters into
their value */
for (mant_s = str1; *str != 0; str++)
{
if (*str == '@'
|| (base <= 10 && (*str == 'e' || *str == 'E')))
{
char *endptr[1];
/* the exponent digits are kept in ASCII */
exp_s += (mp_exp_t) strtol (str + 1, endptr, 10);
if (**endptr != '\0')
{
res = -1; /* invalid input: garbage after exponent */
goto end;
}
break;
}
else if (base == 16 && (*str == 'p' || *str == 'P'))
{
char *endptr[1];
binexp = (mp_exp_t) strtol (str + 1, endptr, 10);
if (**endptr != '\0')
{
res = -1; /* invalid input: garbage after exponent */
goto end;
}
break;
}
else if (*str == '.')
{
point = 1;
continue; /* go to next character */
}
else if ((c = digit_value_in_base (*str, base)) != -1)
*mant_s = c; /* valid character */
else
{
res = -1; /* invalid input */
goto end;
}
if (!point)
exp_s ++;
mant_s ++;
}
prec_s = mant_s - str1; /* number of characters in the mantissa */
mant_s = str1;
/* remove 0's at the beginning and end of mant_s[0..prec_s-1] */
for (; (prec_s > 0) && (*mant_s == 0); mant_s++, prec_s--, exp_s--);
for (; (prec_s > 0) && (mant_s[prec_s - 1] == 0); prec_s--);
/* test if x = 0 */
if (prec_s == 0)
{
MPFR_SET_ZERO (x);
res = 0;
goto sign_and_flags;
}
/* now we have str = 0.mant_s[0]...mant_s[prec_s-1]*base^exp_s*2^binexp */
/* determine the minimal precision for the computation */
prec_x = MPFR_PREC(x) + (mp_exp_t) __gmpfr_ceil_log2 ((double) MPFR_PREC(x));
/* compute y as long as rounding is not possible */
for (;;cboucle ++)
{
TMP_MARK(marker);
/* number of limbs needed to compute x */
n = (prec_x - 1) / BITS_PER_MP_LIMB + 1;
/* initialize y to the value of 0.mant_s[0]...mant_s[pr-1] */
y = TMP_ALLOC ((2 * n + 1) * sizeof (mp_limb_t));
y += n;
/* remember that y - n is allocated for n limbs */
/* required precision for str */
pr = (mp_exp_t) __gmpfr_ceil
(((double) (n * BITS_PER_MP_LIMB) - 1.0) * log_b2[base-2]) + 1;
/* check is there are enough digits in str */
if (pr >= prec_s)
pr = prec_s;
/* convert str into binary */
i = mpn_set_str (y, (unsigned char *) mant_s, pr, base);
/* normalize y */
count_leading_zeros (j, *(y + i - 1));
if ((exact = (i <= n))) /* shift y to the left
in that case y shoud be exact */
{
/* shift {y, i} for j bits to the left */
if (j != 0)
mpn_lshift (y, y, i, j);
/* shift {y, i} for (n-i) limbs to the left */
if (i != n)
{
MPN_COPY_DECR (y + n - i, y, i);
MPN_ZERO (y, n - i);
}
/* for each bit shift decrease exponent of y */
exp_y = - ((n - i) * BITS_PER_MP_LIMB + j);
}
else /* shift y for the right */
{
/* shift {y, i} for (BITS_PER_MP_LIMB - j) bits to the right */
mpn_rshift (y, y, i, BITS_PER_MP_LIMB - j);
/* for each bit shift increase exponent of y */
exp_y = BITS_PER_MP_LIMB - j;
}
/* compute base^(exp_s-pr) on n limbs */
if (IS_POW2 (base))
{
int pow2;
count_leading_zeros (pow2, (mp_limb_t) base);
pow2 = BITS_PER_MP_LIMB - pow2 - 1; /* base = 2^pow2 */
exp_y += pow2 * (exp_s - (mp_exp_t) pr) + binexp;
result = y - n;
}
/* case exp_s > pr */
else if (exp_s > (mp_exp_t) pr)
{
result = TMP_ALLOC ((2 * n + 1) * sizeof (mp_limb_t));
/* (z, exp_z) = base^(exp_s-pr), then result = y*z */
/* z is allocated at y - n */
z = y - n;
err = mpn_exp (z, &exp_z, base, exp_s - (mp_exp_t) pr, n);
exact = (exact && (err == -1));
/* multiply (y = 0.mant_s[0]...mant_s[pr-1])_base by base^(exp_s-g) */
mpn_mul_n (result, y, z, n);
/* compute the error on the product */
if (err == -1)
err = 0;
err ++;
/* compute the exponent of y */
exp_y += exp_z + n * BITS_PER_MP_LIMB;
/* normalize result */
if ((result[2 * n - 1] & MPFR_LIMB_HIGHBIT) == 0)
{
mpn_lshift (result + n - 1, result + n - 1, n + 1, 1);
exp_y --;
}
exact = (exact && (mpn_scan1 (result, 0) >= n * BITS_PER_MP_LIMB));
}
/* cass exp_s < pr */
else if (exp_s < (mp_exp_t) pr)
{
result = TMP_ALLOC ((2 * n + 1) * sizeof (mp_limb_t));
/* set y to y * K^n */
y = y - n; /* we have allocated n limbs at y - n */
MPN_ZERO (y, n);
/* (z, exp_z) = base^(exp_s-pr) */
z = TMP_ALLOC (n * sizeof (mp_limb_t));
err = mpn_exp (z, &exp_z, base, pr - exp_s, n);
exact = (exact && (err == -1));
if (err == -1)
err = 0;
/* compute y / z */
/* result will be put into result + n, and remainder into result */
mpn_tdiv_qr (result + n, result, (mp_size_t) 0, y, 2*n, z, n);
exp_y = exp_y - exp_z - n * BITS_PER_MP_LIMB;
err += 2;
exact = (exact && (mpn_popcount (result, n) == 0));
/* normalize result */
if (result[2 * n] == 1)
{
exact = (exact && ((result[n] & 1) == 0));
mpn_rshift (result + n, result + n, n + 1, 1);
exp_y ++;
}
}
else
{
/* cass exp_s = pr : base^(exp_s-pr) = 1
nothing to compute, but we must put y into result and free it */
result = y - n;
}
/* test if rounding is possible, and if so exit the loop */
if (exact || mpfr_can_round_raw (result + n, n, (negative) ? -1 : 1,
n * BITS_PER_MP_LIMB - err - 1, GMP_RNDN, rnd, MPFR_PREC(x)))
break;
/* update for next loop */
if (cboucle == 2)
prec_x = (mp_exp_t)
__gmpfr_ceil ((double) prec_s / log_b2[base - 2]) + 3;
else
{
mp_exp_t ajout = __gmpfr_ceil_log2 ((double) prec_x);
prec_x += (ajout < BITS_PER_MP_LIMB) ? BITS_PER_MP_LIMB : ajout;
}
TMP_FREE(marker);
}
/* round y */
if (mpfr_round_raw_generic (MPFR_MANT(x), result + n, n * BITS_PER_MP_LIMB,
negative, MPFR_PREC(x), rnd, NULL, (int) 0))
{
/* overflaw when rounding y */
MPFR_MANT(x)[MPFR_ESIZE(x) - 1]
= MPFR_LIMB_HIGHBIT;
exp_y ++;
}
TMP_FREE(marker);
MPFR_SET_EXP (x, exp_y + n * BITS_PER_MP_LIMB);
sign_and_flags:
MPFR_CLEAR_FLAGS(x);
if (negative)
MPFR_SET_NEG(x);
else
MPFR_SET_POS(x);
end:
(*__gmp_free_func) (str1, size_str1 * sizeof (char));
return res;
}
int
mpfr_init_set_str (mpfr_ptr x, const char *str, int base, mp_rnd_t rnd)
{
mpfr_init (x);
return mpfr_set_str (x, str, base, rnd);
}
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