mpfr-2.4.1.zip

/* mpfr_get_str -- output a floating-point number to a string Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. Contributed by the Arenaire and Cacao projects, INRIA. Contributed by Alain Delplanque and Paul Zimmermann. This file is part of the GNU MPFR Library. The GNU 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 GNU 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 GNU MPFR Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ #include <string.h> /* For strlen */ #define MPFR_NEED_LONGLONG_H #include "mpfr-impl.h" static int mpfr_get_str_aux (char *const, mp_exp_t *const, mp_limb_t *const, mp_size_t, mp_exp_t, long, int, size_t, mp_rnd_t); /* The implicit \0 is useless, but we do not write num_to_text[36] otherwise g++ complains. */ static const char num_to_text[] = "0123456789abcdefghijklmnopqrstuvwxyz"; /* copy most important limbs of {op, n2} in {rp, n1} */ /* if n1 > n2 put 0 in low limbs of {rp, n1} */ #define MPN_COPY2(rp, n1, op, n2) \ if ((n1) <= (n2)) \ { \ MPN_COPY ((rp), (op) + (n2) - (n1), (n1)); \ } \ else \ { \ MPN_COPY ((rp) + (n1) - (n2), (op), (n2)); \ MPN_ZERO ((rp), (n1) - (n2)); \ } #define MPFR_ROUND_FAILED 3 /* Input: an approximation r*2^f of an real Y, with |r*2^f-Y| <= 2^(e+f). Returns if possible in the string s the mantissa corresponding to the integer nearest to Y, within the direction rnd, and returns the exponent in exp. n is the number of limbs of r. e represents the maximal error in the approximation of Y (e < 0 iff the approximation is exact, i.e. r*2^f = Y). b is the wanted base (2 <= b <= 36). m is the number of wanted digits in the mantissa. rnd is the rounding mode. It is assumed that b^(m-1) <= Y < b^(m+1), thus the returned value satisfies b^(m-1) <= rnd(Y) < b^(m+1). Rounding may fail for two reasons: - the error is too large to determine the integer N nearest to Y - either the number of digits of N in base b is too large (m+1), N=2*N1+(b/2) and the rounding mode is to nearest. This can only happen when b is even. Return value: - the direction of rounding (-1, 0, 1) if rounding is possible - -MPFR_ROUND_FAILED if rounding not possible because m+1 digits - MPFR_ROUND_FAILED otherwise (too large error) */ static int mpfr_get_str_aux (char *const str, mp_exp_t *const exp, mp_limb_t *const r, mp_size_t n, mp_exp_t f, long e, int b, size_t m, mp_rnd_t rnd) { int dir; /* direction of the rounded result */ mp_limb_t ret = 0; /* possible carry in addition */ mp_size_t i0, j0; /* number of limbs and bits of Y */ unsigned char *str1; /* string of m+2 characters */ size_t size_s1; /* length of str1 */ mp_rnd_t rnd1; size_t i; int exact = (e < 0); MPFR_TMP_DECL(marker); /* if f > 0, then the maximal error 2^(e+f) is larger than 2 so we can't determine the integer Y */ MPFR_ASSERTN(f <= 0); /* if f is too small, then r*2^f is smaller than 1 */ MPFR_ASSERTN(f > (-n * BITS_PER_MP_LIMB)); MPFR_TMP_MARK(marker); /* R = 2^f sum r[i]K^(i) r[i] = (r_(i,k-1)...r_(i,0))_2 R = sum r(i,j)2^(j+ki+f) the bits from R are referenced by pairs (i,j) */ /* check if is possible to round r with rnd mode where |r*2^f-Y| <= 2^(e+f) the exponent of R is: f + n*BITS_PER_MP_LIMB we must have e + f == f + n*BITS_PER_MP_LIMB - err err = n*BITS_PER_MP_LIMB - e R contains exactly -f bits after the integer point: to determine the nearest integer, we thus need a precision of n * BITS_PER_MP_LIMB + f */ if (exact || mpfr_can_round_raw (r, n, (mp_size_t) 1, n * BITS_PER_MP_LIMB - e, GMP_RNDN, rnd, n * BITS_PER_MP_LIMB + f)) { /* compute the nearest integer to R */ /* bit of weight 0 in R has position j0 in limb r[i0] */ i0 = (-f) / BITS_PER_MP_LIMB; j0 = (-f) % BITS_PER_MP_LIMB; ret = mpfr_round_raw (r + i0, r, n * BITS_PER_MP_LIMB, 0, n * BITS_PER_MP_LIMB + f, rnd, &dir); MPFR_ASSERTD(dir != MPFR_ROUND_FAILED); /* warning: mpfr_round_raw_generic returns MPFR_EVEN_INEX (2) or -MPFR_EVEN_INEX (-2) in case of even rounding */ if (ret) /* Y is a power of 2 */ { if (j0) r[n - 1] = MPFR_LIMB_HIGHBIT >> (j0 - 1); else /* j0=0, necessarily i0 >= 1 otherwise f=0 and r is exact */ { r[n - 1] = ret; r[--i0] = 0; /* set to zero the new low limb */ } } else /* shift r to the right by (-f) bits (i0 already done) */ { if (j0) mpn_rshift (r + i0, r + i0, n - i0, j0); } /* now the rounded value Y is in {r+i0, n-i0} */ /* convert r+i0 into base b */ str1 = (unsigned char*) MPFR_TMP_ALLOC (m + 3); /* need one extra character for mpn_get_str */ size_s1 = mpn_get_str (str1, b, r + i0, n - i0); /* round str1 */ MPFR_ASSERTN(size_s1 >= m); *exp = size_s1 - m; /* number of superfluous characters */ /* if size_s1 = m + 2, necessarily we have b^(m+1) as result, and the result will not change */ /* so we have to double-round only when size_s1 = m + 1 and (i) the result is inexact (ii) or the last digit is non-zero */ if ((size_s1 == m + 1) && ((dir != 0) || (str1[size_s1 - 1] != 0))) { /* rounding mode */ rnd1 = rnd; /* round to nearest case */ if (rnd == GMP_RNDN) { if (2 * str1[size_s1 - 1] == b) { if (dir == 0 && exact) /* exact: even rounding */ { rnd1 = ((str1[size_s1-2] & 1) == 0) ? GMP_RNDD : GMP_RNDU; } else { /* otherwise we cannot round correctly: for example if b=10, we might have a mantissa of xxxxxxx5.00000000 which can be rounded to nearest to 8 digits but not to 7 */ dir = -MPFR_ROUND_FAILED; MPFR_ASSERTD(dir != MPFR_EVEN_INEX); goto free_and_return; } } else if (2 * str1[size_s1 - 1] < b) rnd1 = GMP_RNDD; else rnd1 = GMP_RNDU; } /* now rnd1 is either GMP_RNDD or GMP_RNDZ -> truncate or GMP_RDNU -> round towards infinity */ /* round away from zero */ if (rnd1 == GMP_RNDU) { if (str1[size_s1 - 1] != 0) { /* the carry cannot propagate to the whole string, since Y = x*b^(m-g) < 2*b^m <= b^(m+1)-b where x is the input float */ MPFR_ASSERTN(size_s1 >= 2); i = size_s1 - 2; while (str1[i] == b - 1) { MPFR_ASSERTD(i > 0); str1[i--] = 0; } str1[i]++; } dir = 1;