X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=mpfr%2Fcbrt.c;fp=mpfr%2Fcbrt.c;h=923f4c304da64b57c9edd777bc56f4e97bdd60d1;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/mpfr/cbrt.c b/mpfr/cbrt.c new file mode 100644 index 00000000..923f4c30 --- /dev/null +++ b/mpfr/cbrt.c @@ -0,0 +1,148 @@ +/* mpfr_cbrt -- cube root function. + +Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao projects, INRIA. + +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. */ + +#define MPFR_NEED_LONGLONG_H +#include "mpfr-impl.h" + + /* The computation of y = x^(1/3) is done as follows: + + Let x = sign * m * 2^(3*e) where m is an integer + + with 2^(3n-3) <= m < 2^(3n) where n = PREC(y) + + and m = s^3 + r where 0 <= r and m < (s+1)^3 + + we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(3n-3) + i.e. m must have at least 3n-2 bits + + then x^(1/3) = s * 2^e if r=0 + x^(1/3) = (s+1) * 2^e if round up + x^(1/3) = (s-1) * 2^e if round down + x^(1/3) = s * 2^e if nearest and r < 3/2*s^2+3/4*s+1/8 + (s+1) * 2^e otherwise + */ + +int +mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) +{ + mpz_t m; + mp_exp_t e, r, sh; + mp_prec_t n, size_m, tmp; + int inexact, negative; + MPFR_SAVE_EXPO_DECL (expo); + + /* special values */ + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN (x)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF (x)) + { + MPFR_SET_INF (y); + MPFR_SET_SAME_SIGN (y, x); + MPFR_RET (0); + } + /* case 0: cbrt(+/- 0) = +/- 0 */ + else /* x is necessarily 0 */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_ZERO (y); + MPFR_SET_SAME_SIGN (y, x); + MPFR_RET (0); + } + } + + /* General case */ + MPFR_SAVE_EXPO_MARK (expo); + mpz_init (m); + + e = mpfr_get_z_exp (m, x); /* x = m * 2^e */ + if ((negative = MPFR_IS_NEG(x))) + mpz_neg (m, m); + r = e % 3; + if (r < 0) + r += 3; + /* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */ + + MPFR_MPZ_SIZEINBASE2 (size_m, m); + n = MPFR_PREC (y) + (rnd_mode == GMP_RNDN); + + /* we want 3*n-2 <= size_m + 3*sh + r <= 3*n + i.e. 3*sh + size_m + r <= 3*n */ + sh = (3 * (mp_exp_t) n - (mp_exp_t) size_m - r) / 3; + sh = 3 * sh + r; + if (sh >= 0) + { + mpz_mul_2exp (m, m, sh); + e = e - sh; + } + else if (r > 0) + { + mpz_mul_2exp (m, m, r); + e = e - r; + } + + /* invariant: x = m*2^e, with e divisible by 3 */ + + /* we reuse the variable m to store the cube root, since it is not needed + any more: we just need to know if the root is exact */ + inexact = mpz_root (m, m, 3) == 0; + + MPFR_MPZ_SIZEINBASE2 (tmp, m); + sh = tmp - n; + if (sh > 0) /* we have to flush to 0 the last sh bits from m */ + { + inexact = inexact || ((mp_exp_t) mpz_scan1 (m, 0) < sh); + mpz_div_2exp (m, m, sh); + e += 3 * sh; + } + + if (inexact) + { + if (negative) + rnd_mode = MPFR_INVERT_RND (rnd_mode); + if (rnd_mode == GMP_RNDU + || (rnd_mode == GMP_RNDN && mpz_tstbit (m, 0))) + inexact = 1, mpz_add_ui (m, m, 1); + else + inexact = -1; + } + + /* either inexact is not zero, and the conversion is exact, i.e. inexact + is not changed; or inexact=0, and inexact is set only when + rnd_mode=GMP_RNDN and bit (n+1) from m is 1 */ + inexact += mpfr_set_z (y, m, GMP_RNDN); + MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3); + + if (negative) + { + MPFR_CHANGE_SIGN (y); + inexact = -inexact; + } + + mpz_clear (m); + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +}