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author | Akira Kakuto <kakuto@fuk.kindai.ac.jp> | 2016-02-22 06:02:38 +0000 |
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committer | Akira Kakuto <kakuto@fuk.kindai.ac.jp> | 2016-02-22 06:02:38 +0000 |
commit | b2ef5d127f546fa32f303b1dedfc4a6390ad677e (patch) | |
tree | 17cd90adb54888579df0e08223bf4909332380c2 /Build/source/libs/mpfr/mpfr-src/src/cbrt.c | |
parent | 05d739843a7c50294efbda2abf2ab4ea3fc146b1 (diff) |
libs/mpfr: New convention
git-svn-id: svn://tug.org/texlive/trunk@39814 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/cbrt.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/cbrt.c | 153 |
1 files changed, 153 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/cbrt.c b/Build/source/libs/mpfr/mpfr-src/src/cbrt.c new file mode 100644 index 00000000000..d6858bc92fa --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-src/src/cbrt.c @@ -0,0 +1,153 @@ +/* mpfr_cbrt -- cube root function. + +Copyright 2002-2015 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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 3 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.LESSER. If not, see +http://www.gnu.org/licenses/ or 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, mpfr_rnd_t rnd_mode) +{ + mpz_t m; + mpfr_exp_t e, r, sh; + mpfr_prec_t n, size_m, tmp; + int inexact, negative; + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_LOG_FUNC ( + ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), + ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, + inexact)); + + /* 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_2exp (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 == MPFR_RNDN); + + /* we want 3*n-2 <= size_m + 3*sh + r <= 3*n + i.e. 3*sh + size_m + r <= 3*n */ + sh = (3 * (mpfr_exp_t) n - (mpfr_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 || ((mpfr_exp_t) mpz_scan1 (m, 0) < sh); + mpz_fdiv_q_2exp (m, m, sh); + e += 3 * sh; + } + + if (inexact) + { + if (negative) + rnd_mode = MPFR_INVERT_RND (rnd_mode); + if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA + || (rnd_mode == MPFR_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=MPFR_RNDN and bit (n+1) from m is 1 */ + inexact += mpfr_set_z (y, m, MPFR_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); +} |