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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
88 lines
2.8 KiB
C
88 lines
2.8 KiB
C
/* mpfr_tan -- tangent of a floating-point number
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Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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/* computes tan(x) = sign(x)*sqrt(1/cos(x)^2-1) */
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int
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mpfr_tan (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
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{
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mpfr_prec_t precy, m;
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int inexact;
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mpfr_t s, c;
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MPFR_ZIV_DECL (loop);
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_GROUP_DECL (group);
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
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("y[%#R]=%R inexact=%d", y, y, inexact));
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if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
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{
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if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
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{
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MPFR_SET_NAN(y);
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MPFR_RET_NAN;
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}
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else /* x is zero */
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{
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MPFR_ASSERTD(MPFR_IS_ZERO(x));
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MPFR_SET_ZERO(y);
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MPFR_SET_SAME_SIGN(y, x);
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MPFR_RET(0);
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}
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}
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/* tan(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 1, 1,
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rnd_mode, {});
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MPFR_SAVE_EXPO_MARK (expo);
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/* Compute initial precision */
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precy = MPFR_PREC (y);
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m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13;
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MPFR_ASSERTD (m >= 2); /* needed for the error analysis in algorithms.tex */
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MPFR_GROUP_INIT_2 (group, m, s, c);
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MPFR_ZIV_INIT (loop, m);
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for (;;)
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{
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/* The only way to get an overflow is to get ~ Pi/2
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But the result will be ~ 2^Prec(y). */
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mpfr_sin_cos (s, c, x, MPFR_RNDN); /* err <= 1/2 ulp on s and c */
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mpfr_div (c, s, c, MPFR_RNDN); /* err <= 4 ulps */
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MPFR_ASSERTD (!MPFR_IS_SINGULAR (c));
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if (MPFR_LIKELY (MPFR_CAN_ROUND (c, m - 2, precy, rnd_mode)))
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break;
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MPFR_ZIV_NEXT (loop, m);
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MPFR_GROUP_REPREC_2 (group, m, s, c);
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}
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MPFR_ZIV_FREE (loop);
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inexact = mpfr_set (y, c, rnd_mode);
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MPFR_GROUP_CLEAR (group);
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (y, inexact, rnd_mode);
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}
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