| /* mpfr_tan -- tangent of a floating-point number |
| |
| Copyright 2001, 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" |
| |
| /* computes tan(x) = sign(x)*sqrt(1/cos(x)^2-1) */ |
| int |
| mpfr_tan (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) |
| { |
| mp_prec_t precy, m; |
| int inexact; |
| mpfr_t s, c; |
| MPFR_ZIV_DECL (loop); |
| MPFR_SAVE_EXPO_DECL (expo); |
| MPFR_GROUP_DECL (group); |
| |
| MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), |
| ("y[%#R]=%R inexact=%d", y, y, inexact)); |
| |
| if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x))) |
| { |
| if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) |
| { |
| MPFR_SET_NAN(y); |
| MPFR_RET_NAN; |
| } |
| else /* x is zero */ |
| { |
| MPFR_ASSERTD(MPFR_IS_ZERO(x)); |
| MPFR_SET_ZERO(y); |
| MPFR_SET_SAME_SIGN(y, x); |
| MPFR_RET(0); |
| } |
| } |
| |
| /* tan(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */ |
| MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 1, 1, |
| rnd_mode, {}); |
| |
| MPFR_SAVE_EXPO_MARK (expo); |
| |
| /* Compute initial precision */ |
| precy = MPFR_PREC (y); |
| m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13; |
| MPFR_ASSERTD (m >= 2); /* needed for the error analysis in algorithms.tex */ |
| |
| MPFR_GROUP_INIT_2 (group, m, s, c); |
| MPFR_ZIV_INIT (loop, m); |
| for (;;) |
| { |
| /* The only way to get an overflow is to get ~ Pi/2 |
| But the result will be ~ 2^Prec(y). */ |
| mpfr_sin_cos (s, c, x, GMP_RNDN); /* err <= 1/2 ulp on s and c */ |
| mpfr_div (c, s, c, GMP_RNDN); /* err <= 4 ulps */ |
| MPFR_ASSERTD (!MPFR_IS_SINGULAR (c)); |
| if (MPFR_LIKELY (MPFR_CAN_ROUND (c, m - 2, precy, rnd_mode))) |
| break; |
| MPFR_ZIV_NEXT (loop, m); |
| MPFR_GROUP_REPREC_2 (group, m, s, c); |
| } |
| MPFR_ZIV_FREE (loop); |
| inexact = mpfr_set (y, c, rnd_mode); |
| MPFR_GROUP_CLEAR (group); |
| |
| MPFR_SAVE_EXPO_FREE (expo); |
| return mpfr_check_range (y, inexact, rnd_mode); |
| } |