1/* mpfr_tan -- tangent of a floating-point number 2 3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. 4Contributed by the AriC and Caramel projects, INRIA. 5 6This file is part of the GNU MPFR Library. 7 8The GNU MPFR Library is free software; you can redistribute it and/or modify 9it under the terms of the GNU Lesser General Public License as published by 10the Free Software Foundation; either version 3 of the License, or (at your 11option) any later version. 12 13The GNU MPFR Library is distributed in the hope that it will be useful, but 14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 15or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 16License for more details. 17 18You should have received a copy of the GNU Lesser General Public License 19along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see 20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ 22 23#define MPFR_NEED_LONGLONG_H 24#include "mpfr-impl.h" 25 26/* computes tan(x) = sign(x)*sqrt(1/cos(x)^2-1) */ 27int 28mpfr_tan (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) 29{ 30 mpfr_prec_t precy, m; 31 int inexact; 32 mpfr_t s, c; 33 MPFR_ZIV_DECL (loop); 34 MPFR_SAVE_EXPO_DECL (expo); 35 MPFR_GROUP_DECL (group); 36 37 MPFR_LOG_FUNC 38 (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), 39 ("y[%Pu]=%.*Rg inexact=%d", 40 mpfr_get_prec (y), mpfr_log_prec, y, inexact)); 41 42 if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x))) 43 { 44 if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) 45 { 46 MPFR_SET_NAN(y); 47 MPFR_RET_NAN; 48 } 49 else /* x is zero */ 50 { 51 MPFR_ASSERTD(MPFR_IS_ZERO(x)); 52 MPFR_SET_ZERO(y); 53 MPFR_SET_SAME_SIGN(y, x); 54 MPFR_RET(0); 55 } 56 } 57 58 /* tan(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */ 59 MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 1, 1, 60 rnd_mode, {}); 61 62 MPFR_SAVE_EXPO_MARK (expo); 63 64 /* Compute initial precision */ 65 precy = MPFR_PREC (y); 66 m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13; 67 MPFR_ASSERTD (m >= 2); /* needed for the error analysis in algorithms.tex */ 68 69 MPFR_GROUP_INIT_2 (group, m, s, c); 70 MPFR_ZIV_INIT (loop, m); 71 for (;;) 72 { 73 /* The only way to get an overflow is to get ~ Pi/2 74 But the result will be ~ 2^Prec(y). */ 75 mpfr_sin_cos (s, c, x, MPFR_RNDN); /* err <= 1/2 ulp on s and c */ 76 mpfr_div (c, s, c, MPFR_RNDN); /* err <= 4 ulps */ 77 MPFR_ASSERTD (!MPFR_IS_SINGULAR (c)); 78 if (MPFR_LIKELY (MPFR_CAN_ROUND (c, m - 2, precy, rnd_mode))) 79 break; 80 MPFR_ZIV_NEXT (loop, m); 81 MPFR_GROUP_REPREC_2 (group, m, s, c); 82 } 83 MPFR_ZIV_FREE (loop); 84 inexact = mpfr_set (y, c, rnd_mode); 85 MPFR_GROUP_CLEAR (group); 86 87 MPFR_SAVE_EXPO_FREE (expo); 88 return mpfr_check_range (y, inexact, rnd_mode); 89} 90