source/libs/mpfr/mpfr-3.1.3/src/tan.c

   1 /* mpfr_tan -- tangent of a floating-point number
   2
   3 Copyright 2001-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 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) */
  27 int
  28 mpfr_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 }