/* mpfr_sin_cos -- sine and cosine of a floating-point number

Copyright 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"

/* (y, z) <- (sin(x), cos(x)), return value is 0 iff both results are exact
   ie, iff x = 0 */
int
mpfr_sin_cos (mpfr_ptr y, mpfr_ptr z, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mp_prec_t prec, m;
  int neg, reduce;
  mpfr_t c, xr;
  mpfr_srcptr xx;
  mp_exp_t err, expx;
  int inexy, inexz;
  MPFR_ZIV_DECL (loop);
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_ASSERTN (y != z);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
        {
          MPFR_SET_NAN (y);
          MPFR_SET_NAN (z);
          MPFR_RET_NAN;
        }
      else /* x is zero */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (x));
          MPFR_SET_ZERO (y);
          MPFR_SET_SAME_SIGN (y, x);
          /* y = 0, thus exact, but z is inexact in case of underflow
             or overflow */
          return mpfr_set_ui (z, 1, rnd_mode);
        }
    }

  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
                  ("sin[%#R]=%R cos[%#R]=%R", y, y, z, z));

  MPFR_SAVE_EXPO_MARK (expo);

  prec = MAX (MPFR_PREC (y), MPFR_PREC (z));
  m = prec + MPFR_INT_CEIL_LOG2 (prec) + 13;
  expx = MPFR_GET_EXP (x);

  /* When x is close to 0, say 2^(-k), then there is a cancellation of about
     2k bits in 1-cos(x)^2. FIXME: in that case, it would be more efficient
     to compute sin(x) directly. VL: This is partly done by using
     MPFR_FAST_COMPUTE_IF_SMALL_INPUT from the mpfr_sin and mpfr_cos
     functions. Moreover, any overflow on m is avoided. */
  if (expx < 0)
    {
      /* Warning: in case y = x, and the first call to
         MPFR_FAST_COMPUTE_IF_SMALL_INPUT succeeds but the second fails,
         we will have clobbered the original value of x.
         The workaround is to first compute z = cos(x) in that case, since
         y and z are different. */
      if (y != x)
        /* y and x differ, thus we can safely try to compute y first */
        {
          MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * expx, 2, 0, rnd_mode,
                                            { inexy = _inexact;
                                              goto small_input; });
          if (0)
            {
            small_input:
              /* we can go here only if we can round sin(x) */
              MPFR_FAST_COMPUTE_IF_SMALL_INPUT (z, __gmpfr_one, -2 * expx,
                                                1, 0, rnd_mode,
                                                { inexz = _inexact;
                                                  goto end; });
            }

          /* if we go here, one of the two MPFR_FAST_COMPUTE_IF_SMALL_INPUT
             calls failed */
        }
      else /* y and x are the same variable: try to compute z first, which
              necessarily differs */
        {
          MPFR_FAST_COMPUTE_IF_SMALL_INPUT (z, __gmpfr_one, -2 * expx,
                                            1, 0, rnd_mode,
                                            { inexz = _inexact;
                                              goto small_input2; });
          if (0)
            {
            small_input2:
              /* we can go here only if we can round cos(x) */
              MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * expx, 2, 0,
                                                rnd_mode,
                                                { inexy = _inexact;
                                                  goto end; });
            }
        }
      m += 2 * (-expx);
    }

  mpfr_init (c);
  mpfr_init (xr);

  MPFR_ZIV_INIT (loop, m);
  for (;;)
    {
      /* the following is copied from sin.c */
      if (expx >= 2) /* reduce the argument */
        {
          reduce = 1;
          mpfr_set_prec (c, expx + m - 1);
          mpfr_set_prec (xr, m);
          mpfr_const_pi (c, GMP_RNDN);
          mpfr_mul_2ui (c, c, 1, GMP_RNDN);
          mpfr_remainder (xr, x, c, GMP_RNDN);
          mpfr_div_2ui (c, c, 1, GMP_RNDN);
          if (MPFR_SIGN (xr) > 0)
            mpfr_sub (c, c, xr, GMP_RNDZ);
          else
            mpfr_add (c, c, xr, GMP_RNDZ);
          if (MPFR_IS_ZERO(xr) || MPFR_EXP(xr) < (mp_exp_t) 3 - (mp_exp_t) m
              || MPFR_EXP(c) < (mp_exp_t) 3 - (mp_exp_t) m)
            goto next_step;
          xx = xr;
        }
      else /* the input argument is already reduced */
        {
          reduce = 0;
          xx = x;
        }

      neg = MPFR_IS_NEG (xx); /* gives sign of sin(x) */
      mpfr_set_prec (c, m);
      mpfr_cos (c, xx, GMP_RNDZ);
      /* If no argument reduction was performed, the error is at most ulp(c),
         otherwise it is at most ulp(c) + 2^(2-m). Since |c| < 1, we have
         ulp(c) <= 2^(-m), thus the error is bounded by 2^(3-m) in that later
         case. */
      if (reduce == 0)
        err = m;
      else
        err = MPFR_GET_EXP (c) + (mp_exp_t) (m - 3);
      if (!mpfr_can_round (c, err, GMP_RNDN, GMP_RNDZ,
                           MPFR_PREC (z) + (rnd_mode == GMP_RNDN)))
        goto next_step;

      /* we can't set z now, because in case z = x, and the mpfr_can_round()
         call below fails, we will have clobbered the input */
      mpfr_set_prec (xr, MPFR_PREC(c));
      mpfr_swap (xr, c); /* save the approximation of the cosine in xr */
      mpfr_sqr (c, xr, GMP_RNDU); /* the absolute error is bounded by
                                     2^(5-m) if reduce=1, and by 2^(2-m)
                                     otherwise */
      mpfr_ui_sub (c, 1, c, GMP_RNDN); /* error bounded by 2^(6-m) if reduce
                                          is 1, and 2^(3-m) otherwise */
      mpfr_sqrt (c, c, GMP_RNDN); /* the absolute error is bounded by
                                     2^(6-m-Exp(c)) if reduce=1, and
                                     2^(3-m-Exp(c)) otherwise */
      err = 3 + 3 * reduce - MPFR_GET_EXP (c);
      if (neg)
        MPFR_CHANGE_SIGN (c);

      /* the absolute error on c is at most 2^(err-m), which we must put
         in the form 2^(EXP(c)-err). */
      err = MPFR_GET_EXP (c) + (mp_exp_t) m - err;
      if (mpfr_can_round (c, err, GMP_RNDN, GMP_RNDZ,
                          MPFR_PREC (y) + (rnd_mode == GMP_RNDN)))
        break;
      /* check for huge cancellation */
      if (err < (mp_exp_t) MPFR_PREC (y))
        m += MPFR_PREC (y) - err;
      /* Check if near 1 */
      if (MPFR_GET_EXP (c) == 1
          && MPFR_MANT (c)[MPFR_LIMB_SIZE (c)-1] == MPFR_LIMB_HIGHBIT)
        m += m;

    next_step:
      MPFR_ZIV_NEXT (loop, m);
      mpfr_set_prec (c, m);
    }
  MPFR_ZIV_FREE (loop);

  inexy = mpfr_set (y, c, rnd_mode);
  inexz = mpfr_set (z, xr, rnd_mode);

  mpfr_clear (c);
  mpfr_clear (xr);

 end:
  /* FIXME: update the underflow flag if need be. */
  MPFR_SAVE_EXPO_FREE (expo);
  mpfr_check_range (y, inexy, rnd_mode);
  mpfr_check_range (z, inexz, rnd_mode);
  MPFR_RET (1); /* Always inexact */
}
