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Annotation of OpenXM_contrib/gmp/mpfr/sin_cos.c, Revision 1.1

1.1     ! ohara       1: /* mpfr_sin_cos -- sine and cosine of a floating-point number
        !             2:
        !             3: Copyright 2002 Free Software Foundation, Inc.
        !             4:
        !             5: This file is part of the MPFR Library.
        !             6:
        !             7: The MPFR Library is free software; you can redistribute it and/or modify
        !             8: it under the terms of the GNU Lesser General Public License as published by
        !             9: the Free Software Foundation; either version 2.1 of the License, or (at your
        !            10: option) any later version.
        !            11:
        !            12: The MPFR Library is distributed in the hope that it will be useful, but
        !            13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
        !            14: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
        !            15: License for more details.
        !            16:
        !            17: You should have received a copy of the GNU Lesser General Public License
        !            18: along with the MPFR Library; see the file COPYING.LIB.  If not, write to
        !            19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
        !            20: MA 02111-1307, USA. */
        !            21:
        !            22: #include "gmp.h"
        !            23: #include "gmp-impl.h"
        !            24: #include "mpfr.h"
        !            25: #include "mpfr-impl.h"
        !            26:
        !            27: /* (y, z) <- (sin(x), cos(x)), return value is 0 iff both results are exact */
        !            28: int
        !            29: mpfr_sin_cos (mpfr_ptr y, mpfr_ptr z, mpfr_srcptr x, mp_rnd_t rnd_mode)
        !            30: {
        !            31:   int prec, m, ok, e, inexact, neg;
        !            32:   mpfr_t c, k;
        !            33:
        !            34:   if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
        !            35:     {
        !            36:       MPFR_SET_NAN(y);
        !            37:       MPFR_SET_NAN(z);
        !            38:       MPFR_RET_NAN;
        !            39:     }
        !            40:
        !            41:   if (MPFR_IS_ZERO(x))
        !            42:     {
        !            43:       MPFR_CLEAR_FLAGS(y);
        !            44:       MPFR_SET_ZERO(y);
        !            45:       MPFR_SET_SAME_SIGN(y, x);
        !            46:       mpfr_set_ui (z, 1, GMP_RNDN);
        !            47:       MPFR_RET(0);
        !            48:     }
        !            49:
        !            50:   prec = MAX(MPFR_PREC(y), MPFR_PREC(z));
        !            51:   m = prec + _mpfr_ceil_log2 ((double) prec) + ABS(MPFR_EXP(x)) + 13;
        !            52:
        !            53:   mpfr_init2 (c, m);
        !            54:   mpfr_init2 (k, m);
        !            55:
        !            56:   /* first determine sign */
        !            57:   mpfr_const_pi (c, GMP_RNDN);
        !            58:   mpfr_mul_2ui (c, c, 1, GMP_RNDN); /* 2*Pi */
        !            59:   mpfr_div (k, x, c, GMP_RNDN);      /* x/(2*Pi) */
        !            60:   mpfr_floor (k, k);                 /* floor(x/(2*Pi)) */
        !            61:   mpfr_mul (c, k, c, GMP_RNDN);
        !            62:   mpfr_sub (k, x, c, GMP_RNDN);      /* 0 <= k < 2*Pi */
        !            63:   mpfr_const_pi (c, GMP_RNDN); /* cached */
        !            64:   neg = mpfr_cmp (k, c) > 0;
        !            65:   mpfr_clear (k);
        !            66:
        !            67:   do
        !            68:     {
        !            69:       mpfr_cos (c, x, GMP_RNDZ);
        !            70:       if ((ok = mpfr_can_round (c, m, GMP_RNDZ, rnd_mode, MPFR_PREC(z))))
        !            71:         {
        !            72:           inexact = mpfr_set (z, c, rnd_mode);
        !            73:           mpfr_mul (c, c, c, GMP_RNDU);
        !            74:           mpfr_ui_sub (c, 1, c, GMP_RNDN);
        !            75:           e = 2 + (-MPFR_EXP(c)) / 2;
        !            76:           mpfr_sqrt (c, c, GMP_RNDN);
        !            77:           if (neg)
        !            78:             mpfr_neg (c, c, GMP_RNDN);
        !            79:
        !            80:           /* the absolute error on c is at most 2^(e-m) = 2^(EXP(c)-err) */
        !            81:           e = MPFR_EXP(c) + m - e;
        !            82:           ok = (e >= 0) && mpfr_can_round (c, e, GMP_RNDN, rnd_mode,
        !            83:                                            MPFR_PREC(y));
        !            84:         }
        !            85:
        !            86:       if (ok == 0)
        !            87:        {
        !            88:          m += _mpfr_ceil_log2 ((double) m);
        !            89:          mpfr_set_prec (c, m);
        !            90:        }
        !            91:     }
        !            92:   while (ok == 0);
        !            93:
        !            94:   inexact = mpfr_set (y, c, rnd_mode) || inexact;
        !            95:
        !            96:   mpfr_clear (c);
        !            97:
        !            98:   return inexact; /* inexact */
        !            99: }