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

1.1     ! ohara       1: /* mpfr_cos -- cosine of a floating-point number
        !             2:
        !             3: Copyright 2001, 2002 Free Software Foundation.
        !             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 <stdio.h>
        !            23: #include "gmp.h"
        !            24: #include "gmp-impl.h"
        !            25: #include "mpfr.h"
        !            26: #include "mpfr-impl.h"
        !            27:
        !            28: static int mpfr_cos2_aux       _PROTO ((mpfr_ptr, mpfr_srcptr));
        !            29:
        !            30: int
        !            31: mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
        !            32: {
        !            33:   int K0, K, precy, m, k, l, inexact;
        !            34:   mpfr_t r, s;
        !            35:
        !            36:   if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
        !            37:     {
        !            38:       MPFR_SET_NAN(y);
        !            39:       MPFR_RET_NAN;
        !            40:     }
        !            41:
        !            42:   if (MPFR_IS_ZERO(x))
        !            43:     {
        !            44:       mpfr_set_ui (y, 1, GMP_RNDN);
        !            45:       return 0;
        !            46:     }
        !            47:
        !            48:   precy = MPFR_PREC(y);
        !            49:
        !            50:   K0 = _mpfr_isqrt(precy / 2);
        !            51:   /* we need at least K + log2(precy/K) extra bits */
        !            52:   m = precy + 3 * K0 + 3;
        !            53:
        !            54:   mpfr_init2 (r, m);
        !            55:   mpfr_init2 (s, m);
        !            56:
        !            57:   do
        !            58:     {
        !            59:       mpfr_mul (r, x, x, GMP_RNDU); /* err <= 1 ulp */
        !            60:
        !            61:       /* we need that |r| < 1 for mpfr_cos2_aux, i.e. up(x^2)/2^(2K) < 1 */
        !            62:       K = K0 + MAX(MPFR_EXP(r), 0);
        !            63:
        !            64:       mpfr_div_2ui (r, r, 2 * K, GMP_RNDN); /* r = (x/2^K)^2, err <= 1 ulp */
        !            65:
        !            66:       /* s <- 1 - r/2! + ... + (-1)^l r^l/(2l)! */
        !            67:       l = mpfr_cos2_aux (s, r);
        !            68:
        !            69:       for (k = 0; k < K; k++)
        !            70:        {
        !            71:          mpfr_mul (s, s, s, GMP_RNDU); /* err <= 2*olderr */
        !            72:          mpfr_mul_2ui (s, s, 1, GMP_RNDU); /* err <= 4*olderr */
        !            73:          mpfr_sub_ui (s, s, 1, GMP_RNDN);
        !            74:        }
        !            75:
        !            76:       /* absolute error on s is bounded by (2l+1/3)*2^(2K-m) */
        !            77:       for (k = 2 * K, l = 2 * l + 1; l > 1; k++, l = (l + 1) >> 1);
        !            78:       /* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */
        !            79:
        !            80:       l = mpfr_can_round (s, MPFR_EXP(s) + m - k, GMP_RNDN, rnd_mode, precy);
        !            81:
        !            82:       if (l == 0)
        !            83:        {
        !            84:          m += BITS_PER_MP_LIMB;
        !            85:          mpfr_set_prec (r, m);
        !            86:          mpfr_set_prec (s, m);
        !            87:        }
        !            88:     }
        !            89:   while (l == 0);
        !            90:
        !            91:   inexact = mpfr_set (y, s, rnd_mode);
        !            92:
        !            93:   mpfr_clear (r);
        !            94:   mpfr_clear (s);
        !            95:
        !            96:   return inexact;
        !            97: }
        !            98:
        !            99: /* s <- 1 - r/2! + r^2/4! + ... + (-1)^l r^l/(2l)! + ...
        !           100:    Assumes |r| < 1.
        !           101:    Returns the index l0 of the last term (-1)^l r^l/(2l)!.
        !           102:    The absolute error on s is at most 2 * l0 * 2^(-m).
        !           103: */
        !           104: static int
        !           105: mpfr_cos2_aux (mpfr_ptr s, mpfr_srcptr r)
        !           106: {
        !           107:   unsigned int l, b = 2;
        !           108:   long int prec_t, m = MPFR_PREC(s);
        !           109:   mpfr_t t;
        !           110:
        !           111:   MPFR_ASSERTN (MPFR_EXP(r) <= 0);
        !           112:   mpfr_init2 (t, m);
        !           113:   mpfr_set_ui (t, 1, GMP_RNDN);
        !           114:   mpfr_set_ui(s, 1, GMP_RNDN);
        !           115:
        !           116:   for (l = 1; MPFR_EXP(t) + m >= 0; l++)
        !           117:     {
        !           118:       mpfr_mul (t, t, r, GMP_RNDU); /* err <= (3l-1) ulp */
        !           119:       mpfr_div_ui (t, t, (2*l-1)*(2*l), GMP_RNDU); /* err <= 3l ulp */
        !           120:       if (l % 2 == 0)
        !           121:        mpfr_add (s, s, t, GMP_RNDD);
        !           122:       else
        !           123:        mpfr_sub (s, s, t, GMP_RNDD);
        !           124:       MPFR_ASSERTN (MPFR_EXP(s) == 0); /* check 1/2 <= s < 1 */
        !           125:       /* err(s) <= l * 2^(-m) */
        !           126:       if (3 * l > (1 << b))
        !           127:        b++;
        !           128:       /* now 3l <= 2^b, we want 3l*ulp(t) <= 2^(-m)
        !           129:         i.e. b+EXP(t)-PREC(t) <= -m */
        !           130:       prec_t = m + MPFR_EXP(t) + b;
        !           131:       if (prec_t >= MPFR_PREC_MIN)
        !           132:        mpfr_round_prec (t, GMP_RNDN, prec_t);
        !           133:     }
        !           134:
        !           135:   mpfr_clear (t);
        !           136:
        !           137:   return l;
        !           138: }
        !           139: