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Annotation of OpenXM_contrib/gmp/mpfr/cos.c, Revision 1.1.1.1

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: