Annotation of OpenXM_contrib/gmp/mpfr/exp.c, Revision 1.1.1.2
1.1 maekawa 1: /* mpfr_exp -- exponential of a floating-point number
2:
1.1.1.2 ! ohara 3: Copyright 1999, 2000, 2001, 2002 Free Software Foundation.
! 4: Contributed by the Spaces project.
1.1 maekawa 5:
6: This file is part of the MPFR Library.
7:
8: The MPFR Library is free software; you can redistribute it and/or modify
1.1.1.2 ! ohara 9: it under the terms of the GNU Lesser General Public License as published by
! 10: the Free Software Foundation; either version 2.1 of the License, or (at your
1.1 maekawa 11: option) any later version.
12:
13: The MPFR Library is distributed in the hope that it will be useful, but
14: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
1.1.1.2 ! ohara 15: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
1.1 maekawa 16: License for more details.
17:
1.1.1.2 ! ohara 18: You should have received a copy of the GNU Lesser General Public License
1.1 maekawa 19: along with the MPFR Library; see the file COPYING.LIB. If not, write to
20: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
21: MA 02111-1307, USA. */
22:
23: #include <stdio.h>
24: #include "gmp.h"
25: #include "gmp-impl.h"
26: #include "mpfr.h"
1.1.1.2 ! ohara 27: #include "mpfr-impl.h"
1.1 maekawa 28:
29: /* #define DEBUG */
30:
31: /* use Brent's formula exp(x) = (1+r+r^2/2!+r^3/3!+...)^(2^K)*2^n
32: where x = n*log(2)+(2^K)*r
33: number of operations = O(K+prec(r)/K)
34: */
35: int
1.1.1.2 ! ohara 36: mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
1.1 maekawa 37: {
1.1.1.2 ! ohara 38: int expx, precy;
! 39: double d;
1.1 maekawa 40:
1.1.1.2 ! ohara 41: if (MPFR_IS_NAN(x))
! 42: {
! 43: MPFR_SET_NAN(y);
! 44: MPFR_RET_NAN;
! 45: }
! 46:
! 47: MPFR_CLEAR_NAN(y);
! 48:
! 49: if (MPFR_IS_INF(x))
! 50: {
! 51: if (MPFR_SIGN(x) > 0)
! 52: {
! 53: MPFR_SET_INF(y);
! 54: }
! 55: else
! 56: {
! 57: MPFR_CLEAR_INF(y);
! 58: MPFR_SET_ZERO(y);
! 59: }
! 60: MPFR_SET_POS(y);
! 61: MPFR_RET(0);
! 62: }
! 63:
! 64: MPFR_CLEAR_INF(y);
! 65:
! 66: if (MPFR_IS_ZERO(x))
! 67: return mpfr_set_ui (y, 1, GMP_RNDN);
! 68:
! 69: expx = MPFR_EXP(x);
! 70: precy = MPFR_PREC(y);
! 71:
! 72: /* result is +Inf when exp(x) >= 2^(__mpfr_emax), i.e.
! 73: x >= __mpfr_emax * log(2) */
! 74: d = mpfr_get_d1 (x);
! 75: if (d >= (double) __mpfr_emax * LOG2)
! 76: return mpfr_set_overflow(y, rnd_mode, 1);
! 77:
! 78: /* result is 0 when exp(x) < 1/2*2^(__mpfr_emin), i.e.
! 79: x < (__mpfr_emin-1) * LOG2 */
! 80: if (d < ((double) __mpfr_emin - 1.0) * LOG2)
! 81: return mpfr_set_underflow(y, rnd_mode, 1);
1.1 maekawa 82:
83: /* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
1.1.1.2 ! ohara 84: if (expx < -precy)
! 85: {
! 86: int signx = MPFR_SIGN(x);
! 87:
! 88: mpfr_set_ui (y, 1, rnd_mode);
! 89: if (signx > 0 && rnd_mode == GMP_RNDU)
! 90: {
! 91: mpfr_add_one_ulp (y, rnd_mode);
! 92: return 1;
! 93: }
! 94: else if (signx < 0 && (rnd_mode == GMP_RNDD || rnd_mode == GMP_RNDZ))
! 95: {
! 96: mpfr_sub_one_ulp (y, rnd_mode);
! 97: return -1;
! 98: }
! 99: return -signx;
! 100: }
! 101:
! 102: if (precy > 13000)
! 103: return mpfr_exp3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
! 104: else
! 105: return mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
1.1 maekawa 106: }
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