1 /* mpfr_log10 -- logarithm in base 10.
3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
4 Contributed by the Arenaire and Cacao projects, INRIA.
6 This file is part of the GNU MPFR Library.
8 The GNU MPFR Library is free software; you can redistribute it and/or modify
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
11 option) any later version.
13 The GNU MPFR Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MPFR Library; see the file COPYING.LIB. If not, write to
20 the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
21 MA 02110-1301, USA. */
23 #define MPFR_NEED_LONGLONG_H
24 #include "mpfr-impl.h"
26 /* The computation of r=log10(a)
28 r=log10(a)=log(a)/log(10)
32 mpfr_log10 (mpfr_ptr r
, mpfr_srcptr a
, mp_rnd_t rnd_mode
)
35 MPFR_SAVE_EXPO_DECL (expo
);
37 /* If a is NaN, the result is NaN */
38 if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (a
)))
45 /* check for infinity before zero */
46 else if (MPFR_IS_INF (a
))
49 /* log10(-Inf) = NaN */
54 else /* log10(+Inf) = +Inf */
58 MPFR_RET (0); /* exact */
63 MPFR_ASSERTD (MPFR_IS_ZERO (a
));
66 MPFR_RET (0); /* log10(0) is an exact -infinity */
70 /* If a is negative, the result is NaN */
71 if (MPFR_UNLIKELY (MPFR_IS_NEG (a
)))
77 /* If a is 1, the result is 0 */
78 if (mpfr_cmp_ui (a
, 1) == 0)
82 MPFR_RET (0); /* result is exact */
85 MPFR_SAVE_EXPO_MARK (expo
);
89 /* Declaration of the intermediary variable */
92 /* Declaration of the size variable */
93 mp_prec_t Ny
= MPFR_PREC(r
); /* Precision of output variable */
94 mp_prec_t Nt
; /* Precision of the intermediary variable */
95 mp_exp_t err
; /* Precision of error */
97 /* compute the precision of intermediary variable */
98 /* the optimal number of bits : see algorithms.tex */
99 Nt
= Ny
+ 4 + MPFR_INT_CEIL_LOG2 (Ny
);
101 /* initialise of intermediary variables */
105 /* First computation of log10 */
106 MPFR_ZIV_INIT (loop
, Nt
);
110 mpfr_set_ui (t
, 10, GMP_RNDN
); /* 10 */
111 mpfr_log (t
, t
, GMP_RNDD
); /* log(10) */
112 mpfr_log (tt
, a
, GMP_RNDN
); /* log(a) */
113 mpfr_div (t
, tt
, t
, GMP_RNDN
); /* log(a)/log(10) */
115 /* estimation of the error */
117 if (MPFR_LIKELY (MPFR_CAN_ROUND (t
, err
, Ny
, rnd_mode
)))
120 /* log10(10^n) is exact:
121 FIXME: Can we have 10^n exactly representable as a mpfr_t
122 but n can't fit an unsigned long? */
124 && mpfr_integer_p (t
) && mpfr_fits_ulong_p (t
, GMP_RNDN
)
125 && !mpfr_ui_pow_ui (tt
, 10, mpfr_get_ui (t
, GMP_RNDN
), GMP_RNDN
)
126 && mpfr_cmp (a
, tt
) == 0)
129 /* actualisation of the precision */
130 MPFR_ZIV_NEXT (loop
, Nt
);
131 mpfr_set_prec (t
, Nt
);
132 mpfr_set_prec (tt
, Nt
);
134 MPFR_ZIV_FREE (loop
);
136 inexact
= mpfr_set (r
, t
, rnd_mode
);
142 MPFR_SAVE_EXPO_FREE (expo
);
143 return mpfr_check_range (r
, inexact
, rnd_mode
);