1 /* mpfr_const_log2 -- compute natural logarithm of 2
3 Copyright 1999, 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 /* Declare the cache */
27 MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_log2
, mpfr_const_log2_internal
);
29 /* Set User interface */
30 #undef mpfr_const_log2
32 mpfr_const_log2 (mpfr_ptr x
, mp_rnd_t rnd_mode
) {
33 return mpfr_cache (x
, __gmpfr_cache_const_log2
, rnd_mode
);
36 /* Auxiliary function: Compute the terms from n1 to n2 (excluded)
37 3/4*sum((-1)^n*n!^2/2^n/(2*n+1)!, n = n1..n2-1).
38 Numerator is T[0], denominator is Q[0],
39 Compute P[0] only when need_P is non-zero.
40 Need 1+ceil(log(n2-n1)/log(2)) cells in T[],P[],Q[].
43 S (mpz_t
*T
, mpz_t
*P
, mpz_t
*Q
, unsigned long n1
, unsigned long n2
, int need_P
)
51 mpz_set_ui (P
[0], n1
);
54 if (n1
<= (ULONG_MAX
/ 4 - 1) / 2)
55 mpz_set_ui (Q
[0], 4 * (2 * n1
+ 1));
56 else /* to avoid overflow in 4 * (2 * n1 + 1) */
58 mpz_set_ui (Q
[0], n1
);
59 mpz_mul_2exp (Q
[0], Q
[0], 1);
60 mpz_add_ui (Q
[0], Q
[0], 1);
61 mpz_mul_2exp (Q
[0], Q
[0], 2);
67 unsigned long m
= (n1
/ 2) + (n2
/ 2) + (n1
& 1UL & n2
);
70 S (T
, P
, Q
, n1
, m
, 1);
71 S (T
+ 1, P
+ 1, Q
+ 1, m
, n2
, need_P
);
72 mpz_mul (T
[0], T
[0], Q
[1]);
73 mpz_mul (T
[1], T
[1], P
[0]);
74 mpz_add (T
[0], T
[0], T
[1]);
76 mpz_mul (P
[0], P
[0], P
[1]);
77 mpz_mul (Q
[0], Q
[0], Q
[1]);
79 /* remove common trailing zeroes if any */
80 v
= mpz_scan1 (T
[0], 0);
83 w
= mpz_scan1 (Q
[0], 0);
88 w
= mpz_scan1 (P
[0], 0);
92 /* now v = min(val(T), val(Q), val(P)) */
95 mpz_div_2exp (T
[0], T
[0], v
);
96 mpz_div_2exp (Q
[0], Q
[0], v
);
98 mpz_div_2exp (P
[0], P
[0], v
);
104 /* Don't need to save / restore exponent range: the cache does it */
106 mpfr_const_log2_internal (mpfr_ptr x
, mp_rnd_t rnd_mode
)
108 unsigned long n
= MPFR_PREC (x
);
109 mp_prec_t w
; /* working precision */
114 int ok
= 1; /* ensures that the 1st try will give correct rounding */
115 unsigned long lgN
, i
;
116 MPFR_ZIV_DECL (loop
);
118 MPFR_LOG_FUNC (("rnd_mode=%d", rnd_mode
), ("x[%#R]=%R inex=%d",x
,x
,inexact
));
120 mpfr_init2 (t
, MPFR_PREC_MIN
);
121 mpfr_init2 (q
, MPFR_PREC_MIN
);
124 w
= n
+ 10; /* ensures correct rounding for the four rounding modes,
125 together with N = w / 3 + 1 (see below). */
127 w
= n
+ 11; /* idem */
140 MPFR_ZIV_INIT (loop
, w
);
143 N
= w
/ 3 + 1; /* Warning: do not change that (even increasing N!)
144 without checking correct rounding in the above
147 /* the following are needed for error analysis (see algorithms.tex) */
148 MPFR_ASSERTD(w
>= 3 && N
>= 2);
150 lgN
= MPFR_INT_CEIL_LOG2 (N
) + 1;
151 T
= (mpz_t
*) (*__gmp_allocate_func
) (3 * lgN
* sizeof (mpz_t
));
154 for (i
= 0; i
< lgN
; i
++)
161 S (T
, P
, Q
, 0, N
, 0);
163 mpfr_set_prec (t
, w
);
164 mpfr_set_prec (q
, w
);
166 mpfr_set_z (t
, T
[0], GMP_RNDN
);
167 mpfr_set_z (q
, Q
[0], GMP_RNDN
);
168 mpfr_div (t
, t
, q
, GMP_RNDN
);
170 for (i
= 0; i
< lgN
; i
++)
176 (*__gmp_free_func
) (T
, 3 * lgN
* sizeof (mpz_t
));
178 if (MPFR_LIKELY (ok
!= 0
179 || mpfr_can_round (t
, w
- 2, GMP_RNDN
, rnd_mode
, n
)))
182 MPFR_ZIV_NEXT (loop
, w
);
184 MPFR_ZIV_FREE (loop
);
186 inexact
= mpfr_set (x
, t
, rnd_mode
);