1 /* mpfr_const_log2 -- compute natural logarithm of 2
2
3 Copyright 1999, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4 Contributed by the AriC and Caramel projects, INRIA.
5
6 This file is part of the GNU MPFR Library.
7
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 3 of the License, or (at your
11 option) any later version.
12
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.
17
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.LESSER. If not, see
20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23 #define MPFR_NEED_LONGLONG_H
24 #include "mpfr-impl.h"
25
26 /* Declare the cache */
27 #ifndef MPFR_USE_LOGGING
28 MPFR_DECL_INIT_CACHE(__gmpfr_cache_const_log2, mpfr_const_log2_internal);
29 #else
30 MPFR_DECL_INIT_CACHE(__gmpfr_normal_log2, mpfr_const_log2_internal);
31 MPFR_DECL_INIT_CACHE(__gmpfr_logging_log2, mpfr_const_log2_internal);
32 mpfr_cache_ptr MPFR_THREAD_ATTR __gmpfr_cache_const_log2 = __gmpfr_normal_log2;
33 #endif
34
35 /* Set User interface */
36 #undef mpfr_const_log2
37 int
mpfr_const_log2(mpfr_ptr x,mpfr_rnd_t rnd_mode)38 mpfr_const_log2 (mpfr_ptr x, mpfr_rnd_t rnd_mode) {
39 return mpfr_cache (x, __gmpfr_cache_const_log2, rnd_mode);
40 }
41
42 /* Auxiliary function: Compute the terms from n1 to n2 (excluded)
43 3/4*sum((-1)^n*n!^2/2^n/(2*n+1)!, n = n1..n2-1).
44 Numerator is T[0], denominator is Q[0],
45 Compute P[0] only when need_P is non-zero.
46 Need 1+ceil(log(n2-n1)/log(2)) cells in T[],P[],Q[].
47 */
48 static void
S(mpz_t * T,mpz_t * P,mpz_t * Q,unsigned long n1,unsigned long n2,int need_P)49 S (mpz_t *T, mpz_t *P, mpz_t *Q, unsigned long n1, unsigned long n2, int need_P)
50 {
51 if (n2 == n1 + 1)
52 {
53 if (n1 == 0)
54 mpz_set_ui (P[0], 3);
55 else
56 {
57 mpz_set_ui (P[0], n1);
58 mpz_neg (P[0], P[0]);
59 }
60 if (n1 <= (ULONG_MAX / 4 - 1) / 2)
61 mpz_set_ui (Q[0], 4 * (2 * n1 + 1));
62 else /* to avoid overflow in 4 * (2 * n1 + 1) */
63 {
64 mpz_set_ui (Q[0], n1);
65 mpz_mul_2exp (Q[0], Q[0], 1);
66 mpz_add_ui (Q[0], Q[0], 1);
67 mpz_mul_2exp (Q[0], Q[0], 2);
68 }
69 mpz_set (T[0], P[0]);
70 }
71 else
72 {
73 unsigned long m = (n1 / 2) + (n2 / 2) + (n1 & 1UL & n2);
74 unsigned long v, w;
75
76 S (T, P, Q, n1, m, 1);
77 S (T + 1, P + 1, Q + 1, m, n2, need_P);
78 mpz_mul (T[0], T[0], Q[1]);
79 mpz_mul (T[1], T[1], P[0]);
80 mpz_add (T[0], T[0], T[1]);
81 if (need_P)
82 mpz_mul (P[0], P[0], P[1]);
83 mpz_mul (Q[0], Q[0], Q[1]);
84
85 /* remove common trailing zeroes if any */
86 v = mpz_scan1 (T[0], 0);
87 if (v > 0)
88 {
89 w = mpz_scan1 (Q[0], 0);
90 if (w < v)
91 v = w;
92 if (need_P)
93 {
94 w = mpz_scan1 (P[0], 0);
95 if (w < v)
96 v = w;
97 }
98 /* now v = min(val(T), val(Q), val(P)) */
99 if (v > 0)
100 {
101 mpz_fdiv_q_2exp (T[0], T[0], v);
102 mpz_fdiv_q_2exp (Q[0], Q[0], v);
103 if (need_P)
104 mpz_fdiv_q_2exp (P[0], P[0], v);
105 }
106 }
107 }
108 }
109
110 /* Don't need to save / restore exponent range: the cache does it */
111 int
mpfr_const_log2_internal(mpfr_ptr x,mpfr_rnd_t rnd_mode)112 mpfr_const_log2_internal (mpfr_ptr x, mpfr_rnd_t rnd_mode)
113 {
114 unsigned long n = MPFR_PREC (x);
115 mpfr_prec_t w; /* working precision */
116 unsigned long N;
117 mpz_t *T, *P, *Q;
118 mpfr_t t, q;
119 int inexact;
120 int ok = 1; /* ensures that the 1st try will give correct rounding */
121 unsigned long lgN, i;
122 MPFR_ZIV_DECL (loop);
123
124 MPFR_LOG_FUNC (
125 ("rnd_mode=%d", rnd_mode),
126 ("x[%Pu]=%.*Rg inex=%d", mpfr_get_prec(x), mpfr_log_prec, x, inexact));
127
128 mpfr_init2 (t, MPFR_PREC_MIN);
129 mpfr_init2 (q, MPFR_PREC_MIN);
130
131 if (n < 1253)
132 w = n + 10; /* ensures correct rounding for the four rounding modes,
133 together with N = w / 3 + 1 (see below). */
134 else if (n < 2571)
135 w = n + 11; /* idem */
136 else if (n < 3983)
137 w = n + 12;
138 else if (n < 4854)
139 w = n + 13;
140 else if (n < 26248)
141 w = n + 14;
142 else
143 {
144 w = n + 15;
145 ok = 0;
146 }
147
148 MPFR_ZIV_INIT (loop, w);
149 for (;;)
150 {
151 N = w / 3 + 1; /* Warning: do not change that (even increasing N!)
152 without checking correct rounding in the above
153 ranges for n. */
154
155 /* the following are needed for error analysis (see algorithms.tex) */
156 MPFR_ASSERTD(w >= 3 && N >= 2);
157
158 lgN = MPFR_INT_CEIL_LOG2 (N) + 1;
159 T = (mpz_t *) (*__gmp_allocate_func) (3 * lgN * sizeof (mpz_t));
160 P = T + lgN;
161 Q = T + 2*lgN;
162 for (i = 0; i < lgN; i++)
163 {
164 mpz_init (T[i]);
165 mpz_init (P[i]);
166 mpz_init (Q[i]);
167 }
168
169 S (T, P, Q, 0, N, 0);
170
171 mpfr_set_prec (t, w);
172 mpfr_set_prec (q, w);
173
174 mpfr_set_z (t, T[0], MPFR_RNDN);
175 mpfr_set_z (q, Q[0], MPFR_RNDN);
176 mpfr_div (t, t, q, MPFR_RNDN);
177
178 for (i = 0; i < lgN; i++)
179 {
180 mpz_clear (T[i]);
181 mpz_clear (P[i]);
182 mpz_clear (Q[i]);
183 }
184 (*__gmp_free_func) (T, 3 * lgN * sizeof (mpz_t));
185
186 if (MPFR_LIKELY (ok != 0
187 || mpfr_can_round (t, w - 2, MPFR_RNDN, rnd_mode, n)))
188 break;
189
190 MPFR_ZIV_NEXT (loop, w);
191 }
192 MPFR_ZIV_FREE (loop);
193
194 inexact = mpfr_set (x, t, rnd_mode);
195
196 mpfr_clear (t);
197 mpfr_clear (q);
198
199 return inexact;
200 }
201