0cbfe12e |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mptext-len.c,v 1.1 2002/10/15 22:58:29 mdw Exp $ |
4 | * |
5 | * Work out length of a number's string representation |
6 | * |
7 | * (c) 2002 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mptext-len.c,v $ |
33 | * Revision 1.1 2002/10/15 22:58:29 mdw |
34 | * Fast estimation of number representation lengths. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | #include "mptext.h" |
42 | |
43 | /*----- Main code ---------------------------------------------------------*/ |
44 | |
45 | /* --- @mptext_len@ --- * |
46 | * |
47 | * Arguments: @mp *x@ = number to work on |
48 | * @int r@ = radix the number will be expressed in |
49 | * |
50 | * Returns: The number of digits needed to represent the number in the |
51 | * given base. This will not include space for a leading sign |
52 | * (use @MP_ISNEG@ to check that, or just add one on for luck); |
53 | * neither will it add space for a terminating null. In general |
54 | * the answer will be an overestimate. |
55 | */ |
56 | |
57 | size_t mptext_len(mp *x, int r) |
58 | { |
59 | unsigned long b = mp_bits(x); |
60 | int s, ss = 2; |
61 | size_t n; |
62 | unsigned d = 0; |
63 | |
64 | /* --- Huh? --- * |
65 | * |
66 | * The number of digits is at most %$\lceil b \log 2/\log r \rceil$%. We |
67 | * produce an underestimate of %$\log_2 r = \log r/\log 2$% and divide by |
68 | * that. How? By linear interpolation between known points on the curve. |
69 | * The known points are precisely the powers of 2, so we can find a pair |
70 | * efficiently by doubling up. The log curve is convex, so linear |
71 | * interpolation between points on the curve is always an underestimate. |
72 | * |
73 | * The integer maths here is a bit weird, so here's how it works. If |
74 | * %$s = 2^d$% is the power of 2 below %$r$% then we want to compute |
75 | * %$\lceil b/(d + (r - s)/s) \rceil = \lceil (b s)/(s(d - 1) + r \rceil$% |
76 | * which is %$\lfloor (r + s (b + d - 1) - 1)/(r + s(d - 1)) \rfloor$%. |
77 | * Gluing the whole computation together like this makes the code hard to |
78 | * read, but means that there are fewer possibilities for rounding errors |
79 | * and thus we get a tighter bound. |
80 | */ |
81 | |
82 | /* --- Find the right pair of points --- */ |
83 | |
84 | do { |
85 | s = ss; |
86 | d++; |
87 | if (r == s) { |
88 | n = (b + (d - 1))/d; |
89 | goto done; |
90 | } |
91 | ss = s << 1; |
92 | } while (ss <= r); |
93 | |
94 | /* --- Do the interpolation --- */ |
95 | |
96 | n = (r + s*(b + d - 1) - 1)/(r + s*(d - 1)); |
97 | |
98 | /* --- Fixups --- */ |
99 | |
100 | done: |
101 | if (!n) |
102 | n = 1; |
103 | return (n); |
104 | } |
105 | |
106 | /*----- That's all, folks -------------------------------------------------*/ |