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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | #include "mptext.h" |
34 | |
35 | /*----- Main code ---------------------------------------------------------*/ |
36 | |
37 | /* --- @mptext_len@ --- * |
38 | * |
39 | * Arguments: @mp *x@ = number to work on |
40 | * @int r@ = radix the number will be expressed in |
41 | * |
42 | * Returns: The number of digits needed to represent the number in the |
43 | * given base. This will not include space for a leading sign |
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44 | * (use @MP_NEGP@ to check that, or just add one on for luck); |
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45 | * neither will it add space for a terminating null. In general |
46 | * the answer will be an overestimate. |
47 | */ |
48 | |
49 | size_t mptext_len(mp *x, int r) |
50 | { |
51 | unsigned long b = mp_bits(x); |
52 | int s, ss = 2; |
53 | size_t n; |
54 | unsigned d = 0; |
55 | |
56 | /* --- Huh? --- * |
57 | * |
58 | * The number of digits is at most %$\lceil b \log 2/\log r \rceil$%. We |
59 | * produce an underestimate of %$\log_2 r = \log r/\log 2$% and divide by |
60 | * that. How? By linear interpolation between known points on the curve. |
61 | * The known points are precisely the powers of 2, so we can find a pair |
62 | * efficiently by doubling up. The log curve is convex, so linear |
63 | * interpolation between points on the curve is always an underestimate. |
64 | * |
65 | * The integer maths here is a bit weird, so here's how it works. If |
66 | * %$s = 2^d$% is the power of 2 below %$r$% then we want to compute |
67 | * %$\lceil b/(d + (r - s)/s) \rceil = \lceil (b s)/(s(d - 1) + r \rceil$% |
68 | * which is %$\lfloor (r + s (b + d - 1) - 1)/(r + s(d - 1)) \rfloor$%. |
69 | * Gluing the whole computation together like this makes the code hard to |
70 | * read, but means that there are fewer possibilities for rounding errors |
71 | * and thus we get a tighter bound. |
72 | */ |
73 | |
74 | /* --- Find the right pair of points --- */ |
75 | |
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76 | if (r < 0) r = -r; |
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77 | do { |
78 | s = ss; |
79 | d++; |
80 | if (r == s) { |
81 | n = (b + (d - 1))/d; |
82 | goto done; |
83 | } |
84 | ss = s << 1; |
85 | } while (ss <= r); |
86 | |
87 | /* --- Do the interpolation --- */ |
88 | |
89 | n = (r + s*(b + d - 1) - 1)/(r + s*(d - 1)); |
90 | |
91 | /* --- Fixups --- */ |
92 | |
93 | done: |
94 | if (!n) |
95 | n = 1; |
96 | return (n); |
97 | } |
98 | |
99 | /*----- That's all, folks -------------------------------------------------*/ |