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