| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Work out length of a number's string representation |
| 4 | * |
| 5 | * (c) 2002 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 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. |
| 16 | * |
| 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. |
| 21 | * |
| 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 | |
| 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 |
| 42 | * (use @MP_NEGP@ to check that, or just add one on for luck); |
| 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 | |
| 74 | if (r < 0) r = -r; |
| 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 -------------------------------------------------*/ |