Tristan Matthews | 0a329cc | 2013-07-17 13:20:14 -0400 | [diff] [blame] | 1 | /* $Id: math.h 3553 2011-05-05 06:14:19Z nanang $ */ |
| 2 | /* |
| 3 | * Copyright (C) 2008-2011 Teluu Inc. (http://www.teluu.com) |
| 4 | * Copyright (C) 2003-2008 Benny Prijono <benny@prijono.org> |
| 5 | * |
| 6 | * This program is free software; you can redistribute it and/or modify |
| 7 | * it under the terms of the GNU General Public License as published by |
| 8 | * the Free Software Foundation; either version 2 of the License, or |
| 9 | * (at your option) any later version. |
| 10 | * |
| 11 | * This program is distributed in the hope that it will be useful, |
| 12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 14 | * GNU General Public License for more details. |
| 15 | * |
| 16 | * You should have received a copy of the GNU General Public License |
| 17 | * along with this program; if not, write to the Free Software |
| 18 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
| 19 | */ |
| 20 | |
| 21 | #ifndef __PJ_MATH_H__ |
| 22 | #define __PJ_MATH_H__ |
| 23 | |
| 24 | /** |
| 25 | * @file math.h |
| 26 | * @brief Mathematics and Statistics. |
| 27 | */ |
| 28 | |
| 29 | #include <pj/string.h> |
| 30 | #include <pj/compat/high_precision.h> |
| 31 | |
| 32 | PJ_BEGIN_DECL |
| 33 | |
| 34 | /** |
| 35 | * @defgroup pj_math Mathematics and Statistics |
| 36 | * @ingroup PJ_MISC |
| 37 | * @{ |
| 38 | * |
| 39 | * Provides common mathematics constants and operations, and also standard |
| 40 | * statistics calculation (min, max, mean, standard deviation). Statistics |
| 41 | * calculation is done in realtime (statistics state is updated on time each |
| 42 | * new sample comes). |
| 43 | */ |
| 44 | |
| 45 | /** |
| 46 | * Mathematical constants |
| 47 | */ |
| 48 | #define PJ_PI 3.14159265358979323846 /* pi */ |
| 49 | #define PJ_1_PI 0.318309886183790671538 /* 1/pi */ |
| 50 | |
| 51 | /** |
| 52 | * Mathematical macro |
| 53 | */ |
| 54 | #define PJ_ABS(x) ((x) > 0 ? (x) : -(x)) |
| 55 | #define PJ_MAX(x, y) ((x) > (y)? (x) : (y)) |
| 56 | #define PJ_MIN(x, y) ((x) < (y)? (x) : (y)) |
| 57 | |
| 58 | /** |
| 59 | * This structure describes statistics state. |
| 60 | */ |
| 61 | typedef struct pj_math_stat |
| 62 | { |
| 63 | int n; /* number of samples */ |
| 64 | int max; /* maximum value */ |
| 65 | int min; /* minimum value */ |
| 66 | int last; /* last value */ |
| 67 | int mean; /* mean */ |
| 68 | |
| 69 | /* Private members */ |
| 70 | #if PJ_HAS_FLOATING_POINT |
| 71 | float fmean_; /* mean(floating point) */ |
| 72 | #else |
| 73 | int mean_res_; /* mean residu */ |
| 74 | #endif |
| 75 | pj_highprec_t m2_; /* variance * n */ |
| 76 | } pj_math_stat; |
| 77 | |
| 78 | /** |
| 79 | * Calculate integer square root of an integer. |
| 80 | * |
| 81 | * @param i Integer to be calculated. |
| 82 | * |
| 83 | * @return Square root result. |
| 84 | */ |
| 85 | PJ_INLINE(unsigned) pj_isqrt(unsigned i) |
| 86 | { |
| 87 | unsigned res = 1, prev; |
| 88 | |
| 89 | /* Rough guess, calculate half bit of input */ |
| 90 | prev = i >> 2; |
| 91 | while (prev) { |
| 92 | prev >>= 2; |
| 93 | res <<= 1; |
| 94 | } |
| 95 | |
| 96 | /* Babilonian method */ |
| 97 | do { |
| 98 | prev = res; |
| 99 | res = (prev + i/prev) >> 1; |
| 100 | } while ((prev+res)>>1 != res); |
| 101 | |
| 102 | return res; |
| 103 | } |
| 104 | |
| 105 | /** |
| 106 | * Initialize statistics state. |
| 107 | * |
| 108 | * @param stat Statistic state. |
| 109 | */ |
| 110 | PJ_INLINE(void) pj_math_stat_init(pj_math_stat *stat) |
| 111 | { |
| 112 | pj_bzero(stat, sizeof(pj_math_stat)); |
| 113 | } |
| 114 | |
| 115 | /** |
| 116 | * Update statistics state as a new sample comes. |
| 117 | * |
| 118 | * @param stat Statistic state. |
| 119 | * @param val The new sample data. |
| 120 | */ |
| 121 | PJ_INLINE(void) pj_math_stat_update(pj_math_stat *stat, int val) |
| 122 | { |
| 123 | #if PJ_HAS_FLOATING_POINT |
| 124 | float delta; |
| 125 | #else |
| 126 | int delta; |
| 127 | #endif |
| 128 | |
| 129 | stat->last = val; |
| 130 | |
| 131 | if (stat->n++) { |
| 132 | if (stat->min > val) |
| 133 | stat->min = val; |
| 134 | if (stat->max < val) |
| 135 | stat->max = val; |
| 136 | } else { |
| 137 | stat->min = stat->max = val; |
| 138 | } |
| 139 | |
| 140 | #if PJ_HAS_FLOATING_POINT |
| 141 | delta = val - stat->fmean_; |
| 142 | stat->fmean_ += delta/stat->n; |
| 143 | |
| 144 | /* Return mean value with 'rounding' */ |
| 145 | stat->mean = (int) (stat->fmean_ + 0.5); |
| 146 | |
| 147 | stat->m2_ += (int)(delta * (val-stat->fmean_)); |
| 148 | #else |
| 149 | delta = val - stat->mean; |
| 150 | stat->mean += delta/stat->n; |
| 151 | stat->mean_res_ += delta % stat->n; |
| 152 | if (stat->mean_res_ >= stat->n) { |
| 153 | ++stat->mean; |
| 154 | stat->mean_res_ -= stat->n; |
| 155 | } else if (stat->mean_res_ <= -stat->n) { |
| 156 | --stat->mean; |
| 157 | stat->mean_res_ += stat->n; |
| 158 | } |
| 159 | |
| 160 | stat->m2_ += delta * (val-stat->mean); |
| 161 | #endif |
| 162 | } |
| 163 | |
| 164 | /** |
| 165 | * Get the standard deviation of specified statistics state. |
| 166 | * |
| 167 | * @param stat Statistic state. |
| 168 | * |
| 169 | * @return The standard deviation. |
| 170 | */ |
| 171 | PJ_INLINE(unsigned) pj_math_stat_get_stddev(const pj_math_stat *stat) |
| 172 | { |
| 173 | if (stat->n == 0) return 0; |
| 174 | return (pj_isqrt((unsigned)(stat->m2_/stat->n))); |
| 175 | } |
| 176 | |
| 177 | /** |
| 178 | * Set the standard deviation of statistics state. This is useful when |
| 179 | * the statistic state is operated in 'read-only' mode as a storage of |
| 180 | * statistical data. |
| 181 | * |
| 182 | * @param stat Statistic state. |
| 183 | * |
| 184 | * @param dev The standard deviation. |
| 185 | */ |
| 186 | PJ_INLINE(void) pj_math_stat_set_stddev(pj_math_stat *stat, unsigned dev) |
| 187 | { |
| 188 | if (stat->n == 0) |
| 189 | stat->n = 1; |
| 190 | stat->m2_ = dev*dev*stat->n; |
| 191 | } |
| 192 | |
| 193 | /** @} */ |
| 194 | |
| 195 | PJ_END_DECL |
| 196 | |
| 197 | #endif /* __PJ_MATH_H__ */ |