WDL/cmath/factorial.h

   1 /*
   2   factorial.h
   3   Copyright (C) 2011 and later Lubomir I. Ivanov (neolit123 [at] gmail)
   4
   5   This software is provided 'as-is', without any express or implied
   6   warranty.  In no event will the authors be held liable for any damages
   7   arising from the use of this software.
   8
   9   Permission is granted to anyone to use this software for any purpose,
  10   including commercial applications, and to alter it and redistribute it
  11   freely, subject to the following restrictions:
  12
  13   1. The origin of this software must not be misrepresented; you must not
  14      claim that you wrote the original software. If you use this software
  15      in a product, an acknowledgment in the product documentation would be
  16      appreciated but is not required.
  17   2. Altered source versions must be plainly marked as such, and must not be
  18      misrepresented as being the original software.
  19   3. This notice may not be removed or altered from any source distribution.
  20 */
  21
  22 /*
  23   methods to return low-order factorials depending on allowed data types.
  24
  25   20! = 2432902008176640000 is the maximum factorial to be held
  26   in a unsigned 64bit integer.
  27   13! = 479001600 is the maximum factorial to be held in a unsigned
  28   32bit integer.
  29 */
  30
  31 #ifndef _FACTORIAL_H_
  32 #define _FACTORIAL_H_
  33
  34 #include "custom_math.h"
  35
  36 #define FACTORIAL_LOWER         \
  37   MK_ULL(1),                    \
  38   MK_ULL(1),                    \
  39   MK_ULL(2),                    \
  40   MK_ULL(6),                    \
  41   MK_ULL(24),                   \
  42   MK_ULL(120),                  \
  43   MK_ULL(720),                  \
  44   MK_ULL(5040),                 \
  45   MK_ULL(40320),                \
  46   MK_ULL(362880),               \
  47   MK_ULL(3628800),              \
  48   MK_ULL(39916800),             \
  49   MK_ULL(479001600)
  50
  51 #define FACTORIAL_HIGHER        \
  52   MK_ULL(6227020800),           \
  53   MK_ULL(87178291200),          \
  54   MK_ULL(1307674368000),        \
  55   MK_ULL(20922789888000),       \
  56   MK_ULL(355687428096000),      \
  57   MK_ULL(6402373705728000),     \
  58   MK_ULL(121645100408832000),   \
  59   MK_ULL(2432902008176640000)
  60
  61 static const cmath_std_uint_t _factorials[] =
  62 {
  63   #ifdef _CMATH_ANSI
  64     FACTORIAL_LOWER
  65   #else
  66     FACTORIAL_LOWER,
  67     FACTORIAL_HIGHER
  68   #endif
  69 };
  70
  71 static const cmath_t _inv_factorials[] =
  72 {
  73   1.00000000000000000000000000000000,
  74   1.00000000000000000000000000000000,
  75   0.50000000000000000000000000000000,
  76   0.16666666666666666666666666666667,
  77   0.04166666666666666666666666666666,
  78   0.00833333333333333333333333333333,
  79   0.00138888888888888888888888888888,
  80   0.00019841269841269841269841269841,
  81   0.00002480158730158730158730158730,
  82   0.00000275573192239858906525573192,
  83   0.00000027557319223985890652557319,
  84   0.00000002505210838544171877505210,
  85   0.00000000208767569878680989792100,
  86   0.00000000016059043836821614599390,
  87   0.00000000001147074559772972471385,
  88   0.00000000000076471637318198164750,
  89   0.00000000000004779477332387385297,
  90   0.00000000000000281145725434552076,
  91   0.00000000000000015619206968586225,
  92   0.00000000000000000822063524662433,
  93   0.00000000000000000041103176233122
  94 };
  95
  96 _CMATH_INLINE
  97 cmath_std_uint_t factorial(const cmath_uint32_t x)
  98 {
  99   if(x >= cmath_array_size(_factorials))
 100     return 0;
 101   else
 102     return _factorials[x];
 103 }
 104
 105 _CMATH_INLINE
 106 cmath_t inv_factorial(const cmath_uint32_t x)
 107 {
 108   if(x >= cmath_array_size(_inv_factorials))
 109     return 0;
 110   else
 111     return _inv_factorials[x];
 112 }
 113
 114 #endif /* _FACTORIAL_H_ */