limits.hpp 20 KB

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  1. ///////////////////////////////////////////////////////////////
  2. // Copyright 2012 John Maddock. Distributed under the Boost
  3. // Software License, Version 1.0. (See accompanying file
  4. // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
  5. //
  6. // Comparison operators for cpp_int_backend:
  7. //
  8. #ifndef BOOST_MP_CPP_INT_LIM_HPP
  9. #define BOOST_MP_CPP_INT_LIM_HPP
  10. namespace std{
  11. namespace detail{
  12. #ifdef _MSC_VER
  13. #pragma warning(push)
  14. #pragma warning(disable:4307)
  15. #endif
  16. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  17. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  18. get_min(const boost::mpl::true_&, const boost::mpl::true_&)
  19. {
  20. // Bounded and signed.
  21. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> result_type;
  22. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MaxBits, MaxBits, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked>, ExpressionTemplates> ui_type;
  23. static const result_type val = -result_type(~ui_type(0));
  24. return val;
  25. }
  26. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  27. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  28. get_min(const boost::mpl::true_&, const boost::mpl::false_&)
  29. {
  30. // Bounded and unsigned:
  31. static const boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> val(0u);
  32. return val;
  33. }
  34. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  35. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  36. get_min(const boost::mpl::false_&, const boost::mpl::true_&)
  37. {
  38. // Unbounded and signed.
  39. // There is no minimum value, just return 0:
  40. static const boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> val(0u);
  41. return val;
  42. }
  43. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  44. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  45. get_min(const boost::mpl::false_&, const boost::mpl::false_&)
  46. {
  47. // Unbound and unsigned:
  48. static const boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> val(0u);
  49. return val;
  50. }
  51. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  52. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  53. get_max(const boost::mpl::true_&, const boost::mpl::true_&)
  54. {
  55. // Bounded and signed.
  56. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> result_type;
  57. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MaxBits, MaxBits, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked>, ExpressionTemplates> ui_type;
  58. static const result_type val = ~ui_type(0);
  59. return val;
  60. }
  61. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  62. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  63. get_max(const boost::mpl::true_&, const boost::mpl::false_&)
  64. {
  65. // Bound and unsigned:
  66. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> result_type;
  67. typedef boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, boost::multiprecision::unsigned_magnitude, boost::multiprecision::unchecked, Allocator>, ExpressionTemplates> ui_type;
  68. static const result_type val = ~ui_type(0);
  69. return val;
  70. }
  71. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  72. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  73. get_max(const boost::mpl::false_&, const boost::mpl::true_&)
  74. {
  75. // Unbounded and signed.
  76. // There is no maximum value, just return 0:
  77. static const boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> val(0u);
  78. return val;
  79. }
  80. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  81. inline boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates>
  82. get_max(const boost::mpl::false_&, const boost::mpl::false_&)
  83. {
  84. // Unbound and unsigned:
  85. static const boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> val(0u);
  86. return val;
  87. }
  88. }
  89. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  90. class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >
  91. {
  92. typedef boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> backend_type;
  93. typedef boost::multiprecision::number<backend_type, ExpressionTemplates> number_type;
  94. struct inititializer
  95. {
  96. inititializer()
  97. {
  98. (std::numeric_limits<number_type>::max)();
  99. (std::numeric_limits<number_type>::min)();
  100. }
  101. void do_nothing()const{}
  102. };
  103. static const inititializer init;
  104. public:
  105. BOOST_STATIC_CONSTEXPR bool is_specialized = true;
  106. //
  107. // Largest and smallest numbers are bounded only by available memory, set
  108. // to zero:
  109. //
  110. static number_type (min)()
  111. {
  112. init.do_nothing();
  113. return detail::get_min<MinBits, MaxBits, SignType, Checked, Allocator, ExpressionTemplates>(boost::multiprecision::backends::is_fixed_precision<backend_type>(), boost::multiprecision::is_signed_number<backend_type>());
  114. }
  115. static number_type (max)()
  116. {
  117. init.do_nothing();
  118. return detail::get_max<MinBits, MaxBits, SignType, Checked, Allocator, ExpressionTemplates>(boost::multiprecision::backends::is_fixed_precision<backend_type>(), boost::multiprecision::is_signed_number<backend_type>());
  119. }
  120. static number_type lowest() { return (min)(); }
  121. BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::backends::max_precision<backend_type>::value == UINT_MAX ? INT_MAX : boost::multiprecision::backends::max_precision<backend_type>::value;
  122. BOOST_STATIC_CONSTEXPR int digits10 = (digits > INT_MAX / 301) ? (digits / 1000) * 301L : (digits * 301) / 1000;
  123. BOOST_STATIC_CONSTEXPR int max_digits10 = digits10 + 3;
  124. BOOST_STATIC_CONSTEXPR bool is_signed = boost::multiprecision::is_signed_number<backend_type>::value;
  125. BOOST_STATIC_CONSTEXPR bool is_integer = true;
  126. BOOST_STATIC_CONSTEXPR bool is_exact = true;
  127. BOOST_STATIC_CONSTEXPR int radix = 2;
  128. static number_type epsilon() { return 0; }
  129. static number_type round_error() { return 0; }
  130. BOOST_STATIC_CONSTEXPR int min_exponent = 0;
  131. BOOST_STATIC_CONSTEXPR int min_exponent10 = 0;
  132. BOOST_STATIC_CONSTEXPR int max_exponent = 0;
  133. BOOST_STATIC_CONSTEXPR int max_exponent10 = 0;
  134. BOOST_STATIC_CONSTEXPR bool has_infinity = false;
  135. BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = false;
  136. BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
  137. BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
  138. BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
  139. static number_type infinity() { return 0; }
  140. static number_type quiet_NaN() { return 0; }
  141. static number_type signaling_NaN() { return 0; }
  142. static number_type denorm_min() { return 0; }
  143. BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
  144. BOOST_STATIC_CONSTEXPR bool is_bounded = boost::multiprecision::backends::is_fixed_precision<backend_type>::value;
  145. BOOST_STATIC_CONSTEXPR bool is_modulo = (boost::multiprecision::backends::is_fixed_precision<backend_type>::value && (Checked == boost::multiprecision::unchecked));
  146. BOOST_STATIC_CONSTEXPR bool traps = false;
  147. BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
  148. BOOST_STATIC_CONSTEXPR float_round_style round_style = round_toward_zero;
  149. };
  150. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  151. const typename numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::inititializer numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::init;
  152. #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
  153. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  154. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::digits;
  155. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  156. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::digits10;
  157. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  158. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::max_digits10;
  159. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  160. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_signed;
  161. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  162. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_integer;
  163. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  164. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_exact;
  165. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  166. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::radix;
  167. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  168. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::min_exponent;
  169. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  170. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::min_exponent10;
  171. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  172. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::max_exponent;
  173. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  174. BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::max_exponent10;
  175. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  176. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::has_infinity;
  177. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  178. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::has_quiet_NaN;
  179. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  180. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::has_signaling_NaN;
  181. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  182. BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::has_denorm;
  183. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  184. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::has_denorm_loss;
  185. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  186. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_iec559;
  187. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  188. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_bounded;
  189. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  190. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::is_modulo;
  191. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  192. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::traps;
  193. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  194. BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::tinyness_before;
  195. template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, boost::multiprecision::cpp_int_check_type Checked, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
  196. BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, ExpressionTemplates> >::round_style;
  197. #endif
  198. #ifdef _MSC_VER
  199. #pragma warning(pop)
  200. #endif
  201. } // namespace std
  202. #endif