ceph/src/boost/boost/multiprecision/cpp_int/add.hpp

   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 https://www.boost.org/LICENSE_1_0.txt
   5 //
   6 // Comparison operators for cpp_int_backend:
   7 //
   8 #ifndef BOOST_MP_CPP_INT_ADD_HPP
   9 #define BOOST_MP_CPP_INT_ADD_HPP
  10
  11 #include <boost/multiprecision/detail/constexpr.hpp>
  12 #include <boost/multiprecision/cpp_int/add_unsigned.hpp>
  13
  14 namespace boost { namespace multiprecision { namespace backends {
  15
  16 //
  17 // As above, but for adding a single limb to a non-trivial cpp_int:
  18 //
  19 template <class CppInt1, class CppInt2>
  20 inline BOOST_MP_CXX14_CONSTEXPR void add_unsigned(CppInt1& result, const CppInt2& a, const limb_type& o) noexcept(is_non_throwing_cpp_int<CppInt1>::value)
  21 {
  22    // Addition using modular arithmetic.
  23    // Nothing fancy, just let uintmax_t take the strain:
  24    if (&result != &a)
  25       result.resize(a.size(), a.size());
  26    double_limb_type                     carry = o;
  27    typename CppInt1::limb_pointer       pr    = result.limbs();
  28    typename CppInt2::const_limb_pointer pa    = a.limbs();
  29    std::size_t                             i     = 0;
  30    // Addition with carry until we either run out of digits or carry is zero:
  31    for (; carry && (i < result.size()); ++i)
  32    {
  33       carry += static_cast<double_limb_type>(pa[i]);
  34 #ifdef __MSVC_RUNTIME_CHECKS
  35       pr[i] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
  36 #else
  37       pr[i] = static_cast<limb_type>(carry);
  38 #endif
  39       carry >>= CppInt1::limb_bits;
  40    }
  41    // Just copy any remaining digits:
  42    if (&a != &result)
  43    {
  44       std_constexpr::copy(pa + i, pa + a.size(), pr + i);
  45    }
  46    if (carry)
  47    {
  48       // We overflowed, need to add one more limb:
  49       std::size_t x = result.size();
  50       result.resize(x + 1, x + 1);
  51       if (result.size() > x)
  52          result.limbs()[x] = static_cast<limb_type>(carry);
  53    }
  54    result.normalize();
  55    result.sign(a.sign());
  56 }
  57 //
  58 // And again to subtract a single limb:
  59 //
  60 template <class CppInt1, class CppInt2>
  61 inline BOOST_MP_CXX14_CONSTEXPR void subtract_unsigned(CppInt1& result, const CppInt2& a, const limb_type& b) noexcept(is_non_throwing_cpp_int<CppInt1>::value)
  62 {
  63    // Subtract one limb.
  64    // Nothing fancy, just let uintmax_t take the strain:
  65    constexpr double_limb_type borrow = static_cast<double_limb_type>(CppInt1::max_limb_value) + 1;
  66    result.resize(a.size(), a.size());
  67    typename CppInt1::limb_pointer       pr = result.limbs();
  68    typename CppInt2::const_limb_pointer pa = a.limbs();
  69    if (*pa >= b)
  70    {
  71       *pr = *pa - b;
  72       if (&result != &a)
  73       {
  74          std_constexpr::copy(pa + 1, pa + a.size(), pr + 1);
  75          result.sign(a.sign());
  76       }
  77       else if ((result.size() == 1) && (*pr == 0))
  78       {
  79          result.sign(false); // zero is unsigned.
  80       }
  81    }
  82    else if (result.size() == 1)
  83    {
  84       *pr = b - *pa;
  85       result.sign(!a.sign());
  86    }
  87    else
  88    {
  89       *pr        = static_cast<limb_type>((borrow + *pa) - b);
  90       std::size_t i = 1;
  91       while (!pa[i])
  92       {
  93          pr[i] = CppInt1::max_limb_value;
  94          ++i;
  95       }
  96       pr[i] = pa[i] - 1;
  97       if (&result != &a)
  98       {
  99          ++i;
 100          std_constexpr::copy(pa + i, pa + a.size(), pr + i);
 101       }
 102       result.normalize();
 103       result.sign(a.sign());
 104    }
 105 }
 106
 107 //
 108 // Now the actual functions called by the front end, all of which forward to one of the above:
 109 //
 110 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 111 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 112 eval_add(
 113     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 114     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 115 {
 116    eval_add(result, result, o);
 117 }
 118 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2, std::size_t MinBits3, std::size_t MaxBits3, cpp_integer_type SignType3, cpp_int_check_type Checked3, class Allocator3>
 119 inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3> >::value>::type
 120 eval_add(
 121     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 122     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 123     const cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>& b) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 124 {
 125    if (a.sign() != b.sign())
 126    {
 127       subtract_unsigned(result, a, b);
 128       return;
 129    }
 130    add_unsigned(result, a, b);
 131 }
 132 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 133 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 134 eval_add(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const limb_type& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 135 {
 136    if (result.sign())
 137    {
 138       subtract_unsigned(result, result, o);
 139    }
 140    else
 141       add_unsigned(result, result, o);
 142 }
 143 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 144 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 145 eval_add(
 146     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 147     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 148     const limb_type&                                                            o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 149 {
 150    if (a.sign())
 151    {
 152       subtract_unsigned(result, a, o);
 153    }
 154    else
 155       add_unsigned(result, a, o);
 156 }
 157 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 158 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 159 eval_add(
 160     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 161     const signed_limb_type&                                               o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 162 {
 163    if (o < 0)
 164       eval_subtract(result, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(o)));
 165    else if (o > 0)
 166       eval_add(result, static_cast<limb_type>(o));
 167 }
 168 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 169 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 170 eval_add(
 171     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 172     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 173     const signed_limb_type&                                                     o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 174 {
 175    if (o < 0)
 176       eval_subtract(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(o)));
 177    else if (o > 0)
 178       eval_add(result, a, static_cast<limb_type>(o));
 179    else if (&result != &a)
 180       result = a;
 181 }
 182 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 183 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 184 eval_subtract(
 185     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 186     const limb_type&                                                      o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 187 {
 188    if (result.sign())
 189    {
 190       add_unsigned(result, result, o);
 191    }
 192    else
 193       subtract_unsigned(result, result, o);
 194 }
 195 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 196 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 197 eval_subtract(
 198     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 199     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 200     const limb_type&                                                            o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 201 {
 202    if (a.sign())
 203    {
 204       add_unsigned(result, a, o);
 205    }
 206    else
 207    {
 208       subtract_unsigned(result, a, o);
 209    }
 210 }
 211 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 212 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 213 eval_subtract(
 214     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 215     const signed_limb_type&                                               o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 216 {
 217    if (o)
 218    {
 219       if (o < 0)
 220          eval_add(result, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(o)));
 221       else
 222          eval_subtract(result, static_cast<limb_type>(o));
 223    }
 224 }
 225 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 226 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 227 eval_subtract(
 228     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 229     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 230     const signed_limb_type&                                                     o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 231 {
 232    if (o)
 233    {
 234       if (o < 0)
 235          eval_add(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(o)));
 236       else
 237          eval_subtract(result, a, static_cast<limb_type>(o));
 238    }
 239    else if (&result != &a)
 240       result = a;
 241 }
 242
 243 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 244 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 245 eval_increment(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 246 {
 247    constexpr const limb_type one = 1;
 248
 249    if (!result.sign() && (result.limbs()[0] < cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value))
 250       ++result.limbs()[0];
 251    else if (result.sign() && result.limbs()[0])
 252    {
 253       --result.limbs()[0];
 254       if (!result.limbs()[0] && (result.size() == 1))
 255          result.sign(false);
 256    }
 257    else
 258       eval_add(result, one);
 259 }
 260 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 261 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 262 eval_decrement(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 263 {
 264    constexpr const limb_type one = 1;
 265
 266    if (!result.sign() && result.limbs()[0])
 267       --result.limbs()[0];
 268    else if (result.sign() && (result.limbs()[0] < cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value))
 269       ++result.limbs()[0];
 270    else
 271       eval_subtract(result, one);
 272 }
 273 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 274 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>::type
 275 eval_subtract(
 276     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 277     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 278 {
 279    eval_subtract(result, result, o);
 280 }
 281 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, std::size_t MinBits2, std::size_t MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2, std::size_t MinBits3, std::size_t MaxBits3, cpp_integer_type SignType3, cpp_int_check_type Checked3, class Allocator3>
 282 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3> >::value>::type
 283 eval_subtract(
 284     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 285     const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 286     const cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>& b) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 287 {
 288    if (a.sign() != b.sign())
 289    {
 290       add_unsigned(result, a, b);
 291       return;
 292    }
 293    subtract_unsigned(result, a, b);
 294 }
 295
 296 //
 297 // Simple addition and subtraction routine for trivial cpp_int's come last:
 298 //
 299 // One of the arguments is signed:
 300 //
 301 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 302 inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
 303     is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)>::type
 304 eval_add(
 305     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 306     const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 307 {
 308    if (result.sign() != o.sign())
 309    {
 310       if (*o.limbs() > *result.limbs())
 311       {
 312          *result.limbs() = detail::checked_subtract(*o.limbs(), *result.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 313          result.negate();
 314       }
 315       else
 316          *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 317    }
 318    else
 319       *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 320    result.normalize();
 321 }
 322 // Simple version for two unsigned arguments:
 323 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 324 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
 325     is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 326 eval_add(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 327          const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 328 {
 329    *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 330    result.normalize();
 331 }
 332
 333 // signed subtraction:
 334 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 335 inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
 336     is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)>::type
 337 eval_subtract(
 338     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 339     const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 340 {
 341    if (result.sign() != o.sign())
 342    {
 343       *result.limbs() = detail::checked_add(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 344    }
 345    else if (*result.limbs() < *o.limbs())
 346    {
 347       *result.limbs() = detail::checked_subtract(*o.limbs(), *result.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 348       result.negate();
 349    }
 350    else
 351       *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 352    result.normalize();
 353 }
 354
 355 template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 356 BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
 357     is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 358 eval_subtract(
 359     cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&       result,
 360     const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 361 {
 362    *result.limbs() = detail::checked_subtract(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 363    result.normalize();
 364 }
 365
 366 }}} // namespace boost::multiprecision::backends
 367
 368 #endif