ceph/src/boost/boost/multiprecision/cpp_int/multiply.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 http://www.boost.org/LICENSE_1_
   5 //
   6 // Comparison operators for cpp_int_backend:
   7 //
   8 #ifndef BOOST_MP_CPP_INT_MUL_HPP
   9 #define BOOST_MP_CPP_INT_MUL_HPP
  10
  11 namespace boost{ namespace multiprecision{ namespace backends{
  12
  13 #ifdef _MSC_VER
  14 #pragma warning(push)
  15 #pragma warning(disable:4127) // conditional expression is constant
  16 #endif
  17
  18    template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
  19 inline typename enable_if_c<!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
  20    eval_multiply(
  21       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
  22       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
  23       const limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
  24 {
  25    if(!val)
  26    {
  27       result = static_cast<limb_type>(0);
  28       return;
  29    }
  30    if((void*)&a != (void*)&result)
  31       result.resize(a.size(), a.size());
  32    double_limb_type carry = 0;
  33    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer p = result.limbs();
  34    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pe = result.limbs() + result.size();
  35    typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
  36    while(p != pe)
  37    {
  38       carry += static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(val);
  39 #ifdef __MSVC_RUNTIME_CHECKS
  40       *p = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
  41 #else
  42       *p = static_cast<limb_type>(carry);
  43 #endif
  44       carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
  45       ++p, ++pa;
  46    }
  47    if(carry)
  48    {
  49       unsigned i = result.size();
  50       result.resize(i + 1, i + 1);
  51       if(result.size() > i)
  52          result.limbs()[i] = static_cast<limb_type>(carry);
  53    }
  54    result.sign(a.sign());
  55    if(!cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable)
  56       result.normalize();
  57 }
  58
  59 //
  60 // resize_for_carry forces a resize of the underlying buffer only if a previous request
  61 // for "required" elements could possibly have failed, *and* we have checking enabled.
  62 // This will cause an overflow error inside resize():
  63 //
  64 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
  65 inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& /*result*/, unsigned /*required*/){}
  66
  67 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, class Allocator1>
  68 inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, checked, Allocator1>& result, unsigned required)
  69 {
  70    if(result.size() < required)
  71       result.resize(required, required);
  72 }
  73
  74 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2, unsigned MinBits3, unsigned MaxBits3, cpp_integer_type SignType3, cpp_int_check_type Checked3, class Allocator3>
  75 inline typename enable_if_c<!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
  76    eval_multiply(
  77       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
  78       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
  79       const cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>& b) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
  80 {
  81    // Very simple long multiplication, only usable for small numbers of limb_type's
  82    // but that's the typical use case for this type anyway:
  83    //
  84    // Special cases first:
  85    //
  86    unsigned as = a.size();
  87    unsigned bs = b.size();
  88    typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
  89    typename cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>::const_limb_pointer pb = b.limbs();
  90    if(as == 1)
  91    {
  92       bool s = b.sign() != a.sign();
  93       if(bs == 1)
  94       {
  95          result = static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(*pb);
  96       }
  97       else
  98       {
  99          limb_type l = *pa;
 100          eval_multiply(result, b, l);
 101       }
 102       result.sign(s);
 103       return;
 104    }
 105    if(bs == 1)
 106    {
 107       bool s = b.sign() != a.sign();
 108       limb_type l = *pb;
 109       eval_multiply(result, a, l);
 110       result.sign(s);
 111       return;
 112    }
 113
 114    if((void*)&result == (void*)&a)
 115    {
 116       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(a);
 117       eval_multiply(result, t, b);
 118       return;
 119    }
 120    if((void*)&result == (void*)&b)
 121    {
 122       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(b);
 123       eval_multiply(result, a, t);
 124       return;
 125    }
 126
 127    result.resize(as + bs, as + bs - 1);
 128    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pr = result.limbs();
 129
 130    static const double_limb_type limb_max = ~static_cast<limb_type>(0u);
 131    static const double_limb_type double_limb_max = ~static_cast<double_limb_type>(0u);
 132    BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
 133
 134    double_limb_type carry = 0;
 135    std::memset(pr, 0, result.size() * sizeof(limb_type));
 136    for(unsigned i = 0; i < as; ++i)
 137    {
 138       unsigned inner_limit = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable ? bs : (std::min)(result.size() - i, bs);
 139       unsigned j;
 140       for(j = 0; j < inner_limit; ++j)
 141       {
 142          BOOST_ASSERT(i+j < result.size());
 143 #if (!defined(__GLIBCXX__) && !defined(__GLIBCPP__)) || !BOOST_WORKAROUND(BOOST_GCC_VERSION, <= 50100)
 144          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized
 145             || ((std::numeric_limits<double_limb_type>::max)() - carry
 146                   >
 147                 static_cast<double_limb_type>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value) * static_cast<double_limb_type>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value)));
 148 #endif
 149          carry += static_cast<double_limb_type>(pa[i]) * static_cast<double_limb_type>(pb[j]);
 150          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized || ((std::numeric_limits<double_limb_type>::max)() - carry >= pr[i+j]));
 151          carry += pr[i + j];
 152 #ifdef __MSVC_RUNTIME_CHECKS
 153          pr[i + j] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 154 #else
 155          pr[i + j] = static_cast<limb_type>(carry);
 156 #endif
 157          carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
 158          BOOST_ASSERT(carry <= (cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value));
 159       }
 160       if(carry)
 161       {
 162          resize_for_carry(result, i + j + 1);  // May throw if checking is enabled
 163          if(i + j < result.size())
 164 #ifdef __MSVC_RUNTIME_CHECKS
 165             pr[i + j] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 166 #else
 167             pr[i + j] = static_cast<limb_type>(carry);
 168 #endif
 169       }
 170       carry = 0;
 171    }
 172    result.normalize();
 173    //
 174    // Set the sign of the result:
 175    //
 176    result.sign(a.sign() != b.sign());
 177 }
 178
 179 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 180 BOOST_MP_FORCEINLINE typename enable_if_c<!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
 181    eval_multiply(
 182       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 183       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 184 {
 185     eval_multiply(result, result, a);
 186 }
 187
 188 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 189 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 190    eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 191 {
 192    eval_multiply(result, result, val);
 193 }
 194
 195 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 196 BOOST_MP_FORCEINLINE typename enable_if_c<!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_multiply(
 198       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 199       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 200       const double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 201 {
 202    if(val <= (std::numeric_limits<limb_type>::max)())
 203    {
 204       eval_multiply(result, a, static_cast<limb_type>(val));
 205    }
 206    else
 207    {
 208 #if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
 209       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
 210 #else
 211       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
 212       t = val;
 213 #endif
 214       eval_multiply(result, a, t);
 215    }
 216 }
 217
 218 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 219 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 220    eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 221 {
 222    eval_multiply(result, result, val);
 223 }
 224
 225 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 226 BOOST_MP_FORCEINLINE typename enable_if_c<!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_multiply(
 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& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 231 {
 232    if(val > 0)
 233       eval_multiply(result, a, static_cast<limb_type>(val));
 234    else
 235    {
 236       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
 237       result.negate();
 238    }
 239 }
 240
 241 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 242 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 243    eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 244 {
 245    eval_multiply(result, result, val);
 246 }
 247
 248 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 249 inline typename enable_if_c<!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
 250    eval_multiply(
 251       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 252       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 253       const signed_double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 254 {
 255    if(val > 0)
 256    {
 257       if(val <= (std::numeric_limits<limb_type>::max)())
 258       {
 259          eval_multiply(result, a, static_cast<limb_type>(val));
 260          return;
 261       }
 262    }
 263    else if(val >= -static_cast<signed_double_limb_type>((std::numeric_limits<limb_type>::max)()))
 264    {
 265       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
 266       result.negate();
 267       return;
 268    }
 269 #if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
 270    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
 271 #else
 272    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
 273    t = val;
 274 #endif
 275    eval_multiply(result, a, t);
 276 }
 277
 278 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 279 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 280    eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 281 {
 282    eval_multiply(result, result, val);
 283 }
 284
 285 //
 286 // Now over again for trivial cpp_int's:
 287 //
 288 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 289 BOOST_MP_FORCEINLINE typename enable_if_c<
 290          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 291          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 292          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 293             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
 294          >::type
 295    eval_multiply(
 296       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 297       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 298 {
 299    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 300    result.sign(result.sign() != o.sign());
 301    result.normalize();
 302 }
 303
 304 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 305 BOOST_MP_FORCEINLINE typename enable_if_c<
 306          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 307          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 308          >::type
 309    eval_multiply(
 310       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 311       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 312 {
 313    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 314    result.normalize();
 315 }
 316
 317 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 318 BOOST_MP_FORCEINLINE typename enable_if_c<
 319          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 320          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 321          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 322             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
 323          >::type
 324    eval_multiply(
 325       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 326       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
 327       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 328 {
 329    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 330    result.sign(a.sign() != b.sign());
 331    result.normalize();
 332 }
 333
 334 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 335 BOOST_MP_FORCEINLINE typename enable_if_c<
 336          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 337          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 338          >::type
 339    eval_multiply(
 340       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 341       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
 342       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 343 {
 344    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 345    result.normalize();
 346 }
 347
 348 //
 349 // Special routines for multiplying two integers to obtain a multiprecision result:
 350 //
 351 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 352 BOOST_MP_FORCEINLINE typename enable_if_c<
 353             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 354          >::type
 355    eval_multiply(
 356       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 357       signed_double_limb_type a, signed_double_limb_type b)
 358 {
 359    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
 360    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 361    bool s = false;
 362    double_limb_type w, x, y, z;
 363    if(a < 0)
 364    {
 365       a = -a;
 366       s = true;
 367    }
 368    if(b < 0)
 369    {
 370       b = -b;
 371       s = !s;
 372    }
 373    w = a & mask;
 374    x = a >> limb_bits;
 375    y = b & mask;
 376    z = b >> limb_bits;
 377
 378    result.resize(4, 4);
 379    limb_type* pr = result.limbs();
 380
 381    double_limb_type carry = w * y;
 382 #ifdef __MSVC_RUNTIME_CHECKS
 383    pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 384    carry >>= limb_bits;
 385    carry += w * z + x * y;
 386    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 387    carry >>= limb_bits;
 388    carry += x * z;
 389    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 390    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 391 #else
 392    pr[0] = static_cast<limb_type>(carry);
 393    carry >>= limb_bits;
 394    carry += w * z + x * y;
 395    pr[1] = static_cast<limb_type>(carry);
 396    carry >>= limb_bits;
 397    carry += x * z;
 398    pr[2] = static_cast<limb_type>(carry);
 399    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 400 #endif
 401    result.sign(s);
 402    result.normalize();
 403 }
 404
 405 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 406 BOOST_MP_FORCEINLINE typename enable_if_c<
 407             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 408          >::type
 409    eval_multiply(
 410       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 411       double_limb_type a, double_limb_type b)
 412 {
 413    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
 414    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 415
 416    double_limb_type w, x, y, z;
 417    w = a & mask;
 418    x = a >> limb_bits;
 419    y = b & mask;
 420    z = b >> limb_bits;
 421
 422    result.resize(4, 4);
 423    limb_type* pr = result.limbs();
 424
 425    double_limb_type carry = w * y;
 426 #ifdef __MSVC_RUNTIME_CHECKS
 427    pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 428    carry >>= limb_bits;
 429    carry += w * z;
 430    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 431    carry >>= limb_bits;
 432    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 433    carry = x * y + pr[1];
 434    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 435    carry >>= limb_bits;
 436    carry += pr[2] + x * z;
 437    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 438    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 439 #else
 440    pr[0] = static_cast<limb_type>(carry);
 441    carry >>= limb_bits;
 442    carry += w * z;
 443    pr[1] = static_cast<limb_type>(carry);
 444    carry >>= limb_bits;
 445    pr[2] = static_cast<limb_type>(carry);
 446    carry = x * y + pr[1];
 447    pr[1] = static_cast<limb_type>(carry);
 448    carry >>= limb_bits;
 449    carry += pr[2] + x * z;
 450    pr[2] = static_cast<limb_type>(carry);
 451    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 452 #endif
 453    result.sign(false);
 454    result.normalize();
 455 }
 456
 457 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1,
 458           unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 459 BOOST_MP_FORCEINLINE typename enable_if_c<
 460             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 461             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
 462             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
 463          >::type
 464    eval_multiply(
 465       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 466       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& a,
 467       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& b)
 468 {
 469    typedef typename boost::multiprecision::detail::canonical<typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::local_limb_type, cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::type canonical_type;
 470    eval_multiply(result, static_cast<canonical_type>(*a.limbs()), static_cast<canonical_type>(*b.limbs()));
 471    result.sign(a.sign() != b.sign());
 472 }
 473
 474 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class SI>
 475 BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<SI>::value && (sizeof(SI) <= sizeof(signed_double_limb_type) / 2)>::type
 476    eval_multiply(
 477       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 478       SI a, SI b)
 479 {
 480    result = static_cast<signed_double_limb_type>(a) * static_cast<signed_double_limb_type>(b);
 481 }
 482
 483 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class UI>
 484 BOOST_MP_FORCEINLINE typename enable_if_c<is_unsigned<UI>::value && (sizeof(UI) <= sizeof(signed_double_limb_type) / 2)>::type
 485    eval_multiply(
 486       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 487       UI a, UI b)
 488 {
 489    result = static_cast<double_limb_type>(a) * static_cast<double_limb_type>(b);
 490 }
 491
 492 #ifdef _MSC_VER
 493 #pragma warning(pop)
 494 #endif
 495
 496 }}} // namespaces
 497
 498 #endif