ceph/src/boost/libs/multiprecision/include/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(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (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, cpp_int_check_type Checked1, class Allocator1>
  68 inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, checked, void>& 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       for(unsigned j = 0; j < inner_limit; ++j)
 140       {
 141          BOOST_ASSERT(i+j < result.size());
 142 #if (!defined(__GLIBCXX__) && !defined(__GLIBCPP__)) || !BOOST_WORKAROUND(BOOST_GCC_VERSION, <= 50100)
 143          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized
 144             || ((std::numeric_limits<double_limb_type>::max)() - carry
 145                   >
 146                 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)));
 147 #endif
 148          carry += static_cast<double_limb_type>(pa[i]) * static_cast<double_limb_type>(pb[j]);
 149          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized || ((std::numeric_limits<double_limb_type>::max)() - carry >= pr[i+j]));
 150          carry += pr[i + j];
 151 #ifdef __MSVC_RUNTIME_CHECKS
 152          pr[i + j] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 153 #else
 154          pr[i + j] = static_cast<limb_type>(carry);
 155 #endif
 156          carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
 157          BOOST_ASSERT(carry <= (cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value));
 158       }
 159       resize_for_carry(result, as + bs);  // May throw if checking is enabled
 160       if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (i + bs < result.size()))
 161          pr[i + bs] = static_cast<limb_type>(carry);
 162       carry = 0;
 163    }
 164    result.normalize();
 165    //
 166    // Set the sign of the result:
 167    //
 168    result.sign(a.sign() != b.sign());
 169 }
 170
 171 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>
 172 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
 173    eval_multiply(
 174       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 175       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))
 176 {
 177     eval_multiply(result, result, a);
 178 }
 179
 180 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 181 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 182    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))
 183 {
 184    eval_multiply(result, result, val);
 185 }
 186
 187 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>
 188 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
 189    eval_multiply(
 190       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 191       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 192       const double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 193 {
 194    if(val <= (std::numeric_limits<limb_type>::max)())
 195    {
 196       eval_multiply(result, a, static_cast<limb_type>(val));
 197    }
 198    else
 199    {
 200 #if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
 201       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
 202 #else
 203       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
 204       t = val;
 205 #endif
 206       eval_multiply(result, a, t);
 207    }
 208 }
 209
 210 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 211 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 212    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))
 213 {
 214    eval_multiply(result, result, val);
 215 }
 216
 217 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>
 218 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
 219    eval_multiply(
 220       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 221       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 222       const signed_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 223 {
 224    if(val > 0)
 225       eval_multiply(result, a, static_cast<limb_type>(val));
 226    else
 227    {
 228       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
 229       result.negate();
 230    }
 231 }
 232
 233 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 234 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 235    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))
 236 {
 237    eval_multiply(result, result, val);
 238 }
 239
 240 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>
 241 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
 242    eval_multiply(
 243       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 244       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
 245       const signed_double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
 246 {
 247    if(val > 0)
 248    {
 249       if(val <= (std::numeric_limits<limb_type>::max)())
 250       {
 251          eval_multiply(result, a, static_cast<limb_type>(val));
 252          return;
 253       }
 254    }
 255    else if(val >= -static_cast<signed_double_limb_type>((std::numeric_limits<limb_type>::max)()))
 256    {
 257       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
 258       result.negate();
 259       return;
 260    }
 261 #if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
 262    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
 263 #else
 264    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
 265    t = val;
 266 #endif
 267    eval_multiply(result, a, t);
 268 }
 269
 270 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 271 BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
 272    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))
 273 {
 274    eval_multiply(result, result, val);
 275 }
 276
 277 //
 278 // Now over again for trivial cpp_int's:
 279 //
 280 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 281 BOOST_MP_FORCEINLINE typename enable_if_c<
 282          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 283          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 284          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 285             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
 286          >::type
 287    eval_multiply(
 288       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 289       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))
 290 {
 291    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 292    result.sign(result.sign() != o.sign());
 293    result.normalize();
 294 }
 295
 296 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 297 BOOST_MP_FORCEINLINE typename enable_if_c<
 298          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 299          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 300          >::type
 301    eval_multiply(
 302       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 303       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))
 304 {
 305    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 306    result.normalize();
 307 }
 308
 309 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 310 BOOST_MP_FORCEINLINE typename enable_if_c<
 311          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 312          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 313          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 314             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
 315          >::type
 316    eval_multiply(
 317       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 318       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
 319       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))
 320 {
 321    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 322    result.sign(a.sign() != b.sign());
 323    result.normalize();
 324 }
 325
 326 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 327 BOOST_MP_FORCEINLINE typename enable_if_c<
 328          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 329          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 330          >::type
 331    eval_multiply(
 332       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 333       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
 334       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))
 335 {
 336    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
 337    result.normalize();
 338 }
 339
 340 //
 341 // Special routines for multiplying two integers to obtain a multiprecision result:
 342 //
 343 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 344 BOOST_MP_FORCEINLINE typename enable_if_c<
 345             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 346          >::type
 347    eval_multiply(
 348       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 349       signed_double_limb_type a, signed_double_limb_type b)
 350 {
 351    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
 352    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 353    bool s = false;
 354    double_limb_type w, x, y, z;
 355    if(a < 0)
 356    {
 357       a = -a;
 358       s = true;
 359    }
 360    if(b < 0)
 361    {
 362       b = -b;
 363       s = !s;
 364    }
 365    w = a & mask;
 366    x = a >> limb_bits;
 367    y = b & mask;
 368    z = b >> limb_bits;
 369
 370    result.resize(4, 4);
 371    limb_type* pr = result.limbs();
 372
 373    double_limb_type carry = w * y;
 374 #ifdef __MSVC_RUNTIME_CHECKS
 375    pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 376    carry >>= limb_bits;
 377    carry += w * z + x * y;
 378    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 379    carry >>= limb_bits;
 380    carry += x * z;
 381    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 382    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 383 #else
 384    pr[0] = static_cast<limb_type>(carry);
 385    carry >>= limb_bits;
 386    carry += w * z + x * y;
 387    pr[1] = static_cast<limb_type>(carry);
 388    carry >>= limb_bits;
 389    carry += x * z;
 390    pr[2] = static_cast<limb_type>(carry);
 391    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 392 #endif
 393    result.sign(s);
 394    result.normalize();
 395 }
 396
 397 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
 398 BOOST_MP_FORCEINLINE typename enable_if_c<
 399             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 400          >::type
 401    eval_multiply(
 402       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 403       double_limb_type a, double_limb_type b)
 404 {
 405    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
 406    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 407
 408    double_limb_type w, x, y, z;
 409    w = a & mask;
 410    x = a >> limb_bits;
 411    y = b & mask;
 412    z = b >> limb_bits;
 413
 414    result.resize(4, 4);
 415    limb_type* pr = result.limbs();
 416
 417    double_limb_type carry = w * y;
 418 #ifdef __MSVC_RUNTIME_CHECKS
 419    pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 420    carry >>= limb_bits;
 421    carry += w * z;
 422    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 423    carry >>= limb_bits;
 424    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 425    carry = x * y + pr[1];
 426    pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 427    carry >>= limb_bits;
 428    carry += pr[2] + x * z;
 429    pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
 430    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 431 #else
 432    pr[0] = static_cast<limb_type>(carry);
 433    carry >>= limb_bits;
 434    carry += w * z;
 435    pr[1] = static_cast<limb_type>(carry);
 436    carry >>= limb_bits;
 437    pr[2] = static_cast<limb_type>(carry);
 438    carry = x * y + pr[1];
 439    pr[1] = static_cast<limb_type>(carry);
 440    carry >>= limb_bits;
 441    carry += pr[2] + x * z;
 442    pr[2] = static_cast<limb_type>(carry);
 443    pr[3] = static_cast<limb_type>(carry >> limb_bits);
 444 #endif
 445    result.sign(false);
 446    result.normalize();
 447 }
 448
 449 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1,
 450           unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
 451 BOOST_MP_FORCEINLINE typename enable_if_c<
 452             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
 453             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
 454             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
 455          >::type
 456    eval_multiply(
 457       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 458       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& a,
 459       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& b)
 460 {
 461    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;
 462    eval_multiply(result, static_cast<canonical_type>(*a.limbs()), static_cast<canonical_type>(*b.limbs()));
 463    result.sign(a.sign() != b.sign());
 464 }
 465
 466 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class SI>
 467 BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<SI>::value && (sizeof(SI) <= sizeof(signed_double_limb_type) / 2)>::type
 468    eval_multiply(
 469       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 470       SI a, SI b)
 471 {
 472    result = static_cast<signed_double_limb_type>(a) * static_cast<signed_double_limb_type>(b);
 473 }
 474
 475 template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class UI>
 476 BOOST_MP_FORCEINLINE typename enable_if_c<is_unsigned<UI>::value && (sizeof(UI) <= sizeof(signed_double_limb_type) / 2)>::type
 477    eval_multiply(
 478       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
 479       UI a, UI b)
 480 {
 481    result = static_cast<double_limb_type>(a) * static_cast<double_limb_type>(b);
 482 }
 483
 484 #ifdef _MSC_VER
 485 #pragma warning(pop)
 486 #endif
 487
 488 }}} // namespaces
 489
 490 #endif