C++ default_ops::eval_subtract方法代码示例

BOOST_MP_FORCEINLINE number<B, et_off> operator - (const number<B, et_off>& a, const number<B, et_off>& b)
{
   number<B, et_off> result;
   using default_ops::eval_subtract;
   eval_subtract(result.backend(), a.backend(), b.backend());
   return BOOST_MP_MOVE(result);
}

BOOST_MP_FORCEINLINE typename enable_if<is_compatible_arithmetic_type<V, number<B, et_off> >, number<B, et_off> >::type
   operator - (number<B, et_off>&& a, const V& b)
{
   using default_ops::eval_subtract;
   eval_subtract(a.backend(), number<B, et_off>::canonical_value(b));
   return static_cast<number<B, et_off>&&>(a);
}

BOOST_MP_FORCEINLINE number<B, et_off> operator - (number<B, et_off>&& a, number<B, et_off>&& b)
{
   using default_ops::eval_subtract;
   detail::scoped_default_precision<multiprecision::number<B, et_off> > precision_guard(a, b);
   eval_subtract(a.backend(), b.backend());
   return static_cast<number<B, et_off>&&>(a);
}

BOOST_MP_FORCEINLINE number<B, et_off> operator - (const number<B, et_off>& a, const number<B, et_off>& b)
{
   detail::scoped_default_precision<multiprecision::number<B, et_off> > precision_guard(a, b);
   number<B, et_off> result;
   using default_ops::eval_subtract;
   eval_subtract(result.backend(), a.backend(), b.backend());
   return result;
}

void generic_interconvert(To& to, const From& from, const mpl::int_<number_kind_floating_point>& /*to_type*/, const mpl::int_<number_kind_floating_point>& /*from_type*/)
{
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif
   //
   // The code here only works when the radix of "From" is 2, we could try shifting by other
   // radixes but it would complicate things.... use a string conversion when the radix is other
   // than 2:
   //
   if(std::numeric_limits<number<From> >::radix != 2)
   {
      to = from.str(0, std::ios_base::fmtflags()).c_str();
      return;
   }


   typedef typename canonical<unsigned char, To>::type ui_type;

   using default_ops::eval_fpclassify;
   using default_ops::eval_add;
   using default_ops::eval_subtract;
   using default_ops::eval_convert_to;

   //
   // First classify the input, then handle the special cases:
   //
   int c = eval_fpclassify(from);

   if(c == FP_ZERO)
   {
      to = ui_type(0);
      return;
   }
   else if(c == FP_NAN)
   {
      to = "nan";
      return;
   }
   else if(c == FP_INFINITE)
   {
      to = "inf";
      if(eval_get_sign(from) < 0)
         to.negate();
      return;
   }

   typename From::exponent_type e;
   From f, term;
   to = ui_type(0);

   eval_frexp(f, from, &e);

   static const int shift = std::numeric_limits<boost::intmax_t>::digits - 1;

   while(!eval_is_zero(f))
   {
      // extract int sized bits from f:
      eval_ldexp(f, f, shift);
      eval_floor(term, f);
      e -= shift;
      eval_ldexp(to, to, shift);
      typename boost::multiprecision::detail::canonical<boost::intmax_t, To>::type ll;
      eval_convert_to(&ll, term);
      eval_add(to, ll);
      eval_subtract(f, term);
   }
   typedef typename To::exponent_type to_exponent;
   if((e > (std::numeric_limits<to_exponent>::max)()) || (e < (std::numeric_limits<to_exponent>::min)()))
   {
      to = "inf";
      if(eval_get_sign(from) < 0)
         to.negate();
      return;
   }
   eval_ldexp(to, to, static_cast<to_exponent>(e));
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}

void divide_unsigned_helper(
   CppInt1* result, 
   const CppInt2& x, 
   const CppInt3& y, 
   CppInt1& r)
{
   if(((void*)result == (void*)&x) || ((void*)&r == (void*)&x))
   {
      CppInt2 t(x);
      divide_unsigned_helper(result, t, y, r);
      return;
   }
   if(((void*)result == (void*)&y) || ((void*)&r == (void*)&y))
   {
      CppInt3 t(y);
      divide_unsigned_helper(result, x, t, r);
      return;
   }

   /*
    Very simple, fairly braindead long division.
    Start by setting the remainder equal to x, and the
    result equal to 0.  Then in each loop we calculate our
    "best guess" for how many times y divides into r,
    add our guess to the result, and subtract guess*y
    from the remainder r.  One wrinkle is that the remainder
    may go negative, in which case we subtract the current guess
    from the result rather than adding.  The value of the guess
    is determined by dividing the most-significant-limb of the
    current remainder by the most-significant-limb of y.

    Note that there are more efficient algorithms than this
    available, in particular see Knuth Vol 2.  However for small
    numbers of limbs this generally outperforms the alternatives
    and avoids the normalisation step which would require extra storage.
    */


   using default_ops::eval_subtract;

   if(result == &r)
   {
      CppInt1 rem;
      divide_unsigned_helper(result, x, y, rem);
      r = rem;
      return;
   }

   //
   // Find the most significant words of numerator and denominator.
   //
   limb_type y_order = y.size() - 1;

   if(y_order == 0)
   {
      //
      // Only a single non-zero limb in the denominator, in this case
      // we can use a specialized divide-by-single-limb routine which is
      // much faster.  This also handles division by zero:
      //
      divide_unsigned_helper(result, x, y.limbs()[y_order], r);
      return;
   }

   typename CppInt2::const_limb_pointer px = x.limbs();
   typename CppInt3::const_limb_pointer py = y.limbs();

   limb_type r_order = x.size() - 1;
   if((r_order == 0) && (*px == 0))
   {
      // x is zero, so is the result:
      r = x;
      if(result)
         *result = x;
      return;
   }

   r = x;
   r.sign(false);
   if(result)
      *result = static_cast<limb_type>(0u);
   //
   // Check if the remainder is already less than the divisor, if so
   // we already have the result.  Note we try and avoid a full compare
   // if we can:
   //
   if(r_order <= y_order)
   {
      if((r_order < y_order) || (r.compare_unsigned(y) < 0))
      {
         return;
      }
   }

   CppInt1 t;
   bool r_neg = false;

   //
   // See if we can short-circuit long division, and use basic arithmetic instead:
   //
//.........这里部分代码省略.........

void eval_exp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> &arg)
{
   //
   // This is based on MPFR's method, let:
   //
   // n = floor(x / ln(2))
   //
   // Then:
   //
   // r = x - n ln(2) : 0 <= r < ln(2)
   //
   // We can reduce r further by dividing by 2^k, with k ~ sqrt(n),
   // so if:
   //
   // e0 = exp(r / 2^k) - 1
   //
   // With e0 evaluated by taylor series for small arguments, then:
   //
   // exp(x) = 2^n (1 + e0)^2^k
   //
   // Note that to preserve precision we actually square (1 + e0) k times, calculating
   // the result less one each time, i.e.
   //
   // (1 + e0)^2 - 1 = e0^2 + 2e0
   //
   // Then add the final 1 at the end, given that e0 is small, this effectively wipes
   // out the error in the last step.
   //
   using default_ops::eval_multiply;
   using default_ops::eval_subtract;
   using default_ops::eval_add;
   using default_ops::eval_convert_to;

   int type = eval_fpclassify(arg);
   bool isneg = eval_get_sign(arg) < 0;
   if(type == (int)FP_NAN)
   {
      res = arg;
      errno = EDOM;
      return;
   }
   else if(type == (int)FP_INFINITE)
   {
      res = arg;
      if(isneg)
         res = limb_type(0u);
      else
         res = arg;
      return;
   }
   else if(type == (int)FP_ZERO)
   {
      res = limb_type(1);
      return;
   }
   cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> t, n;
   if(isneg)
   {
      t = arg;
      t.negate();
      eval_exp(res, t);
      t.swap(res);
      res = limb_type(1);
      eval_divide(res, t);
      return;
   }

   eval_divide(n, arg, default_ops::get_constant_ln2<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >());
   eval_floor(n, n);
   eval_multiply(t, n, default_ops::get_constant_ln2<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >());
   eval_subtract(t, arg);
   t.negate();
   if(eval_get_sign(t) < 0)
   {
      // There are some very rare cases where arg/ln2 is an integer, and the subsequent multiply
      // rounds up, in that situation t ends up negative at this point which breaks our invariants below:
      t = limb_type(0);
   }

   Exponent k, nn;
   eval_convert_to(&nn, n);

   if (nn == (std::numeric_limits<Exponent>::max)())
   {
      // The result will necessarily oveflow:
      res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
      return;
   }

   BOOST_ASSERT(t.compare(default_ops::get_constant_ln2<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >()) < 0);

   k = nn ? Exponent(1) << (msb(nn) / 2) : 0;
   eval_ldexp(t, t, -k);

   eval_exp_taylor(res, t);
   //
   // Square 1 + res k times:
   //
   for(int s = 0; s < k; ++s)
   {
//.........这里部分代码省略.........

std::string convert_to_string(Backend b, std::streamsize digits, std::ios_base::fmtflags f)
{
   using default_ops::eval_log10;
   using default_ops::eval_floor;
   using default_ops::eval_pow;
   using default_ops::eval_convert_to;
   using default_ops::eval_multiply;
   using default_ops::eval_divide;
   using default_ops::eval_subtract;
   using default_ops::eval_fpclassify;

   typedef typename mpl::front<typename Backend::unsigned_types>::type ui_type;
   typedef typename Backend::exponent_type exponent_type;

   std::string result;
   bool iszero = false;
   bool isneg = false;
   exponent_type expon = 0;
   std::streamsize org_digits = digits;
   BOOST_ASSERT(digits > 0);

   int fpt = eval_fpclassify(b);

   if(fpt == (int)FP_ZERO)
   {
      result = "0";
      iszero = true;
   }
   else if(fpt == (int)FP_INFINITE)
   {
      if(b.compare(ui_type(0)) < 0)
         return "-inf";
      else
         return ((f & std::ios_base::showpos) == std::ios_base::showpos) ? "+inf" : "inf";
   }
   else if(fpt == (int)FP_NAN)
   {
      return "nan";
   }
   else
   {
      //
      // Start by figuring out the exponent:
      //
      isneg = b.compare(ui_type(0)) < 0;
      if(isneg)
         b.negate();
      Backend t;
      Backend ten;
      ten = ui_type(10);

      eval_log10(t, b);
      eval_floor(t, t);
      eval_convert_to(&expon, t);
      if(-expon > std::numeric_limits<number<Backend> >::max_exponent10 - 3)
      {
         int e = -expon / 2;
         Backend t2;
         eval_pow(t2, ten, e);
         eval_multiply(t, t2, b);
         eval_multiply(t, t2);
         if(expon & 1)
            eval_multiply(t, ten);
      }
      else
      {
         eval_pow(t, ten, -expon);
         eval_multiply(t, b);
      }
      //
      // Make sure we're between [1,10) and adjust if not:
      //
      if(t.compare(ui_type(1)) < 0)
      {
         eval_multiply(t, ui_type(10));
         --expon;
      }
      else if(t.compare(ui_type(10)) >= 0)
      {
         eval_divide(t, ui_type(10));
         ++expon;
      }
      Backend digit;
      ui_type cdigit;
      //
      // Adjust the number of digits required based on formatting options:
      //
      if(((f & std::ios_base::fixed) == std::ios_base::fixed) && (expon != -1))
         digits += expon + 1;
      if((f & std::ios_base::scientific) == std::ios_base::scientific)
         ++digits;
      //
      // Extract the digits one at a time:
      //
      for(unsigned i = 0; i < digits; ++i)
      {
         eval_floor(digit, t);
         eval_convert_to(&cdigit, digit);
         result += static_cast<char>('0' + cdigit);
         eval_subtract(t, digit);
//.........这里部分代码省略.........