ceph/src/boost/libs/multiprecision/test/test_arithmetic.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 #ifdef TEST_VLD
   7 #include <vld.h>
   8 #endif
   9
  10 #include <boost/math/special_functions/pow.hpp>
  11 #include <boost/integer/common_factor_rt.hpp>
  12 #include <boost/functional/hash.hpp>
  13 #include <functional>
  14 #include "test.hpp"
  15
  16 template <class T>
  17 struct is_boost_rational : public boost::mpl::false_
  18 {};
  19 template <class T>
  20 struct is_checked_cpp_int : public boost::mpl::false_
  21 {};
  22
  23 #ifdef BOOST_MSVC
  24 // warning C4127: conditional expression is constant
  25 #pragma warning(disable : 4127)
  26 #endif
  27
  28 template <class Target, class Source>
  29 Target checked_lexical_cast(const Source& val)
  30 {
  31 #ifndef BOOST_NO_EXCEPTIONS
  32    try
  33    {
  34 #endif
  35       return boost::lexical_cast<Target>(val);
  36 #ifndef BOOST_NO_EXCEPTIONS
  37    }
  38    catch (...)
  39    {
  40       std::cerr << "Error in lexical cast\nSource type = " << typeid(Source).name() << " \"" << val << "\"\n";
  41       std::cerr << "Target type = " << typeid(Target).name() << std::endl;
  42       throw;
  43    }
  44 #endif
  45 }
  46
  47 bool isfloat(float) { return true; }
  48 bool isfloat(double) { return true; }
  49 bool isfloat(long double) { return true; }
  50 template <class T>
  51 bool isfloat(T) { return false; }
  52
  53 namespace detail {
  54
  55 template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
  56 typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type
  57 abs(boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4> const& v)
  58 {
  59    typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type result_type;
  60    return v < 0 ? result_type(-v) : result_type(v);
  61 }
  62
  63 } // namespace detail
  64
  65 template <class T>
  66 struct is_twos_complement_integer : public boost::mpl::true_
  67 {};
  68
  69 template <class T>
  70 struct related_type
  71 {
  72    typedef T type;
  73 };
  74
  75 template <class Real, class Val>
  76 void test_comparisons(Val, Val, const boost::mpl::false_)
  77 {}
  78
  79 int normalize_compare_result(int r)
  80 {
  81    return r > 0 ? 1 : r < 0 ? -1 : 0;
  82 }
  83
  84 template <class Real, class Val>
  85 typename boost::disable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type
  86 test_comparisons(Val a, Val b, const boost::mpl::true_)
  87 {
  88    Real r1(a);
  89    Real r2(b);
  90    Real z(1);
  91
  92    int cr = a < b ? -1 : a > b ? 1 : 0;
  93
  94    BOOST_CHECK_EQUAL(r1 == r2, a == b);
  95    BOOST_CHECK_EQUAL(r1 != r2, a != b);
  96    BOOST_CHECK_EQUAL(r1 <= r2, a <= b);
  97    BOOST_CHECK_EQUAL(r1 < r2, a < b);
  98    BOOST_CHECK_EQUAL(r1 >= r2, a >= b);
  99    BOOST_CHECK_EQUAL(r1 > r2, a > b);
 100
 101    BOOST_CHECK_EQUAL(r1 == b, a == b);
 102    BOOST_CHECK_EQUAL(r1 != b, a != b);
 103    BOOST_CHECK_EQUAL(r1 <= b, a <= b);
 104    BOOST_CHECK_EQUAL(r1 < b, a < b);
 105    BOOST_CHECK_EQUAL(r1 >= b, a >= b);
 106    BOOST_CHECK_EQUAL(r1 > b, a > b);
 107
 108    BOOST_CHECK_EQUAL(a == r2, a == b);
 109    BOOST_CHECK_EQUAL(a != r2, a != b);
 110    BOOST_CHECK_EQUAL(a <= r2, a <= b);
 111    BOOST_CHECK_EQUAL(a < r2, a < b);
 112    BOOST_CHECK_EQUAL(a >= r2, a >= b);
 113    BOOST_CHECK_EQUAL(a > r2, a > b);
 114
 115    BOOST_CHECK_EQUAL(r1 * z == r2, a == b);
 116    BOOST_CHECK_EQUAL(r1 * z != r2, a != b);
 117    BOOST_CHECK_EQUAL(r1 * z <= r2, a <= b);
 118    BOOST_CHECK_EQUAL(r1 * z < r2, a < b);
 119    BOOST_CHECK_EQUAL(r1 * z >= r2, a >= b);
 120    BOOST_CHECK_EQUAL(r1 * z > r2, a > b);
 121
 122    BOOST_CHECK_EQUAL(r1 == r2 * z, a == b);
 123    BOOST_CHECK_EQUAL(r1 != r2 * z, a != b);
 124    BOOST_CHECK_EQUAL(r1 <= r2 * z, a <= b);
 125    BOOST_CHECK_EQUAL(r1 < r2 * z, a < b);
 126    BOOST_CHECK_EQUAL(r1 >= r2 * z, a >= b);
 127    BOOST_CHECK_EQUAL(r1 > r2 * z, a > b);
 128
 129    BOOST_CHECK_EQUAL(r1 * z == r2 * z, a == b);
 130    BOOST_CHECK_EQUAL(r1 * z != r2 * z, a != b);
 131    BOOST_CHECK_EQUAL(r1 * z <= r2 * z, a <= b);
 132    BOOST_CHECK_EQUAL(r1 * z < r2 * z, a < b);
 133    BOOST_CHECK_EQUAL(r1 * z >= r2 * z, a >= b);
 134    BOOST_CHECK_EQUAL(r1 * z > r2 * z, a > b);
 135
 136    BOOST_CHECK_EQUAL(r1 * z == b, a == b);
 137    BOOST_CHECK_EQUAL(r1 * z != b, a != b);
 138    BOOST_CHECK_EQUAL(r1 * z <= b, a <= b);
 139    BOOST_CHECK_EQUAL(r1 * z < b, a < b);
 140    BOOST_CHECK_EQUAL(r1 * z >= b, a >= b);
 141    BOOST_CHECK_EQUAL(r1 * z > b, a > b);
 142
 143    BOOST_CHECK_EQUAL(a == r2 * z, a == b);
 144    BOOST_CHECK_EQUAL(a != r2 * z, a != b);
 145    BOOST_CHECK_EQUAL(a <= r2 * z, a <= b);
 146    BOOST_CHECK_EQUAL(a < r2 * z, a < b);
 147    BOOST_CHECK_EQUAL(a >= r2 * z, a >= b);
 148    BOOST_CHECK_EQUAL(a > r2 * z, a > b);
 149
 150    BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), cr);
 151    BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), -cr);
 152    BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), cr);
 153    BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), -cr);
 154 }
 155
 156 template <class Real, class Val>
 157 typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type
 158 test_comparisons(Val a, Val b, const boost::mpl::true_)
 159 {
 160    Real r1(a);
 161    Real r2(b);
 162    Real z(1);
 163
 164    int cr = a < b ? -1 : a > b ? 1 : 0;
 165    (void)cr;
 166
 167    BOOST_CHECK_EQUAL(r1 == r2, a == b);
 168    BOOST_CHECK_EQUAL(r1 != r2, a != b);
 169
 170    BOOST_CHECK_EQUAL(r1 == b, a == b);
 171    BOOST_CHECK_EQUAL(r1 != b, a != b);
 172
 173    BOOST_CHECK_EQUAL(a == r2, a == b);
 174    BOOST_CHECK_EQUAL(a != r2, a != b);
 175
 176    BOOST_CHECK_EQUAL(r1 * z == r2, a == b);
 177    BOOST_CHECK_EQUAL(r1 * z != r2, a != b);
 178
 179    BOOST_CHECK_EQUAL(r1 == r2 * z, a == b);
 180    BOOST_CHECK_EQUAL(r1 != r2 * z, a != b);
 181
 182    BOOST_CHECK_EQUAL(r1 * z == r2 * z, a == b);
 183    BOOST_CHECK_EQUAL(r1 * z != r2 * z, a != b);
 184
 185    BOOST_CHECK_EQUAL(r1 * z == b, a == b);
 186    BOOST_CHECK_EQUAL(r1 * z != b, a != b);
 187
 188    BOOST_CHECK_EQUAL(a == r2 * z, a == b);
 189    BOOST_CHECK_EQUAL(a != r2 * z, a != b);
 190
 191    if (r1 == r2)
 192    {
 193       BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), 0);
 194       BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), 0);
 195       BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), 0);
 196       BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), 0);
 197    }
 198    else
 199    {
 200       BOOST_CHECK_NE(normalize_compare_result(r1.compare(r2)), 0);
 201       BOOST_CHECK_NE(normalize_compare_result(r2.compare(r1)), 0);
 202       BOOST_CHECK_NE(normalize_compare_result(r1.compare(b)), 0);
 203       BOOST_CHECK_NE(normalize_compare_result(r2.compare(a)), 0);
 204    }
 205 }
 206
 207 template <class Real, class Exp>
 208 void test_conditional(Real v, Exp e)
 209 {
 210    //
 211    // Verify that Exp is usable in Boolean contexts, and has the same value as v:
 212    //
 213    if (e)
 214    {
 215       BOOST_CHECK(v);
 216    }
 217    else
 218    {
 219       BOOST_CHECK(!v);
 220    }
 221    if (!e)
 222    {
 223       BOOST_CHECK(!v);
 224    }
 225    else
 226    {
 227       BOOST_CHECK(v);
 228    }
 229 }
 230
 231 template <class Real>
 232 void test_complement(Real a, Real b, Real c, const boost::mpl::true_&)
 233 {
 234    int i         = 1020304;
 235    int j         = 56789123;
 236    int sign_mask = ~0;
 237    if (std::numeric_limits<Real>::is_signed)
 238    {
 239       BOOST_CHECK_EQUAL(~a, (~i & sign_mask));
 240       c = a & ~b;
 241       BOOST_CHECK_EQUAL(c, (i & (~j & sign_mask)));
 242       c = ~(a | b);
 243       BOOST_CHECK_EQUAL(c, (~(i | j) & sign_mask));
 244    }
 245    else
 246    {
 247       BOOST_CHECK_EQUAL((~a & a), 0);
 248    }
 249 }
 250
 251 template <class Real>
 252 void test_complement(Real, Real, Real, const boost::mpl::false_&)
 253 {
 254 }
 255
 256 template <class Real, class T>
 257 void test_integer_ops(const T&) {}
 258
 259 template <class Real>
 260 void test_rational(const boost::mpl::true_&)
 261 {
 262    Real a(2);
 263    a /= 3;
 264    BOOST_CHECK_EQUAL(numerator(a), 2);
 265    BOOST_CHECK_EQUAL(denominator(a), 3);
 266    Real b(4);
 267    b /= 6;
 268    BOOST_CHECK_EQUAL(a, b);
 269
 270    //
 271    // Check IO code:
 272    //
 273    std::stringstream ss;
 274    ss << a;
 275    ss >> b;
 276    BOOST_CHECK_EQUAL(a, b);
 277 }
 278
 279 template <class Real>
 280 void test_rational(const boost::mpl::false_&)
 281 {
 282    Real a(2);
 283    a /= 3;
 284    BOOST_CHECK_EQUAL(numerator(a), 2);
 285    BOOST_CHECK_EQUAL(denominator(a), 3);
 286    Real b(4);
 287    b /= 6;
 288    BOOST_CHECK_EQUAL(a, b);
 289
 290 #ifndef BOOST_NO_EXCEPTIONS
 291    BOOST_CHECK_THROW(Real(a / 0), std::overflow_error);
 292    BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
 293 #endif
 294    b = Real("2/3");
 295    BOOST_CHECK_EQUAL(a, b);
 296    //
 297    // Check IO code:
 298    //
 299    std::stringstream ss;
 300    ss << a;
 301    ss >> b;
 302    BOOST_CHECK_EQUAL(a, b);
 303 }
 304
 305 template <class Real>
 306 void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&)
 307 {
 308    test_rational<Real>(is_boost_rational<Real>());
 309 }
 310
 311 template <class Real>
 312 void test_signed_integer_ops(const boost::mpl::true_&)
 313 {
 314    Real a(20);
 315    Real b(7);
 316    Real c(5);
 317    BOOST_CHECK_EQUAL(-a % c, 0);
 318    BOOST_CHECK_EQUAL(-a % b, -20 % 7);
 319    BOOST_CHECK_EQUAL(-a % -b, -20 % -7);
 320    BOOST_CHECK_EQUAL(a % -b, 20 % -7);
 321    BOOST_CHECK_EQUAL(-a % 7, -20 % 7);
 322    BOOST_CHECK_EQUAL(-a % -7, -20 % -7);
 323    BOOST_CHECK_EQUAL(a % -7, 20 % -7);
 324    BOOST_CHECK_EQUAL(-a % 7u, -20 % 7);
 325    BOOST_CHECK_EQUAL(-a % a, 0);
 326    BOOST_CHECK_EQUAL(-a % 5, 0);
 327    BOOST_CHECK_EQUAL(-a % -5, 0);
 328    BOOST_CHECK_EQUAL(a % -5, 0);
 329
 330    b = -b;
 331    BOOST_CHECK_EQUAL(a % b, 20 % -7);
 332    a = -a;
 333    BOOST_CHECK_EQUAL(a % b, -20 % -7);
 334    BOOST_CHECK_EQUAL(a % -7, -20 % -7);
 335    b = 7;
 336    BOOST_CHECK_EQUAL(a % b, -20 % 7);
 337    BOOST_CHECK_EQUAL(a % 7, -20 % 7);
 338    BOOST_CHECK_EQUAL(a % 7u, -20 % 7);
 339
 340    a = 20;
 341    a %= b;
 342    BOOST_CHECK_EQUAL(a, 20 % 7);
 343    a = -20;
 344    a %= b;
 345    BOOST_CHECK_EQUAL(a, -20 % 7);
 346    a = 20;
 347    a %= -b;
 348    BOOST_CHECK_EQUAL(a, 20 % -7);
 349    a = -20;
 350    a %= -b;
 351    BOOST_CHECK_EQUAL(a, -20 % -7);
 352    a = 5;
 353    a %= b - a;
 354    BOOST_CHECK_EQUAL(a, 5 % (7 - 5));
 355    a = -20;
 356    a %= 7;
 357    BOOST_CHECK_EQUAL(a, -20 % 7);
 358    a = 20;
 359    a %= -7;
 360    BOOST_CHECK_EQUAL(a, 20 % -7);
 361    a = -20;
 362    a %= -7;
 363    BOOST_CHECK_EQUAL(a, -20 % -7);
 364 #ifndef BOOST_NO_LONG_LONG
 365    a = -20;
 366    a %= 7uLL;
 367    BOOST_CHECK_EQUAL(a, -20 % 7);
 368    a = 20;
 369    a %= -7LL;
 370    BOOST_CHECK_EQUAL(a, 20 % -7);
 371    a = -20;
 372    a %= -7LL;
 373    BOOST_CHECK_EQUAL(a, -20 % -7);
 374 #endif
 375    a = 400;
 376    b = 45;
 377    BOOST_CHECK_EQUAL(gcd(a, -45), boost::integer::gcd(400, 45));
 378    BOOST_CHECK_EQUAL(lcm(a, -45), boost::integer::lcm(400, 45));
 379    BOOST_CHECK_EQUAL(gcd(-400, b), boost::integer::gcd(400, 45));
 380    BOOST_CHECK_EQUAL(lcm(-400, b), boost::integer::lcm(400, 45));
 381    a = -20;
 382    BOOST_CHECK_EQUAL(abs(a), 20);
 383    BOOST_CHECK_EQUAL(abs(-a), 20);
 384    BOOST_CHECK_EQUAL(abs(+a), 20);
 385    a = 20;
 386    BOOST_CHECK_EQUAL(abs(a), 20);
 387    BOOST_CHECK_EQUAL(abs(-a), 20);
 388    BOOST_CHECK_EQUAL(abs(+a), 20);
 389    a = -400;
 390    b = 45;
 391    BOOST_CHECK_EQUAL(gcd(a, b), boost::integer::gcd(-400, 45));
 392    BOOST_CHECK_EQUAL(lcm(a, b), boost::integer::lcm(-400, 45));
 393    BOOST_CHECK_EQUAL(gcd(a, 45), boost::integer::gcd(-400, 45));
 394    BOOST_CHECK_EQUAL(lcm(a, 45), boost::integer::lcm(-400, 45));
 395    BOOST_CHECK_EQUAL(gcd(-400, b), boost::integer::gcd(-400, 45));
 396    BOOST_CHECK_EQUAL(lcm(-400, b), boost::integer::lcm(-400, 45));
 397    Real r;
 398    divide_qr(a, b, c, r);
 399    BOOST_CHECK_EQUAL(c, a / b);
 400    BOOST_CHECK_EQUAL(r, a % b);
 401    BOOST_CHECK_EQUAL(integer_modulus(a, 57), abs(a % 57));
 402    b = -57;
 403    divide_qr(a, b, c, r);
 404    BOOST_CHECK_EQUAL(c, a / b);
 405    BOOST_CHECK_EQUAL(r, a % b);
 406    BOOST_CHECK_EQUAL(integer_modulus(a, -57), abs(a % -57));
 407    a = 458;
 408    divide_qr(a, b, c, r);
 409    BOOST_CHECK_EQUAL(c, a / b);
 410    BOOST_CHECK_EQUAL(r, a % b);
 411    BOOST_CHECK_EQUAL(integer_modulus(a, -57), abs(a % -57));
 412 #ifndef TEST_CHECKED_INT
 413    if (is_checked_cpp_int<Real>::value)
 414    {
 415       a = -1;
 416 #ifndef BOOST_NO_EXCEPTIONS
 417       BOOST_CHECK_THROW(a << 2, std::range_error);
 418       BOOST_CHECK_THROW(a >> 2, std::range_error);
 419       BOOST_CHECK_THROW(a <<= 2, std::range_error);
 420       BOOST_CHECK_THROW(a >>= 2, std::range_error);
 421 #endif
 422    }
 423    else
 424    {
 425       a = -1;
 426       BOOST_CHECK_EQUAL(a << 10, -1024);
 427       a = -23;
 428       BOOST_CHECK_EQUAL(a << 10, -23552);
 429       a = -23456;
 430       BOOST_CHECK_EQUAL(a >> 10, -23);
 431       a = -3;
 432       BOOST_CHECK_EQUAL(a >> 10, -1);
 433    }
 434 #endif
 435 }
 436 template <class Real>
 437 void test_signed_integer_ops(const boost::mpl::false_&)
 438 {
 439 }
 440
 441 template <class Real>
 442 inline Real negate_if_signed(Real r, const boost::mpl::bool_<true>&)
 443 {
 444    return -r;
 445 }
 446 template <class Real>
 447 inline Real negate_if_signed(Real r, const boost::mpl::bool_<false>&)
 448 {
 449    return r;
 450 }
 451
 452 template <class Real, class Int>
 453 void test_integer_overflow()
 454 {
 455    if (std::numeric_limits<Real>::digits > std::numeric_limits<Int>::digits)
 456    {
 457       Real m((std::numeric_limits<Int>::max)());
 458       Int  r;
 459       ++m;
 460       if (is_checked_cpp_int<Real>::value)
 461       {
 462          BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
 463       }
 464       else if (boost::is_signed<Int>::value)
 465       {
 466          r = m.template convert_to<Int>();
 467          BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::max)());
 468       }
 469       else
 470       {
 471          r = m.template convert_to<Int>();
 472          BOOST_CHECK_EQUAL(r, 0);
 473       }
 474       // Again with much larger value:
 475       m = 1u;
 476       m <<= (std::min)(std::numeric_limits<Real>::digits - 1, 1000);
 477       if (is_checked_cpp_int<Real>::value)
 478       {
 479          BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
 480       }
 481       else if (boost::is_signed<Int>::value)
 482       {
 483          r = m.template convert_to<Int>();
 484          BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::max)());
 485       }
 486       else
 487       {
 488          r = m.template convert_to<Int>();
 489          BOOST_CHECK_EQUAL(r, 0);
 490       }
 491
 492       if (std::numeric_limits<Real>::is_signed && (boost::is_signed<Int>::value))
 493       {
 494          m = (std::numeric_limits<Int>::min)();
 495          --m;
 496          if (is_checked_cpp_int<Real>::value)
 497          {
 498             BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
 499          }
 500          else
 501          {
 502             r = m.template convert_to<Int>();
 503             BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::min)());
 504          }
 505          // Again with much larger value:
 506          m = 2u;
 507          m = pow(m, (std::min)(std::numeric_limits<Real>::digits - 1, 1000));
 508          ++m;
 509          m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
 510          if (is_checked_cpp_int<Real>::value)
 511          {
 512             BOOST_CHECK_THROW(m.template convert_to<Int>(), std::overflow_error);
 513          }
 514          else
 515          {
 516             r = m.template convert_to<Int>();
 517             BOOST_CHECK_EQUAL(r, (std::numeric_limits<Int>::min)());
 518          }
 519       }
 520       else if (std::numeric_limits<Real>::is_signed && !boost::is_signed<Int>::value)
 521       {
 522          // signed to unsigned converison with overflow, it's really not clear what should happen here!
 523          m = (std::numeric_limits<Int>::max)();
 524          ++m;
 525          m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
 526          BOOST_CHECK_THROW(m.template convert_to<Int>(), std::range_error);
 527          // Again with much larger value:
 528          m = 2u;
 529          m = pow(m, (std::min)(std::numeric_limits<Real>::digits - 1, 1000));
 530          m = negate_if_signed(m, boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
 531          BOOST_CHECK_THROW(m.template convert_to<Int>(), std::range_error);
 532       }
 533    }
 534 }
 535
 536 template <class Real, class Int>
 537 void test_integer_round_trip()
 538 {
 539    if (std::numeric_limits<Real>::digits >= std::numeric_limits<Int>::digits)
 540    {
 541       Real m((std::numeric_limits<Int>::max)());
 542       Int  r = m.template convert_to<Int>();
 543       BOOST_CHECK_EQUAL(m, r);
 544       if (std::numeric_limits<Real>::is_signed && (std::numeric_limits<Real>::digits > std::numeric_limits<Int>::digits))
 545       {
 546          m = (std::numeric_limits<Int>::min)();
 547          r = m.template convert_to<Int>();
 548          BOOST_CHECK_EQUAL(m, r);
 549       }
 550    }
 551    test_integer_overflow<Real, Int>();
 552 }
 553
 554 template <class Real>
 555 void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&)
 556 {
 557    test_signed_integer_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
 558
 559    Real a(20);
 560    Real b(7);
 561    Real c(5);
 562    BOOST_CHECK_EQUAL(a % b, 20 % 7);
 563    BOOST_CHECK_EQUAL(a % 7, 20 % 7);
 564    BOOST_CHECK_EQUAL(a % 7u, 20 % 7);
 565    BOOST_CHECK_EQUAL(a % a, 0);
 566    BOOST_CHECK_EQUAL(a % c, 0);
 567    BOOST_CHECK_EQUAL(a % 5, 0);
 568    a = a % (b + 0);
 569    BOOST_CHECK_EQUAL(a, 20 % 7);
 570    a = 20;
 571    c = (a + 2) % (a - 1);
 572    BOOST_CHECK_EQUAL(c, 22 % 19);
 573    c = 5;
 574    a = b % (a - 15);
 575    BOOST_CHECK_EQUAL(a, 7 % 5);
 576    a = 20;
 577
 578    a = 20;
 579    a %= 7;
 580    BOOST_CHECK_EQUAL(a, 20 % 7);
 581 #ifndef BOOST_NO_LONG_LONG
 582    a = 20;
 583    a %= 7uLL;
 584    BOOST_CHECK_EQUAL(a, 20 % 7);
 585 #endif
 586    a = 20;
 587    ++a;
 588    BOOST_CHECK_EQUAL(a, 21);
 589    --a;
 590    BOOST_CHECK_EQUAL(a, 20);
 591    BOOST_CHECK_EQUAL(a++, 20);
 592    BOOST_CHECK_EQUAL(a, 21);
 593    BOOST_CHECK_EQUAL(a--, 21);
 594    BOOST_CHECK_EQUAL(a, 20);
 595    a = 2000;
 596    a <<= 20;
 597    BOOST_CHECK_EQUAL(a, 2000L << 20);
 598    a >>= 20;
 599    BOOST_CHECK_EQUAL(a, 2000);
 600    a <<= 20u;
 601    BOOST_CHECK_EQUAL(a, 2000L << 20);
 602    a >>= 20u;
 603    BOOST_CHECK_EQUAL(a, 2000);
 604 #ifndef BOOST_NO_EXCEPTIONS
 605    BOOST_CHECK_THROW(a <<= -20, std::out_of_range);
 606    BOOST_CHECK_THROW(a >>= -20, std::out_of_range);
 607    BOOST_CHECK_THROW(Real(a << -20), std::out_of_range);
 608    BOOST_CHECK_THROW(Real(a >> -20), std::out_of_range);
 609 #endif
 610 #ifndef BOOST_NO_LONG_LONG
 611    if (sizeof(long long) > sizeof(std::size_t))
 612    {
 613       // extreme values should trigger an exception:
 614 #ifndef BOOST_NO_EXCEPTIONS
 615       BOOST_CHECK_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 616       BOOST_CHECK_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 617       BOOST_CHECK_THROW(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 618       BOOST_CHECK_THROW(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 619       BOOST_CHECK_THROW(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 620       BOOST_CHECK_THROW(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
 621 #endif
 622       // Unless they fit within range:
 623       a = 2000L;
 624       a <<= 20uLL;
 625       BOOST_CHECK_EQUAL(a, (2000L << 20));
 626       a = 2000;
 627       a <<= 20LL;
 628       BOOST_CHECK_EQUAL(a, (2000L << 20));
 629
 630 #ifndef BOOST_NO_EXCEPTIONS
 631       BOOST_CHECK_THROW(Real(a >> (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 632       BOOST_CHECK_THROW(Real(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 633       BOOST_CHECK_THROW(Real(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 634       BOOST_CHECK_THROW(Real(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 635       BOOST_CHECK_THROW(Real(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 636       BOOST_CHECK_THROW(Real(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
 637 #endif
 638       // Unless they fit within range:
 639       a = 2000L;
 640       BOOST_CHECK_EQUAL(Real(a << 20uLL), (2000L << 20));
 641       a = 2000;
 642       BOOST_CHECK_EQUAL(Real(a << 20LL), (2000L << 20));
 643    }
 644 #endif
 645    a = 20;
 646    b = a << 20;
 647    BOOST_CHECK_EQUAL(b, (20 << 20));
 648    b = a >> 2;
 649    BOOST_CHECK_EQUAL(b, (20 >> 2));
 650    b = (a + 2) << 10;
 651    BOOST_CHECK_EQUAL(b, (22 << 10));
 652    b = (a + 3) >> 3;
 653    BOOST_CHECK_EQUAL(b, (23 >> 3));
 654    //
 655    // Bit fiddling:
 656    //
 657    int i = 1020304;
 658    int j = 56789123;
 659    int k = 4523187;
 660    a     = i;
 661    b     = j;
 662    c     = a;
 663    c &= b;
 664    BOOST_CHECK_EQUAL(c, (i & j));
 665    c = a;
 666    c &= j;
 667    BOOST_CHECK_EQUAL(c, (i & j));
 668    c = a;
 669    c &= a + b;
 670    BOOST_CHECK_EQUAL(c, (i & (i + j)));
 671    BOOST_CHECK_EQUAL((a & b), (i & j));
 672    c = k;
 673    a = a & (b + k);
 674    BOOST_CHECK_EQUAL(a, (i & (j + k)));
 675    a = i;
 676    a = (b + k) & a;
 677    BOOST_CHECK_EQUAL(a, (i & (j + k)));
 678    a = i;
 679    c = a & b & k;
 680    BOOST_CHECK_EQUAL(c, (i & j & k));
 681    c = a;
 682    c &= (c + b);
 683    BOOST_CHECK_EQUAL(c, (i & (i + j)));
 684    c = a & (b | 1);
 685    BOOST_CHECK_EQUAL(c, (i & (j | 1)));
 686
 687    test_complement<Real>(a, b, c, typename is_twos_complement_integer<Real>::type());
 688
 689    a = i;
 690    b = j;
 691    c = a;
 692    c |= b;
 693    BOOST_CHECK_EQUAL(c, (i | j));
 694    c = a;
 695    c |= j;
 696    BOOST_CHECK_EQUAL(c, (i | j));
 697    c = a;
 698    c |= a + b;
 699    BOOST_CHECK_EQUAL(c, (i | (i + j)));
 700    BOOST_CHECK_EQUAL((a | b), (i | j));
 701    c = k;
 702    a = a | (b + k);
 703    BOOST_CHECK_EQUAL(a, (i | (j + k)));
 704    a = i;
 705    a = (b + k) | a;
 706    BOOST_CHECK_EQUAL(a, (i | (j + k)));
 707    a = i;
 708    c = a | b | k;
 709    BOOST_CHECK_EQUAL(c, (i | j | k));
 710    c = a;
 711    c |= (c + b);
 712    BOOST_CHECK_EQUAL(c, (i | (i + j)));
 713    c = a | (b | 1);
 714    BOOST_CHECK_EQUAL(c, (i | (j | 1)));
 715
 716    a = i;
 717    b = j;
 718    c = a;
 719    c ^= b;
 720    BOOST_CHECK_EQUAL(c, (i ^ j));
 721    c = a;
 722    c ^= j;
 723    BOOST_CHECK_EQUAL(c, (i ^ j));
 724    c = a;
 725    c ^= a + b;
 726    BOOST_CHECK_EQUAL(c, (i ^ (i + j)));
 727    BOOST_CHECK_EQUAL((a ^ b), (i ^ j));
 728    c = k;
 729    a = a ^ (b + k);
 730    BOOST_CHECK_EQUAL(a, (i ^ (j + k)));
 731    a = i;
 732    a = (b + k) ^ a;
 733    BOOST_CHECK_EQUAL(a, (i ^ (j + k)));
 734    a = i;
 735    c = a ^ b ^ k;
 736    BOOST_CHECK_EQUAL(c, (i ^ j ^ k));
 737    c = a;
 738    c ^= (c + b);
 739    BOOST_CHECK_EQUAL(c, (i ^ (i + j)));
 740    c = a ^ (b | 1);
 741    BOOST_CHECK_EQUAL(c, (i ^ (j | 1)));
 742
 743    a = i;
 744    b = j;
 745    c = k;
 746    //
 747    // Non-member functions:
 748    //
 749    a = 400;
 750    b = 45;
 751    BOOST_CHECK_EQUAL(gcd(a, b), boost::integer::gcd(400, 45));
 752    BOOST_CHECK_EQUAL(lcm(a, b), boost::integer::lcm(400, 45));
 753    BOOST_CHECK_EQUAL(gcd(a, 45), boost::integer::gcd(400, 45));
 754    BOOST_CHECK_EQUAL(lcm(a, 45), boost::integer::lcm(400, 45));
 755    BOOST_CHECK_EQUAL(gcd(a, 45u), boost::integer::gcd(400, 45));
 756    BOOST_CHECK_EQUAL(lcm(a, 45u), boost::integer::lcm(400, 45));
 757    BOOST_CHECK_EQUAL(gcd(400, b), boost::integer::gcd(400, 45));
 758    BOOST_CHECK_EQUAL(lcm(400, b), boost::integer::lcm(400, 45));
 759    BOOST_CHECK_EQUAL(gcd(400u, b), boost::integer::gcd(400, 45));
 760    BOOST_CHECK_EQUAL(lcm(400u, b), boost::integer::lcm(400, 45));
 761
 762    //
 763    // Conditionals involving 2 arg functions:
 764    //
 765    test_conditional(Real(gcd(a, b)), gcd(a, b));
 766
 767    Real r;
 768    divide_qr(a, b, c, r);
 769    BOOST_CHECK_EQUAL(c, a / b);
 770    BOOST_CHECK_EQUAL(r, a % b);
 771    divide_qr(a + 0, b, c, r);
 772    BOOST_CHECK_EQUAL(c, a / b);
 773    BOOST_CHECK_EQUAL(r, a % b);
 774    divide_qr(a, b + 0, c, r);
 775    BOOST_CHECK_EQUAL(c, a / b);
 776    BOOST_CHECK_EQUAL(r, a % b);
 777    divide_qr(a + 0, b + 0, c, r);
 778    BOOST_CHECK_EQUAL(c, a / b);
 779    BOOST_CHECK_EQUAL(r, a % b);
 780    BOOST_CHECK_EQUAL(integer_modulus(a, 57), a % 57);
 781    for (i = 0; i < 20; ++i)
 782    {
 783       if (std::numeric_limits<Real>::is_specialized && (!std::numeric_limits<Real>::is_bounded || ((int)i * 17 < std::numeric_limits<Real>::digits)))
 784       {
 785          BOOST_CHECK_EQUAL(lsb(Real(1) << (i * 17)), static_cast<unsigned>(i * 17));
 786          BOOST_CHECK_EQUAL(msb(Real(1) << (i * 17)), static_cast<unsigned>(i * 17));
 787          BOOST_CHECK(bit_test(Real(1) << (i * 17), i * 17));
 788          BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 + 1));
 789          if (i)
 790          {
 791             BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 - 1));
 792          }
 793          Real zero(0);
 794          BOOST_CHECK(bit_test(bit_set(zero, i * 17), i * 17));
 795          zero = 0;
 796          BOOST_CHECK_EQUAL(bit_flip(zero, i * 17), Real(1) << i * 17);
 797          zero = Real(1) << i * 17;
 798          BOOST_CHECK_EQUAL(bit_flip(zero, i * 17), 0);
 799          zero = Real(1) << i * 17;
 800          BOOST_CHECK_EQUAL(bit_unset(zero, i * 17), 0);
 801       }
 802    }
 803    //
 804    // pow, powm:
 805    //
 806    BOOST_CHECK_EQUAL(pow(Real(3), 4u), 81);
 807    BOOST_CHECK_EQUAL(pow(Real(3) + Real(0), 4u), 81);
 808    BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13)), 81 % 13);
 809    BOOST_CHECK_EQUAL(powm(Real(3), Real(4), 13), 81 % 13);
 810    BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13) + 0), 81 % 13);
 811    BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13)), 81 % 13);
 812    BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, 13), 81 % 13);
 813    BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13) + 0), 81 % 13);
 814    BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13)), 81 % 13);
 815    BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, 13), 81 % 13);
 816    BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13) + 0), 81 % 13);
 817    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13)), 81 % 13);
 818    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), 13), 81 % 13);
 819    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13) + 0), 81 % 13);
 820    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13)), 81 % 13);
 821    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, 13), 81 % 13);
 822    BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13) + 0), 81 % 13);
 823    BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13)), 81 % 13);
 824    BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, 13), 81 % 13);
 825    BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13) + 0), 81 % 13);
 826    //
 827    // Conditionals involving 3 arg functions:
 828    //
 829    test_conditional(Real(powm(Real(3), Real(4), Real(13))), powm(Real(3), Real(4), Real(13)));
 830
 831 #ifndef BOOST_NO_EXCEPTIONS
 832    //
 833    // Things that are expected errors:
 834    //
 835    BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
 836    BOOST_CHECK_THROW(Real("3L"), std::runtime_error);
 837    BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error);
 838 #endif
 839    //
 840    // Extra tests added for full coverage:
 841    //
 842    a = 20;
 843    b = 7;
 844    c = 20 % b;
 845    BOOST_CHECK_EQUAL(c, (20 % 7));
 846    c = 20 % (b + 0);
 847    BOOST_CHECK_EQUAL(c, (20 % 7));
 848    c = a & 10;
 849    BOOST_CHECK_EQUAL(c, (20 & 10));
 850    c = 10 & a;
 851    BOOST_CHECK_EQUAL(c, (20 & 10));
 852    c = (a + 0) & (b + 0);
 853    BOOST_CHECK_EQUAL(c, (20 & 7));
 854    c = 10 & (a + 0);
 855    BOOST_CHECK_EQUAL(c, (20 & 10));
 856    c = 10 | a;
 857    BOOST_CHECK_EQUAL(c, (20 | 10));
 858    c = (a + 0) | (b + 0);
 859    BOOST_CHECK(c == (20 | 7))
 860    c = 20 | (b + 0);
 861    BOOST_CHECK_EQUAL(c, (20 | 7));
 862    c = a ^ 7;
 863    BOOST_CHECK_EQUAL(c, (20 ^ 7));
 864    c = 20 ^ b;
 865    BOOST_CHECK_EQUAL(c, (20 ^ 7));
 866    c = (a + 0) ^ (b + 0);
 867    BOOST_CHECK_EQUAL(c, (20 ^ 7));
 868    c = 20 ^ (b + 0);
 869    BOOST_CHECK_EQUAL(c, (20 ^ 7));
 870
 871    //
 872    // Round tripping of built in integers:
 873    //
 874    test_integer_round_trip<Real, short>();
 875    test_integer_round_trip<Real, unsigned short>();
 876    test_integer_round_trip<Real, int>();
 877    test_integer_round_trip<Real, unsigned int>();
 878    test_integer_round_trip<Real, long>();
 879    test_integer_round_trip<Real, unsigned long>();
 880 #ifndef BOOST_NO_CXX11_LONG_LONG
 881    test_integer_round_trip<Real, long long>();
 882    test_integer_round_trip<Real, unsigned long long>();
 883 #endif
 884 }
 885
 886 template <class Real, class T>
 887 void test_float_funcs(const T&) {}
 888
 889 template <class Real>
 890 void test_float_funcs(const boost::mpl::true_&)
 891 {
 892    if (boost::multiprecision::is_interval_number<Real>::value)
 893       return;
 894    //
 895    // Test variable reuse in function calls, see https://svn.boost.org/trac/boost/ticket/8326
 896    //
 897    Real a(2), b(10), c, d;
 898    a = pow(a, b);
 899    BOOST_CHECK_EQUAL(a, 1024);
 900    a = 2;
 901    b = pow(a, b);
 902    BOOST_CHECK_EQUAL(b, 1024);
 903    b = 10;
 904    a = pow(a, 10);
 905    BOOST_CHECK_EQUAL(a, 1024);
 906    a = -2;
 907    a = abs(a);
 908    BOOST_CHECK_EQUAL(a, 2);
 909    a = -2;
 910    a = fabs(a);
 911    BOOST_CHECK_EQUAL(a, 2);
 912    a = 2.5;
 913    a = floor(a);
 914    BOOST_CHECK_EQUAL(a, 2);
 915    a = 2.5;
 916    a = ceil(a);
 917    BOOST_CHECK_EQUAL(a, 3);
 918    a = 2.5;
 919    a = trunc(a);
 920    BOOST_CHECK_EQUAL(a, 2);
 921    a = 2.25;
 922    a = round(a);
 923    BOOST_CHECK_EQUAL(a, 2);
 924    a = 2;
 925    a = ldexp(a, 1);
 926    BOOST_CHECK_EQUAL(a, 4);
 927    int i;
 928    a = frexp(a, &i);
 929    BOOST_CHECK_EQUAL(a, 0.5);
 930
 931    Real tol = std::numeric_limits<Real>::epsilon() * 3;
 932    a        = 4;
 933    a        = sqrt(a);
 934    BOOST_CHECK_CLOSE_FRACTION(a, 2, tol);
 935    a = 3;
 936    a = exp(a);
 937    BOOST_CHECK_CLOSE_FRACTION(a, Real(exp(Real(3))), tol);
 938    a = 3;
 939    a = log(a);
 940    BOOST_CHECK_CLOSE_FRACTION(a, Real(log(Real(3))), tol);
 941    a = 3;
 942    a = log10(a);
 943    BOOST_CHECK_CLOSE_FRACTION(a, Real(log10(Real(3))), tol);
 944
 945    a = 0.5;
 946    a = sin(a);
 947    BOOST_CHECK_CLOSE_FRACTION(a, Real(sin(Real(0.5))), tol);
 948    a = 0.5;
 949    a = cos(a);
 950    BOOST_CHECK_CLOSE_FRACTION(a, Real(cos(Real(0.5))), tol);
 951    a = 0.5;
 952    a = tan(a);
 953    BOOST_CHECK_CLOSE_FRACTION(a, Real(tan(Real(0.5))), tol);
 954    a = 0.5;
 955    a = asin(a);
 956    BOOST_CHECK_CLOSE_FRACTION(a, Real(asin(Real(0.5))), tol);
 957    a = 0.5;
 958    a = acos(a);
 959    BOOST_CHECK_CLOSE_FRACTION(a, Real(acos(Real(0.5))), tol);
 960    a = 0.5;
 961    a = atan(a);
 962    BOOST_CHECK_CLOSE_FRACTION(a, Real(atan(Real(0.5))), tol);
 963    a = 0.5;
 964    a = sinh(a);
 965    BOOST_CHECK_CLOSE_FRACTION(a, Real(sinh(Real(0.5))), tol);
 966    a = 0.5;
 967    a = cosh(a);
 968    BOOST_CHECK_CLOSE_FRACTION(a, Real(cosh(Real(0.5))), tol);
 969    a = 0.5;
 970    a = tanh(a);
 971    BOOST_CHECK_CLOSE_FRACTION(a, Real(tanh(Real(0.5))), tol);
 972    // fmod, need to check all the sign permutations:
 973    a = 4;
 974    b = 2;
 975    a = fmod(a, b);
 976    BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), Real(2))), tol);
 977    a = 4;
 978    b = fmod(a, b);
 979    BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), Real(2))), tol);
 980    a = 4;
 981    b = 2;
 982    a = fmod(-a, b);
 983    BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(-Real(4), Real(2))), tol);
 984    a = 4;
 985    b = fmod(-a, b);
 986    BOOST_CHECK_CLOSE_FRACTION(b, Real(-fmod(Real(4), Real(2))), tol);
 987    a = 4;
 988    b = 2;
 989    a = fmod(a, -b);
 990    BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), -Real(2))), tol);
 991    a = 4;
 992    b = fmod(a, -b);
 993    BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), -Real(2))), tol);
 994    a = 4;
 995    b = 2;
 996    a = fmod(-a, -b);
 997    BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(-Real(4), -Real(2))), tol);
 998    a = 4;
 999    b = fmod(-a, -b);
1000    BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(-Real(4), -Real(2))), tol);
1001    // modf:
1002    a = 5;
1003    a /= 2;
1004    b = modf(a, &c);
1005    BOOST_CHECK_EQUAL(b + c, a);
1006    BOOST_CHECK_EQUAL(b > 0, a > 0);
1007    BOOST_CHECK_EQUAL(c > 0, a > 0);
1008    a = -a;
1009    b = modf(a, &c);
1010    BOOST_CHECK_EQUAL(b + c, a);
1011    BOOST_CHECK_EQUAL(b > 0, a > 0);
1012    BOOST_CHECK_EQUAL(c > 0, a > 0);
1013    b = modf(a, &c);
1014    c = 0;
1015    modf(a, &c);
1016    BOOST_CHECK_EQUAL(b + c, a);
1017    BOOST_CHECK_EQUAL(b > 0, a > 0);
1018    BOOST_CHECK_EQUAL(c > 0, a > 0);
1019    a = -a;
1020    b = modf(a, &c);
1021    c = 0;
1022    modf(a, &c);
1023    BOOST_CHECK_EQUAL(b + c, a);
1024    BOOST_CHECK_EQUAL(b > 0, a > 0);
1025    BOOST_CHECK_EQUAL(c > 0, a > 0);
1026
1027    if (std::numeric_limits<Real>::has_infinity)
1028    {
1029       a = std::numeric_limits<Real>::infinity();
1030       b = modf(a, &c);
1031       BOOST_CHECK_EQUAL(a, c);
1032       BOOST_CHECK_EQUAL(b, 0);
1033       a = -std::numeric_limits<Real>::infinity();
1034       b = modf(a, &c);
1035       BOOST_CHECK_EQUAL(a, c);
1036       BOOST_CHECK_EQUAL(b, 0);
1037    }
1038    if (std::numeric_limits<Real>::has_quiet_NaN)
1039    {
1040       a = std::numeric_limits<Real>::quiet_NaN();
1041       b = modf(a, &c);
1042       BOOST_CHECK((boost::math::isnan)(b));
1043       BOOST_CHECK((boost::math::isnan)(c));
1044    }
1045
1046    a = 4;
1047    b = 2;
1048    a = atan2(a, b);
1049    BOOST_CHECK_CLOSE_FRACTION(a, Real(atan2(Real(4), Real(2))), tol);
1050    a = 4;
1051    b = atan2(a, b);
1052    BOOST_CHECK_CLOSE_FRACTION(b, Real(atan2(Real(4), Real(2))), tol);
1053
1054    // fma:
1055    a = 2;
1056    b = 4;
1057    c = 6;
1058    BOOST_CHECK_EQUAL(fma(a, b, c), 14);
1059    BOOST_CHECK_EQUAL(fma(a, 4, c), 14);
1060    BOOST_CHECK_EQUAL(fma(a, b, 6), 14);
1061    BOOST_CHECK_EQUAL(fma(a, 4, 6), 14);
1062    BOOST_CHECK_EQUAL(fma(a + 0, b, c), 14);
1063    BOOST_CHECK_EQUAL(fma(a - 0, 4, c), 14);
1064    BOOST_CHECK_EQUAL(fma(a * 1, b, 6), 14);
1065    BOOST_CHECK_EQUAL(fma(a / 1, 4, 6), 14);
1066    BOOST_CHECK_EQUAL(fma(2, b, c), 14);
1067    BOOST_CHECK_EQUAL(fma(2, b, 6), 14);
1068    BOOST_CHECK_EQUAL(fma(2, b * 1, c), 14);
1069    BOOST_CHECK_EQUAL(fma(2, b + 0, 6), 14);
1070    BOOST_CHECK_EQUAL(fma(2, 4, c), 14);
1071    BOOST_CHECK_EQUAL(fma(2, 4, c + 0), 14);
1072
1073    // Default construct, for consistency with native floats, default constructed values are zero:
1074    Real zero;
1075    BOOST_CHECK_EQUAL(zero, 0);
1076
1077    //
1078    // Complex number functions on scalars:
1079    //
1080    a = 40;
1081    BOOST_CHECK_EQUAL(Real(arg(a)), 0);
1082    BOOST_CHECK_EQUAL(Real(arg(a + 0)), 0);
1083    a - 20;
1084    BOOST_CHECK_EQUAL(Real(arg(a)), 0);
1085    BOOST_CHECK_EQUAL(Real(arg(a - 20)), 0);
1086 }
1087
1088 template <class T, class U>
1089 void compare_NaNs(const T& a, const U& b)
1090 {
1091    BOOST_CHECK_EQUAL(a == b, false);
1092    BOOST_CHECK_EQUAL(a != b, true);
1093    BOOST_CHECK_EQUAL(a <= b, false);
1094    BOOST_CHECK_EQUAL(a >= b, false);
1095    BOOST_CHECK_EQUAL(a > b, false);
1096    BOOST_CHECK_EQUAL(a < b, false);
1097    //
1098    // Again where LHS may be an expression template:
1099    //
1100    BOOST_CHECK_EQUAL(1 * a == b, false);
1101    BOOST_CHECK_EQUAL(1 * a != b, true);
1102    BOOST_CHECK_EQUAL(1 * a <= b, false);
1103    BOOST_CHECK_EQUAL(1 * a >= b, false);
1104    BOOST_CHECK_EQUAL(1 * a > b, false);
1105    BOOST_CHECK_EQUAL(1 * a < b, false);
1106    //
1107    // Again where RHS may be an expression template:
1108    //
1109    BOOST_CHECK_EQUAL(a == b * 1, false);
1110    BOOST_CHECK_EQUAL(a != b * 1, true);
1111    BOOST_CHECK_EQUAL(a <= b * 1, false);
1112    BOOST_CHECK_EQUAL(a >= b * 1, false);
1113    BOOST_CHECK_EQUAL(a > b * 1, false);
1114    BOOST_CHECK_EQUAL(a < b * 1, false);
1115    //
1116    // Again where LHS and RHS may be an expression templates:
1117    //
1118    BOOST_CHECK_EQUAL(1 * a == b * 1, false);
1119    BOOST_CHECK_EQUAL(1 * a != b * 1, true);
1120    BOOST_CHECK_EQUAL(1 * a <= b * 1, false);
1121    BOOST_CHECK_EQUAL(1 * a >= b * 1, false);
1122    BOOST_CHECK_EQUAL(1 * a > b * 1, false);
1123    BOOST_CHECK_EQUAL(1 * a < b * 1, false);
1124 }
1125
1126 template <class Real, class T>
1127 void test_float_ops(const T&) {}
1128
1129 template <class Real>
1130 void test_float_ops(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&)
1131 {
1132    BOOST_CHECK_EQUAL(abs(Real(2)), 2);
1133    BOOST_CHECK_EQUAL(abs(Real(-2)), 2);
1134    BOOST_CHECK_EQUAL(fabs(Real(2)), 2);
1135    BOOST_CHECK_EQUAL(fabs(Real(-2)), 2);
1136    BOOST_CHECK_EQUAL(floor(Real(5) / 2), 2);
1137    BOOST_CHECK_EQUAL(ceil(Real(5) / 2), 3);
1138    BOOST_CHECK_EQUAL(floor(Real(-5) / 2), -3);
1139    BOOST_CHECK_EQUAL(ceil(Real(-5) / 2), -2);
1140    BOOST_CHECK_EQUAL(trunc(Real(5) / 2), 2);
1141    BOOST_CHECK_EQUAL(trunc(Real(-5) / 2), -2);
1142    //
1143    // ldexp and frexp, these pretty much have to be implemented by each backend:
1144    //
1145    typedef typename Real::backend_type::exponent_type e_type;
1146    BOOST_CHECK_EQUAL(ldexp(Real(2), 5), 64);
1147    BOOST_CHECK_EQUAL(ldexp(Real(2), -5), Real(2) / 32);
1148    Real   v(512);
1149    e_type exponent;
1150    Real   r = frexp(v, &exponent);
1151    BOOST_CHECK_EQUAL(r, 0.5);
1152    BOOST_CHECK_EQUAL(exponent, 10);
1153    BOOST_CHECK_EQUAL(v, 512);
1154    v = 1 / v;
1155    r = frexp(v, &exponent);
1156    BOOST_CHECK_EQUAL(r, 0.5);
1157    BOOST_CHECK_EQUAL(exponent, -8);
1158    BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(5)), 64);
1159    BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(-5)), Real(2) / 32);
1160    v = 512;
1161    e_type exp2;
1162    r = frexp(v, &exp2);
1163    BOOST_CHECK_EQUAL(r, 0.5);
1164    BOOST_CHECK_EQUAL(exp2, 10);
1165    BOOST_CHECK_EQUAL(v, 512);
1166    v = 1 / v;
1167    r = frexp(v, &exp2);
1168    BOOST_CHECK_EQUAL(r, 0.5);
1169    BOOST_CHECK_EQUAL(exp2, -8);
1170    //
1171    // scalbn and logb, these are the same as ldexp and frexp unless the radix is
1172    // something other than 2:
1173    //
1174    if (std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::radix)
1175    {
1176       BOOST_CHECK_EQUAL(scalbn(Real(2), 5), 2 * pow(double(std::numeric_limits<Real>::radix), 5));
1177       BOOST_CHECK_EQUAL(scalbn(Real(2), -5), Real(2) / pow(double(std::numeric_limits<Real>::radix), 5));
1178       v        = 512;
1179       exponent = ilogb(v);
1180       r        = scalbn(v, -exponent);
1181       BOOST_CHECK(r >= 1);
1182       BOOST_CHECK(r < std::numeric_limits<Real>::radix);
1183       BOOST_CHECK_EQUAL(exponent, logb(v));
1184       BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
1185       v        = 1 / v;
1186       exponent = ilogb(v);
1187       r        = scalbn(v, -exponent);
1188       BOOST_CHECK(r >= 1);
1189       BOOST_CHECK(r < std::numeric_limits<Real>::radix);
1190       BOOST_CHECK_EQUAL(exponent, logb(v));
1191       BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
1192    }
1193    //
1194    // pow and exponent:
1195    //
1196    v = 3.25;
1197    r = pow(v, 0);
1198    BOOST_CHECK_EQUAL(r, 1);
1199    r = pow(v, 1);
1200    BOOST_CHECK_EQUAL(r, 3.25);
1201    r = pow(v, 2);
1202    BOOST_CHECK_EQUAL(r, boost::math::pow<2>(3.25));
1203    r = pow(v, 3);
1204    BOOST_CHECK_EQUAL(r, boost::math::pow<3>(3.25));
1205    r = pow(v, 4);
1206    BOOST_CHECK_EQUAL(r, boost::math::pow<4>(3.25));
1207    r = pow(v, 5);
1208    BOOST_CHECK_EQUAL(r, boost::math::pow<5>(3.25));
1209    r = pow(v, 6);
1210    BOOST_CHECK_EQUAL(r, boost::math::pow<6>(3.25));
1211    r = pow(v, 25);
1212    BOOST_CHECK_EQUAL(r, boost::math::pow<25>(Real(3.25)));
1213
1214 #ifndef BOOST_NO_EXCEPTIONS
1215    //
1216    // Things that are expected errors:
1217    //
1218    BOOST_CHECK_THROW(Real("3.14L"), std::runtime_error);
1219    if (std::numeric_limits<Real>::is_specialized)
1220    {
1221       if (std::numeric_limits<Real>::has_infinity)
1222       {
1223          BOOST_CHECK((boost::math::isinf)(Real(20) / 0u));
1224       }
1225       else
1226       {
1227          BOOST_CHECK_THROW(r = Real(Real(20) / 0u), std::overflow_error);
1228       }
1229    }
1230 #endif
1231    //
1232    // Comparisons of NaN's should always fail:
1233    //
1234    if (std::numeric_limits<Real>::has_quiet_NaN)
1235    {
1236       r = v = std::numeric_limits<Real>::quiet_NaN();
1237       compare_NaNs(r, v);
1238       v = 0;
1239       compare_NaNs(r, v);
1240       r.swap(v);
1241       compare_NaNs(r, v);
1242       //
1243       // Conmpare NaN to int:
1244       //
1245       compare_NaNs(v, 0);
1246       compare_NaNs(0, v);
1247       //
1248       // Compare to floats:
1249       //
1250       compare_NaNs(v, 0.5);
1251       compare_NaNs(0.5, v);
1252       if (std::numeric_limits<double>::has_quiet_NaN)
1253       {
1254          compare_NaNs(r, std::numeric_limits<double>::quiet_NaN());
1255          compare_NaNs(std::numeric_limits<double>::quiet_NaN(), r);
1256       }
1257    }
1258
1259    //
1260    // Operations involving NaN's as one argument:
1261    //
1262    if (std::numeric_limits<Real>::has_quiet_NaN)
1263    {
1264       v = 20.25;
1265       r = std::numeric_limits<Real>::quiet_NaN();
1266       BOOST_CHECK((boost::math::isnan)(v + r));
1267       BOOST_CHECK((boost::math::isnan)(r + v));
1268       BOOST_CHECK((boost::math::isnan)(r - v));
1269       BOOST_CHECK((boost::math::isnan)(v - r));
1270       BOOST_CHECK((boost::math::isnan)(r * v));
1271       BOOST_CHECK((boost::math::isnan)(v * r));
1272       BOOST_CHECK((boost::math::isnan)(r / v));
1273       BOOST_CHECK((boost::math::isnan)(v / r));
1274       Real t = v;
1275       BOOST_CHECK((boost::math::isnan)(t += r));
1276       t = r;
1277       BOOST_CHECK((boost::math::isnan)(t += v));
1278       t = r;
1279       BOOST_CHECK((boost::math::isnan)(t -= v));
1280       t = v;
1281       BOOST_CHECK((boost::math::isnan)(t -= r));
1282       t = r;
1283       BOOST_CHECK((boost::math::isnan)(t *= v));
1284       t = v;
1285       BOOST_CHECK((boost::math::isnan)(t *= r));
1286       t = r;
1287       BOOST_CHECK((boost::math::isnan)(t /= v));
1288       t = v;
1289       BOOST_CHECK((boost::math::isnan)(t /= r));
1290    }
1291    //
1292    // Operations involving infinities as one argument:
1293    //
1294    if (std::numeric_limits<Real>::has_infinity)
1295    {
1296       v = 20.25;
1297       r = std::numeric_limits<Real>::infinity();
1298       BOOST_CHECK((boost::math::isinf)(v + r));
1299       BOOST_CHECK((boost::math::isinf)(r + v));
1300       BOOST_CHECK((boost::math::isinf)(r - v));
1301       BOOST_CHECK((boost::math::isinf)(v - r));
1302       BOOST_CHECK_LT(v - r, 0);
1303       BOOST_CHECK((boost::math::isinf)(r * v));
1304       BOOST_CHECK((boost::math::isinf)(v * r));
1305       BOOST_CHECK((boost::math::isinf)(r / v));
1306       BOOST_CHECK_EQUAL(v / r, 0);
1307       Real t = v;
1308       BOOST_CHECK((boost::math::isinf)(t += r));
1309       t = r;
1310       BOOST_CHECK((boost::math::isinf)(t += v));
1311       t = r;
1312       BOOST_CHECK((boost::math::isinf)(t -= v));
1313       t = v;
1314       BOOST_CHECK((boost::math::isinf)(t -= r));
1315       t = v;
1316       BOOST_CHECK(t -= r < 0);
1317       t = r;
1318       BOOST_CHECK((boost::math::isinf)(t *= v));
1319       t = v;
1320       BOOST_CHECK((boost::math::isinf)(t *= r));
1321       t = r;
1322       BOOST_CHECK((boost::math::isinf)(t /= v));
1323       t = v;
1324       BOOST_CHECK((t /= r) == 0);
1325    }
1326    //
1327    // Operations that should produce NaN as a result:
1328    //
1329    if (std::numeric_limits<Real>::has_quiet_NaN)
1330    {
1331       v = r  = 0;
1332       Real t = v / r;
1333       BOOST_CHECK((boost::math::isnan)(t));
1334       v /= r;
1335       BOOST_CHECK((boost::math::isnan)(v));
1336       t = v / 0;
1337       BOOST_CHECK((boost::math::isnan)(v));
1338       if (std::numeric_limits<Real>::has_infinity)
1339       {
1340          v = 0;
1341          r = std::numeric_limits<Real>::infinity();
1342          t = v * r;
1343          if (!boost::multiprecision::is_interval_number<Real>::value)
1344          {
1345             BOOST_CHECK((boost::math::isnan)(t));
1346             t = r * 0;
1347             BOOST_CHECK((boost::math::isnan)(t));
1348          }
1349          v = r;
1350          t = r / v;
1351          BOOST_CHECK((boost::math::isnan)(t));
1352       }
1353    }
1354
1355    test_float_funcs<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
1356 }
1357
1358 template <class T>
1359 struct lexical_cast_target_type
1360 {
1361    typedef typename boost::mpl::if_<
1362        boost::is_signed<T>,
1363        boost::intmax_t,
1364        typename boost::mpl::if_<
1365            boost::is_unsigned<T>,
1366            boost::uintmax_t,
1367            T>::type>::type type;
1368 };
1369
1370 template <class Real, class Num>
1371 void test_negative_mixed_minmax(boost::mpl::true_ const&)
1372 {
1373    if (!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits >= std::numeric_limits<Num>::digits))
1374    {
1375       Real mx1((std::numeric_limits<Num>::max)() - 1);
1376       ++mx1;
1377       Real mx2((std::numeric_limits<Num>::max)());
1378       BOOST_CHECK_EQUAL(mx1, mx2);
1379       mx1 = (std::numeric_limits<Num>::max)() - 1;
1380       ++mx1;
1381       mx2 = (std::numeric_limits<Num>::max)();
1382       BOOST_CHECK_EQUAL(mx1, mx2);
1383
1384       if (!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits > std::numeric_limits<Num>::digits))
1385       {
1386          Real mx3((std::numeric_limits<Num>::min)() + 1);
1387          --mx3;
1388          Real mx4((std::numeric_limits<Num>::min)());
1389          BOOST_CHECK_EQUAL(mx3, mx4);
1390          mx3 = (std::numeric_limits<Num>::min)() + 1;
1391          --mx3;
1392          mx4 = (std::numeric_limits<Num>::min)();
1393          BOOST_CHECK_EQUAL(mx3, mx4);
1394       }
1395    }
1396 }
1397 template <class Real, class Num>
1398 void test_negative_mixed_minmax(boost::mpl::false_ const&)
1399 {
1400 }
1401
1402 template <class Real, class Num>
1403 void test_negative_mixed_numeric_limits(boost::mpl::true_ const&)
1404 {
1405    typedef typename lexical_cast_target_type<Num>::type target_type;
1406 #if defined(TEST_MPFR)
1407    Num tol = 10 * std::numeric_limits<Num>::epsilon();
1408 #else
1409    Num tol = 0;
1410 #endif
1411    static const int        left_shift      = std::numeric_limits<Num>::digits - 1;
1412    Num                     n1              = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
1413    Num                     n2              = -1;
1414    Num                     n3              = 0;
1415    Num                     n4              = -20;
1416    std::ios_base::fmtflags f               = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
1417    int                     digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
1418                              ? std::numeric_limits<Num>::digits10 + 5
1419                              : 0;
1420    if (std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
1421    {
1422       BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
1423    }
1424    BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
1425    BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
1426    BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
1427 }
1428
1429 template <class Real, class Num>
1430 void test_negative_mixed_numeric_limits(boost::mpl::false_ const&) {}
1431
1432 template <class Real, class Num>
1433 void test_negative_mixed(boost::mpl::true_ const&)
1434 {
1435    typedef typename boost::mpl::if_<
1436        boost::is_convertible<Num, Real>,
1437        typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
1438        Real>::type cast_type;
1439    typedef typename boost::mpl::if_<
1440        boost::is_convertible<Num, Real>,
1441        Num,
1442        Real>::type simple_cast_type;
1443    std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
1444    static const int left_shift = std::numeric_limits<Num>::digits - 1;
1445    Num              n1         = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
1446    Num              n2         = -1;
1447    Num              n3         = 0;
1448    Num              n4         = -20;
1449    Num              n5         = -8;
1450
1451    test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
1452    test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
1453    test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
1454    test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
1455    test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
1456    test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
1457
1458    // Default construct:
1459    BOOST_CHECK_EQUAL(Real(n1), static_cast<cast_type>(n1));
1460    BOOST_CHECK_EQUAL(Real(n2), static_cast<cast_type>(n2));
1461    BOOST_CHECK_EQUAL(Real(n3), static_cast<cast_type>(n3));
1462    BOOST_CHECK_EQUAL(Real(n4), static_cast<cast_type>(n4));
1463    BOOST_CHECK_EQUAL(static_cast<cast_type>(n1), Real(n1));
1464    BOOST_CHECK_EQUAL(static_cast<cast_type>(n2), Real(n2));
1465    BOOST_CHECK_EQUAL(static_cast<cast_type>(n3), Real(n3));
1466    BOOST_CHECK_EQUAL(static_cast<cast_type>(n4), Real(n4));
1467    BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>(), n1);
1468    BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>(), n2);
1469    BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>(), n3);
1470    BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>(), n4);
1471 #ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
1472    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)), n1);
1473    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)), n2);
1474    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)), n3);
1475    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)), n4);
1476 #endif
1477    // Conversions when source is an expression template:
1478    BOOST_CHECK_EQUAL((Real(n1) + 0).template convert_to<Num>(), n1);
1479    BOOST_CHECK_EQUAL((Real(n2) + 0).template convert_to<Num>(), n2);
1480    BOOST_CHECK_EQUAL((Real(n3) + 0).template convert_to<Num>(), n3);
1481    BOOST_CHECK_EQUAL((Real(n4) + 0).template convert_to<Num>(), n4);
1482 #ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
1483    BOOST_CHECK_EQUAL(static_cast<Num>((Real(n1) + 0)), n1);
1484    BOOST_CHECK_EQUAL(static_cast<Num>((Real(n2) + 0)), n2);
1485    BOOST_CHECK_EQUAL(static_cast<Num>((Real(n3) + 0)), n3);
1486    BOOST_CHECK_EQUAL(static_cast<Num>((Real(n4) + 0)), n4);
1487 #endif
1488    test_negative_mixed_numeric_limits<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
1489    // Assignment:
1490    Real r(0);
1491    BOOST_CHECK(r != static_cast<cast_type>(n1));
1492    r = static_cast<simple_cast_type>(n1);
1493    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1));
1494    r = static_cast<simple_cast_type>(n2);
1495    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2));
1496    r = static_cast<simple_cast_type>(n3);
1497    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n3));
1498    r = static_cast<simple_cast_type>(n4);
1499    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
1500    // Addition:
1501    r = static_cast<simple_cast_type>(n2);
1502    BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 + n4));
1503    BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 + n4));
1504    r += static_cast<simple_cast_type>(n4);
1505    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 + n4));
1506    // subtraction:
1507    r = static_cast<simple_cast_type>(n4);
1508    BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5), static_cast<cast_type>(n4 - n5));
1509    BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n4 - n5));
1510    r -= static_cast<simple_cast_type>(n5);
1511    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
1512    // Multiplication:
1513    r = static_cast<simple_cast_type>(n2);
1514    BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 * n4));
1515    BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 * n4));
1516    r *= static_cast<simple_cast_type>(n4);
1517    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 * n4));
1518    // Division:
1519    r = static_cast<simple_cast_type>(n1);
1520    BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5), static_cast<cast_type>(n1 / n5));
1521    BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n1 / n5));
1522    r /= static_cast<simple_cast_type>(n5);
1523    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1 / n5));
1524    //
1525    // Extra cases for full coverage:
1526    //
1527    r = Real(n4) + static_cast<simple_cast_type>(n5);
1528    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
1529    r = static_cast<simple_cast_type>(n4) + Real(n5);
1530    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
1531    r = Real(n4) - static_cast<simple_cast_type>(n5);
1532    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
1533    r = static_cast<simple_cast_type>(n4) - Real(n5);
1534    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
1535    r = static_cast<simple_cast_type>(n4) * Real(n5);
1536    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 * n5));
1537    r = static_cast<cast_type>(Num(4) * n4) / Real(4);
1538    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
1539
1540    Real a, b, c;
1541    a = 20;
1542    b = 30;
1543    c = -a + b;
1544    BOOST_CHECK_EQUAL(c, 10);
1545    c = b + -a;
1546    BOOST_CHECK_EQUAL(c, 10);
1547    n4 = 30;
1548    c  = -a + static_cast<cast_type>(n4);
1549    BOOST_CHECK_EQUAL(c, 10);
1550    c = static_cast<cast_type>(n4) + -a;
1551    BOOST_CHECK_EQUAL(c, 10);
1552    c = -a + -b;
1553    BOOST_CHECK_EQUAL(c, -50);
1554    n4 = 4;
1555    c  = -(a + b) + static_cast<cast_type>(n4);
1556    BOOST_CHECK_EQUAL(c, -50 + 4);
1557    n4 = 50;
1558    c  = (a + b) - static_cast<cast_type>(n4);
1559    BOOST_CHECK_EQUAL(c, 0);
1560    c = (a + b) - static_cast<cast_type>(n4);
1561    BOOST_CHECK_EQUAL(c, 0);
1562    c = a - -(b + static_cast<cast_type>(n4));
1563    BOOST_CHECK_EQUAL(c, 20 - -(30 + 50));
1564    c = -(b + static_cast<cast_type>(n4)) - a;
1565    BOOST_CHECK_EQUAL(c, -(30 + 50) - 20);
1566    c = a - -b;
1567    BOOST_CHECK_EQUAL(c, 50);
1568    c = -a - b;
1569    BOOST_CHECK_EQUAL(c, -50);
1570    c = -a - static_cast<cast_type>(n4);
1571    BOOST_CHECK_EQUAL(c, -20 - 50);
1572    c = static_cast<cast_type>(n4) - -a;
1573    BOOST_CHECK_EQUAL(c, 50 + 20);
1574    c = -(a + b) - Real(n4);
1575    BOOST_CHECK_EQUAL(c, -(20 + 30) - 50);
1576    c = static_cast<cast_type>(n4) - (a + b);
1577    BOOST_CHECK_EQUAL(c, 0);
1578    c = (a + b) * static_cast<cast_type>(n4);
1579    BOOST_CHECK_EQUAL(c, 50 * 50);
1580    c = static_cast<cast_type>(n4) * (a + b);
1581    BOOST_CHECK_EQUAL(c, 50 * 50);
1582    c = a * -(b + static_cast<cast_type>(n4));
1583    BOOST_CHECK_EQUAL(c, 20 * -(30 + 50));
1584    c = -(b + static_cast<cast_type>(n4)) * a;
1585    BOOST_CHECK_EQUAL(c, 20 * -(30 + 50));
1586    c = a * -b;
1587    BOOST_CHECK_EQUAL(c, 20 * -30);
1588    c = -a * b;
1589    BOOST_CHECK_EQUAL(c, 20 * -30);
1590    c = -a * static_cast<cast_type>(n4);
1591    BOOST_CHECK_EQUAL(c, -20 * 50);
1592    c = static_cast<cast_type>(n4) * -a;
1593    BOOST_CHECK_EQUAL(c, -20 * 50);
1594    c = -(a + b) + a;
1595    BOOST_CHECK(-50 + 20);
1596    c = static_cast<cast_type>(n4) - (a + b);
1597    BOOST_CHECK_EQUAL(c, 0);
1598    Real d = 10;
1599    c      = (a + b) / d;
1600    BOOST_CHECK_EQUAL(c, 5);
1601    c = (a + b) / (d + 0);
1602    BOOST_CHECK_EQUAL(c, 5);
1603    c = (a + b) / static_cast<cast_type>(n4);
1604    BOOST_CHECK_EQUAL(c, 1);
1605    c = static_cast<cast_type>(n4) / (a + b);
1606    BOOST_CHECK_EQUAL(c, 1);
1607    d = 50;
1608    c = d / -(a + b);
1609    BOOST_CHECK_EQUAL(c, -1);
1610    c = -(a + b) / d;
1611    BOOST_CHECK_EQUAL(c, -1);
1612    d = 2;
1613    c = a / -d;
1614    BOOST_CHECK_EQUAL(c, 20 / -2);
1615    c = -a / d;
1616    BOOST_CHECK_EQUAL(c, 20 / -2);
1617    d = 50;
1618    c = -d / static_cast<cast_type>(n4);
1619    BOOST_CHECK_EQUAL(c, -1);
1620    c = static_cast<cast_type>(n4) / -d;
1621    BOOST_CHECK_EQUAL(c, -1);
1622    c = static_cast<cast_type>(n4) + a;
1623    BOOST_CHECK_EQUAL(c, 70);
1624    c = static_cast<cast_type>(n4) - a;
1625    BOOST_CHECK_EQUAL(c, 30);
1626    c = static_cast<cast_type>(n4) * a;
1627    BOOST_CHECK_EQUAL(c, 50 * 20);
1628
1629    n1 = -2;
1630    n2 = -3;
1631    n3 = -4;
1632    a  = static_cast<cast_type>(n1);
1633    b  = static_cast<cast_type>(n2);
1634    c  = static_cast<cast_type>(n3);
1635    d  = a + b * c;
1636    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1637    d = static_cast<cast_type>(n1) + b * c;
1638    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1639    d = a + static_cast<cast_type>(n2) * c;
1640    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1641    d = a + b * static_cast<cast_type>(n3);
1642    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1643    d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
1644    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1645    d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
1646    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1647    a += static_cast<cast_type>(n2) * c;
1648    BOOST_CHECK_EQUAL(a, -2 + -3 * -4);
1649    a = static_cast<cast_type>(n1);
1650    a += b * static_cast<cast_type>(n3);
1651    BOOST_CHECK_EQUAL(a, -2 + -3 * -4);
1652    a = static_cast<cast_type>(n1);
1653
1654    d = b * c + a;
1655    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1656    d = b * c + static_cast<cast_type>(n1);
1657    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1658    d = static_cast<cast_type>(n2) * c + a;
1659    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1660    d = b * static_cast<cast_type>(n3) + a;
1661    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1662    d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
1663    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1664    d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
1665    BOOST_CHECK_EQUAL(d, -2 + -3 * -4);
1666
1667    a = -20;
1668    d = a - b * c;
1669    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1670    n1 = -20;
1671    d  = static_cast<cast_type>(n1) - b * c;
1672    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1673    d = a - static_cast<cast_type>(n2) * c;
1674    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1675    d = a - b * static_cast<cast_type>(n3);
1676    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1677    d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
1678    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1679    d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
1680    BOOST_CHECK_EQUAL(d, -20 - -3 * -4);
1681    a -= static_cast<cast_type>(n2) * c;
1682    BOOST_CHECK_EQUAL(a, -20 - -3 * -4);
1683    a = static_cast<cast_type>(n1);
1684    a -= b * static_cast<cast_type>(n3);
1685    BOOST_CHECK_EQUAL(a, -20 - -3 * -4);
1686
1687    a = -2;
1688    d = b * c - a;
1689    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1690    n1 = -2;
1691    d  = b * c - static_cast<cast_type>(n1);
1692    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1693    d = static_cast<cast_type>(n2) * c - a;
1694    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1695    d = b * static_cast<cast_type>(n3) - a;
1696    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1697    d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
1698    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1699    d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
1700    BOOST_CHECK_EQUAL(d, -3 * -4 - -2);
1701    //
1702    // Conversion from min and max values:
1703    //
1704    test_negative_mixed_minmax<Real, Num>(boost::mpl::bool_ < std::numeric_limits<Real>::is_integer && std::numeric_limits<Num>::is_integer > ());
1705 }
1706
1707 template <class Real, class Num>
1708 void test_negative_mixed(boost::mpl::false_ const&)
1709 {
1710 }
1711
1712 template <class Real, class Num>
1713 void test_mixed(const boost::mpl::false_&)
1714 {
1715 }
1716
1717 template <class Real>
1718 inline bool check_is_nan(const Real& val, const boost::mpl::true_&)
1719 {
1720    return (boost::math::isnan)(val);
1721 }
1722 template <class Real>
1723 inline bool check_is_nan(const Real&, const boost::mpl::false_&)
1724 {
1725    return false;
1726 }
1727 template <class Real>
1728 inline Real negate_value(const Real& val, const boost::mpl::true_&)
1729 {
1730    return -val;
1731 }
1732 template <class Real>
1733 inline Real negate_value(const Real& val, const boost::mpl::false_&)
1734 {
1735    return val;
1736 }
1737
1738 template <class Real, class Num>
1739 void test_mixed_numeric_limits(const boost::mpl::true_&)
1740 {
1741    typedef typename lexical_cast_target_type<Num>::type target_type;
1742 #if defined(TEST_MPFR)
1743    Num tol = 10 * std::numeric_limits<Num>::epsilon();
1744 #else
1745    Num tol = 0;
1746 #endif
1747
1748    Real d;
1749    if (std::numeric_limits<Real>::has_infinity && std::numeric_limits<Num>::has_infinity)
1750    {
1751       d = static_cast<Real>(std::numeric_limits<Num>::infinity());
1752       BOOST_CHECK_GT(d, (std::numeric_limits<Real>::max)());
1753       d = static_cast<Real>(negate_value(std::numeric_limits<Num>::infinity(), boost::mpl::bool_<std::numeric_limits<Num>::is_signed>()));
1754       BOOST_CHECK_LT(d, negate_value((std::numeric_limits<Real>::max)(), boost::mpl::bool_<std::numeric_limits<Real>::is_signed>()));
1755    }
1756    if (std::numeric_limits<Real>::has_quiet_NaN && std::numeric_limits<Num>::has_quiet_NaN)
1757    {
1758       d = static_cast<Real>(std::numeric_limits<Num>::quiet_NaN());
1759       BOOST_CHECK(check_is_nan(d, boost::mpl::bool_<std::numeric_limits<Real>::has_quiet_NaN>()));
1760       d = static_cast<Real>(negate_value(std::numeric_limits<Num>::quiet_NaN(), boost::mpl::bool_<std::numeric_limits<Num>::is_signed>()));
1761       BOOST_CHECK(check_is_nan(d, boost::mpl::bool_<std::numeric_limits<Real>::has_quiet_NaN>()));
1762    }
1763
1764    static const int left_shift = std::numeric_limits<Num>::digits - 1;
1765    Num              n1         = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
1766    Num              n2         = 1;
1767    Num              n3         = 0;
1768    Num              n4         = 20;
1769
1770    std::ios_base::fmtflags f               = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
1771    int                     digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
1772                              ? std::numeric_limits<Num>::digits10 + 5
1773                              : 0;
1774    if (std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
1775    {
1776       BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
1777    }
1778    BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
1779    BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
1780    BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
1781 }
1782 template <class Real, class Num>
1783 void test_mixed_numeric_limits(const boost::mpl::false_&)
1784 {
1785 }
1786
1787 template <class Real, class Num>
1788 void test_mixed(const boost::mpl::true_&)
1789 {
1790    typedef typename boost::mpl::if_<
1791        boost::is_convertible<Num, Real>,
1792        typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
1793        Real>::type cast_type;
1794    typedef typename boost::mpl::if_<
1795        boost::is_convertible<Num, Real>,
1796        Num,
1797        Real>::type simple_cast_type;
1798
1799    if (std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::is_bounded && std::numeric_limits<Real>::digits < std::numeric_limits<Num>::digits)
1800       return;
1801
1802    std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
1803    static const int left_shift = std::numeric_limits<Num>::digits - 1;
1804    Num              n1         = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
1805    Num              n2         = 1;
1806    Num              n3         = 0;
1807    Num              n4         = 20;
1808    Num              n5         = 8;
1809
1810    test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
1811    test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
1812    test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
1813    test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
1814    test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
1815    test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
1816
1817    // Default construct:
1818    BOOST_CHECK_EQUAL(Real(n1), static_cast<cast_type>(n1));
1819    BOOST_CHECK_EQUAL(Real(n2), static_cast<cast_type>(n2));
1820    BOOST_CHECK_EQUAL(Real(n3), static_cast<cast_type>(n3));
1821    BOOST_CHECK_EQUAL(Real(n4), static_cast<cast_type>(n4));
1822    BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>(), n1);
1823    BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>(), n2);
1824    BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>(), n3);
1825    BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>(), n4);
1826 #ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
1827    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)), n1);
1828    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)), n2);
1829    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)), n3);
1830    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)), n4);
1831 #endif
1832    // Again with expression templates:
1833    BOOST_CHECK_EQUAL((Real(n1) + 0).template convert_to<Num>(), n1);
1834    BOOST_CHECK_EQUAL((Real(n2) + 0).template convert_to<Num>(), n2);
1835    BOOST_CHECK_EQUAL((Real(n3) + 0).template convert_to<Num>(), n3);
1836    BOOST_CHECK_EQUAL((Real(n4) + 0).template convert_to<Num>(), n4);
1837 #ifndef BOOST_MP_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
1838    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1) + 0), n1);
1839    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2) + 0), n2);
1840    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3) + 0), n3);
1841    BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4) + 0), n4);
1842 #endif
1843    BOOST_CHECK_EQUAL(static_cast<cast_type>(n1), Real(n1));
1844    BOOST_CHECK_EQUAL(static_cast<cast_type>(n2), Real(n2));
1845    BOOST_CHECK_EQUAL(static_cast<cast_type>(n3), Real(n3));
1846    BOOST_CHECK_EQUAL(static_cast<cast_type>(n4), Real(n4));
1847    // Assignment:
1848    Real r(0);
1849    BOOST_CHECK(r != static_cast<cast_type>(n1));
1850    r = static_cast<simple_cast_type>(n1);
1851    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1));
1852    r = static_cast<simple_cast_type>(n2);
1853    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2));
1854    r = static_cast<simple_cast_type>(n3);
1855    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n3));
1856    r = static_cast<simple_cast_type>(n4);
1857    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
1858    // Addition:
1859    r = static_cast<simple_cast_type>(n2);
1860    BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 + n4));
1861    BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 + n4));
1862    r += static_cast<simple_cast_type>(n4);
1863    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 + n4));
1864    // subtraction:
1865    r = static_cast<simple_cast_type>(n4);
1866    BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5), static_cast<cast_type>(n4 - n5));
1867    BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n4 - n5));
1868    r -= static_cast<simple_cast_type>(n5);
1869    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
1870    // Multiplication:
1871    r = static_cast<simple_cast_type>(n2);
1872    BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4), static_cast<cast_type>(n2 * n4));
1873    BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)), static_cast<cast_type>(n2 * n4));
1874    r *= static_cast<simple_cast_type>(n4);
1875    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n2 * n4));
1876    // Division:
1877    r = static_cast<simple_cast_type>(n1);
1878    BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5), static_cast<cast_type>(n1 / n5));
1879    BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)), static_cast<cast_type>(n1 / n5));
1880    r /= static_cast<simple_cast_type>(n5);
1881    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n1 / n5));
1882    //
1883    // special cases for full coverage:
1884    //
1885    r = static_cast<simple_cast_type>(n5) + Real(n4);
1886    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 + n5));
1887    r = static_cast<simple_cast_type>(n4) - Real(n5);
1888    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 - n5));
1889    r = static_cast<simple_cast_type>(n4) * Real(n5);
1890    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4 * n5));
1891    r = static_cast<cast_type>(Num(4) * n4) / Real(4);
1892    BOOST_CHECK_EQUAL(r, static_cast<cast_type>(n4));
1893
1894    typedef boost::mpl::bool_<
1895        (!std::numeric_limits<Num>::is_specialized || std::numeric_limits<Num>::is_signed) && (!std::numeric_limits<Real>::is_specialized || std::numeric_limits<Real>::is_signed)>
1896        signed_tag;
1897
1898    test_negative_mixed<Real, Num>(signed_tag());
1899
1900    n1 = 2;
1901    n2 = 3;
1902    n3 = 4;
1903    Real a(n1), b(n2), c(n3), d;
1904    d = a + b * c;
1905    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1906    d = static_cast<cast_type>(n1) + b * c;
1907    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1908    d = a + static_cast<cast_type>(n2) * c;
1909    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1910    d = a + b * static_cast<cast_type>(n3);
1911    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1912    d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
1913    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1914    d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
1915    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1916    a += static_cast<cast_type>(n2) * c;
1917    BOOST_CHECK_EQUAL(a, 2 + 3 * 4);
1918    a = static_cast<cast_type>(n1);
1919    a += b * static_cast<cast_type>(n3);
1920    BOOST_CHECK_EQUAL(a, 2 + 3 * 4);
1921    a = static_cast<cast_type>(n1);
1922
1923    d = b * c + a;
1924    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1925    d = b * c + static_cast<cast_type>(n1);
1926    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1927    d = static_cast<cast_type>(n2) * c + a;
1928    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1929    d = b * static_cast<cast_type>(n3) + a;
1930    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1931    d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
1932    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1933    d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
1934    BOOST_CHECK_EQUAL(d, 2 + 3 * 4);
1935
1936    a = 20;
1937    d = a - b * c;
1938    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1939    n1 = 20;
1940    d  = static_cast<cast_type>(n1) - b * c;
1941    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1942    d = a - static_cast<cast_type>(n2) * c;
1943    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1944    d = a - b * static_cast<cast_type>(n3);
1945    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1946    d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
1947    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1948    d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
1949    BOOST_CHECK_EQUAL(d, 20 - 3 * 4);
1950    a -= static_cast<cast_type>(n2) * c;
1951    BOOST_CHECK_EQUAL(a, 20 - 3 * 4);
1952    a = static_cast<cast_type>(n1);
1953    a -= b * static_cast<cast_type>(n3);
1954    BOOST_CHECK_EQUAL(a, 20 - 3 * 4);
1955
1956    a = 2;
1957    d = b * c - a;
1958    BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
1959    n1 = 2;
1960    d  = b * c - static_cast<cast_type>(n1);
1961    BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
1962    d = static_cast<cast_type>(n2) * c - a;
1963    BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
1964    d = b * static_cast<cast_type>(n3) - a;
1965    BOOST_CHECK_EQUAL(d, 3 * 4 - a);
1966    d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
1967    BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
1968    d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
1969    BOOST_CHECK_EQUAL(d, 3 * 4 - 2);
1970
1971    test_mixed_numeric_limits<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
1972 }
1973
1974 template <class Real>
1975 typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex>::type test_members(Real)
1976 {
1977    //
1978    // Test sign and zero functions:
1979    //
1980    Real a = 20;
1981    Real b = 30;
1982    BOOST_CHECK(!a.is_zero());
1983    a = -20;
1984    BOOST_CHECK(!a.is_zero());
1985    a = 0;
1986    BOOST_CHECK(a.is_zero());
1987
1988    a = 20;
1989    b = 30;
1990    a.swap(b);
1991    BOOST_CHECK_EQUAL(a, 30);
1992    BOOST_CHECK_EQUAL(b, 20);
1993
1994    Real c(2, 3);
1995
1996    BOOST_CHECK_EQUAL(a.real(), 30);
1997    BOOST_CHECK_EQUAL(a.imag(), 0);
1998    BOOST_CHECK_EQUAL(c.real(), 2);
1999    BOOST_CHECK_EQUAL(c.imag(), 3);
2000
2001    //
2002    // try some more 2-argument constructors:
2003    //
2004    {
2005       Real d(40.5, 2);
2006       BOOST_CHECK_EQUAL(d.real(), 40.5);
2007       BOOST_CHECK_EQUAL(d.imag(), 2);
2008    }
2009    {
2010       Real d("40.5", "2");
2011       BOOST_CHECK_EQUAL(d.real(), 40.5);
2012       BOOST_CHECK_EQUAL(d.imag(), 2);
2013    }
2014    {
2015       Real d("40.5", std::string("2"));
2016       BOOST_CHECK_EQUAL(d.real(), 40.5);
2017       BOOST_CHECK_EQUAL(d.imag(), 2);
2018    }
2019 #ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
2020    {
2021       std::string      sx("40.550"), sy("222");
2022       std::string_view vx(sx.c_str(), 4), vy(sy.c_str(), 1);
2023       Real             d(vx, vy);
2024       BOOST_CHECK_EQUAL(d.real(), 40.5);
2025       BOOST_CHECK_EQUAL(d.imag(), 2);
2026    }
2027 #endif
2028    {
2029       typename Real::value_type x(40.5), y(2);
2030       Real                      d(x, y);
2031       BOOST_CHECK_EQUAL(d.real(), 40.5);
2032       BOOST_CHECK_EQUAL(d.imag(), 2);
2033    }
2034 #ifdef TEST_MPC
2035    {
2036       typename Real::value_type x(40.5), y(2);
2037       Real                      d(x.backend().data(), y.backend().data());
2038       BOOST_CHECK_EQUAL(d.real(), 40.5);
2039       BOOST_CHECK_EQUAL(d.imag(), 2);
2040    }
2041 #endif
2042    {
2043       typename Real::value_type x(40.5);
2044       Real                      d(x, 2);
2045       BOOST_CHECK_EQUAL(d.real(), 40.5);
2046       BOOST_CHECK_EQUAL(d.imag(), 2);
2047    }
2048    {
2049       typename Real::value_type x(40.5);
2050       Real                      d(2, x);
2051       BOOST_CHECK_EQUAL(d.imag(), 40.5);
2052       BOOST_CHECK_EQUAL(d.real(), 2);
2053    }
2054    {
2055       typename Real::value_type x(real(a) * real(b) + imag(a) * imag(b)), y(imag(a) * real(b) - real(a) * imag(b));
2056       Real                      d(real(a) * real(b) + imag(a) * imag(b), imag(a) * real(b) - real(a) * imag(b));
2057       Real                      e(x, y);
2058       BOOST_CHECK_EQUAL(d, e);
2059    }
2060    //
2061    // real and imag setters:
2062    //
2063    c.real(4);
2064    BOOST_CHECK_EQUAL(real(c), 4);
2065    c.imag(-55);
2066    BOOST_CHECK_EQUAL(imag(c), -55);
2067    typename Real::value_type z(20);
2068    c.real(z);
2069    BOOST_CHECK_EQUAL(real(c), 20);
2070    c.real(21L);
2071    BOOST_CHECK_EQUAL(real(c), 21);
2072    c.real(22L);
2073    BOOST_CHECK_EQUAL(real(c), 22);
2074    c.real(23UL);
2075    BOOST_CHECK_EQUAL(real(c), 23);
2076    c.real(24U);
2077    BOOST_CHECK_EQUAL(real(c), 24);
2078    c.real(25.0f);
2079    BOOST_CHECK_EQUAL(real(c), 25);
2080    c.real(26.0);
2081    BOOST_CHECK_EQUAL(real(c), 26);
2082    c.real(27.0L);
2083    BOOST_CHECK_EQUAL(real(c), 27);
2084 #if defined(BOOST_HAS_LONG_LONG)
2085    c.real(28LL);
2086    BOOST_CHECK_EQUAL(real(c), 28);
2087    c.real(29ULL);
2088    BOOST_CHECK_EQUAL(real(c), 29);
2089 #endif
2090    c.imag(z);
2091    BOOST_CHECK_EQUAL(imag(c), 20);
2092    c.imag(21L);
2093    BOOST_CHECK_EQUAL(imag(c), 21);
2094    c.imag(22L);
2095    BOOST_CHECK_EQUAL(imag(c), 22);
2096    c.imag(23UL);
2097    BOOST_CHECK_EQUAL(imag(c), 23);
2098    c.imag(24U);
2099    BOOST_CHECK_EQUAL(imag(c), 24);
2100    c.imag(25.0f);
2101    BOOST_CHECK_EQUAL(imag(c), 25);
2102    c.imag(26.0);
2103    BOOST_CHECK_EQUAL(imag(c), 26);
2104    c.imag(27.0L);
2105    BOOST_CHECK_EQUAL(imag(c), 27);
2106 #if defined(BOOST_HAS_LONG_LONG)
2107    c.imag(28LL);
2108    BOOST_CHECK_EQUAL(imag(c), 28);
2109    c.imag(29ULL);
2110    BOOST_CHECK_EQUAL(imag(c), 29);
2111 #endif
2112
2113    c.real(2).imag(3);
2114
2115    BOOST_CHECK_EQUAL(real(a), 30);
2116    BOOST_CHECK_EQUAL(imag(a), 0);
2117    BOOST_CHECK_EQUAL(real(c), 2);
2118    BOOST_CHECK_EQUAL(imag(c), 3);
2119    BOOST_CHECK_EQUAL(real(a + 0), 30);
2120    BOOST_CHECK_EQUAL(imag(a + 0), 0);
2121    BOOST_CHECK_EQUAL(real(c + 0), 2);
2122    BOOST_CHECK_EQUAL(imag(c + 0), 3);
2123
2124    // string construction:
2125    a = Real("2");
2126    BOOST_CHECK_EQUAL(real(a), 2);
2127    BOOST_CHECK_EQUAL(imag(a), 0);
2128    a = Real("(2)");
2129    BOOST_CHECK_EQUAL(real(a), 2);
2130    BOOST_CHECK_EQUAL(imag(a), 0);
2131    a = Real("(,2)");
2132    BOOST_CHECK_EQUAL(real(a), 0);
2133    BOOST_CHECK_EQUAL(imag(a), 2);
2134    a = Real("(2,3)");
2135    BOOST_CHECK_EQUAL(real(a), 2);
2136    BOOST_CHECK_EQUAL(imag(a), 3);
2137
2138    typedef typename boost::multiprecision::component_type<Real>::type real_type;
2139
2140    real_type r(3);
2141    real_type tol = std::numeric_limits<real_type>::epsilon() * 30;
2142
2143    a = r;
2144    BOOST_CHECK_EQUAL(real(a), 3);
2145    BOOST_CHECK_EQUAL(imag(a), 0);
2146
2147    a += r;
2148    BOOST_CHECK_EQUAL(real(a), 6);
2149    BOOST_CHECK_EQUAL(imag(a), 0);
2150
2151    a *= r;
2152    BOOST_CHECK_EQUAL(real(a), 18);
2153    BOOST_CHECK_EQUAL(imag(a), 0);
2154
2155    a = a / r;
2156    BOOST_CHECK_EQUAL(real(a), 6);
2157    BOOST_CHECK_EQUAL(imag(a), 0);
2158    a = a - r;
2159    BOOST_CHECK_EQUAL(real(a), 3);
2160    BOOST_CHECK_EQUAL(imag(a), 0);
2161    a = r + a;
2162    BOOST_CHECK_EQUAL(real(a), 6);
2163    BOOST_CHECK_EQUAL(imag(a), 0);
2164
2165    r = abs(c);
2166    BOOST_CHECK_CLOSE_FRACTION(real_type("3.60555127546398929311922126747049594625129657384524621271045305622716694829301044520461908201849071767351418202406"), r, tol);
2167    r = arg(c);
2168    BOOST_CHECK_CLOSE_FRACTION(real_type("0.98279372324732906798571061101466601449687745363162855676142508831798807154979603538970653437281731110816513970201"), r, tol);
2169    r = norm(c);
2170    BOOST_CHECK_CLOSE_FRACTION(real_type(13), r, tol);
2171    a = conj(c);
2172    BOOST_CHECK_EQUAL(real(a), 2);
2173    BOOST_CHECK_EQUAL(imag(a), -3);
2174    a = proj(c);
2175    BOOST_CHECK_EQUAL(real(a), 2);
2176    BOOST_CHECK_EQUAL(imag(a), 3);
2177    a = polar(real_type(3), real_type(-10));
2178    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2179    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2180    a = polar(real_type(3) + 0, real_type(-10));
2181    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2182    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2183    a = polar(real_type(3), real_type(-10) + 0);
2184    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2185    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2186    a = polar(real_type(3) + 0, real_type(-10) + 0);
2187    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2188    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2189    a = polar(3, real_type(-10));
2190    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2191    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2192    a = polar(3.0, real_type(-10) + 0);
2193    BOOST_CHECK_CLOSE_FRACTION(real_type("-2.517214587229357356776591843472194503559790495399505640507861193146377760598812305202801138281266416782353163216"), real(a), tol);
2194    BOOST_CHECK_CLOSE_FRACTION(real_type("1.63206333266810944021424298555413184505092903874867167472255203785027162892148027712122702168494964847488147271478"), imag(a), tol);
2195
2196    a = polar(real_type(3));
2197    BOOST_CHECK_EQUAL(3, real(a));
2198    BOOST_CHECK_EQUAL(0, imag(a));
2199    a = polar(real_type(3) + 0);
2200    BOOST_CHECK_EQUAL(3, real(a));
2201    BOOST_CHECK_EQUAL(0, imag(a));
2202
2203    r = abs(c + 0);
2204    BOOST_CHECK_CLOSE_FRACTION(real_type("3.60555127546398929311922126747049594625129657384524621271045305622716694829301044520461908201849071767351418202406"), r, tol);
2205    r = arg(c + 0);
2206    BOOST_CHECK_CLOSE_FRACTION(real_type("0.98279372324732906798571061101466601449687745363162855676142508831798807154979603538970653437281731110816513970201"), r, tol);
2207    r = norm(c + 0);
2208    BOOST_CHECK_CLOSE_FRACTION(real_type(13), r, tol);
2209    a = conj(c + 0);
2210    BOOST_CHECK_EQUAL(real(a), 2);
2211    BOOST_CHECK_EQUAL(imag(a), -3);
2212    a = proj(c + 0);
2213    BOOST_CHECK_EQUAL(real(a), 2);
2214    BOOST_CHECK_EQUAL(imag(a), 3);
2215
2216    a = exp(c);
2217    BOOST_CHECK_CLOSE_FRACTION(real_type("-7.3151100949011025174865361510507893218698794489446322367845159660828327860599907104337742108443234172141249777"), real(a), tol);
2218    BOOST_CHECK_CLOSE_FRACTION(real_type("1.0427436562359044141015039404625521939183300604422348975424523449538886779880818796291971422701951470533151185"), imag(a), tol);
2219
2220    a = log(c);
2221    BOOST_CHECK_CLOSE_FRACTION(real_type("1.282474678730768368026743720782659302402633972380103558209522755331732333662205089699787331720244744384629096046"), real(a), tol);
2222    BOOST_CHECK_CLOSE_FRACTION(real_type("0.9827937232473290679857106110146660144968774536316285567614250883179880715497960353897065343728173111081651397020"), imag(a), tol);
2223
2224    a = log10(c);
2225    BOOST_CHECK_CLOSE_FRACTION(real_type("0.556971676153418384603252578971164215414864594193534135900595487498776545815097120403823727129449829836488977743"), real(a), tol);
2226    BOOST_CHECK_CLOSE_FRACTION(real_type("0.426821890855466638944275673291166123449562356934437957244904971730668088711719757900679614536803436424488603794"), imag(a), tol);
2227
2228    a = exp(c + 0);
2229    BOOST_CHECK_CLOSE_FRACTION(real_type("-7.3151100949011025174865361510507893218698794489446322367845159660828327860599907104337742108443234172141249777"), real(a), tol);
2230    BOOST_CHECK_CLOSE_FRACTION(real_type("1.0427436562359044141015039404625521939183300604422348975424523449538886779880818796291971422701951470533151185"), imag(a), tol);
2231
2232    a = log(c + 0);
2233    BOOST_CHECK_CLOSE_FRACTION(real_type("1.282474678730768368026743720782659302402633972380103558209522755331732333662205089699787331720244744384629096046"), real(a), tol);
2234    BOOST_CHECK_CLOSE_FRACTION(real_type("0.9827937232473290679857106110146660144968774536316285567614250883179880715497960353897065343728173111081651397020"), imag(a), tol);
2235
2236    a = log10(c + 0);
2237    BOOST_CHECK_CLOSE_FRACTION(real_type("0.556971676153418384603252578971164215414864594193534135900595487498776545815097120403823727129449829836488977743"), real(a), tol);
2238    BOOST_CHECK_CLOSE_FRACTION(real_type("0.426821890855466638944275673291166123449562356934437957244904971730668088711719757900679614536803436424488603794"), imag(a), tol);
2239
2240    // Powers where one arg is an integer.
2241    b = Real(5, -2);
2242    a = pow(c, b);
2243    BOOST_CHECK_CLOSE_FRACTION(real_type("-3053.8558566606567369633610140423321260211388217942246293871310470377722279440084474789529228008638668934381183"), real(a), tol);
2244    BOOST_CHECK_CLOSE_FRACTION(real_type("3097.9975862915005132449772136982559285192410496951232473245540634244845290672745578327467396750607773968246915"), imag(a), tol);
2245    a = pow(c, 3);
2246    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2247    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2248    a = pow(3, c);
2249    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2250    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2251    a = pow(c + 0, b);
2252    BOOST_CHECK_CLOSE_FRACTION(real_type("-3053.8558566606567369633610140423321260211388217942246293871310470377722279440084474789529228008638668934381183"), real(a), tol);
2253    BOOST_CHECK_CLOSE_FRACTION(real_type("3097.9975862915005132449772136982559285192410496951232473245540634244845290672745578327467396750607773968246915"), imag(a), tol);
2254    a = pow(c + 0, 3);
2255    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2256    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2257    a = pow(3, c + 0);
2258    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2259    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2260
2261    r = 3;
2262    // Powers where one arg is a real_type.
2263    a = pow(c, r);
2264    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2265    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2266    a = pow(r, c);
2267    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2268    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2269    a = pow(c + 0, r);
2270    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2271    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2272    a = pow(r, c + 0);
2273    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2274    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2275    a = pow(c, r + 0);
2276    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2277    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2278    a = pow(r + 0, c);
2279    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2280    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2281
2282    // Powers where one arg is an float.
2283    a = pow(c, 3.0);
2284    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2285    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2286    a = pow(3.0, c);
2287    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2288    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2289    a = pow(c + 0, 3.0);
2290    BOOST_CHECK_CLOSE_FRACTION(real_type(-46), real(a), tol);
2291    BOOST_CHECK_CLOSE_FRACTION(real_type(9), imag(a), tol);
2292    a = pow(3.0, c + 0);
2293    BOOST_CHECK_CLOSE_FRACTION(real_type("-8.8931513442797186948734782808862447235385767991868219480917324534839621090167050538805196124711247247992169338"), real(a), tol);
2294    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.3826999557878897572499699021550296885662132089951379549068064961882821777067532977546360861176011175070188118"), imag(a), tol * 3);
2295
2296    a = sqrt(c);
2297    BOOST_CHECK_CLOSE_FRACTION(real_type("1.674149228035540040448039300849051821674708677883920366727287836003399240343274891876712629708287692163156802065"), real(a), tol);
2298    BOOST_CHECK_CLOSE_FRACTION(real_type("0.8959774761298381247157337552900434410433241995549314932449006989874470582160955817053273057885402621549320588976"), imag(a), tol);
2299    a = sin(c);
2300    BOOST_CHECK_CLOSE_FRACTION(real_type("9.154499146911429573467299544609832559158860568765182977899828142590020335321896403936690014669532606510294425039"), real(a), tol);
2301    BOOST_CHECK_CLOSE_FRACTION(real_type("-4.168906959966564350754813058853754843573565604758055889965478710592666260138453299795649308385497563475115931624"), imag(a), tol);
2302    a = cos(c);
2303    BOOST_CHECK_CLOSE_FRACTION(real_type("-4.1896256909688072301325550196159737286219454041279210357407905058369727912162626993926269783331491034500484583"), real(a), tol);
2304    BOOST_CHECK_CLOSE_FRACTION(real_type("-9.1092278937553365979791972627788621213326202389201695649104967309554222940748568716960841549279996556547993373"), imag(a), tol);
2305    a = tan(c);
2306    BOOST_CHECK_CLOSE_FRACTION(real_type("-0.0037640256415042482927512211303226908396306202016580864328644932511249097100916559688254811519914564480500042311"), real(a), tol * 5);
2307    BOOST_CHECK_CLOSE_FRACTION(real_type("1.0032386273536098014463585978219272598077897241071003399272426939850671219193120708438426543945017427085738411"), imag(a), tol);
2308    a = asin(c);
2309    BOOST_CHECK_CLOSE_FRACTION(real_type("0.5706527843210994007102838796856696501828032450960401365302732598209740064262509342420347149436326252483895113827"), real(a), tol);
2310    BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
2311    a = acos(c);
2312    BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), real(a), tol);
2313    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
2314    a = atan(c);
2315    BOOST_CHECK_CLOSE_FRACTION(real_type("1.409921049596575522530619384460420782588207051908724814771070766475530084440199227135813201495737846771570458568"), real(a), tol);
2316    BOOST_CHECK_CLOSE_FRACTION(real_type("0.2290726829685387662958818029420027678625253049770656169479919704951963414344907622560676377741902308144912055002"), imag(a), tol);
2317    a = sqrt(c + 0);
2318    BOOST_CHECK_CLOSE_FRACTION(real_type("1.674149228035540040448039300849051821674708677883920366727287836003399240343274891876712629708287692163156802065"), real(a), tol);
2319    BOOST_CHECK_CLOSE_FRACTION(real_type("0.8959774761298381247157337552900434410433241995549314932449006989874470582160955817053273057885402621549320588976"), imag(a), tol);
2320    a = sin(c + 0);
2321    BOOST_CHECK_CLOSE_FRACTION(real_type("9.154499146911429573467299544609832559158860568765182977899828142590020335321896403936690014669532606510294425039"), real(a), tol);
2322    BOOST_CHECK_CLOSE_FRACTION(real_type("-4.168906959966564350754813058853754843573565604758055889965478710592666260138453299795649308385497563475115931624"), imag(a), tol);
2323    a = cos(c + 0);
2324    BOOST_CHECK_CLOSE_FRACTION(real_type("-4.1896256909688072301325550196159737286219454041279210357407905058369727912162626993926269783331491034500484583"), real(a), tol);
2325    BOOST_CHECK_CLOSE_FRACTION(real_type("-9.1092278937553365979791972627788621213326202389201695649104967309554222940748568716960841549279996556547993373"), imag(a), tol);
2326    a = tan(c + 0);
2327    BOOST_CHECK_CLOSE_FRACTION(real_type("-0.0037640256415042482927512211303226908396306202016580864328644932511249097100916559688254811519914564480500042311"), real(a), tol * 5);
2328    BOOST_CHECK_CLOSE_FRACTION(real_type("1.0032386273536098014463585978219272598077897241071003399272426939850671219193120708438426543945017427085738411"), imag(a), tol);
2329    a = asin(c + 0);
2330    BOOST_CHECK_CLOSE_FRACTION(real_type("0.5706527843210994007102838796856696501828032450960401365302732598209740064262509342420347149436326252483895113827"), real(a), tol);
2331    BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
2332    a = acos(c + 0);
2333    BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), real(a), tol);
2334    BOOST_CHECK_CLOSE_FRACTION(real_type("-1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), imag(a), tol);
2335    a = atan(c + 0);
2336    BOOST_CHECK_CLOSE_FRACTION(real_type("1.409921049596575522530619384460420782588207051908724814771070766475530084440199227135813201495737846771570458568"), real(a), tol);
2337    BOOST_CHECK_CLOSE_FRACTION(real_type("0.2290726829685387662958818029420027678625253049770656169479919704951963414344907622560676377741902308144912055002"), imag(a), tol);
2338
2339    a = sinh(c);
2340    BOOST_CHECK_CLOSE_FRACTION(real_type("-3.5905645899857799520125654477948167931949136757293015099986213974178826801534614215227593814301490087307920223"), real(a), tol);
2341    BOOST_CHECK_CLOSE_FRACTION(real_type("0.53092108624851980526704009066067655967277345095149103008706855371803528753067068552935673000832252607835087747"), imag(a), tol);
2342    a = cosh(c);
2343    BOOST_CHECK_CLOSE_FRACTION(real_type("-3.7245455049153225654739707032559725286749657732153307267858945686649501059065292889110148294141744084833329553"), real(a), tol);
2344    BOOST_CHECK_CLOSE_FRACTION(real_type("0.51182256998738460883446384980187563424555660949074386745538379123585339045741119409984041226187262097496424111"), imag(a), tol);
2345    a = tanh(c);
2346    BOOST_CHECK_CLOSE_FRACTION(real_type("0.965385879022133124278480269394560685879729650005757773636908240066639772853967550095754361348005358178253777920"), real(a), tol * 5);
2347    BOOST_CHECK_CLOSE_FRACTION(real_type("-0.00988437503832249372031403430350121097961813353467039031861010606115560355679254344335582852193041894874685555114"), imag(a), tol);
2348    a = asinh(c);
2349    BOOST_CHECK_CLOSE_FRACTION(real_type("1.968637925793096291788665095245498189520731012682010573842811017352748255492485345887875752070076230641308014923"), real(a), tol);
2350    BOOST_CHECK_CLOSE_FRACTION(real_type("0.9646585044076027920454110594995323555197773725073316527132580297155508786089335572049608301897631767195194427315"), imag(a), tol);
2351    a = acosh(c);
2352    BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), real(a), tol);
2353    BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), imag(a), tol);
2354    a = atanh(c);
2355    BOOST_CHECK_CLOSE_FRACTION(real_type("0.1469466662255297520474327851547159424423449403442452953891851939502023996823900422792744078835711416939934387775"), real(a), tol);
2356    BOOST_CHECK_CLOSE_FRACTION(real_type("1.338972522294493561124193575909144241084316172544492778582005751793809271060233646663717270678614587712809117131"), imag(a), tol);
2357    a = sinh(c + 0);
2358    BOOST_CHECK_CLOSE_FRACTION(real_type("-3.5905645899857799520125654477948167931949136757293015099986213974178826801534614215227593814301490087307920223"), real(a), tol);
2359    BOOST_CHECK_CLOSE_FRACTION(real_type("0.53092108624851980526704009066067655967277345095149103008706855371803528753067068552935673000832252607835087747"), imag(a), tol);
2360    a = cosh(c + 0);
2361    BOOST_CHECK_CLOSE_FRACTION(real_type("-3.7245455049153225654739707032559725286749657732153307267858945686649501059065292889110148294141744084833329553"), real(a), tol);
2362    BOOST_CHECK_CLOSE_FRACTION(real_type("0.51182256998738460883446384980187563424555660949074386745538379123585339045741119409984041226187262097496424111"), imag(a), tol);
2363    a = tanh(c + 0);
2364    BOOST_CHECK_CLOSE_FRACTION(real_type("0.965385879022133124278480269394560685879729650005757773636908240066639772853967550095754361348005358178253777920"), real(a), tol);
2365    BOOST_CHECK_CLOSE_FRACTION(real_type("-0.00988437503832249372031403430350121097961813353467039031861010606115560355679254344335582852193041894874685555114"), imag(a), tol);
2366    a = asinh(c + 0);
2367    BOOST_CHECK_CLOSE_FRACTION(real_type("1.968637925793096291788665095245498189520731012682010573842811017352748255492485345887875752070076230641308014923"), real(a), tol);
2368    BOOST_CHECK_CLOSE_FRACTION(real_type("0.9646585044076027920454110594995323555197773725073316527132580297155508786089335572049608301897631767195194427315"), imag(a), tol);
2369    a = acosh(c + 0);
2370    BOOST_CHECK_CLOSE_FRACTION(real_type("1.983387029916535432347076902894039565014248302909345356125267430944752731616095111727103650117987412058949254132"), real(a), tol);
2371    BOOST_CHECK_CLOSE_FRACTION(real_type("1.000143542473797218521037811954081791915781454591512773957199036332934196716853565071982697727425908742684531873"), imag(a), tol);
2372    a = atanh(c + 0);
2373    BOOST_CHECK_CLOSE_FRACTION(real_type("0.1469466662255297520474327851547159424423449403442452953891851939502023996823900422792744078835711416939934387775"), real(a), tol);
2374    BOOST_CHECK_CLOSE_FRACTION(real_type("1.338972522294493561124193575909144241084316172544492778582005751793809271060233646663717270678614587712809117131"), imag(a), tol);
2375 }
2376
2377 template <class Real>
2378 typename boost::enable_if_c<boost::multiprecision::number_category<Real>::value != boost::multiprecision::number_kind_complex>::type test_members(Real)
2379 {
2380    //
2381    // Test sign and zero functions:
2382    //
2383    Real a = 20;
2384    Real b = 30;
2385    BOOST_CHECK(a.sign() > 0);
2386    BOOST_CHECK(!a.is_zero());
2387    if (std::numeric_limits<Real>::is_signed)
2388    {
2389       a = -20;
2390       BOOST_CHECK(a.sign() < 0);
2391       BOOST_CHECK(!a.is_zero());
2392    }
2393    a = 0;
2394    BOOST_CHECK_EQUAL(a.sign(), 0);
2395    BOOST_CHECK(a.is_zero());
2396
2397    a = 20;
2398    b = 30;
2399    a.swap(b);
2400    BOOST_CHECK_EQUAL(a, 30);
2401    BOOST_CHECK_EQUAL(b, 20);
2402    //
2403    // Test complex number functions which are also overloaded for scalar type:
2404    //
2405    BOOST_CHECK_EQUAL(real(a), a);
2406    BOOST_CHECK_EQUAL(imag(a), 0);
2407    BOOST_CHECK_EQUAL(real(a + 0), a);
2408    BOOST_CHECK_EQUAL(imag(a + 2), 0);
2409    BOOST_CHECK_EQUAL(norm(a), a * a);
2410    BOOST_CHECK_EQUAL(norm(a * 1), a * a);
2411    BOOST_CHECK_EQUAL(conj(a), a);
2412    BOOST_CHECK_EQUAL(conj(a * 1), a);
2413    BOOST_CHECK_EQUAL(proj(a), a);
2414    BOOST_CHECK_EQUAL(proj(a * 1), a);
2415    BOOST_CHECK_EQUAL(a.real(), a);
2416    BOOST_CHECK_EQUAL(a.imag(), 0);
2417    a.real(55);
2418    BOOST_CHECK_EQUAL(a, 55);
2419 }
2420
2421 template <class Real>
2422 void test_members(boost::rational<Real>)
2423 {
2424 }
2425
2426 template <class Real>
2427 void test_signed_ops(const boost::mpl::true_&)
2428 {
2429    Real a(8);
2430    Real b(64);
2431    Real c(500);
2432    Real d(1024);
2433    Real ac;
2434    BOOST_CHECK_EQUAL(-a, -8);
2435    ac = a;
2436    ac = ac - b;
2437    BOOST_CHECK_EQUAL(ac, 8 - 64);
2438    ac = a;
2439    ac -= a + b;
2440    BOOST_CHECK_EQUAL(ac, -64);
2441    ac = a;
2442    ac -= b - a;
2443    BOOST_CHECK_EQUAL(ac, 16 - 64);
2444    ac = -a;
2445    BOOST_CHECK_EQUAL(ac, -8);
2446    ac = a;
2447    ac -= -a;
2448    BOOST_CHECK_EQUAL(ac, 16);
2449    ac = a;
2450    ac += -a;
2451    BOOST_CHECK_EQUAL(ac, 0);
2452    ac = b;
2453    ac /= -a;
2454    BOOST_CHECK_EQUAL(ac, -8);
2455    ac = a;
2456    ac *= -a;
2457    BOOST_CHECK_EQUAL(ac, -64);
2458    ac = a + -b;
2459    BOOST_CHECK_EQUAL(ac, 8 - 64);
2460    ac = -a + b;
2461    BOOST_CHECK_EQUAL(ac, -8 + 64);
2462    ac = -a + -b;
2463    BOOST_CHECK_EQUAL(ac, -72);
2464    ac = a + -+-b; // lots of unary operators!!
2465    BOOST_CHECK_EQUAL(ac, 72);
2466    test_conditional(Real(-a), -a);
2467 }
2468 template <class Real>
2469 void test_signed_ops(const boost::mpl::false_&)
2470 {
2471 }
2472
2473 template <class Real>
2474 void test_basic_conditionals(Real a, Real b)
2475 {
2476    if (a)
2477    {
2478       BOOST_ERROR("Unexpected non-zero result");
2479    }
2480    if (!a)
2481    {
2482    }
2483    else
2484    {
2485       BOOST_ERROR("Unexpected zero result");
2486    }
2487    b = 2;
2488    if (!b)
2489    {
2490       BOOST_ERROR("Unexpected zero result");
2491    }
2492    if (b)
2493    {
2494    }
2495    else
2496    {
2497       BOOST_ERROR("Unexpected non-zero result");
2498    }
2499    if (a && b)
2500    {
2501       BOOST_ERROR("Unexpected zero result");
2502    }
2503    if (!(a || b))
2504    {
2505       BOOST_ERROR("Unexpected zero result");
2506    }
2507    if (a + b)
2508    {
2509    }
2510    else
2511    {
2512       BOOST_ERROR("Unexpected zero result");
2513    }
2514    if (b - 2)
2515    {
2516       BOOST_ERROR("Unexpected non-zero result");
2517    }
2518 }
2519
2520 template <class T>
2521 typename boost::enable_if_c<boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex>::type
2522 test_relationals(T a, T b)
2523 {
2524    BOOST_CHECK_EQUAL((a == b), false);
2525    BOOST_CHECK_EQUAL((a != b), true);
2526
2527    BOOST_CHECK_EQUAL((a + b == b), false);
2528    BOOST_CHECK_EQUAL((a + b != b), true);
2529
2530    BOOST_CHECK_EQUAL((a == b + a), false);
2531    BOOST_CHECK_EQUAL((a != b + a), true);
2532
2533    BOOST_CHECK_EQUAL((a + b == b + a), true);
2534    BOOST_CHECK_EQUAL((a + b != b + a), false);
2535
2536    BOOST_CHECK_EQUAL((8 == b + a), false);
2537    BOOST_CHECK_EQUAL((8 != b + a), true);
2538    BOOST_CHECK_EQUAL((800 == b + a), false);
2539    BOOST_CHECK_EQUAL((800 != b + a), true);
2540    BOOST_CHECK_EQUAL((72 == b + a), true);
2541    BOOST_CHECK_EQUAL((72 != b + a), false);
2542
2543    BOOST_CHECK_EQUAL((b + a == 8), false);
2544    BOOST_CHECK_EQUAL((b + a != 8), true);
2545    BOOST_CHECK_EQUAL((b + a == 800), false);
2546    BOOST_CHECK_EQUAL((b + a != 800), true);
2547    BOOST_CHECK_EQUAL((b + a == 72), true);
2548    BOOST_CHECK_EQUAL((b + a != 72), false);
2549 }
2550
2551 template <class T>
2552 typename boost::disable_if_c<boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex>::type
2553 test_relationals(T a, T b)
2554 {
2555    BOOST_CHECK_EQUAL((a == b), false);
2556    BOOST_CHECK_EQUAL((a != b), true);
2557    BOOST_CHECK_EQUAL((a <= b), true);
2558    BOOST_CHECK_EQUAL((a < b), true);
2559    BOOST_CHECK_EQUAL((a >= b), false);
2560    BOOST_CHECK_EQUAL((a > b), false);
2561
2562    BOOST_CHECK_EQUAL((a + b == b), false);
2563    BOOST_CHECK_EQUAL((a + b != b), true);
2564    BOOST_CHECK_EQUAL((a + b >= b), true);
2565    BOOST_CHECK_EQUAL((a + b > b), true);
2566    BOOST_CHECK_EQUAL((a + b <= b), false);
2567    BOOST_CHECK_EQUAL((a + b < b), false);
2568
2569    BOOST_CHECK_EQUAL((a == b + a), false);
2570    BOOST_CHECK_EQUAL((a != b + a), true);
2571    BOOST_CHECK_EQUAL((a <= b + a), true);
2572    BOOST_CHECK_EQUAL((a < b + a), true);
2573    BOOST_CHECK_EQUAL((a >= b + a), false);
2574    BOOST_CHECK_EQUAL((a > b + a), false);
2575
2576    BOOST_CHECK_EQUAL((a + b == b + a), true);
2577    BOOST_CHECK_EQUAL((a + b != b + a), false);
2578    BOOST_CHECK_EQUAL((a + b <= b + a), true);
2579    BOOST_CHECK_EQUAL((a + b < b + a), false);
2580    BOOST_CHECK_EQUAL((a + b >= b + a), true);
2581    BOOST_CHECK_EQUAL((a + b > b + a), false);
2582
2583    BOOST_CHECK_EQUAL((8 == b + a), false);
2584    BOOST_CHECK_EQUAL((8 != b + a), true);
2585    BOOST_CHECK_EQUAL((8 <= b + a), true);
2586    BOOST_CHECK_EQUAL((8 < b + a), true);
2587    BOOST_CHECK_EQUAL((8 >= b + a), false);
2588    BOOST_CHECK_EQUAL((8 > b + a), false);
2589    BOOST_CHECK_EQUAL((800 == b + a), false);
2590    BOOST_CHECK_EQUAL((800 != b + a), true);
2591    BOOST_CHECK_EQUAL((800 >= b + a), true);
2592    BOOST_CHECK_EQUAL((800 > b + a), true);
2593    BOOST_CHECK_EQUAL((800 <= b + a), false);
2594    BOOST_CHECK_EQUAL((800 < b + a), false);
2595    BOOST_CHECK_EQUAL((72 == b + a), true);
2596    BOOST_CHECK_EQUAL((72 != b + a), false);
2597    BOOST_CHECK_EQUAL((72 <= b + a), true);
2598    BOOST_CHECK_EQUAL((72 < b + a), false);
2599    BOOST_CHECK_EQUAL((72 >= b + a), true);
2600    BOOST_CHECK_EQUAL((72 > b + a), false);
2601
2602    BOOST_CHECK_EQUAL((b + a == 8), false);
2603    BOOST_CHECK_EQUAL((b + a != 8), true);
2604    BOOST_CHECK_EQUAL((b + a >= 8), true);
2605    BOOST_CHECK_EQUAL((b + a > 8), true);
2606    BOOST_CHECK_EQUAL((b + a <= 8), false);
2607    BOOST_CHECK_EQUAL((b + a < 8), false);
2608    BOOST_CHECK_EQUAL((b + a == 800), false);
2609    BOOST_CHECK_EQUAL((b + a != 800), true);
2610    BOOST_CHECK_EQUAL((b + a <= 800), true);
2611    BOOST_CHECK_EQUAL((b + a < 800), true);
2612    BOOST_CHECK_EQUAL((b + a >= 800), false);
2613    BOOST_CHECK_EQUAL((b + a > 800), false);
2614    BOOST_CHECK_EQUAL((b + a == 72), true);
2615    BOOST_CHECK_EQUAL((b + a != 72), false);
2616    BOOST_CHECK_EQUAL((b + a >= 72), true);
2617    BOOST_CHECK_EQUAL((b + a > 72), false);
2618    BOOST_CHECK_EQUAL((b + a <= 72), true);
2619    BOOST_CHECK_EQUAL((b + a < 72), false);
2620
2621    T c;
2622    //
2623    // min and max overloads:
2624    //
2625 #if !defined(min) && !defined(max)
2626 //   using std::max;
2627 //   using std::min;
2628 // This works, but still causes complaints from inspect.exe, so use brackets to prevent macrosubstitution,
2629 // and to explicitly specify type T seems necessary, for reasons unclear.
2630    a = 2;
2631    b = 5;
2632    c = 6;
2633    BOOST_CHECK_EQUAL( (std::min<T>)(a, b),  a);
2634    BOOST_CHECK_EQUAL( (std::min<T>)(b, a), a);
2635    BOOST_CHECK_EQUAL( (std::max<T>)(a, b), b);
2636    BOOST_CHECK_EQUAL( (std::max<T>)(b, a), b);
2637    BOOST_CHECK_EQUAL( (std::min<T>)(a, b + c), a);
2638    BOOST_CHECK_EQUAL( (std::min<T>)(b + c, a), a);
2639    BOOST_CHECK_EQUAL( (std::min<T>)(a, c - b), 1);
2640    BOOST_CHECK_EQUAL( (std::min<T>)(c - b, a), 1);
2641    BOOST_CHECK_EQUAL( (std::max<T>)(a, b + c), 11);
2642    BOOST_CHECK_EQUAL( (std::max<T>)(b + c, a), 11);
2643    BOOST_CHECK_EQUAL( (std::max<T>)(a, c - b), a);
2644    BOOST_CHECK_EQUAL( (std::max<T>)(c - b, a), a);
2645    BOOST_CHECK_EQUAL( (std::min<T>)(a + b, b + c), 7);
2646    BOOST_CHECK_EQUAL( (std::min<T>)(b + c, a + b), 7);
2647    BOOST_CHECK_EQUAL( (std::max<T>)(a + b, b + c), 11);
2648    BOOST_CHECK_EQUAL( (std::max<T>)(b + c, a + b), 11);
2649    BOOST_CHECK_EQUAL( (std::min<T>)(a + b, c - a), 4);
2650    BOOST_CHECK_EQUAL( (std::min<T>)(c - a, a + b), 4);
2651    BOOST_CHECK_EQUAL( (std::max<T>)(a + b, c - a), 7);
2652    BOOST_CHECK_EQUAL( (std::max<T>)(c - a, a + b), 7);
2653
2654    long l1(2), l2(3), l3;
2655    l3 = (std::min)(l1, l2) + (std::max)(l1, l2) + (std::max<long>)(l1, l2) + (std::min<long>)(l1, l2);
2656    BOOST_CHECK_EQUAL(l3, 10);
2657
2658 #endif
2659 }
2660
2661 template <class T>
2662 const T& self(const T& a) { return a; }
2663
2664 template <class Real>
2665 void test()
2666 {
2667 #if !defined(NO_MIXED_OPS) && !defined(SLOW_COMPILER)
2668    boost::multiprecision::is_number<Real> tag;
2669    test_mixed<Real, unsigned char>(tag);
2670    test_mixed<Real, signed char>(tag);
2671    test_mixed<Real, char>(tag);
2672    test_mixed<Real, short>(tag);
2673    test_mixed<Real, unsigned short>(tag);
2674    test_mixed<Real, int>(tag);
2675    test_mixed<Real, unsigned int>(tag);
2676    test_mixed<Real, long>(tag);
2677    test_mixed<Real, unsigned long>(tag);
2678 #ifdef BOOST_HAS_LONG_LONG
2679    test_mixed<Real, long long>(tag);
2680    test_mixed<Real, unsigned long long>(tag);
2681 #endif
2682    test_mixed<Real, float>(tag);
2683    test_mixed<Real, double>(tag);
2684    test_mixed<Real, long double>(tag);
2685
2686    typedef typename related_type<Real>::type                                                                      related_type;
2687    boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && !boost::is_same<related_type, Real>::value> tag2;
2688
2689    test_mixed<Real, related_type>(tag2);
2690
2691    boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && (boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex)> complex_tag;
2692    test_mixed<Real, std::complex<float> >(complex_tag);
2693    test_mixed<Real, std::complex<double> >(complex_tag);
2694    test_mixed<Real, std::complex<long double> >(complex_tag);
2695
2696 #endif
2697 #ifndef MIXED_OPS_ONLY
2698    //
2699    // Integer only functions:
2700    //
2701    test_integer_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
2702    //
2703    // Real number only functions:
2704    //
2705    test_float_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
2706    //
2707    // Test basic arithmetic:
2708    //
2709    Real a(8);
2710    Real b(64);
2711    Real c(500);
2712    Real d(1024);
2713    BOOST_CHECK_EQUAL(a + b, 72);
2714    a += b;
2715    BOOST_CHECK_EQUAL(a, 72);
2716    BOOST_CHECK_EQUAL(a - b, 8);
2717    a -= b;
2718    BOOST_CHECK_EQUAL(a, 8);
2719    BOOST_CHECK_EQUAL(a * b, 8 * 64L);
2720    a *= b;
2721    BOOST_CHECK_EQUAL(a, 8 * 64L);
2722    BOOST_CHECK_EQUAL(a / b, 8);
2723    a /= b;
2724    BOOST_CHECK_EQUAL(a, 8);
2725    Real ac(a);
2726    BOOST_CHECK_EQUAL(ac, a);
2727    ac = a * c;
2728    BOOST_CHECK_EQUAL(ac, 8 * 500L);
2729    ac = 8 * 500L;
2730    ac = ac + b + c;
2731    BOOST_CHECK_EQUAL(ac, 8 * 500L + 64 + 500);
2732    ac = a;
2733    ac = b + c + ac;
2734    BOOST_CHECK_EQUAL(ac, 8 + 64 + 500);
2735    ac = ac - b + c;
2736    BOOST_CHECK_EQUAL(ac, 8 + 64 + 500 - 64 + 500);
2737    ac = a;
2738    ac = b + c - ac;
2739    BOOST_CHECK_EQUAL(ac, -8 + 64 + 500);
2740    ac = a;
2741    ac = ac * b;
2742    BOOST_CHECK_EQUAL(ac, 8 * 64);
2743    ac = a;
2744    ac *= b * ac;
2745    BOOST_CHECK_EQUAL(ac, 8 * 8 * 64);
2746    ac = b;
2747    ac = ac / a;
2748    BOOST_CHECK_EQUAL(ac, 64 / 8);
2749    ac = b;
2750    ac /= ac / a;
2751    BOOST_CHECK_EQUAL(ac, 64 / (64 / 8));
2752    ac = a;
2753    ac = b + ac * a;
2754    BOOST_CHECK_EQUAL(ac, 64 * 2);
2755    ac = a;
2756    ac = b - ac * a;
2757    BOOST_CHECK_EQUAL(ac, 0);
2758    ac = a;
2759    ac = b * (ac + a);
2760    BOOST_CHECK_EQUAL(ac, 64 * (16));
2761    ac = a;
2762    ac = b / (ac * 1);
2763    BOOST_CHECK_EQUAL(ac, 64 / 8);
2764    ac = a;
2765    ac = ac + b;
2766    BOOST_CHECK_EQUAL(ac, 8 + 64);
2767    ac = a;
2768    ac = a + ac;
2769    BOOST_CHECK_EQUAL(ac, 16);
2770    ac = a;
2771    ac = a - ac;
2772    BOOST_CHECK_EQUAL(ac, 0);
2773    ac = a;
2774    ac += a + b;
2775    BOOST_CHECK_EQUAL(ac, 80);
2776    ac = a;
2777    ac += b + a;
2778    BOOST_CHECK_EQUAL(ac, 80);
2779    ac = +a;
2780    BOOST_CHECK_EQUAL(ac, 8);
2781    ac = 8;
2782    ac = a * ac;
2783    BOOST_CHECK_EQUAL(ac, 8 * 8);
2784    ac = a;
2785    ac = a;
2786    ac += +a;
2787    BOOST_CHECK_EQUAL(ac, 16);
2788    ac = a;
2789    ac += b - a;
2790    BOOST_CHECK_EQUAL(ac, 8 + 64 - 8);
2791    ac = a;
2792    ac += b * c;
2793    BOOST_CHECK_EQUAL(ac, 8 + 64 * 500);
2794    ac = a;
2795    ac = a;
2796    ac -= +a;
2797    BOOST_CHECK_EQUAL(ac, 0);
2798    ac = a;
2799    if (std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
2800    {
2801       ac = a;
2802       ac -= c - b;
2803       BOOST_CHECK_EQUAL(ac, 8 - (500 - 64));
2804       ac = a;
2805       ac -= b * c;
2806       BOOST_CHECK_EQUAL(ac, 8 - 500 * 64);
2807    }
2808    ac = a;
2809    ac += ac * b;
2810    BOOST_CHECK_EQUAL(ac, 8 + 8 * 64);
2811    if (std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
2812    {
2813       ac = a;
2814       ac -= ac * b;
2815       BOOST_CHECK_EQUAL(ac, 8 - 8 * 64);
2816    }
2817    ac = a * 8;
2818    ac *= +a;
2819    BOOST_CHECK_EQUAL(ac, 64 * 8);
2820    ac = a;
2821    ac *= b * c;
2822    BOOST_CHECK_EQUAL(ac, 8 * 64 * 500);
2823    ac = a;
2824    ac *= b / a;
2825    BOOST_CHECK_EQUAL(ac, 8 * 64 / 8);
2826    ac = a;
2827    ac *= b + c;
2828    BOOST_CHECK_EQUAL(ac, 8 * (64 + 500));
2829    ac = b;
2830    ac /= +a;
2831    BOOST_CHECK_EQUAL(ac, 8);
2832    ac = b;
2833    ac /= b / a;
2834    BOOST_CHECK_EQUAL(ac, 64 / (64 / 8));
2835    ac = b;
2836    ac /= a + Real(0);
2837    BOOST_CHECK_EQUAL(ac, 8);
2838    //
2839    // simple tests with immediate values, these calls can be optimised in many backends:
2840    //
2841    ac = a + b;
2842    BOOST_CHECK_EQUAL(ac, 72);
2843    ac = a + +b;
2844    BOOST_CHECK_EQUAL(ac, 72);
2845    ac = +a + b;
2846    BOOST_CHECK_EQUAL(ac, 72);
2847    ac = +a + +b;
2848    BOOST_CHECK_EQUAL(ac, 72);
2849    ac = a;
2850    ac = b / ac;
2851    BOOST_CHECK_EQUAL(ac, b / a);
2852    //
2853    // Comparisons:
2854    //
2855    test_relationals(a, b);
2856    test_members(a);
2857    //
2858    // Use in Boolean context:
2859    //
2860    a = 0;
2861    b = 2;
2862    test_basic_conditionals(a, b);
2863    //
2864    // Test iostreams:
2865    //
2866    std::stringstream ss;
2867    a = 20;
2868    b = 2;
2869    ss << a;
2870    ss >> c;
2871    BOOST_CHECK_EQUAL(a, c);
2872    ss.clear();
2873    ss << a + b;
2874    ss >> c;
2875    BOOST_CHECK_EQUAL(c, 22);
2876    BOOST_CHECK_EQUAL(c, a + b);
2877    //
2878    // More cases for complete code coverage:
2879    //
2880    a = 20;
2881    b = 30;
2882    swap(a, b);
2883    BOOST_CHECK_EQUAL(a, 30);
2884    BOOST_CHECK_EQUAL(b, 20);
2885    a = 20;
2886    b = 30;
2887    std::swap(a, b);
2888    BOOST_CHECK_EQUAL(a, 30);
2889    BOOST_CHECK_EQUAL(b, 20);
2890    a = 20;
2891    b = 30;
2892    a = a + b * 2;
2893    BOOST_CHECK_EQUAL(a, 20 + 30 * 2);
2894    a = 100;
2895    a = a - b * 2;
2896    BOOST_CHECK_EQUAL(a, 100 - 30 * 2);
2897    a = 20;
2898    a = a * (b + 2);
2899    BOOST_CHECK_EQUAL(a, 20 * (32));
2900    a = 20;
2901    a = (b + 2) * a;
2902    BOOST_CHECK_EQUAL(a, 20 * (32));
2903    a = 90;
2904    b = 2;
2905    a = a / (b + 0);
2906    BOOST_CHECK_EQUAL(a, 45);
2907    a = 20;
2908    b = 30;
2909    c = (a * b) + 22;
2910    BOOST_CHECK_EQUAL(c, 20 * 30 + 22);
2911    c = 22 + (a * b);
2912    BOOST_CHECK_EQUAL(c, 20 * 30 + 22);
2913    c  = 10;
2914    ac = a + b * c;
2915    BOOST_CHECK_EQUAL(ac, 20 + 30 * 10);
2916    ac = b * c + a;
2917    BOOST_CHECK_EQUAL(ac, 20 + 30 * 10);
2918    a = a + b * c;
2919    BOOST_CHECK_EQUAL(a, 20 + 30 * 10);
2920    a = 20;
2921    b = a + b * c;
2922    BOOST_CHECK_EQUAL(b, 20 + 30 * 10);
2923    b = 30;
2924    c = a + b * c;
2925    BOOST_CHECK_EQUAL(c, 20 + 30 * 10);
2926    c = 10;
2927    c = a + b / c;
2928    BOOST_CHECK_EQUAL(c, 20 + 30 / 10);
2929
2930    //
2931    // Test conditionals:
2932    //
2933    a = 20;
2934    test_conditional(a, +a);
2935    test_conditional(a, (a + 0));
2936
2937    test_signed_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
2938    //
2939    // Test hashing:
2940    //
2941    boost::hash<Real> hasher;
2942    std::size_t       s = hasher(a);
2943    BOOST_CHECK_NE(s, 0);
2944 #ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
2945    std::hash<Real> hasher2;
2946    s = hasher2(a);
2947    BOOST_CHECK_NE(s, 0);
2948 #endif
2949
2950    //
2951    // Test move:
2952    //
2953 #ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
2954    Real m(static_cast<Real&&>(a));
2955    BOOST_CHECK_EQUAL(m, 20);
2956    // Move from already moved from object:
2957    Real m2(static_cast<Real&&>(a));
2958    // assign from moved from object
2959    // (may result in "a" being left in valid state as implementation artifact):
2960    c = static_cast<Real&&>(a);
2961    // assignment to moved-from objects:
2962    c = static_cast<Real&&>(m);
2963    BOOST_CHECK_EQUAL(c, 20);
2964    m2 = c;
2965    BOOST_CHECK_EQUAL(c, 20);
2966    // Destructor of "a" checks destruction of moved-from-object...
2967    Real m3(static_cast<Real&&>(a));
2968 #endif
2969 #ifndef BOOST_MP_NOT_TESTING_NUMBER
2970    //
2971    // string and string_view:
2972    //
2973    {
2974       std::string s1("2");
2975       Real        x(s1);
2976       BOOST_CHECK_EQUAL(x, 2);
2977       s1 = "3";
2978       x.assign(s1);
2979       BOOST_CHECK_EQUAL(x, 3);
2980 #ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
2981       s1 = "20";
2982       std::string_view v(s1.c_str(), 1);
2983       Real             y(v);
2984       BOOST_CHECK_EQUAL(y, 2);
2985       std::string_view v2(s1.c_str(), 2);
2986       y.assign(v2);
2987       BOOST_CHECK_EQUAL(y, 20);
2988 #endif
2989    }
2990 #endif
2991    //
2992    // Bug cases, self assignment first:
2993    //
2994    a = 20;
2995    a = self(a);
2996    BOOST_CHECK_EQUAL(a, 20);
2997
2998    a = 2;
2999    a = a * a * a;
3000    BOOST_CHECK_EQUAL(a, 8);
3001    a = 2;
3002    a = a + a + a;
3003    BOOST_CHECK_EQUAL(a, 6);
3004    a = 2;
3005    a = a - a + a;
3006    BOOST_CHECK_EQUAL(a, 2);
3007    a = 2;
3008    a = a + a - a;
3009    BOOST_CHECK_EQUAL(a, 2);
3010    a = 2;
3011    a = a * a - a;
3012    BOOST_CHECK_EQUAL(a, 2);
3013    a = 2;
3014    a = a + a * a;
3015    BOOST_CHECK_EQUAL(a, 6);
3016    a = 2;
3017    a = (a + a) * a;
3018    BOOST_CHECK_EQUAL(a, 8);
3019 #endif
3020 }