/usr/include/boost/math/special_functions/next.hpp is in libboost1.55-dev 1.55.0+dfsg-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 | // (C) Copyright John Maddock 2008.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_SPECIAL_NEXT_HPP
#define BOOST_MATH_SPECIAL_NEXT_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/math/special_functions/sign.hpp>
#include <boost/math/special_functions/trunc.hpp>
#ifdef BOOST_MSVC
#include <float.h>
#endif
namespace boost{ namespace math{
namespace detail{
template <class T>
inline T get_smallest_value(mpl::true_ const&)
{
//
// numeric_limits lies about denorms being present - particularly
// when this can be turned on or off at runtime, as is the case
// when using the SSE2 registers in DAZ or FTZ mode.
//
static const T m = std::numeric_limits<T>::denorm_min();
return ((tools::min_value<T>() - m) == tools::min_value<T>()) ? tools::min_value<T>() : m;
}
template <class T>
inline T get_smallest_value(mpl::false_ const&)
{
return tools::min_value<T>();
}
template <class T>
inline T get_smallest_value()
{
#if defined(BOOST_MSVC) && (BOOST_MSVC <= 1310)
return get_smallest_value<T>(mpl::bool_<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == 1)>());
#else
return get_smallest_value<T>(mpl::bool_<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::has_denorm == std::denorm_present)>());
#endif
}
//
// Returns the smallest value that won't generate denorms when
// we calculate the value of the least-significant-bit:
//
template <class T>
T get_min_shift_value();
template <class T>
struct min_shift_initializer
{
struct init
{
init()
{
do_init();
}
static void do_init()
{
get_min_shift_value<T>();
}
void force_instantiate()const{}
};
static const init initializer;
static void force_instantiate()
{
initializer.force_instantiate();
}
};
template <class T>
const typename min_shift_initializer<T>::init min_shift_initializer<T>::initializer;
template <class T>
inline T get_min_shift_value()
{
BOOST_MATH_STD_USING
static const T val = ldexp(tools::min_value<T>(), tools::digits<T>() + 1);
min_shift_initializer<T>::force_instantiate();
return val;
}
template <class T, class Policy>
T float_next_imp(const T& val, const Policy& pol)
{
BOOST_MATH_STD_USING
int expon;
static const char* function = "float_next<%1%>(%1%)";
int fpclass = (boost::math::fpclassify)(val);
if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
{
if(val < 0)
return -tools::max_value<T>();
return policies::raise_domain_error<T>(
function,
"Argument must be finite, but got %1%", val, pol);
}
if(val >= tools::max_value<T>())
return policies::raise_overflow_error<T>(function, 0, pol);
if(val == 0)
return detail::get_smallest_value<T>();
if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value<T>()) && (val != -tools::min_value<T>()))
{
//
// Special case: if the value of the least significant bit is a denorm, and the result
// would not be a denorm, then shift the input, increment, and shift back.
// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
//
return ldexp(float_next(T(ldexp(val, 2 * tools::digits<T>())), pol), -2 * tools::digits<T>());
}
if(-0.5f == frexp(val, &expon))
--expon; // reduce exponent when val is a power of two, and negative.
T diff = ldexp(T(1), expon - tools::digits<T>());
if(diff == 0)
diff = detail::get_smallest_value<T>();
return val + diff;
}
}
template <class T, class Policy>
inline typename tools::promote_args<T>::type float_next(const T& val, const Policy& pol)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::float_next_imp(static_cast<result_type>(val), pol);
}
#if 0 //def BOOST_MSVC
//
// We used to use ::_nextafter here, but doing so fails when using
// the SSE2 registers if the FTZ or DAZ flags are set, so use our own
// - albeit slower - code instead as at least that gives the correct answer.
//
template <class Policy>
inline double float_next(const double& val, const Policy& pol)
{
static const char* function = "float_next<%1%>(%1%)";
if(!(boost::math::isfinite)(val) && (val > 0))
return policies::raise_domain_error<double>(
function,
"Argument must be finite, but got %1%", val, pol);
if(val >= tools::max_value<double>())
return policies::raise_overflow_error<double>(function, 0, pol);
return ::_nextafter(val, tools::max_value<double>());
}
#endif
template <class T>
inline typename tools::promote_args<T>::type float_next(const T& val)
{
return float_next(val, policies::policy<>());
}
namespace detail{
template <class T, class Policy>
T float_prior_imp(const T& val, const Policy& pol)
{
BOOST_MATH_STD_USING
int expon;
static const char* function = "float_prior<%1%>(%1%)";
int fpclass = (boost::math::fpclassify)(val);
if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
{
if(val > 0)
return tools::max_value<T>();
return policies::raise_domain_error<T>(
function,
"Argument must be finite, but got %1%", val, pol);
}
if(val <= -tools::max_value<T>())
return -policies::raise_overflow_error<T>(function, 0, pol);
if(val == 0)
return -detail::get_smallest_value<T>();
if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value<T>()) && (val != tools::min_value<T>()))
{
//
// Special case: if the value of the least significant bit is a denorm, and the result
// would not be a denorm, then shift the input, increment, and shift back.
// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
//
return ldexp(float_prior(T(ldexp(val, 2 * tools::digits<T>())), pol), -2 * tools::digits<T>());
}
T remain = frexp(val, &expon);
if(remain == 0.5)
--expon; // when val is a power of two we must reduce the exponent
T diff = ldexp(T(1), expon - tools::digits<T>());
if(diff == 0)
diff = detail::get_smallest_value<T>();
return val - diff;
}
}
template <class T, class Policy>
inline typename tools::promote_args<T>::type float_prior(const T& val, const Policy& pol)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::float_prior_imp(static_cast<result_type>(val), pol);
}
#if 0 //def BOOST_MSVC
//
// We used to use ::_nextafter here, but doing so fails when using
// the SSE2 registers if the FTZ or DAZ flags are set, so use our own
// - albeit slower - code instead as at least that gives the correct answer.
//
template <class Policy>
inline double float_prior(const double& val, const Policy& pol)
{
static const char* function = "float_prior<%1%>(%1%)";
if(!(boost::math::isfinite)(val) && (val < 0))
return policies::raise_domain_error<double>(
function,
"Argument must be finite, but got %1%", val, pol);
if(val <= -tools::max_value<double>())
return -policies::raise_overflow_error<double>(function, 0, pol);
return ::_nextafter(val, -tools::max_value<double>());
}
#endif
template <class T>
inline typename tools::promote_args<T>::type float_prior(const T& val)
{
return float_prior(val, policies::policy<>());
}
template <class T, class U, class Policy>
inline typename tools::promote_args<T, U>::type nextafter(const T& val, const U& direction, const Policy& pol)
{
typedef typename tools::promote_args<T, U>::type result_type;
return val < direction ? boost::math::float_next<result_type>(val, pol) : val == direction ? val : boost::math::float_prior<result_type>(val, pol);
}
template <class T, class U>
inline typename tools::promote_args<T, U>::type nextafter(const T& val, const U& direction)
{
return nextafter(val, direction, policies::policy<>());
}
namespace detail{
template <class T, class Policy>
T float_distance_imp(const T& a, const T& b, const Policy& pol)
{
BOOST_MATH_STD_USING
//
// Error handling:
//
static const char* function = "float_distance<%1%>(%1%, %1%)";
if(!(boost::math::isfinite)(a))
return policies::raise_domain_error<T>(
function,
"Argument a must be finite, but got %1%", a, pol);
if(!(boost::math::isfinite)(b))
return policies::raise_domain_error<T>(
function,
"Argument b must be finite, but got %1%", b, pol);
//
// Special cases:
//
if(a > b)
return -float_distance(b, a, pol);
if(a == b)
return 0;
if(a == 0)
return 1 + fabs(float_distance(static_cast<T>((b < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), b, pol));
if(b == 0)
return 1 + fabs(float_distance(static_cast<T>((a < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), a, pol));
if(boost::math::sign(a) != boost::math::sign(b))
return 2 + fabs(float_distance(static_cast<T>((b < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), b, pol))
+ fabs(float_distance(static_cast<T>((a < 0) ? T(-detail::get_smallest_value<T>()) : detail::get_smallest_value<T>()), a, pol));
//
// By the time we get here, both a and b must have the same sign, we want
// b > a and both postive for the following logic:
//
if(a < 0)
return float_distance(static_cast<T>(-b), static_cast<T>(-a), pol);
BOOST_ASSERT(a >= 0);
BOOST_ASSERT(b >= a);
int expon;
//
// Note that if a is a denorm then the usual formula fails
// because we actually have fewer than tools::digits<T>()
// significant bits in the representation:
//
frexp(((boost::math::fpclassify)(a) == FP_SUBNORMAL) ? tools::min_value<T>() : a, &expon);
T upper = ldexp(T(1), expon);
T result = 0;
expon = tools::digits<T>() - expon;
//
// If b is greater than upper, then we *must* split the calculation
// as the size of the ULP changes with each order of magnitude change:
//
if(b > upper)
{
result = float_distance(upper, b);
}
//
// Use compensated double-double addition to avoid rounding
// errors in the subtraction:
//
T mb, x, y, z;
if(((boost::math::fpclassify)(a) == FP_SUBNORMAL) || (b - a < tools::min_value<T>()))
{
//
// Special case - either one end of the range is a denormal, or else the difference is.
// The regular code will fail if we're using the SSE2 registers on Intel and either
// the FTZ or DAZ flags are set.
//
T a2 = ldexp(a, tools::digits<T>());
T b2 = ldexp(b, tools::digits<T>());
mb = -(std::min)(T(ldexp(upper, tools::digits<T>())), b2);
x = a2 + mb;
z = x - a2;
y = (a2 - (x - z)) + (mb - z);
expon -= tools::digits<T>();
}
else
{
mb = -(std::min)(upper, b);
x = a + mb;
z = x - a;
y = (a - (x - z)) + (mb - z);
}
if(x < 0)
{
x = -x;
y = -y;
}
result += ldexp(x, expon) + ldexp(y, expon);
//
// Result must be an integer:
//
BOOST_ASSERT(result == floor(result));
return result;
}
}
template <class T, class U, class Policy>
inline typename tools::promote_args<T, U>::type float_distance(const T& a, const U& b, const Policy& pol)
{
typedef typename tools::promote_args<T, U>::type result_type;
return detail::float_distance_imp(static_cast<result_type>(a), static_cast<result_type>(b), pol);
}
template <class T, class U>
typename tools::promote_args<T, U>::type float_distance(const T& a, const U& b)
{
return boost::math::float_distance(a, b, policies::policy<>());
}
namespace detail{
template <class T, class Policy>
T float_advance_imp(T val, int distance, const Policy& pol)
{
BOOST_MATH_STD_USING
//
// Error handling:
//
static const char* function = "float_advance<%1%>(%1%, int)";
int fpclass = (boost::math::fpclassify)(val);
if((fpclass == FP_NAN) || (fpclass == FP_INFINITE))
return policies::raise_domain_error<T>(
function,
"Argument val must be finite, but got %1%", val, pol);
if(val < 0)
return -float_advance(-val, -distance, pol);
if(distance == 0)
return val;
if(distance == 1)
return float_next(val, pol);
if(distance == -1)
return float_prior(val, pol);
if(fabs(val) < detail::get_min_shift_value<T>())
{
//
// Special case: if the value of the least significant bit is a denorm,
// implement in terms of float_next/float_prior.
// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
//
if(distance > 0)
{
do{ val = float_next(val, pol); } while(--distance);
}
else
{
do{ val = float_prior(val, pol); } while(++distance);
}
return val;
}
int expon;
frexp(val, &expon);
T limit = ldexp((distance < 0 ? T(0.5f) : T(1)), expon);
if(val <= tools::min_value<T>())
{
limit = sign(T(distance)) * tools::min_value<T>();
}
T limit_distance = float_distance(val, limit);
while(fabs(limit_distance) < abs(distance))
{
distance -= itrunc(limit_distance);
val = limit;
if(distance < 0)
{
limit /= 2;
expon--;
}
else
{
limit *= 2;
expon++;
}
limit_distance = float_distance(val, limit);
if(distance && (limit_distance == 0))
{
policies::raise_evaluation_error<T>(function, "Internal logic failed while trying to increment floating point value %1%: most likely your FPU is in non-IEEE conforming mode.", val, pol);
}
}
if((0.5f == frexp(val, &expon)) && (distance < 0))
--expon;
T diff = 0;
if(val != 0)
diff = distance * ldexp(T(1), expon - tools::digits<T>());
if(diff == 0)
diff = distance * detail::get_smallest_value<T>();
return val += diff;
}
}
template <class T, class Policy>
inline typename tools::promote_args<T>::type float_advance(T val, int distance, const Policy& pol)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::float_advance_imp(static_cast<result_type>(val), distance, pol);
}
template <class T>
inline typename tools::promote_args<T>::type float_advance(const T& val, int distance)
{
return boost::math::float_advance(val, distance, policies::policy<>());
}
}} // namespaces
#endif // BOOST_MATH_SPECIAL_NEXT_HPP
|