T float_advance(T val, int distance, const Policy& pol)
{
//
// Error handling:
//
static const char* function = "float_advance<%1%>(%1%, int)";
if(!(boost::math::isfinite)(val))
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);
BOOST_MATH_STD_USING
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((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;
}
T float_advance(T val, int distance, const Policy& pol)
{
BOOST_MATH_STD_USING
//
// Error handling:
//
static const char* function = "float_advance<%1%>(%1%, int)";
int fpclass = (pdalboost::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;
}
T float_distance(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);
if(a == b)
return 0;
if(a == 0)
return 1 + fabs(float_distance(boost::math::sign(b) * detail::get_smallest_value<T>(), b, pol));
if(b == 0)
return 1 + fabs(float_distance(boost::math::sign(a) * detail::get_smallest_value<T>(), a, pol));
if(boost::math::sign(a) != boost::math::sign(b))
return 2 + fabs(float_distance(boost::math::sign(b) * detail::get_smallest_value<T>(), b, pol))
+ fabs(float_distance(boost::math::sign(a) * 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(-b, -a);
BOOST_ASSERT(a >= 0);
BOOST_ASSERT(b >= a);
BOOST_MATH_STD_USING
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 = -(std::min)(upper, b);
T x = a + mb;
T z = x - a;
T 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;
}
T float_distance(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(!(pdalboost::math::isfinite)(a))
return policies::raise_domain_error<T>(
function,
"Argument a must be finite, but got %1%", a, pol);
if(!(pdalboost::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) ? -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) ? -detail::get_smallest_value<T>() : detail::get_smallest_value<T>()), a, pol));
if(pdalboost::math::sign(a) != pdalboost::math::sign(b))
return 2 + fabs(float_distance(static_cast<T>((b < 0) ? -detail::get_smallest_value<T>() : detail::get_smallest_value<T>()), b, pol))
+ fabs(float_distance(static_cast<T>((a < 0) ? -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(((pdalboost::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(((pdalboost::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;
}
