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_prior(const T& val, const Policy& pol)
{
BOOST_MATH_STD_USING
int expon;
static const char* function = "float_prior<%1%>(%1%)";
int fpclass = (pdalboost::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;
}
inline T float_prior(const T& val)
{
return float_prior(val, policies::policy<>());
}
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;
}