const T& get_constant_log10()
{
static T result;
static bool b = false;
if(!b)
{
typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
T ten;
ten = ui_type(10u);
eval_log(result, ten);
}
constant_initializer<T, &get_constant_log10<T> >::do_nothing();
return result;
}
inline void eval_pow(T& result, const T& x, const T& a)
{
BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The pow function is only valid for floating point types.");
typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
typedef typename boost::multiprecision::detail::canonical<unsigned, T>::type ui_type;
typedef typename T::exponent_type exp_type;
typedef typename boost::multiprecision::detail::canonical<exp_type, T>::type canonical_exp_type;
typedef typename mpl::front<typename T::float_types>::type fp_type;
if((&result == &x) || (&result == &a))
{
T t;
eval_pow(t, x, a);
result = t;
return;
}
if(a.compare(si_type(1)) == 0)
{
result = x;
return;
}
int type = eval_fpclassify(x);
switch(type)
{
case FP_INFINITE:
result = x;
return;
case FP_ZERO:
result = si_type(1);
return;
case FP_NAN:
result = x;
return;
default: ;
}
if(eval_get_sign(a) == 0)
{
result = si_type(1);
return;
}
if(a.compare(si_type(-1)) < 0)
{
T t, da;
t = a;
t.negate();
eval_pow(da, x, t);
eval_divide(result, si_type(1), da);
return;
}
bool bo_a_isint = false;
typename boost::multiprecision::detail::canonical<boost::intmax_t, T>::type an;
T fa;
try
{
eval_convert_to(&an, a);
if(a.compare(an) == 0)
{
detail::pow_imp(result, x, an, mpl::true_());
return;
}
}
catch(const std::exception&)
{
// conversion failed, just fall through, value is not an integer.
an = (std::numeric_limits<boost::intmax_t>::max)();
}
if((eval_get_sign(x) < 0) && !bo_a_isint)
{
result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
}
T t, da;
eval_subtract(da, a, an);
if((x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0))
{
if(a.compare(fp_type(1e-5f)) <= 0)
{
// Series expansion for small a.
eval_log(t, x);
eval_multiply(t, a);
hyp0F0(result, t);
return;
}
else
{
// Series expansion for moderately sized x. Note that for large power of a,
// the power of the integer part of a is calculated using the pown function.
if(an)
{
da.negate();
t = si_type(1);
eval_subtract(t, x);
hyp1F0(result, da, t);
detail::pow_imp(t, x, an, mpl::true_());
eval_multiply(result, t);
}
else
{
da = a;
da.negate();
t = si_type(1);
eval_subtract(t, x);
hyp1F0(result, da, t);
}
}
}
else
{
// Series expansion for pow(x, a). Note that for large power of a, the power
// of the integer part of a is calculated using the pown function.
if(an)
{
eval_log(t, x);
eval_multiply(t, da);
eval_exp(result, t);
detail::pow_imp(t, x, an, mpl::true_());
eval_multiply(result, t);
}
else
{
eval_log(t, x);
eval_multiply(t, a);
eval_exp(result, t);
}
}
}
void eval_log10(T& result, const T& arg)
{
BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The log10 function is only valid for floating point types.");
eval_log(result, arg);
eval_divide(result, get_constant_log10<T>());
}
inline void eval_pow(T& result, const T& x, const T& a)
{
BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The pow function is only valid for floating point types.");
typedef typename boost::multiprecision::detail::canonical<int, T>::type si_type;
typedef typename mpl::front<typename T::float_types>::type fp_type;
if((&result == &x) || (&result == &a))
{
T t;
eval_pow(t, x, a);
result = t;
return;
}
if(a.compare(si_type(1)) == 0)
{
result = x;
return;
}
int type = eval_fpclassify(x);
switch(type)
{
case FP_INFINITE:
result = x;
return;
case FP_ZERO:
switch(eval_fpclassify(a))
{
case FP_ZERO:
result = si_type(1);
break;
case FP_NAN:
result = a;
break;
default:
result = x;
break;
}
return;
case FP_NAN:
result = x;
return;
default: ;
}
int s = eval_get_sign(a);
if(s == 0)
{
result = si_type(1);
return;
}
if(s < 0)
{
T t, da;
t = a;
t.negate();
eval_pow(da, x, t);
eval_divide(result, si_type(1), da);
return;
}
typename boost::multiprecision::detail::canonical<boost::intmax_t, T>::type an;
T fa;
#ifndef BOOST_NO_EXCEPTIONS
try
{
#endif
eval_convert_to(&an, a);
if(a.compare(an) == 0)
{
detail::pow_imp(result, x, an, mpl::true_());
return;
}
#ifndef BOOST_NO_EXCEPTIONS
}
catch(const std::exception&)
{
// conversion failed, just fall through, value is not an integer.
an = (std::numeric_limits<boost::intmax_t>::max)();
}
#endif
if((eval_get_sign(x) < 0))
{
typename boost::multiprecision::detail::canonical<boost::uintmax_t, T>::type aun;
#ifndef BOOST_NO_EXCEPTIONS
try
{
#endif
eval_convert_to(&aun, a);
if(a.compare(aun) == 0)
{
fa = x;
fa.negate();
eval_pow(result, fa, a);
if(aun & 1u)
result.negate();
return;
}
#ifndef BOOST_NO_EXCEPTIONS
}
catch(const std::exception&)
{
// conversion failed, just fall through, value is not an integer.
}
#endif
if(std::numeric_limits<number<T, et_on> >::has_quiet_NaN)
result = std::numeric_limits<number<T, et_on> >::quiet_NaN().backend();
else
{
BOOST_THROW_EXCEPTION(std::domain_error("Result of pow is undefined or non-real and there is no NaN for this number type."));
}
return;
}
T t, da;
eval_subtract(da, a, an);
if((x.compare(fp_type(0.5)) >= 0) && (x.compare(fp_type(0.9)) < 0))
{
if(a.compare(fp_type(1e-5f)) <= 0)
{
// Series expansion for small a.
eval_log(t, x);
eval_multiply(t, a);
hyp0F0(result, t);
return;
}
else
{
// Series expansion for moderately sized x. Note that for large power of a,
// the power of the integer part of a is calculated using the pown function.
if(an)
{
da.negate();
t = si_type(1);
eval_subtract(t, x);
hyp1F0(result, da, t);
detail::pow_imp(t, x, an, mpl::true_());
eval_multiply(result, t);
}
else
{
da = a;
da.negate();
t = si_type(1);
eval_subtract(t, x);
hyp1F0(result, da, t);
}
}
}
else
{
// Series expansion for pow(x, a). Note that for large power of a, the power
// of the integer part of a is calculated using the pown function.
if(an)
{
eval_log(t, x);
eval_multiply(t, da);
eval_exp(result, t);
detail::pow_imp(t, x, an, mpl::true_());
eval_multiply(result, t);
}
else
{
eval_log(t, x);
eval_multiply(t, a);
eval_exp(result, t);
}
}
}