void eval_atan2(T& result, const T& y, const T& x)
{
BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The atan2 function is only valid for floating point types.");
if(&result == &y)
{
T temp(y);
eval_atan2(result, temp, x);
return;
}
else if(&result == &x)
{
T temp(x);
eval_atan2(result, y, temp);
return;
}
typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
switch(eval_fpclassify(y))
{
case FP_NAN:
result = y;
return;
case FP_ZERO:
{
int c = eval_get_sign(x);
if(c < 0)
result = get_constant_pi<T>();
else if(c >= 0)
result = ui_type(0); // Note we allow atan2(0,0) to be zero, even though it's mathematically undefined
return;
}
case FP_INFINITE:
{
if(eval_fpclassify(x) == FP_INFINITE)
{
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 is undefined or complex and there is no NaN for this number type."));
}
else
{
eval_ldexp(result, get_constant_pi<T>(), -1);
if(eval_get_sign(y) < 0)
result.negate();
}
return;
}
}
switch(eval_fpclassify(x))
{
case FP_NAN:
result = x;
return;
case FP_ZERO:
{
eval_ldexp(result, get_constant_pi<T>(), -1);
if(eval_get_sign(y) < 0)
result.negate();
return;
}
case FP_INFINITE:
if(eval_get_sign(x) > 0)
result = ui_type(0);
else
result = get_constant_pi<T>();
if(eval_get_sign(y) < 0)
result.negate();
return;
}
T xx;
eval_divide(xx, y, x);
if(eval_get_sign(xx) < 0)
xx.negate();
eval_atan(result, xx);
// Determine quadrant (sign) based on signs of x, y
const bool y_neg = eval_get_sign(y) < 0;
const bool x_neg = eval_get_sign(x) < 0;
if(y_neg != x_neg)
result.negate();
if(x_neg)
{
if(y_neg)
eval_subtract(result, get_constant_pi<T>());
else
eval_add(result, get_constant_pi<T>());
}
}
void eval_atan2(T& result, const T& y, const T& x)
{
BOOST_STATIC_ASSERT_MSG(number_category<T>::value == number_kind_floating_point, "The atan2 function is only valid for floating point types.");
if(&result == &y)
{
T temp(y);
eval_atan2(result, temp, x);
return;
}
else if(&result == &x)
{
T temp(x);
eval_atan2(result, y, temp);
return;
}
typedef typename boost::multiprecision::detail::canonical<boost::uint32_t, T>::type ui_type;
switch(eval_fpclassify(y))
{
case FP_NAN:
result = y;
errno = EDOM;
return;
case FP_ZERO:
{
if(eval_signbit(x))
{
result = get_constant_pi<T>();
if(eval_signbit(y))
result.negate();
}
else
{
result = y; // Note we allow atan2(0,0) to be +-zero, even though it's mathematically undefined
}
return;
}
case FP_INFINITE:
{
if(eval_fpclassify(x) == FP_INFINITE)
{
if(eval_signbit(x))
{
// 3Pi/4
eval_ldexp(result, get_constant_pi<T>(), -2);
eval_subtract(result, get_constant_pi<T>());
if(eval_get_sign(y) >= 0)
result.negate();
}
else
{
// Pi/4
eval_ldexp(result, get_constant_pi<T>(), -2);
if(eval_get_sign(y) < 0)
result.negate();
}
}
else
{
eval_ldexp(result, get_constant_pi<T>(), -1);
if(eval_get_sign(y) < 0)
result.negate();
}
return;
}
}
switch(eval_fpclassify(x))
{
case FP_NAN:
result = x;
errno = EDOM;
return;
case FP_ZERO:
{
eval_ldexp(result, get_constant_pi<T>(), -1);
if(eval_get_sign(y) < 0)
result.negate();
return;
}
case FP_INFINITE:
if(eval_get_sign(x) > 0)
result = ui_type(0);
else
result = get_constant_pi<T>();
if(eval_get_sign(y) < 0)
result.negate();
return;
}
T xx;
eval_divide(xx, y, x);
if(eval_get_sign(xx) < 0)
xx.negate();
eval_atan(result, xx);
// Determine quadrant (sign) based on signs of x, y
const bool y_neg = eval_get_sign(y) < 0;
const bool x_neg = eval_get_sign(x) < 0;
if(y_neg != x_neg)
result.negate();
if(x_neg)
{
if(y_neg)
eval_subtract(result, get_constant_pi<T>());
else
eval_add(result, get_constant_pi<T>());
}
}
