4e5f8b4d8d
Use expm1f(x) = exp(x) - 1 for |x| > ln(2). For |x| <= ln(2), divide it into 3 subintervals: [-ln2, -1/8], [-1/8, 1/8], [1/8, ln2] and use a degree-6 polynomial approximation generated by Sollya's fpminmax for each interval. Errors < 1.5 ULPs when we use fma to evaluate the polynomials. Differential Revision: https://reviews.llvm.org/D101134
This directory contains machine independent implementations of floating point
operations. The implementations are nested in the namespace
__llvm_libc::fputil::generic. This is to facilitate calling these generic
implementations from machine dependent implementations. Consider the example of
the fuse-multiply-add operation (FMA). The C standard library requires three
different flavors, fma which operates double precsion numbers, fmaf which
operates on single precision numbers, and fmal which operates on lond double
numbers. On Aarch64, there are hardware instructions which implement the single
and double precision flavors but not the long double flavor. For such targets,
we want to be able to call the generic long double implementation from the
long double flavor. By putting the generic implementations in a separate
nested namespace, we will be to call them as follows:
namespace __llvm_libc {
namespace fputil {
long double fmal(long double x, long double y, long double z) {
return generic::fmal(x, y, z);
}
} // namespace fputil
} // namespace __llvm_libc
Note that actual code might not be as straightforward as above (for example, we might want to prevent implicit type promotions by using some template facilities). But, the general idea is very similar.