[Math] float16 on ARM

From: Phil Endecott (spam_from_boost_dev_at_[hidden])
Date: 2019-10-14 19:15:03

Hi,

There seems to be support for 16-bit floats on iOS, when using 
Apple's XCode clang.  This seems to be a storage-only format 
with the only instruction set support being conversions to 
and from 32- and 64-bit floats.  Quick test:

#if __ARM_FP & 2 
#warning "Have 16-bit FP"
#endif

void test()
{
  __fp16 a = 1.234;
  static_assert(sizeof(a)==2);
  __fp16 b = 2.345;
  auto sum = a+b;
  static_assert(sizeof(sum)==4);
}

There doesn't seem to be a std::numeric_limits specialisation.

I suspect that other platforms have something similar.  It would be 
good to have a boost::float16_t typedef and a portable feature-test 
macro (and maybe a software fallback).  As far as I can see, 
boost/math/cstdfloat/cstdfloat_types.hpp checks the sizes of 
float, double and long double, and checks for 128-bit floats provided 
by the compiler.  Can this be extended to check for __fp16 ?

(P.S. it seems that gcc also has support, see 
https://gcc.gnu.org/onlinedocs/gcc/Half-Precision.html )

Cheers, Phil.