Re: [Math] float16 on ARM

From: pbristow_at_[hidden]
Date: 2019-10-15 13:33:18

> -----Original Message-----
> From: Boost <boost-bounces_at_[hidden]> On Behalf Of Matt Hurd via Boost
> Sent: 15 October 2019 13:05
> To: boost_at_[hidden]
> Cc: Matt Hurd <matthurd_at_[hidden]>
> Subject: Re: [boost] [Math] float16 on ARM
> 
> >
> >
> > Thanks for these useful references.
> >
> n.p.
> 
> 
> > Are bloat16 and IEEE float16
> > I:\boost\libs\math\include\boost\math\cstdfloat\cstdfloat_types.hpp
> >
> > the two layouts that we need to consider?
> >
> 
> Arm also supports another in that it has two similar formats __fp16 and
> _Float16 :-(
> 
> "ARM processors support (via a floating point control register
> <https://en.wikipedia.org/wiki/Control_register> bit) an "alternative half-
> precision" format, which does away with the special case for an exponent value of
> 31 (111112).[10] <https://en.wikipedia.org/wiki/Half-precision_floating-
> point_format#cite_note-10>
> It
> is almost identical to the IEEE format, but there is no encoding for infinity or NaNs;
> instead, an exponent of 31 encodes normalized numbers in the range 65536 to
> 131008." from wiki:
> https://en.wikipedia.org/wiki/Half-precision_floating-point_format
> 
> Arm reference:
> http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.100067_0612_00_
> en/sex1519040854421.html
> gcc ref: https://gcc.gnu.org/onlinedocs/gcc/Half-Precision.html
> 
> Strange complexity within Arm: "The ARM target provides hardware support for
> conversions between __fp16 and float values as an extension to VFP and NEON
> (Advanced SIMD), and from ARMv8-A provides hardware support for conversions
> between __fp16 and double values. GCC generates code using these hardware
> instructions if you compile with options to select an FPU that provides them; for
> example, -mfpu=neon-fp16 -mfloat-abi=softfp, in addition to the -mfp16-format
> option to select a half-precision format."
> 
> Unpleasant, sorry.

I really, really don't wish to know all that! 😉  Paul

> 
> More bfloat16 FWIW (hardware support list is longer):
> https://en.wikichip.org/wiki/brain_floating-point_format
> 
> So that makes at least 3 I guess.
> 
> Facebook has been experimenting with an alternate format Gustafson's post which
> is quite neat and rational and perhaps better than ieee at 64 bit
> too:
> https://www.nextplatform.com/2019/07/08/new-approach-could-sink-floating-
> point-computation/
> Facebook reference:
> https://engineering.fb.com/ai-research/floating-point-math/
> posit "land": https://posithub.org/news
> 
> but posit only lives in FPGA land AFAICT and not yet something to worry about.