Re: [boost] [Math] float16 on ARM

-----Original Message----- From: Boost On Behalf Of Matt Hurd via Boost Sent: 15 October 2019 13:05 To: boost@lists.boost.org Cc: Matt Hurd Subject: Re: [boost] [Math] float16 on ARM

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Thanks for these useful references.

n.p.

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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.