Set_zero_subnormals ineffective for Float16

[milankl]

The set_zero_subnormals function is working fine for Float32/Float64 on x86 and ARM (aarch64) in Julia 1.6-rc3 but has no effect for Float16

julia> set_zero_subnormals(true)
true
julia> floatmin(Float64)/4
0.0
julia> floatmin(Float32)/4
0.0f0
julia> floatmin(Float16)/4
Float16(1.526e-5)

This is an issue as a64fx (tested on Isambard and Fugaku) considerably slows down with subnormals:

julia> A = floatmin(Float16)*rand(Float16,1000,1000)
julia> B = floatmin(Float16)*rand(Float16,1000,1000)
julia> @btime +($A,$B);
  7.116 ms (2 allocations: 1.91 MiB)

compared to computations without subnormals

julia> A = rand(Float16,1000,1000)
julia> B = rand(Float16,1000,1000)
julia> @btime +($A,$B);
  274.681 μs (2 allocations: 1.91 MiB)

(@vchuravy I believe you've switched julia's Float16 to LLVM's half for 1.6?) @samhatfield

[vchuravy]

Switching to Float16 was a joint effort with @maleadt

Can you post the code_llvm on A64fx?

[milankl]

@vchuravy was right, official arm builds convert Float16 to Float32 for arithmetics. A solution is proposed in #40216. Nevertheless the subnormal issue persits: If 1% of operations involve subnormals, the timings are 5x slower

Without subnormals

julia> a,b = rand(Float16,100_000),rand(Float16,100_000);

julia> @btime +($a,$b);
  24.740 μs (2 allocations: 195.39 KiB)

and with 1% subnormals somewhere in the arrays

julia> a[rand(1:100_000,1000)] .*= floatmin(Float16)/2
julia> b[rand(1:100_000,1000)] .*= floatmin(Float16)/2
julia> @btime +($a,$b);
  124.040 μs (2 allocations: 195.39 KiB)

[vchuravy]

Couple notes:

1. set_zero_subnormals is implemented here

   julia/src/processor_arm.cpp

   Lines 1833 to 1839 in 514426d

   	extern "C" JL_DLLEXPORT int32_t jl_set_zero_subnormals(int8_t isZero)
   	{
   	uint32_t fpcr = get_fpcr_aarch64();
   	fpcr = isZero ? (fpcr | fpcr_fz_mask) : (fpcr & ~fpcr_fz_mask);
   	set_fpcr_aarch64(fpcr);
   	return 0;
   	}

2. Instead of manually changing the processor flag we should set the LLVM function attribute: denormal-fp-math, for that it would be great to have a generic function attribute interface like Expr(:loopinfo).

[milankl]

I'd be happy to test if changing manually the processor flag actually flushes subnormals to zero on a64fx, but I don't know how to do this. So if someone posts this here, then I'd be happy to build julia on an a64fx and test it.

[vchuravy]

Looking at: https://developer.arm.com/documentation/100403/0201/register-descriptions/advanced-simd-and-floating-point-registers/aarch64-register-descriptions/fpcr--floating-point-control-register

There seems to be a second control register for fp16 flush to zero. PR incoming