logistic_comparisons.jl

julia> import BenchmarkTools: @btime

julia> @inline _logistic_bounds(x::Float16) = (Float16(-16.64), Float16(7.625))
_logistic_bounds (generic function with 1 method)

julia> @inline _logistic_bounds(x::Float32) = (-103.27893f0, 16.635532f0)
_logistic_bounds (generic function with 2 methods)

julia> @inline _logistic_bounds(x::Float64) = (-744.4400719213812, 36.7368005696771)
_logistic_bounds (generic function with 3 methods)

julia> function logistic_v0(x::Union{Float16, Float32, Float64})
           one(x) / (one(x) + exp(-x))
       end
logistic_v0 (generic function with 1 method)

julia> function logistic_v1(x::Union{Float16, Float32, Float64})
           e = exp(x)
           lower, upper = _logistic_bounds(x)
           ifelse(
               x < lower,
               zero(x),
               ifelse(
                   x > upper,
                   one(x),
                   e / (one(x) + e)
               )
           )
       end
logistic_v1 (generic function with 1 method)

julia> function logistic_v2(x::Union{Float16, Float32, Float64})
           lower, upper = _logistic_bounds(x)
           if x < lower
               zero(x)
           elseif x > upper
               one(x)
           else
               e = exp(x)
               e / (one(x) + e)
           end
       end
logistic_v2 (generic function with 1 method)

julia> @code_llvm logistic_v1(-710.0)

;  @ REPL[6]:2 within `logistic_v1'
define double @julia_logistic_v1_17188(double) {
top:
  %1 = call double @julia_exp_17189(double %0)
;  @ REPL[6]:4 within `logistic_v1'
; ┌ @ float.jl:458 within `<'
   %2 = fcmp uge double %0, 0xC0874385446D71C3
; └
; ┌ @ operators.jl:294 within `>'
; │┌ @ float.jl:458 within `<'
    %3 = fcmp ule double %0, 0x40425E4F7B2737FA
; └└
; ┌ @ float.jl:401 within `+'
   %4 = fadd double %1, 1.000000e+00
; └
; ┌ @ float.jl:407 within `/'
   %5 = fdiv double %1, %4
; └
  %6 = select i1 %3, double %5, double 1.000000e+00
  %7 = select i1 %2, double %6, double 0.000000e+00
  ret double %7
}

julia> @code_llvm logistic_v2(-710.0)

;  @ REPL[7]:2 within `logistic_v2'
define double @julia_logistic_v2_17190(double) {
top:
;  @ REPL[7]:3 within `logistic_v2'
; ┌ @ float.jl:458 within `<'
   %1 = fcmp uge double %0, 0xC0874385446D71C3
; └
  br i1 %1, label %L4, label %L3

L3:                                               ; preds = %L4, %top
  %merge = phi double [ 0.000000e+00, %top ], [ 1.000000e+00, %L4 ]
;  @ REPL[7]:4 within `logistic_v2'
  ret double %merge

L4:                                               ; preds = %top
;  @ REPL[7]:5 within `logistic_v2'
; ┌ @ operators.jl:294 within `>'
; │┌ @ float.jl:458 within `<'
    %2 = fcmp ule double %0, 0x40425E4F7B2737FA
; └└
  br i1 %2, label %L7, label %L3

L7:                                               ; preds = %L4
;  @ REPL[7]:8 within `logistic_v2'
  %3 = call double @julia_exp_17189(double %0)
;  @ REPL[7]:9 within `logistic_v2'
; ┌ @ float.jl:401 within `+'
   %4 = fadd double %3, 1.000000e+00
; └
; ┌ @ float.jl:407 within `/'
   %5 = fdiv double %3, %4
; └
  ret double %5
}

julia> @code_native logistic_v1(-710.0)
	.section	__TEXT,__text,regular,pure_instructions
; ┌ @ REPL[6]:2 within `logistic_v1'
	pushq	%rax
	vmovsd	%xmm0, (%rsp)
	movabsq	$"reinterpret;", %rax
	callq	*%rax
	vmovsd	(%rsp), %xmm2           ## xmm2 = mem[0],zero
	movabsq	$4554540192, %rax       ## imm = 0x10F78C4A0
; │ @ REPL[6]:4 within `logistic_v1'
; │┌ @ operators.jl:294 within `>'
; ││┌ @ float.jl:458 within `<'
	vucomisd	(%rax), %xmm2
	movabsq	$4554540200, %rax       ## imm = 0x10F78C4A8
	vmovsd	(%rax), %xmm1           ## xmm1 = mem[0],zero
; │└└
	ja	L61
; │┌ @ float.jl within `+'
	vaddsd	%xmm1, %xmm0, %xmm1
; │└
; │┌ @ float.jl:407 within `/'
	vdivsd	%xmm1, %xmm0, %xmm1
; └└
; ┌ @ float.jl within `logistic_v1'
L61:
	movabsq	$4554540208, %rax       ## imm = 0x10F78C4B0
; └
; ┌ @ REPL[6]:4 within `logistic_v1'
	vcmpnltsd	(%rax), %xmm2, %xmm0
	vandpd	%xmm1, %xmm0, %xmm0
	popq	%rax
	retq
	nopw	%cs:(%rax,%rax)
	nopl	(%rax)
; └

julia> @code_native logistic_v2(-710.0)
	.section	__TEXT,__text,regular,pure_instructions
; ┌ @ REPL[7]:2 within `logistic_v2'
	pushq	%rbx
	vxorps	%xmm1, %xmm1, %xmm1
	movabsq	$4554543632, %rax       ## imm = 0x10F78D210
	vmovsd	(%rax), %xmm2           ## xmm2 = mem[0],zero
; │ @ REPL[7]:3 within `logistic_v2'
; │┌ @ float.jl:458 within `<'
	vucomisd	%xmm0, %xmm2
; │└
	ja	L77
	movabsq	$4554543640, %rbx       ## imm = 0x10F78D218
	movabsq	$4554543648, %rax       ## imm = 0x10F78D220
; │ @ REPL[7]:5 within `logistic_v2'
; │┌ @ operators.jl:294 within `>'
; ││┌ @ float.jl:458 within `<'
	vucomisd	(%rax), %xmm0
; │└└
	ja	L73
; │ @ REPL[7]:8 within `logistic_v2'
	movabsq	$"reinterpret;", %rax
	callq	*%rax
; │ @ REPL[7]:9 within `logistic_v2'
; │┌ @ float.jl:401 within `+'
	vaddsd	(%rbx), %xmm0, %xmm1
; │└
; │┌ @ float.jl:407 within `/'
	vdivsd	%xmm1, %xmm0, %xmm0
; │└
	popq	%rbx
	retq
L73:
	vmovsd	(%rbx), %xmm1           ## xmm1 = mem[0],zero
; │ @ REPL[7]:4 within `logistic_v2'
L77:
	vmovaps	%xmm1, %xmm0
	popq	%rbx
	retq
	nopw	%cs:(%rax,%rax)
	nopl	(%rax)
; └

julia> z = -710.0
-710.0

julia> @btime logistic_v0($z);
  0.035 ns (0 allocations: 0 bytes)

julia> @btime logistic_v1($z);
  93.639 ns (0 allocations: 0 bytes)

julia> @btime logistic_v2($z);
  93.414 ns (0 allocations: 0 bytes)

julia> @btime logistic_v2($z);
  91.336 ns (0 allocations: 0 bytes)

julia> @btime logistic_v1($z);
  92.003 ns (0 allocations: 0 bytes)

julia> @btime logistic_v0($z);
  0.033 ns (0 allocations: 0 bytes)

julia> z = +710.0
710.0

julia> @btime logistic_v0($z);
  54.049 ns (0 allocations: 0 bytes)

julia> @btime logistic_v1($z);
  0.033 ns (0 allocations: 0 bytes)

julia> @btime logistic_v2($z);
  0.034 ns (0 allocations: 0 bytes)

julia> @btime logistic_v2($z);
  0.034 ns (0 allocations: 0 bytes)

julia> @btime logistic_v1($z);
  0.034 ns (0 allocations: 0 bytes)

julia> @btime logistic_v0($z);
  54.050 ns (0 allocations: 0 bytes)

julia> x = rand(10_000_000);

julia> @btime logistic_v0.($x);
  81.563 ms (2 allocations: 76.29 MiB)

julia> @btime logistic_v1.($x);
  85.935 ms (2 allocations: 76.29 MiB)

julia> @btime logistic_v2.($x);
  87.461 ms (2 allocations: 76.29 MiB)

julia> @btime logistic_v2.($x);
  86.782 ms (2 allocations: 76.29 MiB)

julia> @btime logistic_v1.($x);
  86.505 ms (2 allocations: 76.29 MiB)

julia> @btime logistic_v0.($x);
  82.144 ms (2 allocations: 76.29 MiB)