[e12e]

In Julia it's easy to see the difference between promoting to full number tower and sticking to 64 floats (ed: note difference in result 0 vs 1):

  julia> using Benchmarktools

  julia> @btime floor(0.49999999999999997+0.5)

0.027 ns (0 allocations: 0 bytes)

1.0

  julia> @btime floor(0.49999999999999997+BigFloat(0.5))

280.594 ns (6 allocations: 336 bytes)

0.0

  julia> @code_native floor(0.49999999999999997+BigFloat(0.5))
    .text
  ; ┌ @ floatfuncs.jl:152 within `floor'
    subq    $24, %rsp
    movq    %rsi, 16(%rsp)
    movq    (%rsi), %rax
  ; │┌ @ floatfuncs.jl:152 within `#floor#543'
    movq    %rax, (%rsp)
    movabsq    $jl_system_image_data, %rax
    movq    %rax, 8(%rsp)
    movabsq    $japi1_round_16005, %rax
    movabsq    $jl_system_image_data, %rdi
    movq    %rsp, %rsi
    movl    $2, %edx
    callq    *%rax
  ; │└
    addq    $24, %rsp
    retq
    nopw    %cs:(%rax,%rax)
  ; └

  julia> @code_native floor(0.49999999999999997+0.5)
    .text
  ; ┌ @ floatfuncs.jl:152 within `floor'
  ; │┌ @ floatfuncs.jl:152 within `#floor#543'
  ; ││┌ @ floatfuncs.jl:152 within `round'
    vroundsd    $9, %xmm0, %xmm0, %xmm0
  ; │└└
    retq
    nopw    (%rax,%rax)
  ; └