`fld1` is really buggy when used with floats

[rokke-git]

I don't think this behavior could be considered desirable by anyone:

julia> fld1(-0.533669923120631, 3.430469)
-1.0

julia> fld1(prevfloat(-0.533669923120631), 3.430469)
0.0

julia> fld1(nextfloat(-0.533669923120631), 3.430469)
0.0

(confirmed on 1.12.5 and 1.14.0-DEV.2662)

it seems like the right thing to do here is to make fld1 an alias of cld, and deprecate its use. I don't know why we have a separate fld1 and cld anyways, since they are logically equivalent for integer inputs:

julia> @code_typed fld1(20,3)
CodeInfo(
1 ─ %1  = intrinsic Base.checked_sdiv_int(x, y)::Int64
│   %2  = intrinsic Base.xor_int(x, y)::Int64
│   %3  = intrinsic Base.slt_int(%2, 0)::Bool
│   %4  = intrinsic Base.not_int(%3)::Bool
│   %5  = intrinsic Base.mul_int(%1, y)::Int64
│   %6  =   builtin (%5 === x)::Bool
│   %7  = intrinsic Base.not_int(%6)::Bool
│   %8  = intrinsic Base.and_int(%4, %7)::Bool
│   %9  = intrinsic Core.zext_int(Core.Int64, %8)::Int64
│   %10 = intrinsic Core.and_int(%9, 1)::Int64
│   %11 = intrinsic Base.add_int(%1, %10)::Int64
└──       return %11
) => Int64

julia> @code_typed cld(20,3)
CodeInfo(
1 ─ %1  = intrinsic Base.checked_sdiv_int(a, b)::Int64
│   %2  = intrinsic Base.slt_int(0, a)::Bool
│   %3  = intrinsic Base.slt_int(0, b)::Bool
│   %4  =   builtin (%2 === %3)::Bool
│   %5  = intrinsic Base.mul_int(%1, b)::Int64
│   %6  =   builtin (%5 === a)::Bool
│   %7  = intrinsic Base.not_int(%6)::Bool
│   %8  = intrinsic Base.and_int(%4, %7)::Bool
│   %9  = intrinsic Core.zext_int(Core.Int64, %8)::Int64
│   %10 = intrinsic Core.and_int(%9, 1)::Int64
│   %11 = intrinsic Base.add_int(%1, %10)::Int64
└──       return %11
) => Int64

((0<=a) == (0<=b) and (a⊻b) >= 0 are equivalent statements; and fld1 and cld are trivially equivalent when a or b is zero)

it would also be nice if we could make fldmod1 an alias for cldmod1 and deprecate the fldmod1 name as well.

admire the flickeryness:

julia> using GLMakie

julia> fig = Figure()

julia> ax = Axis(fig[1, 1], xticks = (1:4, ["div", "cld", "fld", "fld1"]), title = "op(a, b)")
Axis with 0 plots:


julia> sl = SliderGrid(fig[2, 1],
       (range = [-logrange(100,.001,100); logrange(.001,100,100)], label = "a", format = "{:.15f}"),
       (range = [-logrange(100,.001,100); logrange(.001,100,100)], label = "b", format = "{:.15f}")
       )
SliderGrid()

julia> bars = lift([s.value for s in sl.sliders]...) do a, b
           [div(a,b), cld(a,b), fld(a,b), fld1(a,b)]
       end
Observable([1.0, 1.0, 1.0, 1.0])

julia> plt = barplot!(ax, bars)
BarPlot{Tuple{Vector{Point{2, Float64}}}}

julia> on(bars) do b
         ylims!(ax, minimum(b)-1, maximum(b)+1)
       end
ObserverFunction defined at REPL[73]:2 operating on Observable([1.0, 1.0, 1.0, 1.0])

julia> while events(fig).window_open[]
          a = sl.sliders[1].selected_index[]
          if a==200
              a=0
              b=sl.sliders[2].selected_index[]
              if b==200 b=0 end
              set_close_to!(sl.sliders[2], sl.sliders[2].range[][b+1])
          end
          set_close_to!(sl.sliders[1], sl.sliders[1].range[][a+1])
          sleep(1/60)
       end

[oscardssmith]

This continues my belief that we really shouldn't have defined fld/mod for floating point.

[rokke-git]

fld is fine, fld1 is the buggy one. very similar names, another reason to deprecate...

we currently have:

consistent with:	RoundToZero	RoundDown	RoundUp	WTF
whole number part:	÷ or div	fld	cld	fld1
fraction part:	% or rem	mod	mod1
combined function:	divrem	fldmod		fldmod1

I'm saying fld1 should be cld, and fldmod1 should be cldmod1

personally, I also feel ÷ and % should mean cld and mod1 since we index arrays starting from 1, but that can't be changed until 2.0

---

example table

table showing fldmod consistent with 0-based indexing, and cldmod1 consistent with 1-based indexing (3x3 array):
a = (-6:10)'; (k->[a; a.÷k; a.%k; fld.(a, k); mod.(a, k); cld.(a, k); mod1.(a,k)])(3)

op(a,3)	-6	-5	-4	-3	-2	-1	0	1	2	3	4	5	6	7	8	9	10
div	-2	-1	-1	-1	0	0	0	0	0	1	1	1	2	2	2	3	3
rem	0	-2	-1	0	-2	-1	0	1	2	0	1	2	0	1	2	0	1
fld	-2	-2	-2	-1	-1	-1	0	0	0	1	1	1	2	2	2	3	3
mod	0	1	2	0	1	2	0	1	2	0	1	2	0	1	2	0	1
cld	-2	-1	-1	-1	0	0	0	1	1	1	2	2	2	3	3	3	4
mod1	3	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3	1

[rokke-git]

holy cow this is so bad:

julia> fig = Figure()

julia> ax = Axis(fig[1, 1])
Axis with 0 plots:


julia> sl = SliderGrid(fig[2, 1],
       (range = [-logrange(100,.001,100); logrange(.001,100,100)], format = "{:.6f}"),
       )
SliderGrid()

julia> points = lift(sl.sliders[].value) do b
           [fld1(a,b)-fld(a,b) for a=-100:.1:100]
       end
Observable([0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0  …  0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0])


julia> plt = scatterlines!(ax, -100:.1:100, points)
ScatterLines{Tuple{Vector{Point{2, Float64}}}}

basically the slider is the denominator and the x-axis is the numerator. there's like no rhyme or reason to when it rounds up or down. I've even seen it hit -1.0 in a couple isolated cases...