fld1 is weird

[jleugeri]

Hi.

I necro-posted this as a comment in a different issue ( #14487 ), which is open since 2015 and thus probably won't get looked at any time soon. So here goes. I was playing around with fld1 on Julia 1.0 on a Ubuntu system, delved too deep and awoke something in Khazad-dum.

fld and cld work as expected:

julia> fld(0.09, 0.1)
0.0
julia> fld(0.08, 0.1)
0.0
julia> fld(0.07, 0.1)
0.0
julia> fld(0.06, 0.1)
0.0

and

julia> cld(0.09, 0.1)
1.0
julia> cld(0.08, 0.1)
1.0
julia> cld(0.07, 0.1)
1.0
julia> cld(0.06, 0.1)
1.0

However:

julia> fld1(0.09, 0.1)
1.0
julia> fld1(0.08, 0.1)
0.0
julia> fld1(0.07, 0.1)
1.0
julia> fld1(0.06, 0.1)
1.0

WAT.

My system:

Julia Version 1.0.0
Commit 5d4eaca0c9 (2018-08-08 20:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
      Ubuntu 16.04.5 LTS
  uname: Linux 4.4.0-127-generic #153-Ubuntu SMP Sat May 19 10:58:46 UTC 2018 x86_64 x86_64
  CPU: Intel(R) Core(TM) i7-2600 CPU @ 3.40GHz: 
              speed         user         nice          sys         idle          irq
       #1  2998 MHz   29220504 s  374401370 s   16316182 s  412409612 s          0 s
       #2  3495 MHz   25098103 s  389922335 s    8533915 s  413120981 s          0 s
       #3  2506 MHz   32293244 s  397619253 s    7969477 s  399074571 s          0 s
       #4  2546 MHz   27990786 s  380869437 s    7981724 s  420045227 s          0 s
       #5  3026 MHz   19610614 s  405248460 s    6253806 s  406291328 s          0 s
       #6  3500 MHz   24186996 s  369161728 s    7044432 s  436747971 s          0 s
       #7  2207 MHz   25446131 s  399302571 s   10678770 s  402065306 s          0 s
       #8  1660 MHz   24326246 s  391760285 s   12716558 s  408596497 s          0 s
       
  Memory: 31.378002166748047 GB (3988.6875 MB free)
  Uptime: 8.380479e6 sec
  Load Avg:  0.2607421875  0.46875  0.4658203125
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.0 (ORCJIT, sandybridge)

Can anyone else reproduce this, or is this a problem uniquely on my system? I could easily live without fld1, but this result ... makes me nervous.

[simonbyrne]

We could just get rid of it? fld1 and fldmod1 aren't actually called anywhere in base or the stdlib.

[simonbyrne]

alternatively, we could make it only defined for integer values (it is somewhat non-sensical for floating point).

[JeffreySarnoff]

julia> vals = (collect(0.09:-0.01:0.06)...,)
(0.09, 0.08, 0.07, 0.06)

julia> xs=vals;ys=(0.1,0.1,0.1,0.1);

julia> # from def of mod1, fld1: x == (fld1(x, y) - 1) * y + mod1(x, y)

julia> (((fld1.(xs,ys)) .- 1) .* ys) .+ mod1.(xs,ys)
(0.09, -0.020000000000000004, 0.07, 0.06)

[JeffreySarnoff]

In calendar calculations, amod [adjusted modulus] is useful:

function amod( x::T , y::T ) where {T<:Signed}
    return y + modulus(x, -y)
end

function modulus( x::T, y::T ) where {T<:Signed}
     return x - y * floor(T, x / y)
end

amod(x::T, y::T) = modulus(x::T, y::T) === zero(T) ? y : modulus(x, y)

[devmotion]

Just ran into this:

julia> fld1(0.4, 0.9)
1.0

julia> fld1(0.41, 0.9)
1.0

julia> fld1(0.401, 0.9)
1.0

julia> fld1(0.4001, 0.9)
1.0

julia> fld1(0.40001, 0.9)
0.0

That's definitely not what I expected.

[JeffreySarnoff]

😢
[from Base, v1.9.0-DEV.1401]

fld1(x::T, y::T) where {T<:Real} = (m = mod1(x, y); fld(x + y - m, y))
fld(x, y) = div(a, b, RoundDown)

julia> x1 = 0.400_100; x2 = 0.400_010; y = 0.9;

julia> mod1(x1, y), mod1(x2, y)
(0.4001, 0.40001)

julia> fld1(x1, y), fld1(x2, y)
(1.0, 0.0)

# the bug is here
julia> a = x1 + y - x1; b = y; a, div(a, b, RoundDown)
(0.9, 1.0)

julia> a = x2 + y - x2; b = y; a, div(a, b, RoundDown)
(0.8999999999999999, 0.0)

# redefining fld1 quashes that bug

Base.fld1(x::T, y::T) where {T<:Real} = (m = mod1(x, y); fld((x - m) + y, y))

I am preparing a PR

[devmotion]

It seems that would also fix the example in the OP:

julia> Base.fld1(x::T, y::T) where {T<:Real} = (m = mod1(x, y); fld((x - m) + y, y))

julia> fld1(0.09, 0.1)
1.0

julia> fld1(0.08, 0.1)
1.0

julia> fld1(0.07, 0.1)
1.0

julia> fld1(0.06, 0.1)
1.0