Why is `fld1` not named `cld1`?

General Usage
,
1

question in title; fld1 seems much more similar to cld than fld:

julia> findall(!iszero, [fld1(a,b)-cld(a,b) for a=-10000:.1:10000, b=[-100:-1; 1:100]]) |> length
0

julia> findall(!iszero, [fld1(a,b)-fld(a,b) for a=-10000:.1:10000, b=[-100:-1; 1:100]]) |> length
39792664

it only seems to match fld when you’re specifically looking for floating pointy weirdness:

julia> fld1(3, 0.3)
10.0

julia> cld(3, 0.3)
11.0

julia> fld(3, 0.3)
10.0

actually, the code for integers appears to be identical, since (0<a) == (0<b) is the same as (a⊻b) >= 0 for non-zero a & b:

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

it seems like it would make more sense to call something that’s pretty much cld as cld1, not fld1. is there some theory reason it’s called fld1?

2

I’ll leave a longer explanation to someone with more time but the short answer is given in its docstring:

  Flooring division, returning a value consistent with mod1(x,y)
3

but couldn’t that just as easily have been written ceiling division, returning a value consistent with mod1(x,y)? it seems to basically always be the ceiling, not the floor; the doc is just saying that its behavior is defined in terms of mod1 rather than in terms of either cld or fld