Use truncation division in mod for floats

[GULPF]

This might just be a pointless breaking change, but it annoys me that modulus for floats uses floor division, when div and mod for integers uses truncating division.

[krux02]

Yes this changes an unnecessary inconsistency. Here is an example how it is now.

import math

echo -3 mod 2
echo -3.0 mod 2.0

output:

-1
1.0

But I am still agains this changes, I would prefer a lot if integers would behave like the float in this case and the result would be:

1
1.0

I only need floor divison modulo. Never needed the truncating divison. Most of the time I use modulo is for indices of arrays arr[i mod arr.len]. But this patters dos not work for i < 0. So I end up writing this ugly code arr[(i mod arr.len + arr.len) mod arr.len] or I wrtie this: assert(arr.len-1 and arr.len == 0) #[ arr.len is power of two #] ; arr[i and (arr.len - 1)]. I really wish I could reliably write arr[i mod arr.len] and it would work reliably for negative numbers.

[GULPF]

Here's a good read on the different ways to implement div and mod

I don't really have an opinion on floor div vs trunc div, but I doubt changing the behavior of div and mod for integers would be accepted since it will break a lot of code.

[data-man]

C++ std::fmod

fmod(+5.1, +3.0) = 2.1
fmod(-5.1, +3.0) = -2.1
fmod(+5.1, -3.0) = 2.1
fmod(-5.1, -3.0) = -2.1
fmod(+0.0, 1.0) = 0
fmod(-0.0, 1.0) = -0
fmod(5.1, Inf) = 5.1
fmod(+5.1, 0) = -nan

C++ std::remainder

remainder(+5.1, +3.0) = -0.9
remainder(-5.1, +3.0) = 0.9
remainder(+5.1, -3.0) = -0.9
remainder(-5.1, -3.0) = 0.9
remainder(+0.0, 1.0) = 0
remainder(-0.0, 1.0) = -0
remainder(5.1, Inf) = 5.1
remainder(+5.1, 0) = -nan

Nim's output:

import math

echo +5.1 mod +3.0
echo -5.1 mod +3.0
echo +5.1 mod -3.0
echo -5.1 mod -3.0
echo +0.0 mod 1.0
echo -0.0 mod  1.0
echo 5.1 mod Inf
echo +5.1 mod  0

2.1
0.9000000000000004
-0.9000000000000004
-2.1
0.0
0.0
nan
5.1

[GULPF]

I changed the PR to simply use use fmod directly for C and % for JS, this is probably the most sane alternative.

[krux02]

and this is what mod does in maxima, a computer algebra system (mathematically correct):

(%i8) mod(+5.1, +3.0);
(%o8)                          2.099999999999999
(%i9) mod(-5.1, +3.0);
(%o9)                         0.9000000000000004
(%i10) mod(+5.1, -3.0);
(%o10)                       - 0.9000000000000004
(%i11) mod(-5.1, -3.0);
(%o11)                        - 2.099999999999999
(%i12) mod(+0.0,+1.0);
(%o12)                                0.0
(%i13) mod(-0.0,+1.0);
(%o13)                               -0.0
(%i14) mod(5.1, inf);
                                             5.1
(%o14)                       5.1 - inf floor(---)
                                             inf
(%i15) mod(5.1, 0);
(%o15)                                5.1

To be honest there are multiple definitions of mod.

[krux02]

I have changed my mind. I agree that this PR should be taken.

@GULPF can you add an entry in the changelog.md?

[Araq]

This needs a changelog entry.

[krux02]

I like how it is now. When the tests are fixed. I would approve it.

[GULPF]

Ready to merge

[data-man]

Changelog's entries for floorDiv/floorMod?