Add @divCeil

[momumi]

The / operator for unsigned integers rounds down, but it's also useful to have division that rounds up. You often see it done like this:

// div round up -> (numerator + (denominator - 1)) / denominator
const num_bytes = (bits + 7) / 8;

However, this will break if (numerator + (denominator - 1)) overflows, so for the general case you need something like this:

fn divCeil(numerator: var, denominator: var) @TypeOf(numerator) {
    const quot = @divTrunc(numerator, denominator);
    const rem = @rem(numerator, denominator);
    const round_up = @intCast(@TypeOf(numerator), @boolToInt(rem > 0));
    return quot + round_up;
}

I'm not sure if you'd want it as a builtin @divCeil or under std.math.divCeil.

[daurnimator]

I'm not sure if you'd want it as a builtin @divCeil or under std.math.divCeil.

It should only be a builtin if this is something that has a matching instruction on some CPU. Otherwise it just goes into the standard library.

[momumi]

In that case, I think we can move all of @divFloor, @divTrunc, @divExact, @mod and @rem to the std library. I'm pretty sure all CPU division/remainder instructions performing rounding towards zero.

Currently we have / and % to perform unsigned division/remainder (div), and we need @divTrunc and @rem for the signed versions (idiv). But why can't we just use / and % for the signed versions as well? With that you wouldn't need any of the builtin functions I listed.

Thinking about it further, something that we currently don't have is unchecked signed integer division. The only way we can signed integer division is with @divTrunc, but it checks for overflow when dividing by -1 @as(i8, -128) / -1

Edit:

Looking at the rest of the builtins, @shlExact and @shrExact can probably be removed. Also, there's no buitins for the ror and rol instructions which are very common in crypto algorithms and supported on quite a few different ISA.

[shawnl]

Also, there's no buitins for the ror and rol instructions

There was once a patch for @fshl and @fshr that I wrote.

[schmee]

This was added to std.math in #6189, so I think this issue can be closed.