Implement proper f128 float printing

[tiehuis]

Right now we cast f128 to a f64 and simply lose any excess precision we otherwise had. This may be fairly involved as errol3 (the current float printing algorithm used) is specified using f64 digits only. Will have to check the algorithm and see the appropriate modifications needed for the wider range.

[shawnl]

negative zero is also printed as positive zero:

    var negative_zero: f32 = -0.0;
    std.debug.warn("\n{}\n", negative_zero);

0.0e+00

[andrewrk]

I would like to propose that the default float printing and default float parsing in Zig should have roundtrip bit-for-bit value preservation for all values for all float types.

So that means that this fuzz test should never fail:

const std = @import("std");

test "fuzz test float printing and parsing" {
    const seed = 0x1234;
    var prng = std.rand.DefaultPrng.init(seed);
    var buf: [1024]u8 = undefined; // i don't know how big this should be
    while (true) {
        inline for ([]type{ f16, f32, f64, f128 }) |F| {
            const I = @IntType(false, F.bit_count);
            const rand_int = prng.random.int(I);
            const rand_float = @bitCast(F, rand_int);
            const serialized = std.fmt.bufPrint(&buf, "{}", rand_float) catch unreachable;
            const deserialized = std.fmt.parseFloat(F, serialized) catch unreachable;
            std.testing.expect(rand_int == @bitCast(I, deserialized));
        }
    }
}

Right now this test is a bug report generator :-)

Maybe an exception should be made for negative NaN? I'm not sure exactly what the rules are about that particular case right now.

[shawnl]

Maybe an exception should be made for negative NaN?

There are more than 2 representations of NaN, and ALL must be normalized to a single representation.