printFloatHex

pub fn printFloatHex(w: *Writer, value: anytype, case: std.fmt.Case, opt_precision: ?usize) Error!void {
    const v = switch (@TypeOf(value)) {
        // comptime_float internally is a f128; this preserves precision.
        comptime_float => @as(f128, value),
        else => value,
    };

    if (std.math.signbit(v)) try w.writeByte('-');
    if (std.math.isNan(v)) return w.writeAll(switch (case) {
        .lower => "nan",
        .upper => "NAN",
    });
    if (std.math.isInf(v)) return w.writeAll(switch (case) {
        .lower => "inf",
        .upper => "INF",
    });

    const T = @TypeOf(v);
    const TU = std.meta.Int(.unsigned, @bitSizeOf(T));

    const mantissa_bits = std.math.floatMantissaBits(T);
    const fractional_bits = std.math.floatFractionalBits(T);
    const exponent_bits = std.math.floatExponentBits(T);
    const mantissa_mask = (1 << mantissa_bits) - 1;
    const exponent_mask = (1 << exponent_bits) - 1;
    const exponent_bias = (1 << (exponent_bits - 1)) - 1;

    const as_bits: TU = @bitCast(v);
    var mantissa = as_bits & mantissa_mask;
    var exponent: i32 = @as(u16, @truncate((as_bits >> mantissa_bits) & exponent_mask));

    const is_denormal = exponent == 0 and mantissa != 0;
    const is_zero = exponent == 0 and mantissa == 0;

    if (is_zero) {
        // Handle this case here to simplify the logic below.
        try w.writeAll("0x0");
        if (opt_precision) |precision| {
            if (precision > 0) {
                try w.writeAll(".");
                try w.splatByteAll('0', precision);
            }
        } else {
            try w.writeAll(".0");
        }
        try w.writeAll("p0");
        return;
    }

    if (is_denormal) {
        // Adjust the exponent for printing.
        exponent += 1;
    } else {
        if (fractional_bits == mantissa_bits)
            mantissa |= 1 << fractional_bits; // Add the implicit integer bit.
    }

    const mantissa_digits = (fractional_bits + 3) / 4;
    // Fill in zeroes to round the fraction width to a multiple of 4.
    mantissa <<= mantissa_digits * 4 - fractional_bits;

    if (opt_precision) |precision| {
        // Round if needed.
        if (precision < mantissa_digits) {
            // We always have at least 4 extra bits.
            var extra_bits = (mantissa_digits - precision) * 4;
            // The result LSB is the Guard bit, we need two more (Round and
            // Sticky) to round the value.
            while (extra_bits > 2) {
                mantissa = (mantissa >> 1) | (mantissa & 1);
                extra_bits -= 1;
            }
            // Round to nearest, tie to even.
            mantissa |= @intFromBool(mantissa & 0b100 != 0);
            mantissa += 1;
            // Drop the excess bits.
            mantissa >>= 2;
            // Restore the alignment.
            mantissa <<= @as(std.math.Log2Int(TU), @intCast((mantissa_digits - precision) * 4));

            const overflow = mantissa & (1 << 1 + mantissa_digits * 4) != 0;
            // Prefer a normalized result in case of overflow.
            if (overflow) {
                mantissa >>= 1;
                exponent += 1;
            }
        }
    }

    // +1 for the decimal part.
    var buf: [1 + mantissa_digits]u8 = undefined;
    assert(std.fmt.printInt(&buf, mantissa, 16, case, .{ .fill = '0', .width = 1 + mantissa_digits }) == buf.len);

    try w.writeAll("0x");
    try w.writeByte(buf[0]);
    const trimmed = std.mem.trimRight(u8, buf[1..], "0");
    if (opt_precision) |precision| {
        if (precision > 0) try w.writeAll(".");
    } else if (trimmed.len > 0) {
        try w.writeAll(".");
    }
    try w.writeAll(trimmed);
    // Add trailing zeros if explicitly requested.
    if (opt_precision) |precision| if (precision > 0) {
        if (precision > trimmed.len)
            try w.splatByteAll('0', precision - trimmed.len);
    };
    try w.writeAll("p");
    try w.printInt(exponent - exponent_bias, 10, case, .{});
}