---
title: "Signed Zero"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Signed Zero}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(discretes)
```

In R, zero has a latent sign: `+0` and `-0` print the same but behave differently under reciprocation:

```{r}
identical(0, -0)
1 / 0
1 / -0
```

When a numeric series contains zero, that sign can matter for derived series (for example, after inversion).

Support for signed zero is included in the discretes package so that the proper signed infinity results by inversion:

```{r}
x <- arithmetic(0, 3, n_left = 1, n_right = 1)
x
1 / x
1 / -x
```

The functions `has_negative_zero()` and `has_positive_zero()` report whether `-0` or `+0` is a discrete value in the series.
For example, the integers contain a single positive zero:

```{r}
has_negative_zero(integers())
has_positive_zero(integers())
```


Rules around signed zero follow those of base R. For example, negation can induce negative zeroes (although note that, in R, -0 is only possible as type "double" and not of type "integer").

```{r}
has_negative_zero(-1.5 * integers())
```

Like numeric vectors, a series can contain both signs of zero:

```{r}
x <- dsct_union(-0, 0)
x
has_positive_zero(x)
has_negative_zero(x)
```

However, since they are both identical values, only one zero is enumerated by `next_discrete()`, `prev_discrete()`, or `get_discretes_*()`:

```{r}
num_discretes(x)
```

But, both signs remain latent and appear when the series is inverted:

```{r}
1 / x
num_discretes(1 / x)
```

When choosing to pull positive or negative zero from the series:

- For numeric vectors, behaviour is delegated to `base::unique()`.
- For combined series through `dsct_union()`, the zero from the first series that has a zero is taken.
- Otherwise, positive zero is selected.
