# Hierarchy of data types In bignum: Arbitrary-Precision Integer and Floating-Point Mathematics

```knitr::opts_chunk\$set(
collapse = TRUE,
comment = "#>"
)
```

This vignette follows terminology outlined by the vctrs package. For further information, see `help("faq-compatibility-types", package = "vctrs")`.

There are three numeric types in base R: `logical`, `integer` and `double`. They form a natural hierarchy from the simplest (`logical`) to the richest (`double`), with richer types able to accommodate simpler types without losing information.

• `integer` expands the set of integer values supported by `logical`.
• `double` expands the set of integer values supported by `integer`, and also supports non-integer values.

The bignum package provides two additional numeric types: `biginteger` and `bigfloat`. These are type-compatible with the existing numeric types because they extend the set of possible values. However, the hierarchy becomes more complex because lossy casts are now possible.

• `biginteger` expands the set of integer values supported by `double`. In fact, it supports any integer value (because `biginteger` uses arbitrary precision). But it does not support non-integer values.
• `bigfloat` expands the set of values supported by `double` (both in precision and range), but does not support the entire range of integers supported by `biginteger` (because `bigfloat` uses fixed precision).
```knitr::include_graphics("type-hierarchy.png", dpi = 300)
```

## Type conversion and lossy casts

As discussed above, casting values from one type to another can lose information.

We see an example in base R, when we cast a non-integer or large `double` to an `integer`:

```# non-integer double
as.integer(1.5)

# large double
as.integer(1e10)
```

For illustrative purposes, we now consider how lossy casts can affect bignum conversions:

```library(bignum)

# double -> biginteger
as_biginteger(1.5)

# biginteger -> double
as.double(biginteger(10)^16L)

# bigfloat -> double
as.double(bigfloat(1) / 3)

# bigfloat -> biginteger
as_biginteger(bigfloat(1.5))

# biginteger -> bigfloat
as_bigfloat(biginteger(10)^51L + 1L)
```

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bignum documentation built on May 4, 2023, 9:10 a.m.