# Float32, Float64 and BFloat16

Floating-point types represent approximate numeric values. They can cover a wide range, but most decimal fractions cannot be represented exactly. Use [Decimal](https://coordinatordb.com/docs/reference/data-types/decimal) when decimal rounding differences are unacceptable.

## Syntax

```text
Float32
Float64
BFloat16
```

## Using floating-point numbers

| Type       | Precision contract                                                  |
| ---------- | ------------------------------------------------------------------- |
| `Float32`  | IEEE single precision, with about 7 significant decimal digits.     |
| `Float64`  | IEEE double precision, with about 15–16 significant decimal digits. |
| `BFloat16` | A truncated Float32 value retaining 7 fraction bits.                |

Converting to a narrower type can change the value. `BFloat16` truncates the low Float32 bits; it does not round to the nearest representable value.

## NaN and Inf

Explicit positive and negative infinity are accepted. NaN is normalized to SQL `NULL`. A finite input that overflows its declared floating-point type raises `NUMERIC_OVERFLOW`.

Top-level columns accept `NULL` unless declared `NOT NULL`. Ordinary numeric comparisons, arithmetic and aggregates can consume these types; each function documents how it handles nonfinite results.

## BFloat16

`BFloat16` represents approximate numbers with seven fraction bits.
Conversion truncates the low Float32 bits. Use it when reduced precision is
acceptable.

```sql
SELECT to_type_name(CAST(1.5 AS BFloat16)), CAST(1.5 AS BFloat16)
FORMAT csv;
```

```text
"BFloat16",1.5
```

## Examples

### Precision loss in Float32

The integer `16777217` is exactly representable in Float64 but lies between two Float32 values:

```sql
SELECT CAST(16777217 AS Float32),
       CAST(16777217 AS Float64)
FORMAT csv;
```

```text
16777216,16777217.0
```

### NaN becomes NULL

```sql
SELECT CAST('nan' AS Float32) IS NULL,
       CAST('nan' AS Float64) IS NULL
FORMAT csv;
```

```text
1,1
```

### Explicit numeric conversion

```sql
SELECT to_float64(42), to_type_name(to_float32(42))
FORMAT csv;
```

```text
42.0,"Float32"
```