## 1.1. Numeric Types

Numeric types consist of two-, four-, and eight-byte integers, as well as eight-byte floating-point numbers and selectable-precision decimals. Table 1.2 lists the available types.

Table 1.2. Numeric Types

NameStorage SizeDescriptionRange
`smallint`2 bytessmall-range integer-32768 to +32767
`integer`4 bytestypical choice for integer-2147483648 to +2147483647
`bigint`8 byteslarge-range integer-9223372036854775808 to +9223372036854775807
`numeric`8 or 16 bytesexact, fixed-length representation of numbers with decimal pointup to 38 digits
`double precision`8 bytesvariable-precision, inexact15 decimal digits precision

### 1.1.1. Integer Types

The types `smallint`, `integer`, and `bigint` store whole numbers, that is, numbers without fractional components, of various ranges. Attempts to store values outside of the allowed range will result in an error.

### 1.1.2. Fixed-point Numbers

The type `numeric` can store fixed-point numbers with up to 38 digits without loss of precision. It is especially recommended for storing monetary amounts and other quantities where exactness is required. Calculations with `numeric` values yield exact results where possible, e.g. addition, subtraction, multiplication.

We use the following terms below: The precision of a `numeric` is the total count of significant digits in the whole number, that is, the number of digits to both sides of the decimal point. The scale of a `numeric` is the count of decimal digits in the fractional part, to the right of the decimal point. So the number 23.5141 has a precision of 6 and a scale of 4. Integers can be considered to have a scale of zero.

The maximum supported precision is 38. Internally, `numeric` values are stored as 64-bit values if the precision is smaller or equal to 18. Precisions over 18 require 128-bit for internal storage. Processing 128-bit `numeric` values is often slower than processing 64-bit values.

Both the maximum precision and the maximum scale of a `numeric` column can be configured. To declare a column of type `numeric` use the syntax:

```NUMERIC(`precision`, `scale`)
```

The precision must be positive, the scale zero or positive. Alternatively:

```NUMERIC(`precision`)
```

selects a scale of 0. Specifying:

```NUMERIC
```

selects the maximum precision of 38 and a scale of 0.

The type propagation rules for arithmetic operations with numerics never decrease the scale and set the precision such that the biggest possible result will fit into the result type. This may lead to undesired growth of both scale and precision, especially when chaining multiple arithmetic operations. Large scale might be undesirable because it takes away from the digits in front of the decimal point, potentially leading to overflow errors. Large precision might also be undesirable because `numeric` values with precision over 18 internally use 128-bit which may slow down processing. To avoid this, explicit casts to the desired scale and precision can be added throughout a query.

Arithmetic operations between a `NUMERIC(p1,s1)` and a `NUMERIC(p2,s2)` have the following results:

Table 1.3. Result Types of Arithmetic Operations with Numeric Operands

OperatorResult Type
+ or -

`NUMERIC(precision, scale)` with:
`scale = max(s1,s2)`
`precision = min(38, max((p1-s1),(p2-s2)) + 1 + scale)`

*

`NUMERIC(precision, scale)` with:
`scale = max(max(s1,s2), min(s1+s2, 38 - (p1-s1) - (p2-s2)))`
`precision = min(p1+p2, 38)`

/

`NUMERIC(precision, scale)` with:
`scale = max(s1,s2)`
`precision = min(38, ((p1-s1) + s2 + scale))`

%

`NUMERIC(precision, scale)` with:
`scale = max(s1,s2)`
`precision = min((p1-s1), (p2-s2)) + scale`

When used in arithmetic operation together with `NUMERIC`, `DOUBLE PRECISION` operands will always give `DOUBLE PRECISION` results, `SMALLINT` behaves the same as `NUMERIC(5,0)`, `INTEGER` as `NUMERIC(10,0)` and `BIGINT` as `NUMERIC(19,0)`.

### Note

In the SQL standard, as well as in PostgreSQL and many other database systems, the types `decimal` and `numeric` are equivalent and both support variable-length precision. This is unlike Hyper, where `numeric` has fixed-length precision and `decimal` is not officially supported.

### Note

Hyper does not support arbitrary-precision decimal numbers.

### Note

If you create an extract of a relational database in Tableau, the extract will always use the Hyper `double precision` type, so you only get 15 digits of precision. However, you can create the extract file using the Hyper API and specify the `numeric` type to get up to 38 digits.

### Note

Once a `numeric` value has a precision of over 18, 128-bit are used for internal storage which can impact the performance of all subsequent operations.

### Note

Storing `numeric` columns with precision larger than 18 is not available, yet.

### 1.1.3. Floating-Point Type

The data type `double precision` is an inexact, variable-precision numeric type. On all currently supported platforms, these types are implementations of IEEE Standard 754 for Binary Floating-Point Arithmetic.

Inexact means that some values cannot be converted exactly to the internal format and are stored as approximations, so that storing and retrieving a value might show slight discrepancies. This is not a limitation of Hyper but an inherent trade-off of using floating-point values. In particular, the following recommendations should be taken into account when using floating-point types:

• If you require exact storage and calculations (such as for monetary amounts), use the `numeric` type instead.

• Aggregations such as `sum()` on floating-point values may yield inconsistent results when executed repeatedly due to parallel computation of aggregates. If you require consistent results, consider using `numeric` instead.

• Comparing two floating-point values for equality might not always work as expected. Using difference to a small epsilon value is recommended instead.

On all currently supported platforms, the `double precision` type has a range of around 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are too large or too small will cause an error. Rounding might take place if the precision of an input number is too high. Numbers too close to zero that are not representable as distinct from zero will cause an underflow error.

By default, floating point values are output in text form in their shortest precise decimal representation; the decimal value produced is closer to the true stored binary value than to any other value representable in the same binary precision. This value will use at most 17 significant decimal digits.

In addition to ordinary numeric values, the floating-point types have several special values:

`Infinity`
`-Infinity`
`NaN`

These represent the IEEE 754 special values infinity, negative infinity, and not-a-number, respectively. When writing these values as constants in an SQL command, you must put quotes around them, for example `UPDATE table SET x = '-Infinity'`. On input, these strings are recognized in a case-insensitive manner.

### Note

IEEE754 specifies that `NaN` should not compare equal to any other floating-point value (including `NaN` itself).

Hyper also supports the SQL-standard notations `float` and `float(p)` for specifying inexact numeric types. Here, `p` specifies the minimum acceptable precision in binary digits. However, the `p` argument is currently ignored and all `float(p)` types are simply mapped to `double precision`. `float` with no precision specified is also mapped to `double precision`.