Numeric Types

Numeric types consist of two-, four-, and eight-byte integers, as well as eight-byte floating-point numbers and selectable-precision decimals:

Name	Description
smallint	small-range integer: -32768 to +32767 (2 bytes)
integer	typical choice for integer: -2147483648 to +2147483647 (4 bytes)
bigint	large-range integer: -9223372036854775808 to +9223372036854775807 (8 bytes)
numeric	exact, fixed-length representation of numbers with decimal point: up to decimal 38 digits
double precision	variable-precision, inexact: 15 decimal digits precision

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.

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, so it is advisable to use a sensible precision for the use case at hand instead of always using the maximum precision by default.

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 often lead to larger precision and scale in 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. The resulting precision is always capped at the maximum of 38.

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

Operator	Result Type
+ or -	NUMERIC(precision, scale) with: scale = max(s1,s2) precision = max((p1-s1),(p2-s2)) + 1 + scale
*	NUMERIC(precision, scale) with: scale* = s1 + s2 precision = p1+p2
/	NUMERIC(precision, scale) with: scale* = max(6, s1 + p2 + 1) precision = p1 - s1 + s2 + max(6, s1 + p2 + 1)
%	NUMERIC(precision, scale) with: scale = max(s1,s2) precision = min((p1-s1), (p2-s2)) + scale

*) An additional rule applies for multiplication and division: If the resulting precision from the above rules exceeds 38, the scale is reduced by the exceeding amount. During this step, the scale is never reduced below 6.

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).

When used in arithmetic operation together with number literals, the literal will be treated as the smallest fitting NUMERIC type. E.g., 100 will be treated as NUMERIC(3,0), 10.0 as NUMERIC(3,1). This rule only applies to literals, not to expressions containing literals. E.g., (1+1) will be treated as NUMERIC(10,0) not NUMERIC(1,0).

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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.

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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.

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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.

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Storing numeric columns with precision larger than 18 in Hyper files is not supported, yet.

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.

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IEEE754 specifies that NaN should not compare equal to any other floating-point value (including NaN itself). In Hyper, NaN compares as equal to NaN, though. This decision was made for compatibility with PostgresQL and many other database systems.

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.