Arithmetic functions

Overview {#overview}

Arithmetic functions work for any two operands of type UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, or Float64.

Before performing the operation, both operands are cast to the result type. The result type is determined as follows (unless specified differently in the function documentation below):

• If both operands are up to 32 bits wide, the size of the result type will be the size of the next bigger type following the bigger of the two operands (integer size promotion). For example, UInt8 + UInt16 = UInt32 or Float32 * Float32 = Float64.
• If one of the operands has 64 or more bits, the size of the result type will be the same size as the bigger of the two operands. For example, UInt32 + UInt128 = UInt128 or Float32 * Float64 = Float64.
• If one of the operands is signed, the result type will also be signed, otherwise it will be unsigned. For example, UInt32 * Int32 = Int64 or UInt32 * UInt32 = UInt64.

These rules make sure that the result type will be the smallest type which can represent all possible results. While this introduces a risk of overflows around the value range boundary, it ensures that calculations are performed quickly using the maximum native integer width of 64 bit. This behavior also guarantees compatibility with many other databases which provide 64 bit integers (BIGINT) as the biggest integer type.

Example:

SELECT toTypeName(0), toTypeName(0 + 0), toTypeName(0 + 0 + 0), toTypeName(0 + 0 + 0 + 0)

┌─toTypeName(0)─┬─toTypeName(plus(0, 0))─┬─toTypeName(plus(plus(0, 0), 0))─┬─toTypeName(plus(plus(plus(0, 0), 0), 0))─┐
│ UInt8         │ UInt16                 │ UInt32                          │ UInt64                                   │
└───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘

Overflows are produced the same way as in C++.