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Merge pull request #52359 from rschu1ze/docs-integer-promotion
Docs: Add another reason for integer promotion rules in ClickHouse
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@ -6,9 +6,20 @@ sidebar_label: Arithmetic
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# Arithmetic Functions
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The result type of all arithmetic functions is the smallest type which can represent all possible results. Size promotion happens for integers up to 32 bit, e.g. `UInt8 + UInt16 = UInt32`. If one of the inters has 64 or more bits, the result is of the same type as the bigger of the input integers, e.g. `UInt16 + UInt128 = UInt128`. 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.
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Arithmetic functions work for any two operands of type `UInt8`, `UInt16`, `UInt32`, `UInt64`, `Int8`, `Int16`, `Int32`, `Int64`, `Float32`, or `Float64`.
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The result of addition or multiplication of two integers is unsigned unless one of the integers is signed.
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Before performing the operation, both operands are casted to the result type. The result type is determined as follows (unless specified
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differently in the function documentation below):
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- 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
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two operands (integer size promotion). For example, `UInt8 + UInt16 = UInt32` or `Float32 * Float32 = Float64`.
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- 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
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example, `UInt32 + UInt128 = UInt128` or `Float32 * Float64 = Float64`.
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- If one of the operands is signed, the result type will also be signed, otherwise it will be signed. For example, `UInt32 * Int32 = Int64`.
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These rules make sure that the result type will be the smallest type which can represent all possible results. While this introduces a risk
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of overflows around the value range boundary, it ensures that calculations are performed quickly using the maximum native integer width of
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64 bit. This behavior also guarantees compatibility with many other databases which provide 64 bit integers (BIGINT) as the biggest integer
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type.
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Example:
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@ -22,8 +33,6 @@ SELECT toTypeName(0), toTypeName(0 + 0), toTypeName(0 + 0 + 0), toTypeName(0 + 0
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└───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘
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```
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Arithmetic functions work for any pair of `UInt8`, `UInt16`, `UInt32`, `UInt64`, `Int8`, `Int16`, `Int32`, `Int64`, `Float32`, or `Float64` values.
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Overflows are produced the same way as in C++.
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## plus
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@ -68,7 +77,7 @@ Alias: `a \* b` (operator)
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## divide
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Calculates the quotient of two values `a` and `b`. The result is always a floating-point value. If you need integer division, you can use the `intDiv` function.
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Calculates the quotient of two values `a` and `b`. The result type is always [Float64](../../sql-reference/data-types/float.md). Integer division is provided by the `intDiv` function.
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Division by 0 returns `inf`, `-inf`, or `nan`.
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@ -84,7 +93,7 @@ Alias: `a / b` (operator)
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Performs an integer division of two values `a` by `b`, i.e. computes the quotient rounded down to the next smallest integer.
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The result has the same type as the dividend (the first parameter).
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The result has the same width as the dividend (the first parameter).
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An exception is thrown when dividing by zero, when the quotient does not fit in the range of the dividend, or when dividing a minimal negative number by minus one.
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@ -135,7 +144,7 @@ intDivOrZero(a, b)
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Calculates the remainder of the division of two values `a` by `b`.
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The result type is an integer if both inputs are integers. If one of the inputs is a floating-point number, the result is a floating-point number.
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The result type is an integer if both inputs are integers. If one of the inputs is a floating-point number, the result type is [Float64](../../sql-reference/data-types/float.md).
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The remainder is computed like in C++. Truncated division is used for negative numbers.
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