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# arith_exp - Arithmetic Operators

The table below shows the possible arithmetic operators for arithmetic expressions, their priority, and the order in which the calculation is performed. Within one parenthesis level, calculations with operators of higher priority are performed before calculations with operators of lower priority. For consecutive operators of the same priority, the calculation is performed in the order specified. In the third column of the table below, 3 indicates the highest priority and 1 the lowest. With the exception of , the operators have no effect on the calculation type. If the operator does not appear in an arithmetic expression, then the calculation type is determined only by the data types involved. When `**` is used, the calculation type is either `decfloat34` or `f`. The calculation type is `decfloat34` if one of the operands used is a decimal floating point number, otherwise it is `f`.

Operator Calculation Priority Order
`+` Addition of the operands 1 From left to right
`-` Subtraction of the right operand from the left 1 From left to right
`*` Multiplication of the operands 2 From left to right
`/` Division of the left operand by the right 2 From left to right
`DIV` Integer part of the division of the left operand by the right, with positive remainder 2 From left to right
`MOD` Positive remainder of the division of the left operand by the right; a remainder other than zero is always between zero and the size of the right operand 2 From left to right
`**` Left operand raised to the power of the right 3 From right to left

Other versions: 7.31 | 7.40 | 7.54

### Programming Guideline

Preventing Division by Zero

Notes

• Division by the value 0 is undefined and raises a handleable exception. The only situation where division by 0 does not raise an exception is if the dividend is also 0. Here, the result is set to 0.

• The result of `DIV` multiplied by `operand2` plus the result of `MOD` always results in `operand1`. Therefore, the rule that the result of `MOD` is always positive also has an impact on the result of `DIV`. The result of an integer division of two positive numbers with a remainder that is not equal to zero differs from the result of an integer division of two negative numbers with the same amounts. Likewise, for operands with different signs, which operand is positive and which is negative is of significance.

• If, when raising to a power, the left operand is 0, the right operand must be greater than or equal to 0. If the left operand is negative, the right operand must be an integer. Otherwise, both cases raise a handleable exception.

• To stop the operator `**` producing the calculation type f, the predefined function `ipow` can be used for integer exponents. Here, the calculation type is determined by the argument.

Example

The following table shows the results of integer divisions and their remainders.

operand1 operand2 DIV MOD
7 3 2 1
-7 3 -3 2
7 -3 -2 1
-7 -3 3 2

Example

Example

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Arithmetic Calculations - Example

Floating Point Numbers, Arithmetic Calculations - Example