Arithmetic operators

REXX arithmetic is performed by the operators +, -, *, /, %, //, and ** (add, subtract, multiply, divide, integer divide, remainder, and power), which all act on two terms, and the prefix plus and minus operators, which both act on a single term. This section describes the way in which these operations are carried out.

Before every arithmetic operation, the term or terms being operated upon have leading zeros removed (noting the position of any decimal point, and leaving only one zero if all the digits in the number are zeros). They are then truncated (if necessary) to DIGITS + 1 significant digits before being used in the computation. (The extra digit is a “guard” digit. It improves accuracy because it is inspected at the end of an operation, when a number is rounded to the required precision.) The operation is then carried out under up to double that precision, as described under the individual operations that follow. When the operation is completed, the result is rounded if necessary to the precision specified by the NUMERIC DIGITS instruction.

Rounding is done in the traditional manner. The digit to the right of the least significant digit in the result (the “guard digit”) is inspected and values of 5 through 9 are rounded up, and values of 0 through 4 are rounded down. Even/odd rounding would require the ability to calculate to arbitrary precision at all times and is, therefore, not the mechanism defined for REXX.

A conventional zero is supplied in front of the decimal point if otherwise there would be no digit before it. Significant trailing zeros are retained for addition, subtraction, and multiplication, according to the rules that follow, except that a result of zero is always expressed as the single digit 0. For division, insignificant trailing zeros are removed after rounding.

The FORMAT built-in function (see FORMAT) allows a number to be represented in a particular format if the standard result provided does not meet your requirements.