The compiler determines the number of integer and decimal places in an intermediate result.
The following table shows the precision theoretically possible as the result of addition, subtraction, multiplication, or division.
| Operation | Integer places | Decimal places |
|---|---|---|
| + or - | (i1 or i2) + 1, whichever is greater | d1 or d2, whichever is greater |
| * | i1 + i2 | d1 + d2 |
| / | i2 + d1 | (d2 - d1) or dmax, whichever is greater |
You must define the operands of any arithmetic statements with enough decimal places to obtain the accuracy you want in the final result.
The following table shows the number of places the compiler carries for fixed-point intermediate results of arithmetic operations that involve addition, subtraction, multiplication, or division in compatibility mode (that is, when the default compiler option ARITH(COMPAT) is in effect):
| Value of i + d | Value of d | Value of i + dmax | Number of places carried for ir |
|---|---|---|---|
| <30 or =30 | Any value | Any value | i integer and d decimal places |
| >30 | <dmax or =dmax | Any value | 30-d integer and d decimal places |
| >dmax | <30 or =30 | i integer and 30-i decimal places | |
| >30 | 30-dmax integer and dmax decimal places |
The following table shows the number of places the compiler carries for fixed-point intermediate results of arithmetic operations that involve addition, subtraction, multiplication, or division in extended mode (that is, when the compiler option ARITH(EXTEND) is in effect):
| Value of i + d | Value of d | Value of i + dmax | Number of places carried for ir |
|---|---|---|---|
| <31 or =31 | Any value | Any value | i integer and d decimal places |
| >31 | <dmax or =dmax | Any value | 31-d integer and d decimal places |
| >dmax | <31 or =31 | i integer and 31-i decimal places | |
| >31 | 31-dmax integer and dmax decimal places |
Exponentiation is represented by the expression op1 ** op2. Based on the characteristics of op2, the compiler handles exponentiation of fixed-point numbers in one of three ways:
d = d1 * |op2|
and the value i is computed based on the characteristics of op1:
i = i1 * |op2|
In compatibility mode (compilation using ARITH(COMPAT)), the compiler having calculated i and d takes the action indicated in the table below to handle the intermediate results ir of the exponentiation.
| Value of i + d | Other conditions | Action taken |
|---|---|---|
| <30 | Any | i integer and d decimal places are carried for ir. |
| =30 | op1 has an odd number of digits. | i integer and d decimal places are carried for ir. |
| op1 has an even number of digits. | Same action as when op2 is an integral data-name or variable (shown below). Exception: for a 30-digit integer raised to the power of literal 1, i integer and d decimal places are carried for ir. | |
| >30 | Any | Same action as when op2 is an integral data-name or variable (shown below) |
In extended mode (compilation using ARITH(EXTEND)), the compiler having calculated i and d takes the action indicated in the table below to handle the intermediate results ir of the exponentiation.
| Value of i + d | Other conditions | Action taken |
|---|---|---|
| <31 | Any | i integer and d decimal places are carried for ir. |
| =31 or >31 | Any | Same action as when op2 is an integral data-name or variable (shown below). Exception: for a 31-digit integer raised to the power of literal 1, i integer and d decimal places are carried for ir. |
If op2 is negative, the value of 1 is then divided by the result produced by the preliminary computation. The values of i and d that are used are calculated following the division rules for fixed-point data already shown above.
If op2 is equal to 0, the result is 1. Division-by-0 and exponentiation SIZE ERROR conditions apply.
Fixed-point exponents with more than nine significant digits are always truncated to nine digits. If the exponent is a literal or constant, an E-level compiler diagnostic message is issued; otherwise, an informational message is issued at run time.
Example: exponentiation in fixed-point arithmetic
related references
Terminology used for intermediate results
Truncated intermediate results
Binary data and intermediate results
Floating-point data and intermediate results
Intrinsic functions evaluated in fixed-point arithmetic
ARITH
SIZE ERROR phrases
(COBOL for Windows Language Reference)