Exponential notation

The preceding description of numbers describes "pure" numbers, in the sense that the character strings that describe numbers can be very long. For example:

10000000000 * 10000000000

would give

100000000000000000000

and

.00000000001 * .00000000001

would give

0.0000000000000000000001

For both large and small numbers some form of exponential notation is useful, both to make long numbers more readable, and to make execution possible in extreme cases. In addition, exponential notation is used whenever the "simple" form would give misleading information.

For example:

numeric digits 5
say 54321*54321

would display 2950800000 in long form. This is clearly misleading, and so the result is expressed as 2.9508E+9 instead.

The definition of numbers is, therefore, extended as:


>>-+--------+--+-----------------+--+-digits--------+----------->
   '-blanks-'  '-sign-+--------+-'  +-digits.digits-+   
                      '-blanks-'    +-.digits-------+   
                                    '-digits.-------'   

>--+-------------------+--+--------+---------------------------><
   '-E-+------+-digits-'  '-blanks-'   
       '-sign-'

The integer following the E represents a power of ten that is to be applied to the number. The E can be in uppercase or lowercase.

Certain character strings are numbers even though they do not appear to be numeric to the user. Specifically, because of the format of numbers in exponential notation, strings, such as 0E123 (0 times 10 raised to the 123 power) and 1E342 (1 times 10 raised to the 342 power), are numeric. In addition, a comparison such as 0E123=0E567 gives a true result of 1 (0 is equal to 0). To prevent problems when comparing nonnumeric strings, use the strict comparison operators.

Here are some examples:

12E7   =    120000000           /* Displays "1" */
12E-5  =    0.00012             /* Displays "1" */
-12e4  =    -120000             /* Displays "1" */
0e123  =    0e456               /* Displays "1" */
0e123  ==   0e456               /* Displays "0" */

The preceding numbers are valid for input data at all times. The results of calculations are returned in either conventional or exponential form, depending on the setting of NUMERIC DIGITS. If the number of places needed before the decimal point exceeds DIGITS, or the number of places after the point exceeds twice DIGITS, exponential form is used. The exponential form REXX generates always has a sign following the E to improve readability. If the exponent is 0, then the exponential part is omitted—that is, an exponential part of E+0 is never generated.

You can explicitly convert numbers to exponential form, or force them to be displayed in long form, by using the FORMAT built-in function (see FORMAT).

Scientific notation is a form of exponential notation that adjusts the power of ten so a single nonzero digit appears to the left of the decimal point. Engineering notation is a form of exponential notation in which from one to three digits (but not simply 0) appear before the decimal point, and the power of ten is always expressed as a multiple of three. The integer part may, therefore, range from 1 through 999. You can control whether Scientific or Engineering notation is used with the instruction:


                 .-SCIENTIFIC-----------.      
>>-NUMERIC FORM--+----------------------+--;-------------------><
                 +-ENGINEERING----------+      
                 '-+-------+-expression-'      
                   '-VALUE-'

Scientific notation is the default.

/* after the instruction */
Numeric form scientific

123.45 * 1e11     ->     1.2345E+13

/* after the instruction */
Numeric form engineering

123.45  * 1e11    ->    12.345E+12