﻿ MAXNUM and EPS

MAXNUM, EPS

MAXNUM function
`MAXNUM`
The largest manipulable number.
MAXNUM is 1E99 on the decimal operation mode.
MAXNUM is about 1.8E308 on the binary operation mode.
MAXNUM is 1E1008 on the decimal 1000 digit mode.
(Note)
MAXNUM is undefined on the rational operation mode. (Compiler stops if any.)
(Note)
MAXNUM is a reserved word.

EPS functions
`EPS(x) `
EPS(x) is the larger of the differences of x and the numbers adjacent to x, provided that if it is smaller than EPS(0), EPS(x) is EPS(0).
EPS(x) means the resolution around x.
Decimal BASIC defines EPS(x) with respect to the precision of numeric variables, while the definition on the standard is vague.
As the precision of variables is 15 digits, `EPS(x)`=1E-14 for a number x not less than 1 and less than 10.
EPS(0) is the smallest positive number. `EPS(0)` is 1E-99 on the decimal mode of Decimal BASIC. If a number of absolute less than EPS(0) is assigned to a variable, the value of the variable becomes 0.
The EPS function can be expressed using a logarithmic function as follows.
` EPS(x)=MAX(10^(INT(LOG10(ABS(x))-14)),1E-99)` for x≠0

(Note) If arithmetic option is NATIVE,
EPS(0)=2^(-1074)≒4.94E-324
```EPS(x)= MAX(2^(INT(LOG2(ABS(x))-52)),EPS(0))``` for x≠0

EPS(0) is 1E-1017 on the decimal 1000 digit mode.
The EPS function is undefined on the rational operation mode.