Exponential function

---

PROBLEM

Compute E**X where E is Euler's number e. E**X is EXP function. This function is defined:

EXP(X)=1+X/FACT(1)+X**2/FACT(2)+...+X**N/FACT(N)+...

where FACT is the factorial function and X is any number.

IMPLEMENTATION

Unit: internal function, external function without procedure statement
 
Parameters: a number X, a positive integer P - number of significant digits of EXP(X), default is 9
 
Interface: the ECONST function, for P<=200 or the E function for P>200
 
Returns: the first P significant decimal digits of EXP(X)

 

EXP: procedure parse arg X, P if P = "" then P = 9; numeric digits P Y = X % 1 if ABS(X - Y) > 0.5 then Y = Y + SIGN(X) X = X - Y Sum = 1; Term = 1 do J = 1   Term = Term * X / J; NewSum = Sum + Term   if NewSum = Sum then leave   Sum = NewSum end if Y = 0 then return Sum return (ECONST() ** Y) * Sum

 

EXAMPLE

EXP(2.1879653,16) returns 8.917051119945531
VISUAL BASIC MsgBox(EXP(2.1879653)) displays 8.91705111994553

CONNECTIONS

Euler's number e
Factorial
Natural logarithms
Technique: Beforehand computed constants
P+n trick by Walter Pachl in Reflexio

---