View source for Expm1

[[category:Math Functions]]
''New to [[Analytica 6.3]]''

== _Expm1(x) ==

This is an internal function that is used to evaluate an expression of the form:
:<code>[[Exp]](x)-1</code>
or
:<code>1-[[Exp]](x)</code>
In the second case, the result is the negation of <code>_Expm1(x)</code>. The expression must have exactly this form, with a literal constant 1.

The result of evaluating <code>_Expm1(x)</code> is <code>[[Exp]](x)-1</code>.  Direct evaluation of <code>Exp(x)-1</code> loses precision when <code>x</code> is small (i.e., <code>abs(x)<<1</code>), so by using <code>_Expm1(x)</code> instead it avoids numeric round-off problems.

When the parser sees an expression in either of the above forms, it replaces the expression with a direct call to <code>_Expm1(x)</code>.

Note: For very small x, <code>Exp(x)-1</code>≈1.

== Examples ==
:<code>Exp(1e-20)-1 &rarr; 1e-20</code>
:<code>Local ex:=Exp(1-20) Do ex-1</code> &rarr; 0   <font color="green">{ This one does not use _Expm1, and hence looses all precision }</font>

== See also ==
* [[Exp]]
* [[_Log1p]]