Logarithmic Functions
=====================

The shift-`L' (`calc-ln') [`ln'] command computes the natural
logarithm of the real or complex number on the top of the stack.  With
the Inverse flag it computes the exponential function instead,
although this is redundant with the `E' command.

The shift-`E' (`calc-exp') [`exp'] command computes the exponential,
i.e., `e' raised to the power of the number on the stack.  The
meanings of the Inverse and Hyperbolic flags follow from those for the
`calc-ln' command.

The `H L' (`calc-log10') [`log10'] command computes the common
(base-10) logarithm of a number.  (With the Inverse flag [`exp10'], it
raises ten to a given power.)  Note that the common logarithm of a
complex number is computed by taking the natural logarithm and
dividing by `ln(10)'.

The `B' (`calc-log') [`log'] command computes a logarithm to any base.
For example, `1024 RET 2 B' produces 10, since `2^10 = 1024'.  In
certain cases like `log(3,9)', the result will be either `1:2' or
`0.5' depending on the current Fraction Mode setting.  With the
Inverse flag [`alog'], this command is similar to `^' except that the
order of the arguments is reversed.

The `f I' (`calc-ilog') [`ilog'] command computes the integer
logarithm of a number to any base.  The number and the base must
themselves be positive integers.  This is the true logarithm, rounded
down to an integer.  Thus `ilog(x,10)' is 3 for all `x' in the range
from 1000 to 9999.  If both arguments are positive integers, exact
integer arithmetic is used; otherwise, this is equivalent to
`floor(log(x,b))'.

The `f E' (`calc-expm1') [`expm1'] command computes `exp(x)-1', but
using an algorithm that produces a more accurate answer when the
result is close to zero, i.e., when `exp(x)' is close to one.

The `f L' (`calc-lnp1') [`lnp1'] command computes `ln(x+1)', producing
a more accurate answer when `x' is close to zero.