Function: logint
Section: number_theoretical
C-Name: logint0
Prototype: lGGD&
Help: logint(x,b,{&z}): return the largest non-negative integer e so that
 b^e <= x, where b > 1 is an integer and x >= 1 is a real number. If the
 parameter z is present, set it to b^e.
Description:
 (int,2):small        expi($1)
 (gen,gen):small      logint0($1, $2, NULL)
 (gen,gen,&int):small logint0($1, $2, &$3)
Doc: Return the largest non-negative integer $e$ so that $b^{e} \leq x$, where
 $b > 1$ is an integer and $x \geq 1$ is a real number. If the parameter $z$
 is present, set it to $b^{e}$.
 \bprog
 ? logint(1000, 2)
 %1 = 9
 ? 2^9
 %2 = 512
 ? logint(1000, 2, &z)
 %3 = 9
 ? z
 %4 = 512
 ? logint(Pi^2, 2, &z)
 %5 = 3
 ? z
 %6 = 8
 @eprog\noindent The number of digits used to write $x$ in base $b$ is
 \kbd{1 + logint(x,b)}:
 \bprog
 ? #digits(1000!, 10)
 %5 = 2568
 ? logint(1000!, 10)
 %6 = 2567
 @eprog\noindent This function may conveniently replace
 \bprog
   floor( log(x) / log(b) )
 @eprog\noindent which may not give the correct answer since PARI
 does not guarantee exact rounding.
