[fill in information about tcl's handling of integers - particular the new Tcl 8.5 longer integer support]
Starting from Tcl 8.5, the expr command is based on LibTomMath arbitrary precision integers :
http://math.libtomcrypt.com/
MB Note that in Tcl releases prior to 8.5, integer calculations were performed with one of the C types long int or Tcl_WideInt. Since a "long int" is based on 32 bits, with one bit for the sign, the maximum positive integer is 2^31. The following is a little algorithm which computes the maximum integer which can be processed without truncation.
#
# searchintmax --
# Compute the maximum integer on Tcl platform.
#
proc searchintmax {imax {fine 0}} {
#
# Search the maximum available power of 2 which keeps multiplication
#
set a 1
for {set i 1} {$i<$imax} {incr i} {
set n [expr {$a*2}]
set p [expr {$n/2}]
puts "a=$a, n=$n, p=$p"
if {$p!=$a} then {
break
}
set a $n
}
#
# Refine process with positivity property of addition
#
if {$fine==1} then {
set shift [expr {int(pow(2,30))}]
for {set i 1} {$i<$imax} {incr i} {
set n [expr {$a+$shift}]
puts "a=$a, shift=$shift, n=$n"
if {$n<=0} then {
set shift [expr {$shift/2}]
if {$shift==0} then {
break
}
}
set a [expr {$a + $shift}]
}
}
return $a
}
If one uses this algorithm with Tcl 8.4, one gets the 2^30=1073741824 value, which is the greatest a such (a * 2)/2 = a.
set intmax [searchintmax 100]
With the fine=1 option, one can get the finer value 2^31=2147483647, which is the greatest a such that (a + 1) - 1 = a.
set intmax [searchintmax 100 1]
With Tcl 8.5, the loop reaches the maximum number of iterations, which is the expected result.
See also wide.