AMG: TIP 232 [L1 ] creates the ::tcl::mathfunc namespace which contains commands implementing the [expr] math functions. The functions are documented in the mathfunc(n) man page [L2 ]. (Previous to TIP 232, the math functions were documented in expr(n).)
List of functions:
Absolute value abs arg Hypotenuse length hypot x y Arc cosine acos arg Coerce to word-sized integer int arg Arc sine asin arg Natural logarithm log arg Arc tangent atan arg Base-10 logarithm log10 arg Four-quadrant arc tangent atan2 y x Greatest value max args Coerce to boolean bool arg Least value min args Round up to whole number ceil arg Power pow x y Cosine cos arg Random float in range [0,1) rand Hyberbolic cosine cosh arg Round to whole number round arg Coerce to float double arg Sine sin arg Coerce to integer entier arg Hyperbolic sine sinh arg Exponential exp arg Square root sqrt arg Round down to whole number floor arg Seed random number generator srand arg Remainder fmod x y Tangent tan arg Coerce to 64-bit integer wide arg Hyperbolic tangent tanh arg Integer part of square root isqrt arg
Thanks to TIP 232, you can create new functions without having to resort to Tcl_CreateMathFunc(3) [L3 ]. This makes it possible for pure Tcl scripts to extend [expr]. Also this makes it possible to rewrite or delete math functions, two things that were previously impossible even for extensions written in C. (I have written code that needed this functionality; I guess it's time to update it!)
This makes math function arguments much more flexible, just as flexible as those of Tcl procs and commands. One possibility worth noting is variadic numbers of arguments, a feature used by the shiny, new min() and max() functions.
One more neat trick is calling math functions without using [expr]; they're regular Tcl commands now. Combine this with TIP 174 Math Operators as Commands, and you can avoid using [expr] altogether, bypassing the problems discussed at brace your expr-essions.
See the TIP for more creative usage ideas.
DKF: If you like doing your computations the Lisp way, add this to your scripts:
namespace path {::tcl::mathop ::tcl::mathfunc}Now you can use all the above functions (and the math operators) as commands without qualification.
AMG: Here's a math function I sometimes find useful. It accepts three arguments, and it returns whichever of the three is between the other two. It's mostly useful to clamp a number to a range.
proc ::tcl::mathfunc::mid {a b c} {
lindex [lsort -real [list $a $b $c]] 1
}It can also be implemented as a bunch of [if]s, which is how I do it in C.
Here is one incorrect implementation you should watch out for:
proc ::tcl::mathfunc::mid {a b c} {
expr {max($a, min($b, $c))}
}This is what Allegro (include/allegro/base.h) has used since the dawn of time. :^( I'm reporting it now; hopefully it'll be fixed. If you're curious, see [L4 ] for my writeup.
KPV The folk algorithm for finding the middle number (or second highest in a longer list) is to take the max of the pair-wise mins. To wit:
max(min($a,$b), min($a,$c), min($b,$c))
LV So what is an example of a case in which the second, incorrect, version of the algorithm fails? Answer: "incorrect_mid 1 0 0" returns 1. The problem is it doesn't (always) handle the case where two of the inputs are the same. Doh.
AMG: I thought the problem was that it doesn't handle the case of the first input being greater than the other two. This wasn't a problem for Allegro because everyone used its MID macro thusly: MID(minimum_value, value_to_clamp, maximum_value).
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