%D \module
%D   [       file=m-mathfun,
%D        version=2021.02.20,
%D          title=\CONTEXT\ Extra Modules,
%D       subtitle=Wried Math Stuff,
%D         author=Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

%D Occasionaly some experiment results in some weird feature. It doesn't make sense
%D to make this core functionality but if also makes no sense to throw it away. By
%D making it a module the user can decide. It's actually an example of abusing a
%D \LUA\ interfacing mechanism that is meant for something else.

\ifdefined\compute \else
    \permanent\protected\def\compute{\thewithproperty\plusone}
\fi

%D At some point this will move to \type {m-mathfun.lmt}:

\startluacode
    local type, load = type, load
    local gmatch = string.gmatch

    local xmath         = xmath
    local xcomplex      = xcomplex
    local xdecimal      = xdecimal

    local context       = context
    local ctx_mfunction = context.mfunctionlabeltext

    local scanoptional  = tokens.scanners.optional
    local scanargument  = tokens.scanners.argument

    local createtoken   = tokens.create
    local defined       = tokens.defined

    local implement     = interfaces.implement

    local compute_code  = 1

    local function smart(what,name,kind)
        if what == "value" or what == compute_code then
            local temp = scanoptional()
            if temp and temp ~= "" then
                temp = "%" .. temp
            else
                temp = "%.6N"
            end
            if kind == "constant" then
                context(temp,math[name])
            else
                local code = scanargument()
                local func = load("return "..name.."("..code..")","mathfunction","t",math)
                if type(func) == "function" then
                    context(temp,func())
                else
                    context(code)
                end
            end
        elseif kind == "constant" then
          -- context[name]() -- recursion
            name = "normal"..name
            if defined(name) then
                context(createtoken(name))
            else
                context(name)
            end
        else
            ctx_mfunction(name)
        end
    end

    local template = { name = false, usage = "value", public = true, protected = true, actions = false, overload = true }

    local function install(str,kind)
        for name in gmatch(str,"[^ ,]+") do
            template.name    = name
            template.actions = function(what) smart(what,name,kind) end
            implement(template)
        end
    end

    local function mathexpr()
        local temp = scanoptional()
        local code = scanargument()
        local func = load("return " .. code,"mathexpr","t",xmath)
        if type(func) == "function" then
            if temp and temp ~= "" then
                temp = "%" .. temp
            else
                temp = "%.6N"
            end
            context(temp,func())
        else
            context(code)
        end
    end

    local tostring    = xdecimal.tostring
    local toengstring = xdecimal.toengstring -- todo

    local function decimalexpr()
        local temp = scanoptional()
        local code = scanargument()
        local func = load("return " .. code,"decimalexpr","t",xdecimal)
        if type(func) == "function" then
            local result = tostring(func())
            if temp and temp ~= "" then
                context("%"..temp,result)
            else
                context(result)
            end
        else
            context(code)
        end
    end

    local topair = xcomplex.topair

    local function complexexpr()
        local temp = scanoptional()
        local code = scanargument()
        local func = load("return " .. code,"complexexpr","t",xcomplex)
        if type(func) == "function" then
         -- local result = tostring(func())
         -- if temp and temp ~= "" then
         --     context("%"..temp,result)
         -- else
         --     context(result)
         -- end
            if temp and temp ~= "" then
                temp = "%" .. temp
            else
                temp = "%.6N + %.6Ni"
            end
            local result = func()
            context(temp,topair(result))
        else
            context(code)
        end
    end

    implement {
        name      = "registermathfunction",
        public    = true,
        protected = true,
        actions   = install,
        arguments = { "optional", "optional" },
    }

    implement {
        name    = "mathexpr",
        public  = true,
        actions = mathexpr,
    }

    implement {
        name    = "decimalexpr",
        public  = true,
        actions = decimalexpr,
    }

    implement {
        name    = "complexexpr",
        public  = true,
        actions = complexexpr,
    }

 -- install("sind cosd tand sin cos tan")
 -- install("sqrt")
\stopluacode

\pushoverloadmode

    \ifdefined\normalpi \else\let\normalpi\pi \fi

    \registermathfunction[sind,cosd,tand,sin,cos,tan]
    \registermathfunction[sqrt]
    \registermathfunction[pi][constant]

\popoverloadmode

\continueifinputfile{m-mathfun.mkxl}

% \pushoverloadmode
% \let\normalpi\pi
% \registermathfunction[sind,cosd,tand,sin,cos,tan]
% \registermathfunction[sqrt]
% \registermathfunction[pi][constant]
% \popoverloadmode

\usemodule[scite] \setupbodyfont[dejavu] \setuplayout[tight] \setuppapersize[A5]

% \mainlanguage[es]

\starttext

\startbuffer
$ \sin (x) = \luaexpr       {math.sin(math.pi/2)} $
$ \sin (x) = \luaexpr [.4N] {math.sin(math.pi/2)} $
$ \sin (x) = \the\sin                     {pi/2}  $
$ \sind(x) = \luaexpr [.4N] {math.sind(120)}      $
$ \sind(x) = \the\sind[.4N]           {120}       $
$ \sqrt(x) = \luaexpr       {math.sqrt(2)}        $
$ \sqrt(x) = \luaexpr [.6N] {math.sqrt(2)}        $
$ \sqrt(x) = \the\sqrt                {2}         $
$ \sqrt(x) = \the\sqrt[.3N]           {2}         $
$ \sqrt(x) = \compute\sqrt[.3N]       {2}         $
$ \sind(x) = \luaexpr [.4N] {math.pi}             $
$ \pi = \compute\pi[.4N]                          $
$ \pi = \mathexpr[.40N]{pi}                       $
$ \pi = \mathexpr[.80N]{sqrt(11)}                 $
$ \pi = \decimalexpr[.80N]{sqrt(11)}              $
$ \pi = \decimalexpr{sqrt(11)}                    $
$ c = \complexexpr{123 + new(456,789)}            $
\stopbuffer

Take your choice:

\typebuffer[option=TEX]

And get:

\startlines
    \getbuffer
\stoplines

\stoptext