#..
    This file defines some common math literals and functions

use "lib/metaprogramming.nom"
use "lib/control_flow.nom"

# Literals:
compile [infinity, inf] to "math.huge"
compile [not a number, NaN, nan] to "(0/0)"
compile [pi, Pi, PI] to "math.pi"
compile [tau, Tau, TAU] to "(2*math.pi)"
compile [golden ratio] to "((1+math.sqrt(5))/2)"
compile [e] to "math.e"

# Functions:
compile [% as number] to "tonumber(\(% as lua))"
compile [absolute value %, | % |, abs %] to "math.abs(\(% as lua))"
compile [square root %, √%, sqrt %] to "math.sqrt(\(% as lua))"
compile [sine %, sin %] to "math.sin(\(% as lua))"
compile [cosine %, cos %] to "math.cos(\(% as lua))"
compile [tangent %, tan %] to "math.tan(\(% as lua))"
compile [arc sine %, asin %] to "math.asin(\(% as lua))"
compile [arc cosine %, acos %] to "math.acos(\(% as lua))"
compile [arc tangent %, atan %] to "math.atan(\(% as lua))"
compile [arc tangent %y/%x, atan2 %y %x] to "math.atan2(\(%y as lua), \(%x as lua))"
compile [hyperbolic sine %, sinh %] to "math.sinh(\(% as lua))"
compile [hyperbolic cosine %, cosh %] to "math.cosh(\(% as lua))"
compile [hyperbolic tangent %, tanh %] to "math.tanh(\(% as lua))"
compile [e^%, exp %] to "math.exp(\(% as lua))"
compile [natural log %, ln %, log %] to "math.log(\(% as lua))"
compile [log % base %base, log_%base %, log base %base %] to "math.log(\(% as lua), \(%base as lua))"
compile [floor %] to "math.floor(\(% as lua))"
compile [ceiling %, ceil %] to "math.ceil(\(% as lua))"
compile [round %, % rounded] to "math.floor(\(% as lua) + .5)"
action [%n to the nearest %rounder]
    =lua "(\%rounder)*math.floor((\%n / \%rounder) + .5)"

# Any/all/none
compile [all of %items, all %items] to
    "(\(join ((% as lua) for all (%items' "value")) with " and "))"
    ..if ((%items' "type") is "List") else "utils.all(\(%items as lua))"
parse [not all of %items, not all %items] as: not (all of %items)
compile [any of %items, any %items] to
    "(\(join ((% as lua) for all (%items' "value")) with " or "))"
    ..if ((%items' "type") is "List") else "utils.any(\(%items as lua))"
parse [none of %items, none %items] as: not (any of %items)
compile [sum of %items, sum %items] to
    "(\(join ((% as lua) for all (%items' "value")) with " + "))"
    ..if ((%items' "type") is "List") else "utils.sum(\(%items as lua))"
compile [product of %items, product %items] to
    "(\(join ((% as lua) for all (%items' "value")) with " * "))"
    ..if ((%items' "type") is "List") else "utils.product(\(%items as lua))"
action [avg of %items, average of %items]
    =lua "(utils.sum(\%items)/#\%items)"
compile [min of %items, smallest of %items, lowest of %items] to
    "utils.min(\(%items as lua))"
compile [max of %items, biggest of %items, largest of %items, highest of %items] to
    "utils.max(\(%items as lua))"
compile [min of %items by %value_expr] to ".."
    utils.min(\(%items as lua), function(\(\% as lua))
        return \(%value_expr as lua)
    end)
compile [max of %items by %value_expr] to ".."
    utils.max(\(%items as lua), function(\(\% as lua))
        return \(%value_expr as lua)
    end)

# Random functions
action [seed random with %]
    lua> ".."
        math.randomseed(\%);
        for i=1,20 do math.random(); end
parse [seed random] as: seed random with (=lua "os.time()")
compile [random number, random, rand] to "math.random()"
compile [random int %n, random integer %n, randint %n] to "math.random(\(%n as lua))"
compile [random from %low to %high, random number from %low to %high, rand %low %high] to
    "math.random(\(%low as lua), \(%high as lua))"
action [random choice from %elements, random choice %elements, random %elements]
    =lua "\%elements[math.random(#\%elements)]"