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

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

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

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

# Any/all/none
compile [all of %items, all %items] to {..}
    expr:
        "(\(joined ((% as lua expr) for all (%items' "value")) with " and "))"
        ..if ((%items' "type") is "List") else "utils.all(\(%items as lua expr))"
parse [not all of %items, not all %items] as: not (all of %items)
compile [any of %items, any %items] to {..}
    expr:
        "(\(joined ((% as lua expr) for all (%items' "value")) with " or "))"
        ..if ((%items' "type") is "List") else "utils.any(\(%items as lua expr))"
parse [none of %items, none %items] as: not (any of %items)
compile [sum of %items, sum %items] to {..}
    expr:
        "(\(joined ((% as lua expr) for all (%items' "value")) with " + "))"
        ..if ((%items' "type") is "List") else "utils.sum(\(%items as lua expr))"
compile [product of %items, product %items] to {..}
    expr:
        "(\(joined ((% as lua expr) for all (%items' "value")) with " * "))"
        ..if ((%items' "type") is "List") else "utils.product(\(%items as lua expr))"
action [avg of %items, average of %items]
    =lua "(utils.sum(\%items)/#\%items)"
compile [min of %items, smallest of %items, lowest of %items] to {..}
    expr:"utils.min(\(%items as lua expr))"
compile [max of %items, biggest of %items, largest of %items, highest of %items] to {..}
    expr:"utils.max(\(%items as lua expr))"
compile [min of %items by %value_expr] to {..}
    expr: ".."
        utils.min(\(%items as lua expr), function(\(\% as lua expr))
            return \(%value_expr as lua expr)
        end)
compile [max of %items by %value_expr] to {..}
    expr: ".."
        utils.max(\(%items as lua expr), function(\(\% as lua expr))
            return \(%value_expr as lua expr)
        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 {expr:"math.random()"}
compile [random int %n, random integer %n, randint %n] to {expr:"math.random(\(%n as lua expr))"}
compile [random from %low to %high, random number from %low to %high, rand %low %high] to
    "math.random(\(%low as lua expr), \(%high as lua expr))"
action [random choice from %elements, random choice %elements, random %elements]
    =lua "\%elements[math.random(#\%elements)]"