#!/usr/bin/env nomsu -V4.8.8.6
#
    This file defines some common math literals and functions

use "core/metaprogramming.nom"
use "core/text.nom"
use "core/operators.nom"
use "core/control_flow.nom"
use "core/collections.nom"

# Literals:
test:
    assume (all of [inf, NaN, pi, tau, golden ratio, e]) or barf "\
        ..math constants failed"
    %nan = (NaN)
    assume (%nan != %nan) or barf "NaN failed"
compile [infinity, inf] to (Lua value "math.huge")
compile [not a number, NaN, nan] to (Lua value "(0/0)")
compile [pi, Pi, PI] to (Lua value "math.pi")
compile [tau, Tau, TAU] to (Lua value "(2*math.pi)")
compile [golden ratio] to (Lua value "((1+math.sqrt(5))/2)")
compile [e] to (Lua value "math.exp(1)")

# Functions:
test:
    assume (("5" as a number) == 5)
compile [% as a number, % as number] to (Lua value "tonumber(\(% as lua expr))")

test:
    assume (..)
        all of [..]
            abs 5, | 5 |, sqrt 5, √ 5, sine 5, cosine 5, tangent 5, arc sine 5, arc cosine 5
            arc tangent 5, arc tangent 5 / 10, hyperbolic sine 5, hyperbolic cosine 5
            hyperbolic tangent 5, e^ 5, ln 5, log base 2 of 5, floor 5, ceiling 5, round 5
    ..or barf "math functions failed"
compile [absolute value %, | % |, abs %] to (..)
    Lua value "math.abs(\(% as lua expr))"

compile [square root %, square root of %, √ %, sqrt %] to (..)
    Lua value "math.sqrt(\(% as lua expr))"

compile [sine %, sin %] to (Lua value "math.sin(\(% as lua expr))")
compile [cosine %, cos %] to (Lua value "math.cos(\(% as lua expr))")
compile [tangent %, tan %] to (Lua value "math.tan(\(% as lua expr))")
compile [arc sine %, asin %] to (Lua value "math.asin(\(% as lua expr))")
compile [arc cosine %, acos %] to (Lua value "math.acos(\(% as lua expr))")
compile [arc tangent %, atan %] to (Lua value "math.atan(\(% as lua expr))")
compile [arc tangent %y / %x, atan2 %y %x] to (..)
    Lua value "math.atan2(\(%y as lua expr), \(%x as lua expr))"

compile [hyperbolic sine %, sinh %] to (Lua value "math.sinh(\(% as lua expr))")
compile [hyperbolic cosine %, cosh %] to (Lua value "math.cosh(\(% as lua expr))")
compile [hyperbolic tangent %, tanh %] to (..)
    Lua value "math.tanh(\(% as lua expr))"

compile [e^ %, exp %] to (Lua value "math.exp(\(% as lua expr))")
compile [natural log %, ln %, log %] to (Lua value "math.log(\(% as lua expr))")
compile [log % base %base, log base %base of %] to (..)
    Lua value "math.log(\(% as lua expr), \(%base as lua expr))"

compile [floor %] to (Lua value "math.floor(\(% as lua expr))")
compile [ceiling %, ceil %] to (Lua value "math.ceil(\(% as lua expr))")
compile [round %, % rounded] to (Lua value "math.floor(\(% as lua expr) + .5)")

test:
    assume ((463 to the nearest 100) == 500) or barf "rounding failed"
    assume ((2.6 to the nearest 0.25) == 2.5) or barf "rounding failed"
action [%n to the nearest %rounder] (..)
    =lua "(\%rounder)*math.floor((\%n / \%rounder) + .5)"

# Any/all/none
compile [all of %items, all %items] to:
    unless (%items.type is "List"):
        return (Lua value "utils.all(\(%items as lua expr))")
    %clauses = ((% as lua expr) for % in %items)
    return (Lua value "(\(%clauses::joined with " and "))")

parse [not all of %items, not all %items] as (not (all of %items))
compile [any of %items, any %items] to:
    unless (%items.type is "List"):
        return (Lua value "utils.any(\(%items as lua expr))")
    %clauses = ((% as lua expr) for % in %items)
    return (Lua value "(\(%clauses::joined with " or "))")

parse [none of %items, none %items] as (not (any of %items))
compile [sum of %items, sum %items] to:
    unless (%items.type is "List"):
        return (Lua value "utils.sum(\(%items as lua expr))")
    %clauses = ((% as lua expr) for % in %items)
    return (Lua value "(\(%clauses::joined with " + "))")

compile [product of %items, product %items] to:
    unless (%items.type is "List"):
        return (Lua value "utils.product(\(%items as lua expr))")
    %clauses = ((% as lua expr) for % in %items)
    return (Lua value "(\(%clauses::joined with " * "))")

action [avg of %items, average of %items] (=lua "(utils.sum(\%items)/#\%items)")
compile [min of %items, smallest of %items, lowest of %items] to (..)
    Lua value "utils.min(\(%items as lua expr))"

compile [max of %items, biggest of %items, largest of %items, highest of %items] to
..(Lua value "utils.max(\(%items as lua expr))")

test:
    assume ((min of [3, -4, 1, 2] by % = (% * %)) == 1)
    assume ((max of [3, -4, 1, 2] by % = (% * %)) == -4)
parse [min of %items by %item = %value_expr] as (..)
    result of:
        set {%best:nil, %best_key:nil}
        for %item in %items:
            %key = %value_expr
            if ((%best == (nil)) or (%key < %best_key)):
                set {%best:%item, %best_key:%key}
        
        return %best

parse [max of %items by %item = %value_expr] as (..)
    result of:
        set {%best:nil, %best_key:nil}
        for %item in %items:
            %key = %value_expr
            if ((%best == (nil)) or (%key > %best_key)):
                set {%best:%item, %best_key:%key}
        
        return %best

# 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 (Lua value "math.random()")
compile [random int %n, random integer %n, randint %n] to (..)
    Lua value "math.random(\(%n as lua expr))"

compile [..]
    random from %low to %high, random number from %low to %high
    rand %low %high
..to (Lua value "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)]"