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#!/usr/bin/env nomsu -V5.12.12.8
#
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 != $nan) or barf "NaN failed"
[infinity, inf] all compile to "math.huge"
[not a number, NaN, nan] all compile to "(0/0)"
[pi, Pi, PI] all compile to "math.pi"
[tau, Tau, TAU] all compile to "(2*math.pi)"
(golden ratio) compiles to "((1+math.sqrt(5))/2)"
(e) compiles to "math.exp(1)"
# Functions:
test:
assume (("5" as a number) == 5)
(($ as a number)'s meaning) = ((tonumber $)'s meaning)
(($ as number)'s meaning) = ((tonumber $)'s meaning)
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"
[absolute value $, | $ |, abs $] all compile to "math.abs(\($ as lua expr))"
[square root $, square root of $, √ $, sqrt $] all compile to \
.."math.sqrt(\($ as lua expr))"
[sine $, sin $] all compile to "math.sin(\($ as lua expr))"
[cosine $, cos $] all compile to "math.cos(\($ as lua expr))"
[tangent $, tan $] all compile to "math.tan(\($ as lua expr))"
[arc sine $, asin $] all compile to "math.asin(\($ as lua expr))"
[arc cosine $, acos $] all compile to "math.acos(\($ as lua expr))"
[arc tangent $, atan $] all compile to "math.atan(\($ as lua expr))"
[arc tangent $y / $x, atan2 $y $x] all compile to \
.."math.atan2(\($y as lua expr), \($x as lua expr))"
[hyperbolic sine $, sinh $] all compile to "math.sinh(\($ as lua expr))"
[hyperbolic cosine $, cosh $] all compile to "math.cosh(\($ as lua expr))"
[hyperbolic tangent $, tanh $] all compile to "math.tanh(\($ as lua expr))"
[e^ $, exp $] all compile to "math.exp(\($ as lua expr))"
[natural log $, ln $, log $] all compile to "math.log(\($ as lua expr))"
[log $ base $base, log base $base of $] all compile to \
.."math.log(\($ as lua expr), \($base as lua expr))"
(floor $) compiles to "math.floor(\($ as lua expr))"
[ceiling $, ceil $] all compile to "math.ceil(\($ as lua expr))"
[round $, $ rounded] all compile to "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"
externally ($n to the nearest $rounder) means (..)
=lua "(\$rounder)*math.floor((\$n / \$rounder) + .5)"
# Any/all
externally [all of $items, all $items] all mean:
for $ in $items:
unless $:
return (no)
return (yes)
#[all of %items, all %items] all compile to:
unless (%items.type is "List"):
return \(all of %items)
if ((size of %items) == 0):
return (Lua "true")
%lua = (Lua "(")
%lua::add [: for % in %items: add (% as lua expr)] joined with " and "
%lua::add ")"
return %lua
[not all of $items, not all $items] all parse as (not (all of $items))
externally [any of $items, any $items] all mean:
for $ in $items:
if $:
return (yes)
return (no)
#[any of %items, any %items] all compile to:
unless (%items.type is "List"):
return \(any of %items)
if ((size of %items) == 0):
return (Lua "false")
%lua = (Lua "(")
%lua::add [: for % in %items: add (% as lua expr)] joined with " or "
%lua::add ")"
return %lua
[none of $items, none $items] all parse as (not (any of $items))
# Sum/product
externally [sum of $items, sum $items] all mean:
$total = 0
for $ in $items:
$total += $
return $total
#[sum of %items, sum %items] all compile to:
unless (%items.type is "List"):
return \(sum of %items)
if ((size of %items) == 0):
return (Lua "0")
%lua = (Lua "(")
%lua::add [: for % in %items: add (% as lua expr)] joined with " + "
%lua::add ")"
return %lua
externally [product of $items, product $items] all mean:
$prod = 1
for $ in $items:
$prod *= $
return $prod
#[product of %items, product %items] all compile to:
unless (%items.type is "List"):
return \(product of %items)
if ((size of %items) == 0):
return (Lua "1")
%lua = (Lua "(")
%lua::add [: for % in %items: add (% as lua expr)] joined with " * "
%lua::add ")"
return %lua
externally [avg of $items, average of $items] all mean (..)
(sum of $items) / (size of $items)
# Min/max
externally [min of $items, smallest of $items, lowest of $items] all mean:
$best = (nil)
for $ in $items:
if (($best == (nil)) or ($ < $best)): $best = $
return $best
externally [..]
max of $items, biggest of $items, largest of $items, highest of $items
..all mean:
$best = (nil)
for $ in $items:
if (($best == (nil)) or ($ > $best)): $best = $
return $best
test:
assume ((min of [3, -4, 1, 2] by $ = ($ * $)) == 1)
assume ((max of [3, -4, 1, 2] by $ = ($ * $)) == -4)
(min of $items by $item = $value_expr) parses as (..)
result of:
$best = (nil)
$best_key = (nil)
for $item in $items:
$key = $value_expr
if (($best == (nil)) or ($key < $best_key)):
$best = $item
$best_key = $key
return $best
(max of $items by $item = $value_expr) parses as (..)
result of:
$best = (nil)
$best_key = (nil)
for $item in $items:
$key = $value_expr
if (($best == (nil)) or ($key > $best_key)):
$best = $item
$best_key = $key
return $best
# Random functions
externally (seed random with $) means:
lua> "math.randomseed(\$);\nfor i=1,20 do math.random(); end"
(seed random) parses as (seed random with (=lua "os.time()"))
[random number, random, rand] all compile to "math.random()"
[random int $n, random integer $n, randint $n] all compile to \
.."math.random(\($n as lua expr))"
[random from $low to $high, random number from $low to $high, rand $low $high] \
..all compile to "math.random(\($low as lua expr), \($high as lua expr))"
externally [..]
random choice from $elements, random choice $elements, random $elements
..all mean (=lua "\$elements[math.random(#\$elements)]")
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