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#!/usr/bin/env nomsu -V6.14
#
This file defines some common math literals and functions
use "core/metaprogramming"
use "core/text"
use "core/operators"
use "core/control_flow"
use "core/collections"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Literals:
test:
unless (all of [inf, NaN, pi, tau, golden ratio, e]):
fail "math constants failed"
$nan = (NaN)
unless ($nan != $nan):
fail "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)
external $($ as a number) = $(tonumber $)
external $($ as number) = $(tonumber $)
test:
unless
all of [
abs 5, | 5 |, sqrt 5, √ 5, sine 5, cosine 5, tangent 5, arc sine 5, arc cosine 5
arc tangent 5, arc tangent 5 / 10, hyperbolic sine 5, hyperbolic cosine 5
hyperbolic tangent 5, e^ 5, ln 5, log 5 base 2, floor 5, ceiling 5, round 5
]
..:
fail "math functions failed"
external [$(absolute value $), $(absolute value of $), $(| $ |), $(abs $)] =
[$math.abs, $math.abs, $math.abs, $math.abs]
external [$(square root $), $(square root of $), $(√ $), $(sqrt $)] =
[$math.sqrt, $math.sqrt, $math.sqrt, $math.sqrt]
external [$(sine $), $(sin $)] = [$math.sin, $math.sin]
external [$(cosine $), $(cos $)] = [$math.cos, $math.cos]
external [$(tangent $), $(tan $)] = [$math.tan, $math.tan]
external [$(arc sine $), $(asin $)] = [$math.asin, $math.asin]
external [$(arc cosine $), $(acos $)] = [$math.acos, $math.acos]
external [$(arc tangent $), $(atan $)] = [$math.atan, $math.atan]
external [$(arc tangent $y / $x), $(atan2 $y $x)] = [$math.atan2, $math.atan2]
external [$(hyperbolic sine $), $(sinh $)] = [$math.sinh, $math.sinh]
external [$(hyperbolic cosine $), $(cosh $)] = [$math.cosh, $math.cosh]
external [$(hyperbolic tangent $), $(tanh $)] = [$math.tanh, $math.tanh]
external [$(e^ $), $(exp $)] = [$math.exp, $math.exp]
external [$(natural log $), $(ln $), $(log $), $(log $ base $)] = [$math.log, $math.log, $math.log, $math.log]
external $(floor $) = $math.floor
external [$(ceiling $), $(ceil $)] = [$math.ceil, $math.ceil]
externally [round $, $ rounded] all mean
floor ($ + 0.5)
test:
unless ((463 to the nearest 100) == 500): fail "rounding failed"
unless ((2.6 to the nearest 0.25) == 2.5): fail "rounding failed"
externally ($n to the nearest $rounder) means
$rounder * (floor ($n / $rounder + 0.5))
# Any/all
externally [all of $items, all $items] all mean:
for $ in $items:
unless $:
return (no)
return (yes)
[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)
[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
externally [product of $items, product $items] all mean:
$prod = 1
for $ in $items:
$prod *= $
return $prod
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 $best
test:
assume (100 clamped between 0 and 10) == 10
externally ($ clamped between $min and $max) means:
when:
($ < $min):
return $min
($ > $max):
return $max
else:
return $
test:
assume (-0.1 smoothed by 2.7) == 0
assume (0 smoothed by 2.7) == 0
assume (0.5 smoothed by 2.7) == 0.5
assume (1 smoothed by 2.7) == 1
assume (1.1 smoothed by 2.7) == 1
externally ($ smoothed by $smoothness) means:
$ = ($ clamped between 0 and 1)
if ($smoothness == 0): return $
$k = (2 ^ $smoothness)
if ($ < 0.5):
return (0.5 * (2 * $) ^ $k)
..else:
return (1 - 0.5 * (2 - 2 * $) ^ $k)
test:
assume (5 to 7 mixed by -1.0) == 5
assume (5 to 7 mixed by 0.0) == 5
assume (5 to 7 mixed by 0.5) == 6
assume (5 to 7 mixed by 1.0) == 7
assume (5 to 7 mixed by 2.0) == 7
externally ($lo to $hi mixed by $amount) means:
$ = ($amount clamped between 0 and 1)
return ((1 - $) * $lo + $ * $hi)
test:
assume ([0, 1, 11] mixed by 0.0) == 0
assume ([0, 1, 11] mixed by 0.25) == 0.5
assume ([0, 1, 11] mixed by 0.5) == 1
assume ([0, 1, 11] mixed by 0.75) == 6
assume ([0, 1, 11] mixed by 1.0) == 11
assume ([99] mixed by 0.5) == 99
externally ($nums mixed by $amount) means:
$ = ($amount clamped between 0 and 1)
$i = (1 + ($ * ((#$nums) - 1)))
if ((floor $i) == (#$nums)):
return $nums.(floor $i)
[$lo, $hi] = [$nums.(floor $i), $nums.(floor ($i + 1))]
return ($lo to $hi mixed by ($i mod 1))
# Random functions
externally (seed random with $) means:
lua> ("
math.randomseed(\$);
for 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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