From c1c32688a4afc43f6addb99b8b5fa878944a70e3 Mon Sep 17 00:00:00 2001
From: Bruce Hill <bruce@bruce-hill.com>
Date: Mon, 14 Jan 2019 15:42:48 -0800
Subject: Overhaul in progress, mostly working. Moved all the nomsu packages
 into lib/, including core/*. Changes to how nomsu environments and importing
 work.

---
 lib/core/math.nom | 212 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 212 insertions(+)
 create mode 100644 lib/core/math.nom

(limited to 'lib/core/math.nom')

diff --git a/lib/core/math.nom b/lib/core/math.nom
new file mode 100644
index 0000000..685ab1e
--- /dev/null
+++ b/lib/core/math.nom
@@ -0,0 +1,212 @@
+#!/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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