diff options
Diffstat (limited to 'lib/core/math.nom')
| -rw-r--r-- | lib/core/math.nom | 392 |
1 files changed, 195 insertions, 197 deletions
diff --git a/lib/core/math.nom b/lib/core/math.nom index 685ab1e..e2c759a 100644 --- a/lib/core/math.nom +++ b/lib/core/math.nom @@ -1,4 +1,4 @@ -#!/usr/bin/env nomsu -V6.14 +#!/usr/bin/env nomsu -V6.15.13.8 # This file defines some common math literals and functions @@ -10,203 +10,201 @@ 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: +external: + # 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) + $($ as a number) = $(tonumber $) + $($ as number) = $(tonumber $) + test: + unless + all of [ + abs 5, | 5 |, sqrt 5, √ 5, sine 5, cosine 5, tangent 5, arc sine 5, arc cosine 5 + arc tangent 5, arc tangent 5 / 10, hyperbolic sine 5, hyperbolic cosine 5 + hyperbolic tangent 5, e^ 5, ln 5, log 5 base 2, floor 5, ceiling 5, round 5 + ] + ..: + fail "math functions failed" + + [$(absolute value $), $(absolute value of $), $(| $ |), $(abs $)] = + [$math.abs, $math.abs, $math.abs, $math.abs] + + [$(square root $), $(square root of $), $(√ $), $(sqrt $)] = + [$math.sqrt, $math.sqrt, $math.sqrt, $math.sqrt] + + [$(sine $), $(sin $)] = [$math.sin, $math.sin] + [$(cosine $), $(cos $)] = [$math.cos, $math.cos] + [$(tangent $), $(tan $)] = [$math.tan, $math.tan] + [$(arc sine $), $(asin $)] = [$math.asin, $math.asin] + [$(arc cosine $), $(acos $)] = [$math.acos, $math.acos] + [$(arc tangent $), $(atan $)] = [$math.atan, $math.atan] + [$(arc tangent $y / $x), $(atan2 $y $x)] = [$math.atan2, $math.atan2] + [$(hyperbolic sine $), $(sinh $)] = [$math.sinh, $math.sinh] + [$(hyperbolic cosine $), $(cosh $)] = [$math.cosh, $math.cosh] + [$(hyperbolic tangent $), $(tanh $)] = [$math.tanh, $math.tanh] + [$(e^ $), $(exp $)] = [$math.exp, $math.exp] + [$(natural log $), $(ln $), $(log $), $(log $ base $)] = + [$math.log, $math.log, $math.log, $math.log] + $(floor $) = $math.floor + [$(ceiling $), $(ceil $)] = [$math.ceil, $math.ceil] + [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" + ($n to the nearest $rounder) means ($rounder * (floor ($n / $rounder + 0.5))) + + # Any/all + [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)) + [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 + [sum of $items, sum $items] all mean: + $total = 0 + for $ in $items: + $total += $ + return $total + + [product of $items, product $items] all mean: + $prod = 1 + for $ in $items: + $prod *= $ + return $prod + + [avg of $items, average of $items] all mean ((sum of $items) / (size of $items)) + + # Min/max + [min of $items, smallest of $items, lowest of $items] all mean: $best = (nil) - $best_key = (nil) - for $item in $items: - $key = $value_expr - if (($best == (nil)) or ($key < $best_key)): - $best = $item - $best_key = $key + for $ in $items: + if (($best == (nil)) or ($ < $best)): $best = $ return $best - -(max of $items by $item = $value_expr) parses as - result of: + + [max of $items, biggest of $items, largest of $items, highest of $items] all mean: $best = (nil) - $best_key = (nil) - for $item in $items: - $key = $value_expr - if (($best == (nil)) or ($key > $best_key)): - $best = $item - $best_key = $key + for $ in $items: + if (($best == (nil)) or ($ > $best)): $best = $ 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)]") + + 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 $best + + test: + assume (100 clamped between 0 and 10) == 10 + + ($ 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 + + ($ 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 * $) ^ $k) + + test: + assume (5 to 7 mixed by -1) == 5 + assume (5 to 7 mixed by 0) == 5 + assume (5 to 7 mixed by 0.5) == 6 + assume (5 to 7 mixed by 1) == 7 + assume (5 to 7 mixed by 2) == 7 + + ($lo to $hi mixed by $amount) means: + $ = ($amount clamped between 0 and 1) + return ((1 - $) * $lo + $ * $hi) + + test: + assume ([0, 1, 11] mixed by 0) == 0 + assume ([0, 1, 11] mixed by 0.25) == 0.5 + assume ([0, 1, 11] mixed by 0.5) == 1 + assume ([0, 1, 11] mixed by 0.75) == 6 + assume ([0, 1, 11] mixed by 1) == 11 + assume ([99] mixed by 0.5) == 99 + + ($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 + (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))" + + [random choice from $elements, random choice $elements, random $elements] + ..all mean (=lua "\$elements[math.random(#\$elements)]") |