diff options
Diffstat (limited to 'core')
| -rw-r--r-- | core/math.nom | 103 |
1 files changed, 77 insertions, 26 deletions
diff --git a/core/math.nom b/core/math.nom index 088da12..94f9b12 100644 --- a/core/math.nom +++ b/core/math.nom @@ -34,37 +34,36 @@ test: 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 + hyperbolic tangent 5, e^ 5, ln 5, log 5 base 2, floor 5, ceiling 5, round 5 ] ..: fail "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)" +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 - =lua "(\$rounder)*math.floor((\$n / \$rounder) + .5)" + $rounder * (floor ($n / $rounder + 0.5)) # Any/all externally [all of $items, all $items] all mean: @@ -137,10 +136,62 @@ test: $best_key = $key return $best +test: + assume (100 clamped between 0 and 10) == 10 + externally ($ clamped between $min and $max) means: - if ($ < $min): return $min - if ($ > $max): return $max - return $ + 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 + $ * $hi) + +test: + assume ([0,1,11] mixed by 0.00) == 0 + assume ([0,1,11] mixed by 0.25) == 0.5 + assume ([0,1,11] mixed by 0.50) == 1 + assume ([0,1,11] mixed by 0.75) == 6 + assume ([0,1,11] mixed by 1.00) == 11 + assume ([99] mixed by 0.5) == 99 + +externally ($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: |