146 lines
5.7 KiB
Plaintext
146 lines
5.7 KiB
Plaintext
#!/usr/bin/env nomsu -V4.8.8.6
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#
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This file defines some common math literals and functions
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use "core/metaprogramming.nom"
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use "core/text.nom"
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use "core/operators.nom"
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use "core/control_flow.nom"
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use "core/collections.nom"
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# Literals:
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test:
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assume (all of [inf, NaN, pi, tau, golden ratio, e]) or barf "\
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..math constants failed"
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%nan = (NaN)
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assume (%nan != %nan) or barf "NaN failed"
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compile [infinity, inf] to (Lua value "math.huge")
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compile [not a number, NaN, nan] to (Lua value "(0/0)")
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compile [pi, Pi, PI] to (Lua value "math.pi")
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compile [tau, Tau, TAU] to (Lua value "(2*math.pi)")
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compile [golden ratio] to (Lua value "((1+math.sqrt(5))/2)")
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compile [e] to (Lua value "math.exp(1)")
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# Functions:
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test:
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assume (("5" as a number) == 5)
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compile [% as a number, % as number] to (Lua value "tonumber(\(% as lua expr))")
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test:
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assume (..)
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all of [..]
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abs 5, | 5 |, sqrt 5, √ 5, sine 5, cosine 5, tangent 5, arc sine 5, arc cosine 5
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arc tangent 5, arc tangent 5 / 10, hyperbolic sine 5, hyperbolic cosine 5
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hyperbolic tangent 5, e^ 5, ln 5, log base 2 of 5, floor 5, ceiling 5, round 5
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..or barf "math functions failed"
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compile [absolute value %, | % |, abs %] to (..)
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Lua value "math.abs(\(% as lua expr))"
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compile [square root %, square root of %, √ %, sqrt %] to (..)
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Lua value "math.sqrt(\(% as lua expr))"
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compile [sine %, sin %] to (Lua value "math.sin(\(% as lua expr))")
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compile [cosine %, cos %] to (Lua value "math.cos(\(% as lua expr))")
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compile [tangent %, tan %] to (Lua value "math.tan(\(% as lua expr))")
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compile [arc sine %, asin %] to (Lua value "math.asin(\(% as lua expr))")
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compile [arc cosine %, acos %] to (Lua value "math.acos(\(% as lua expr))")
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compile [arc tangent %, atan %] to (Lua value "math.atan(\(% as lua expr))")
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compile [arc tangent %y / %x, atan2 %y %x] to (..)
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Lua value "math.atan2(\(%y as lua expr), \(%x as lua expr))"
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compile [hyperbolic sine %, sinh %] to (Lua value "math.sinh(\(% as lua expr))")
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compile [hyperbolic cosine %, cosh %] to (Lua value "math.cosh(\(% as lua expr))")
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compile [hyperbolic tangent %, tanh %] to (..)
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Lua value "math.tanh(\(% as lua expr))"
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compile [e^ %, exp %] to (Lua value "math.exp(\(% as lua expr))")
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compile [natural log %, ln %, log %] to (Lua value "math.log(\(% as lua expr))")
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compile [log % base %base, log base %base of %] to (..)
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Lua value "math.log(\(% as lua expr), \(%base as lua expr))"
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compile [floor %] to (Lua value "math.floor(\(% as lua expr))")
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compile [ceiling %, ceil %] to (Lua value "math.ceil(\(% as lua expr))")
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compile [round %, % rounded] to (Lua value "math.floor(\(% as lua expr) + .5)")
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test:
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assume ((463 to the nearest 100) == 500) or barf "rounding failed"
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assume ((2.6 to the nearest 0.25) == 2.5) or barf "rounding failed"
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action [%n to the nearest %rounder] (..)
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=lua "(\%rounder)*math.floor((\%n / \%rounder) + .5)"
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# Any/all/none
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compile [all of %items, all %items] to:
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unless (%items.type is "List"):
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return (Lua value "utils.all(\(%items as lua expr))")
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%clauses = ((% as lua expr) for % in %items)
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return (Lua value "(\(%clauses::joined with " and "))")
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parse [not all of %items, not all %items] as (not (all of %items))
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compile [any of %items, any %items] to:
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unless (%items.type is "List"):
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return (Lua value "utils.any(\(%items as lua expr))")
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%clauses = ((% as lua expr) for % in %items)
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return (Lua value "(\(%clauses::joined with " or "))")
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parse [none of %items, none %items] as (not (any of %items))
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compile [sum of %items, sum %items] to:
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unless (%items.type is "List"):
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return (Lua value "utils.sum(\(%items as lua expr))")
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%clauses = ((% as lua expr) for % in %items)
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return (Lua value "(\(%clauses::joined with " + "))")
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compile [product of %items, product %items] to:
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unless (%items.type is "List"):
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return (Lua value "utils.product(\(%items as lua expr))")
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%clauses = ((% as lua expr) for % in %items)
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return (Lua value "(\(%clauses::joined with " * "))")
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action [avg of %items, average of %items] (=lua "(utils.sum(\%items)/#\%items)")
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compile [min of %items, smallest of %items, lowest of %items] to (..)
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Lua value "utils.min(\(%items as lua expr))"
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compile [max of %items, biggest of %items, largest of %items, highest of %items] to (..)
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Lua value "utils.max(\(%items as lua expr))"
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test:
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assume ((min of [3, -4, 1, 2] by % = (% * %)) == 1)
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assume ((max of [3, -4, 1, 2] by % = (% * %)) == -4)
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parse [min of %items by %item = %value_expr] as (..)
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result of:
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set {%best:nil, %best_key:nil}
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for %item in %items:
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%key = %value_expr
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if ((%best == (nil)) or (%key < %best_key)):
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set {%best:%item, %best_key:%key}
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return %best
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parse [max of %items by %item = %value_expr] as (..)
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result of:
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set {%best:nil, %best_key:nil}
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for %item in %items:
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%key = %value_expr
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if ((%best == (nil)) or (%key > %best_key)):
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set {%best:%item, %best_key:%key}
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return %best
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# Random functions
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action [seed random with %] (..)
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lua> "\
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..math.randomseed(\%);
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for i=1,20 do math.random(); end"
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parse [seed random] as (seed random with (=lua "os.time()"))
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compile [random number, random, rand] to (Lua value "math.random()")
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compile [random int %n, random integer %n, randint %n] to (..)
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Lua value "math.random(\(%n as lua expr))"
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compile [..]
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random from %low to %high, random number from %low to %high
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rand %low %high
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..to (Lua value "math.random(\(%low as lua expr), \(%high as lua expr))")
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action [random choice from %elements, random choice %elements, random %elements] (..)
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=lua "\%elements[math.random(#\%elements)]"
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