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import PureOp, Constant, T, any from require 'alv.base'
unpack or= table.unpack
---
-- (recursively) wrap/repeat a scalar value to match a (nested) array type.
--
-- For example `expand_to (Array 3, Array 4, T.num), 2` will return
-- `[[2 2 2 2] [2 2 2 2] [2 2 2 2]]`.
expand_to = (type, scalar) ->
return scalar unless type.iter_keys
return for key, inner in type\iter_keys!
expand_to inner, scalar
deep_apply = (fn, type, args) ->
return fn args unless type.iter_keys
return for key, inner in type\iter_keys!
deep_apply fn, inner, [arg[key] for arg in *args]
--- return a function that runs `expand_to` on all arguments
--
-- @treturn function
expand_all_fn = (types) ->
result_type = nil
for type in *types
continue if type == T.num
result_type or= type
assert type == result_type
-- all scalars, don't expand
if not result_type
return T.num, (args) -> args
-- at least one non-scalar
result_type, (args) ->
-- expand all arguments
return for i, arg in ipairs args
if types[i] != result_type
expand_to result_type, arg
else
arg
num = any!! / any.num
reduce_fn = (fn) ->
(accum, ...) ->
for i=1, select '#', ...
accum = fn accum, select i, ...
accum
func_op = (_func, pattern) ->
func = (args) -> _func unpack args
class extends PureOp
pattern: pattern
type: (inputs) =>
types = [input\type! for input in *inputs]
result, @expand = expand_all_fn types
result
tick: =>
@out\set deep_apply func, @out.type, @.expand @unwrap_all!
func_def = (name, args, func, summary, pattern) ->
Constant.meta
meta:
:name
:summary
examples: { "(#{name} #{args})" }
value: func_op func, pattern or num\rep 1, 1
evenodd_op = (remainder) ->
class extends PureOp
pattern: T.num + -T.num
type: T.bool
tick: =>
{ val, div } = @unwrap_all!
@out\set (val % div) == remainder
add = Constant.meta
meta:
name: 'add'
summary: "Add values."
examples: { '(+ a b [c…])', '(add a b [c…])' }
description: "Sum all arguments."
value: func_op (reduce_fn (a, b) -> a + b), num\rep 2, nil
sub = Constant.meta
meta:
name: 'sub'
summary: "Subtract values."
examples: { '(- a b [c…])', '(sub a b [c…])' }
description: "Subtract all other arguments from `a`."
value: func_op (reduce_fn (a, b) -> a - b), num\rep 2, nil
mul = Constant.meta
meta:
name: 'mul'
summary: "Multiply values."
examples: { '(* a b [c…])', '(mul a b [c…])' }
value: func_op (reduce_fn (a, b) -> a * b), num\rep 2, nil
div = Constant.meta
meta:
name: 'div'
summary: "Divide values."
examples: { '(/ a b [c…])', '(div a b [c…])' }
description: "Divide `a` by all other arguments."
value: func_op (reduce_fn (a, b) -> a / b), num\rep 2, nil
pow = Constant.meta
meta:
name: 'pow'
summary: "Raise to a power."
examples: { '(^ base exp)', '(pow base exp' }
description: "Raise `base` to the power `exp`."
value: func_op (reduce_fn (a, b) -> a ^ b), num\rep 2, nil
mod = Constant.meta
meta:
name: 'mod'
summary: 'Modulo operator.'
examples: { '(% num div)', '(mod num div)' }
description: "Calculate remainder of division by `div`."
value: func_op ((a, b) -> a % b), num + num
mix = Constant.meta
meta:
name: 'mix'
summary: 'Linearly interpolate.'
examples: { '(mix a b i)' }
description: "Interpolate between `a` and `b` using `i` in range 0-1."
value: func_op ((a, b, i) -> i*b + (1-i)*a), num + num + num
min = Constant.meta
meta:
name: 'min'
summary: "Find the minimum."
examples: { '(min a b [c…])' }
description: "Return the lowest of arguments."
value: func_op math.min, num*0
max = Constant.meta
meta:
name: 'max'
summary: "Find the maximum."
examples: { '(max a b [c…])' }
description: "Return the highest of arguments."
value: func_op math.max, num*0
inc = func_def 'inc', 'i', ((i) -> i + 1), "Increment by 1."
dec = func_def 'dec', 'i', ((i) -> i - 1), "Decrement by 1."
cos = func_def 'cos', 'alpha', math.cos, "Cosine function (radians)."
sin = func_def 'sin', 'alpha', math.sin, "Sine function (radians)."
tan = func_def 'tan', 'alpha', math.tan, "Tangent function (radians)."
acos = func_def 'acos', 'cos', math.acos, "Inverse cosine function (radians)."
asin = func_def 'asin', 'sin', math.asin, "Inverse sine function (radians)."
atan = func_def 'atan', 'tan', math.atan, "Inverse tangent function (radians)."
atan2 = func_def 'atan2', 'y x', math.atan2, "Inverse tangent function (two argument version).", num + num
cosh = func_def 'cosh', 'alpha', math.cosh, "Hyperbolic cosine function (radians)."
sinh = func_def 'sinh', 'alpha', math.sinh, "Hyperbolic sine function (radians)."
tanh = func_def 'tanh', 'alpha', math.tanh, "Hyperbolic tangent function (radians)."
floor = func_def 'floor', 'val', math.floor, "Round towards negative infinity."
ceil = func_def 'ceil', 'val', math.ceil, "Round towards positive infinity."
abs = func_def 'abs', 'val', math.abs, "Get the absolute value."
exp = func_def 'exp', 'exp', math.floor, "*e* number raised to a power."
log = func_def 'log', 'val [base]', math.log, "Logarithm with optional base.", num + -num
log10 = func_def 'log10', 'val', math.log10, "Logarithm with base 10."
sqrt = func_def 'sqrt', 'val', math.sqrt, "Square root function."
Constant.meta
meta:
name: 'math'
summary: "Mathematical functions, expanded to vectors and matrices."
description: "
These functions are like the ones in [math/][:],
except that they can also operate componentwise on (nested) arrays of numbers.
(+ 1 2 3) #(<num= 6>)
(+ (array 1 2) (array 3 4)) #(<num[2]= [4 6]>)
The arguments for an operator generally have to be of the same type.
However it is also okay to pass in scalar numbers together with a different type.
The scalars will be repeated as necessary to fit the shape of other arguments:
(* (array (array 1 2) (array 3 4))
2)
#(<num[2][2]= [[2 4] [6 8]]>)
"
value:
:add, '+': add
:sub, '-': sub
:mul, '*': mul
:div, '/': div
:pow, '^': pow
:mod, '%': mod
:even, :odd
:mix
:min, :max
:inc, :dec
pi: Constant.meta
value: math.pi
meta: summary: 'The pi constant.'
tau: Constant.meta
value: math.pi*2
meta: summary: 'The tau constant.'
huge: Constant.meta
value: math.huge
meta: summary: 'Positive infinity constant.'
:sin, :cos, :tan
:asin, :acos, :atan, :atan2
:sinh, :cosh, :tanh
:floor, :ceil, :abs
:exp, :log, :log10, :sqrt
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