1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
|
import PureOp, Input, Constant, T, any from require 'alv.base'
unpack or= table.unpack
num = any.num
class ReduceOp extends PureOp
pattern: num\rep 2, nil
type: T.num
tick: =>
args = @unwrap_all!
accum = args[1]
for val in *args[2,]
accum = @.fn accum, val
@out\set accum
func_op = (func, pattern) ->
class extends PureOp
pattern: pattern
type: T.num
tick: => @out\set func unpack @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: num + -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: class extends ReduceOp
fn: (a, b) -> a + b
sub = Constant.meta
meta:
name: 'sub'
summary: "Subtract values."
examples: { '(- a b [c…])', '(- b)', '(sub a b [c…])' }
description: "Subtract all other arguments from `a`.
If only `b` is given, `a` is assumed to be `0`."
value: class extends ReduceOp
setup: (...) =>
super ...
if #@inputs == 1
table.insert @inputs, 1, Input.cold Constant.num 0
pattern: num*0
fn: (a, b) -> a - b
mul = Constant.meta
meta:
name: 'mul'
summary: "Multiply values."
examples: { '(* a b [c…])', '(mul a b [c…])' }
value: class extends ReduceOp
fn: (a, b) -> a * b
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: class extends ReduceOp
fn: (a, b) -> a / b
idiv = Constant.meta
meta:
name: 'idiv'
summary: "Divide values and floor."
examples: { '(// a b [c…])', '(idiv a b [c…])' }
description: "Divide `a` by all other arguments, flooring each time."
value: class extends ReduceOp
fn: (a, b) -> mat.floor a / b
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: class extends ReduceOp
fn: (a, b) -> a ^ b
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
even = Constant.meta
meta:
name: 'even'
summary: 'Check whether val is even.'
examples: { '(even val [div])' }
description: "`true` if dividing `val` by `div` has remainder zero.
`div` defaults to 2."
value: evenodd_op 0
odd = Constant.meta
meta:
name: 'odd'
summary: 'Check whether val is odd.'
examples: { '(odd val [div])' }
description: "`true` if dividing `val` by `div` has remainder one.
`div` defaults to 2."
value: evenodd_op 1
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
clamp = Constant.meta
meta:
name: 'clamp'
summary: "Clamp a value to a range."
examples: { '(clamp min max val)' }
description: "Returns `min` if `val < min`; `max` if `val > max`; and `val` otherwise."
value: func_op ((min, max, val) -> math.min max, math.max min, val), num*3
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-simple'
summary: "Mathematical functions for scalars."
description: "
All operators are PureOps.
They accept only scalar numbers.
For vectorized operators and matrix multiplication, use [math/][]."
value:
:add, '+': add
:sub, '-': sub
:mul, '*': mul
:div, '/': div
:idiv, '//': idiv
:pow, '^': pow
:mod, '%': mod
:even, :odd
:mix
:min, :max, :clamp
:inc, :dec
pi: Constant.meta
value: math.pi
meta: name: 'pi', summary: "The pi constant."
tau: Constant.meta
value: math.pi*2
meta: name: 'tau', summary: "The tau constant."
huge: Constant.meta
value: math.huge
meta: name: 'huge', summary: "Positive infinity constant."
:sin, :cos, :tan
:asin, :acos, :atan, :atan2
:sinh, :cosh, :tanh
:floor, :ceil, :abs
:exp, :log, :log10, :sqrt
|
