7.1 KiB
cxgraph language
cxgraph uses a custom expression language that is compiled to WGSL.
names
names must begin with any alphabetic character (lowercase or capital letters, Greek letters,
etc.) and may contain alphanumeric chararcters as well as underscores (_
) and apostrophes ('
).
the words sum
, prod
, and iter
may not be used for names. names may refer to either
functions or variables.
examples of names include:
a A aaa ω z_3 __5__ f' К'םαl'けx焼__검
names may either be built-in, global, or local. global or local names may shadow built-in names, and local names may shadow global ones.
declarations
a function declaration declares a new function. functions may have zero or more arguments.
f(x) = 3
a constant declaration declares a new constant.
n = 5
declarations are separated by newlines. declarations may only reference functions and constants in
declarations that precede them. the name used in a declaration (f
and n
in the above examples)
is in the global scope
built-ins
arithmetic functions:
name | description |
---|---|
pos(z) |
equivalent to unary + |
neg(z) |
equivalent to unary - |
conj(z) |
complex conjugate, equivalent to unary * |
re(z) |
real part |
im(z) |
imaginary part |
abs(z) |
absolute value (distance from 0 ) |
abs_sq(z) |
square of absolute value |
arg(z) |
argument (angle about 0 ) in the range (-τ/2, τ/2] |
argbr(z,br) |
argument in the range (-τ/2, τ/2] + br |
add(z,w) |
equivalent to z + w |
sub(z,w) |
equivalent to z - w |
mul(z,w) |
equivalent to z * w |
div(z,w) |
equivalent to z / w |
recip(z) |
reciprocal, equivalent to 1/z |
power/exponential functions:
name | description |
---|---|
exp(z) |
exponential function, equivalent to e^z |
log(z) |
logarithm base e |
logbr(z,br) |
logarithm base e with specified branch |
pow(z) |
power, equivalent to ^ |
powbr(z,br) |
pow with specified branch |
sqrt(z) |
square root, equivalent to z^0.5 |
sqrtbr(z,br) |
square root with specified branch |
cbrt(z) |
cube root, equivalent to z^0.5 |
cbrtbr(z,br) |
cube root with specified branch |
trigonometric functions:
name | description |
---|---|
sin(z) |
sine function |
cos(z) |
cosine function |
tan(z) |
tangent function |
sinh(z) |
hyperbolic sine function |
cosh(z) |
hyperbolic cosine function |
tanh(z) |
hyperbolic tangent function |
asin(z) |
inverse sine function |
acos(z) |
inverse cosine function |
atan(z) |
inverse tangent function |
asinh(z) |
inverse hyperbolic sine function |
acosh(z) |
inverse hyperbolic cosine function |
atanh(z) |
inverse hyperbolic tangent function |
special functions:
function | description |
---|---|
gamma(z) , Γ(z) |
gamma function |
invgamma(z) , invΓ(z) |
reciprocal of the gamma function |
loggamma(z) , logΓ(z) |
logarithm of the gamma function |
digamma(z) , ψ(z) |
digamma function |
logic functions:
function | description |
---|---|
signre(z) |
sign of real part (1 if re(z) > 0 , -1 if re(z) < 0 , 0 if re(z) == 0 ) |
signim(z) |
sign of imaginary part |
ifgt(p,q,z,w) |
evaluates to z if re(p) > re(q) , otherwise w |
iflt(p,q,z,w) |
evaluates to z if re(p) < re(q) , otherwise w |
ifge(p,q,z,w) |
evaluates to z if re(p) ≥ re(q) , otherwise w |
ifle(p,q,z,w) |
evaluates to z if re(p) ≤ re(q) , otherwise w |
ifeq(p,q,z,w) |
evaluates to z if re(p) = re(q) , otherwise w |
ifne(p,q,z,w) |
evaluates to z if re(p) ≠ re(q) , otherwise w |
ifnan(p,z,w) |
evaluates to z if p is NaN , otherwise w |
constants:
name | description |
---|---|
i |
the imaginary constant, equal to sqrt(-1) |
e |
the exponential constant, equal to exp(1) |
tau , τ |
the circle constant |
emgamma , γ |
the Euler-Mascheroni constant, equal to -ψ(1) |
phi , φ |
the golden ratio, equal to 1/2 + sqrt(5)/2 |
ebnf grammar
Program := Definitions
Definitions := NEWLINE* (Definition NEWLINE+)* Definition?
Definition := NAME "(" (NAME ",") NAME? ")" "=" Exprs
| NAME "=" Exprs
Exprs := (Expr ",")* Expr ","?
Expr := Store
Store := Store "->" NAME | Sum
Sum := Sum "+" Product
| Sum "-" Product
| Product
Product := Product "*" Unary
| Product "/" Unary
| Unary
Unary := "+" Unary
| "-" Unary
| "*" Unary
| Juxtapose Power
| Power
Juxtapose := Juxtapose PreJuxtapose | PreJuxtapose
Power := FnCall "^" Unary | FnCall
FnCall := NAME "(" Exprs ")" | Item
PreJuxtapose := Number | "(" <Expr> ")"
Item := Number
| NAME
| "(" Expr ")"
| "{" Exprs "}"
| "sum" "(" NAME ":" INT "," INT ")" "{" Exprs "}"
| "prod" "(" NAME ":" INT "," INT ")" "{" Exprs "}"
| "iter" "(" INT "," NAME ":" Expr ")" "{" Exprs "}"
Number = FLOAT | INT