made changes

README.md

@@ -0,0 +1,8 @@
+# cxgraph
+
+cxgraph is a complex function graphing tool built around WebGPU available
+[on the web](https://cx.trimill.xyz/) or (slightly) for desktop.
+
+## documentation
+- [language](docs/language.md)
+- [web interface](docs/web.md)

cxgraph-web/index.html

@@ -8,8 +8,9 @@
 	<div class="canvas-container">
 		<canvas id="canvas"></canvas>
 		<svg id="overlay">
-			<line id="overlay_axis_x" x1="0" y1="0" x2="0" y2="0" stroke="#0006" stroke-width="1.5" visibility="hidden" />
+			<line id="svg_axis_x" x1="0" y1="0" x2="0" y2="0" stroke="#0006" stroke-width="1.5" visibility="hidden" />
-			<line id="overlay_axis_y" x1="0" y1="0" x2="0" y2="0" stroke="#0006" stroke-width="1.5" visibility="hidden" />
+			<line id="svg_axis_y" x1="0" y1="0" x2="0" y2="0" stroke="#0006" stroke-width="1.5" visibility="hidden" />
+			<circle id="svg_unitcircle" cx="0" cy="0" r="0" stroke="#0006" fill="none" stroke-width="1.5" visibility="hidden" />
 			<g id="svg_point_template" visibility="hidden">
 				<circle cx="0" cy="0" r="15" stroke="none" fill="#6664" />
 				<circle cx="0" cy="0" r="5" stroke="none" fill="#6666" />
@@ -39,7 +40,7 @@
 			<summary>Options</summary>
 			<div>
 				<input type="button" id="button_reset_view" value="Reset view">
-				<input type="button" id="button_help" value="Help" onclick="window.open('docs.html')">
+				<input type="button" id="button_help" value="Help" onclick="window.open('https://g.trimill.xyz/trimill/cxgraph')">
 			</div>
 			<div>
 				<div><label for="range_resolution">Resolution</label></div>
@@ -91,9 +92,13 @@
 			<div>
 				Overlay
 				<div>
-					<input type="checkbox" id="overlay_axes" checked>
+					<input type="checkbox" id="overlay_axes">
 					<label for="overlay_axes">Draw axes</label>
 				</div>
+				<div>
+					<input type="checkbox" id="overlay_unitcircle">
+					<label for="overlay_unitcircle">Draw unit circle</label>
+				</div>
 			</div>
 		</details>
 

cxgraph-web/index.js

@@ -70,15 +70,25 @@ function onViewChange() {
 	let bounds = calcBounds();
 	cxgraph.set_bounds(bounds.x_min, bounds.y_min, bounds.x_max, bounds.y_max);
 	let origin = cxToScreen({ re: 0, im: 0 });
+	let one = cxToScreen({ re: 1, im: 0 });
 
-	overlay_axis_x.setAttribute("x1", 0)
+	if(svg_axis_x.visibility != "hidden") {
-	overlay_axis_x.setAttribute("x2", dim.w);
+		svg_axis_x.setAttribute("x1", 0)
-	overlay_axis_x.setAttribute("y1", origin.y);
+		svg_axis_x.setAttribute("x2", dim.w);
-	overlay_axis_x.setAttribute("y2", origin.y);
+		svg_axis_x.setAttribute("y1", origin.y);
-	overlay_axis_y.setAttribute("x1", origin.x);
+		svg_axis_x.setAttribute("y2", origin.y);
-	overlay_axis_y.setAttribute("x2", origin.x);
+	}
-	overlay_axis_y.setAttribute("y1", 0);
+	if(svg_axis_y.visibility != "hidden") {
-	overlay_axis_y.setAttribute("y2", dim.h);
+		svg_axis_y.setAttribute("x1", origin.x);
+		svg_axis_y.setAttribute("x2", origin.x);
+		svg_axis_y.setAttribute("y1", 0);
+		svg_axis_y.setAttribute("y2", dim.h);
+	}
+	if(svg_unitcircle.visibility != "hidden") {
+		svg_unitcircle.setAttribute("cx", origin.x);
+		svg_unitcircle.setAttribute("cy", origin.y);
+		svg_unitcircle.setAttribute("r", one.x - origin.x);
+	}
 
 	for(let point of graphPoints) {
 		point.onViewChange();
@@ -148,7 +158,7 @@ function onGraph() {
 		redraw();
 	} catch(e) {
 		console.log(e);
-		div_error_msg.textContent = e.toString();
+		div_error_msg.textContent = e.toString().replace("\n", "\r\n");
 		div_error_msg.hidden = false;
 	}
 }
@@ -214,10 +224,16 @@ let specialChars = new RegExp(
 console.log(specialChars);
 
 source_text.addEventListener("input", () => {
+	let e = source_text.selectionEnd;
+	let amnt = 0;
 	source_text.value = source_text.value.replace(
 		specialChars,
-		(_m, p) => charMap[p]
+		(m, p) => {
-	)
+			amnt += m.length - charMap[p].length;
+			return charMap[p];
+		}
+	);
+	source_text.selectionEnd = e - amnt;
 });
 
 //
@@ -276,8 +292,13 @@ nameColorMode[0].checked = true;
 
 overlay_axes.addEventListener("change", () => {
 	let vis = overlay_axes.checked ? "visible" : "hidden";
-	overlay_axis_x.setAttribute("visibility", vis);
+	svg_axis_x.setAttribute("visibility", vis);
-	overlay_axis_y.setAttribute("visibility", vis);
+	svg_axis_y.setAttribute("visibility", vis);
+});
+
+overlay_unitcircle.addEventListener("change", () => {
+	let vis = overlay_unitcircle.checked ? "visible" : "hidden";
+	svg_unitcircle.setAttribute("visibility", vis);
 });
 
 //

cxgraph-web/style.css

@@ -71,13 +71,14 @@ summary {
 }
 
 #source_text {
-	width: 300px;
+	width: 400px;
-	height: 500px;
+	height: 150px;
 	font-size: 15px;
 }
 
 #div_error_msg {
 	color: #f9a;
+	white-space: pre-line;
 }
 
 input {

docs/language.md

@@ -0,0 +1,165 @@
+# 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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/E_(mathematical_constant)), equal to `exp(1)` |
+| `tau`, `τ`     | the [circle constant](https://tauday.com/tau-manifesto)                                                |
+| `emgamma`, `γ` | the [Euler-Mascheroni](https://en.wikipedia.org/wiki/Euler%27s_constant) constant, equal to `-ψ(1)`    |
+| `phi`, `φ`     | the [golden ratio](https://en.wikipedia.org/wiki/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
+```

libcxgraph/src/language/ast.rs

@@ -14,6 +14,7 @@ pub enum UnaryOp {
 
 #[derive(Clone, Copy, Debug)]
 pub enum ExpressionType<'a> {
+	Block,
 	Number(Complex),
 	Name(&'a str),
 	Binary(BinaryOp),
@@ -32,6 +33,10 @@ pub struct Expression<'a> {
 }
 
 impl<'a> Expression<'a> {
+	pub fn new_block(exs: Vec<Expression<'a>>) -> Self {
+		Self { ty: ExpressionType::Block, children: exs }
+	}
+
 	pub fn new_number(x: f64) -> Self {
 		Self { ty: ExpressionType::Number(Complex::new(x, 0.0)), children: Vec::with_capacity(0) }
 	}
@@ -87,6 +92,7 @@ pub enum Definition<'a> {
 fn display_expr(w: &mut impl fmt::Write, expr: &Expression, depth: usize) -> fmt::Result {
 	let indent = depth*2;
 	match expr.ty {
+		ExpressionType::Block => write!(w, "{:indent$}BLOCK", "", indent=indent)?,
 		ExpressionType::Number(n) => write!(w, "{:indent$}NUMBER {n:?}", "", indent=indent)?,
 		ExpressionType::Name(n) => write!(w, "{:indent$}NAME {n}", "", indent=indent)?,
 		ExpressionType::Binary(op) => write!(w, "{:indent$}OP {op:?}", "", indent=indent)?,

libcxgraph/src/language/builtins.rs

@@ -10,6 +10,14 @@ thread_local! {
 		m.insert("recip",  ("c_recip",  1));
 		m.insert("conj",   ("c_conj",   1));
 
+		m.insert("ifgt",  ("c_ifgt",  4));
+		m.insert("iflt",  ("c_iflt",  4));
+		m.insert("ifge",  ("c_ifge",  4));
+		m.insert("ifle",  ("c_ifle",  4));
+		m.insert("ifeq",  ("c_ifeq",  4));
+		m.insert("ifne",  ("c_ifne",  4));
+		m.insert("ifnan", ("c_ifnan", 3));
+
 		m.insert("re",       ("c_re",     1));
 		m.insert("im",       ("c_im",     1));
 		m.insert("signre",   ("c_signre", 1));
@@ -24,11 +32,15 @@ thread_local! {
 		m.insert("mul",      ("c_mul",    2));
 		m.insert("div",      ("c_div",    2));
 		m.insert("pow",      ("c_pow",    2));
+		m.insert("powbr",    ("c_powbr",  3));
 
 		m.insert("exp",      ("c_exp",    1));
 		m.insert("log",      ("c_log",    1));
 		m.insert("logbr",    ("c_logbr",  2));
 		m.insert("sqrt",     ("c_sqrt",   1));
+		m.insert("sqrtbr",   ("c_sqrtbr", 2));
+		m.insert("cbrt",     ("c_cbrt",   1));
+		m.insert("cbrtbr",   ("c_cbrtbr", 2));
 
 		m.insert("sin",      ("c_sin",    1));
 		m.insert("cos",      ("c_cos",    1));
@@ -46,6 +58,8 @@ thread_local! {
 
 		m.insert("gamma",       ("c_gamma",    1));
 		m.insert("\u{0393}",    ("c_gamma",    1));
+		m.insert("invgamma",    ("c_invgamma", 1));
+		m.insert("inv\u{0393}", ("c_invgamma", 1));
 		m.insert("loggamma",    ("c_loggamma", 1));
 		m.insert("log\u{0393}", ("c_loggamma", 1));
 		m.insert("digamma",     ("c_digamma",  1));

libcxgraph/src/language/compiler.rs

@@ -148,6 +148,19 @@ impl<'w, 'i, W: fmt::Write> Compiler<'w, 'i, W> {
 	fn compile_expr(&mut self, local: &mut LocalState<'i>, expr: &Expression<'i>)
 	-> Result<String, CompileError> {
 		match expr.ty {
+			ExpressionType::Block => {
+				let tmp = local.next_tmp();
+				writeln!(self.buf, "var {tmp}: vec2f;")?;
+				writeln!(self.buf, "{{")?;
+				let mut block_local = local.clone();
+				let mut last = String::new();
+				for child in &expr.children {
+					last = self.compile_expr(&mut block_local, child)?;
+				}
+				writeln!(self.buf, "{tmp} = {last};")?;
+				writeln!(self.buf, "}}")?;
+				Ok(tmp)
+			}
 			ExpressionType::Name(v) => self.resolve_var(local, v),
 			ExpressionType::Store(var) => {
 				let a = self.compile_expr(local, &expr.children[0])?;

libcxgraph/src/language/syntax.lalrpop

@@ -109,6 +109,7 @@ Item: Expression<'input> = {
 	Number,
 	<n:Name> => Expression::new_name(n),
 	"(" <Expr> ")",
+	"{" <exs:Exprs> "}" => Expression::new_block(exs),
 	"sum" "(" <name:Name> ":" <min:Int> "," <max:Int> ")" "{" <exs:Exprs> "}"
 		=> Expression::new_sum(name, min, max, exs),
 	"prod" "(" <name:Name> ":" <min:Int> "," <max:Int> ")" "{" <exs:Exprs> "}"

libcxgraph/src/language/token.rs

@@ -25,8 +25,8 @@ impl<'i> fmt::Display for Token<'i> {
 			Token::Iter   => f.write_str("iter"),
 			Token::LParen => f.write_str("("),
 			Token::RParen => f.write_str(")"),
-            Token::LBrace => f.write_str("{{"),
+			Token::LBrace => f.write_str("{"),
-            Token::RBrace => f.write_str("}}"),
+			Token::RBrace => f.write_str("}"),
 			Token::Plus   => f.write_str("+"),
 			Token::Minus  => f.write_str("-"),
 			Token::Star   => f.write_str("*"),
@@ -61,6 +61,7 @@ pub type Spanned<T, L, E> = Result<(L, T, L), E>;
 pub struct Lexer<'i> {
 	src: &'i str,
 	chars: Peekable<CharIndices<'i>>,
+	bracket_depth: usize,
 }
 
 fn is_ident_begin(c: char) -> bool {
@@ -73,7 +74,11 @@ fn is_ident_middle(c: char) -> bool {
 
 impl<'i> Lexer<'i> {
 	pub fn new(src: &'i str) -> Self {
-		Self { src, chars: src.char_indices().peekable() }
+		Self {
+			src,
+			chars: src.char_indices().peekable(),
+			bracket_depth: 0,
+	 }
 	}
 
 	fn next_number(&mut self, i: usize, mut has_dot: bool) -> Spanned<Token<'i>, usize, LexerError> {
@@ -117,16 +122,29 @@ impl<'i> Lexer<'i> {
 		}
 	}
 
-	fn next_token(&mut self) -> Option<Spanned<Token<'i>, usize, LexerError>> {
+	fn skip_whitespace(&mut self) {
-		while matches!(self.chars.peek(), Some((_, ' ' | '\t' | '\r'))) {
+		while matches!(self.chars.peek(), Some((_, ' ' | '\t' | '\n' | '\r'))) {
+			if self.bracket_depth == 0 && matches!(self.chars.peek(), Some((_, '\n'))) {
+				break
+			}
 			self.chars.next();
 		}
+	}
+
+	fn next_token(&mut self) -> Option<Spanned<Token<'i>, usize, LexerError>> {
+		self.skip_whitespace();
 
 		Some(match self.chars.next()? {
-			(i, '(') => Ok((i, Token::LParen, i + 1)),
+			(_, '#') => {
-			(i, ')') => Ok((i, Token::RParen, i + 1)),
+				while !matches!(self.chars.peek(), Some((_, '\n')) | None) {
-			(i, '{') => Ok((i, Token::LBrace, i + 1)),
+					self.chars.next();
-			(i, '}') => Ok((i, Token::RBrace, i + 1)),
+				}
+				self.next_token()?
+			}
+			(i, '(') => { self.bracket_depth += 1; Ok((i, Token::LParen, i + 1)) },
+			(i, ')') => { self.bracket_depth -= 1; Ok((i, Token::RParen, i + 1)) },
+			(i, '{') => { self.bracket_depth += 1; Ok((i, Token::LBrace, i + 1)) },
+			(i, '}') => { self.bracket_depth -= 1; Ok((i, Token::RBrace, i + 1)) },
 			(i, '+') => Ok((i, Token::Plus, i + 1)),
 			(i, '-') => match self.chars.peek() {
 				Some((_, '>')) => {

libcxgraph/src/renderer/fragment.wgsl

@@ -31,6 +31,18 @@ fn correct_mod2(x: vec2f, y: vec2f) -> vec2f {
 	return ((x % y) + y) % y;
 }
 
+fn vlength(v: vec2f) -> f32 {
+	let l = length(v);
+	if l != l || l <= 3.4e+38 {
+		return l;
+	}
+	let a = max(abs(v.x), abs(v.y));
+	let b = RECIP_SQRT2 * abs(v.x) + RECIP_SQRT2 * abs(v.y);
+	let c = 2.0 * RECIP_SQRT29 * abs(v.x) + 5.0 * RECIP_SQRT29 * abs(v.y);
+	let d = 5.0 * RECIP_SQRT29 * abs(v.x) + 2.0 * RECIP_SQRT29 * abs(v.y);
+	return max(max(a, b), max(c, d));
+}
+
 /////////////////
 //  constants  //
 /////////////////
@@ -40,6 +52,7 @@ const E = 2.718281828459045;
 const RECIP_SQRT2 = 0.7071067811865475;
 const LOG_TAU = 1.8378770664093453;
 const LOG_2 = 0.6931471805599453;
+const RECIP_SQRT29 = 0.18569533817705186;
 
 const C_TAU = vec2f(TAU, 0.0);
 const C_E = vec2f(E, 0.0);
@@ -67,6 +80,34 @@ fn c_signim(z: vec2f) -> vec2f {
 	return vec2(sign(z.y), 0.0);
 }
 
+fn c_ifgt(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x > q.x);
+}
+
+fn c_iflt(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x < q.x);
+}
+
+fn c_ifge(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x >= q.x);
+}
+
+fn c_ifle(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x <= q.x);
+}
+
+fn c_ifeq(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x == q.x);
+}
+
+fn c_ifne(p: vec2f, q: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x != q.x);
+}
+
+fn c_ifnan(p: vec2f, z: vec2f, w: vec2f) -> vec2f {
+	return select(w, z, p.x != p.x && p.y != p.y);
+}
+
 fn c_conj(z: vec2f) -> vec2f {
 	return z * vec2(1.0, -1.0);
 }
@@ -76,17 +117,20 @@ fn c_abs_sq(z: vec2f) -> vec2f {
 }
 
 fn c_abs(z: vec2f) -> vec2f {
-	return vec2(length(z), 0.0);
+	return vec2(vlength(z), 0.0);
 }
 
 fn c_arg(z: vec2f) -> vec2f {
+	if z.x < 0.0 && z.y == 0.0 {
+		return vec2(TAU/2.0, 0.0);
+	}
 	return vec2(atan2(z.y, z.x), 0.0);
 }
 
 fn c_argbr(z: vec2f, br: vec2f) -> vec2f {
 	let r = vec2(cos(-br.x), sin(-br.x));
 	let zr = c_mul(z, r);
-	return vec2(atan2(zr.y, zr.x) + br.x, 0.0);
+	return c_arg(zr) + vec2(br.x, 0.0);
 }
 
 fn c_add(u: vec2f, v: vec2f) -> vec2f {
@@ -122,7 +166,7 @@ fn c_exp(z: vec2f) -> vec2f {
 }
 
 fn c_log(z: vec2f) -> vec2f {
-	return vec2(0.5 * log(dot(z, z)), atan2(z.y, z.x));
+	return vec2(0.5 * log(dot(z, z)), c_arg(z).x);
 }
 
 fn c_logbr(z: vec2f, br: vec2f) -> vec2f {
@@ -133,10 +177,26 @@ fn c_pow(u: vec2f, v: vec2f) -> vec2f {
 	return c_exp(c_mul(c_log(u), v));
 }
 
+fn c_powbr(u: vec2f, v: vec2f, br: vec2f) -> vec2f {
+	return c_exp(c_mul(c_logbr(u, br), v));
+}
+
 fn c_sqrt(z: vec2f) -> vec2f {
 	return c_pow(z, vec2(0.5, 0.0));
 }
 
+fn c_sqrtbr(z: vec2f, br: vec2f) -> vec2f {
+	return c_powbr(z, vec2(0.5, 0.0), br);
+}
+
+fn c_cbrt(z: vec2f, br: vec2f) -> vec2f {
+	return c_pow(z, vec2(1.0/3.0, 0.0));
+}
+
+fn c_cbrtbr(z: vec2f, br: vec2f) -> vec2f {
+	return c_powbr(z, vec2(1.0/3.0, 0.0), br);
+}
+
 fn c_sin(z: vec2f) -> vec2f {
 	return vec2(sin(z.x)*cosh(z.y), cos(z.x)*sinh(z.y));
 }
@@ -162,84 +222,50 @@ fn c_tanh(z: vec2f) -> vec2f {
 }
 
 fn c_asin(z: vec2f) -> vec2f {
-	let u = c_sqrt(vec2f(1.0, 0.0) - c_mul(z, z));
+	let u = c_sqrt(vec2(1.0, 0.0) - c_mul(z, z));
 	let v = c_log(u + vec2(-z.y, z.x));
 	return vec2(v.y, -v.x);
 }
 
 fn c_acos(z: vec2f) -> vec2f {
-	let u = c_sqrt(vec2f(1.0, 0.0) - c_mul(z, z));
+	let u = c_sqrt(vec2(1.0, 0.0) - c_mul(z, z));
-	let v = c_log(u + vec2f(-z.y, z.x));
+	let v = c_log(u + vec2(-z.y, z.x));
-	return vec2f(TAU*0.25 - v.y, v.x);
+	return vec2(TAU*0.25 - v.y, v.x);
 }
 
 fn c_atan(z: vec2f) -> vec2f {
-	let u = vec2f(1.0, 0.0) - vec2f(-z.y, z.x);
+	let u = vec2(1.0, 0.0) - vec2(-z.y, z.x);
-	let v = vec2f(1.0, 0.0) + vec2f(-z.y, z.x);
+	let v = vec2(1.0, 0.0) + vec2(-z.y, z.x);
 	let w = c_log(c_div(u, v));
-	return 0.5 * vec2f(-w.y, w.x);
+	return 0.5 * vec2(-w.y, w.x);
 }
 
 fn c_asinh(z: vec2f) -> vec2f {
-	let u = c_sqrt(vec2f(1.0, 0.0) + c_mul(z, z));
+	let u = c_sqrt(vec2(1.0, 0.0) + c_mul(z, z));
 	return c_log(u + z);
 }
 
 fn c_acosh(z: vec2f) -> vec2f {
-	let u = c_sqrt(vec2f(-1.0, 0.0) + c_mul(z, z));
+	let u = c_sqrt(vec2(-1.0, 0.0) + c_mul(z, z));
 	return c_log(u + z);
 }
 
 fn c_atanh(z: vec2f) -> vec2f {
-	let u = vec2f(1.0, 0.0) + z;
+	let u = vec2(1.0, 0.0) + z;
-	let v = vec2f(1.0, 0.0) - z;
+	let v = vec2(1.0, 0.0) - z;
 	return 0.5 * c_log(c_div(u, v));
 }
 
-// gamma //
-
-fn c_gamma(z: vec2f) -> vec2f {
-	let reflect = z.x < 0.5;
-	var zp = z;
-	if reflect {
-		zp = vec2(1.0, 0.0) - z;
-	}
-	var w = c_gamma_inner2(zp);
-	if reflect {
-		w = TAU * 0.5 * c_recip(c_mul(c_sin(TAU * 0.5 * z), w));
-	}
-	return w;
-}
-
-// Yang, ZH., Tian, JF. An accurate approximation formula for gamma function. J Inequal Appl 2018, 56 (2018).
-// https://doi.org/10.1186/s13660-018-1646-6
-fn c_gamma_inner(z: vec2f) -> vec2f {
-	let z2 = c_mul(z, z);
-	let z3 = c_mul(z2, z);
-
-	let a = c_sqrt(TAU * z);
-	let b = c_pow(1.0 / (E * E) * c_mul(z3, c_sinh(c_recip(z))), 0.5 * z);
-	let c = c_exp(7.0/324.0 * c_recip(c_mul(z3, 35.0 * z2 + 33.0)));
-
-	return c_mul(c_mul(a, b), c);
-}
-
-fn c_gamma_inner2(z: vec2f) -> vec2f {
-	let w = c_gamma_inner(z + vec2(3.0, 0.0));
-	return c_div(w, c_mul(c_mul(z, z + vec2(1.0, 0.0)), c_mul(z + vec2(2.0, 0.0), z + vec2(3.0, 0.0))));
-}
-
 // log gamma //
 
 fn c_loggamma(z: vec2f) -> vec2f {
-	let reflect = z.x < 0.5 && abs(z.y) < 10.0;
+	let reflect = z.x < 0.5 && abs(z.y) < 13.0;
 	var zp = z;
 	if reflect {
 		zp = vec2(1.0, 0.0) - z;
 	}
 	var w = c_loggamma_inner2(zp);
 	if reflect {
-		//let offset = select(0.0, TAU / 2.0, z % 2.0 < 1.0);
 		let br = 0.5 * TAU * (0.5 - z.x) * sign(z.y);
 		w = vec2(LOG_TAU - LOG_2, 0.0) - c_logbr(c_sin(TAU/2.0 * z), vec2(br, 0.0)) - w;
 	}
@@ -256,10 +282,20 @@ fn c_loggamma_inner2(z: vec2f) -> vec2f {
 	return w - l;
 }
 
+// gamma //
+
+fn c_gamma(z: vec2f) -> vec2f {
+	return c_exp(c_loggamma(z));
+}
+
+fn c_invgamma(z: vec2f) -> vec2f {
+	return c_exp(-c_loggamma(z));
+}
+
 // digamma //
 
 fn c_digamma(z: vec2f) -> vec2f {
-	let reflect = z.x < 0.5;
+	let reflect = z.x < 0.5 && abs(z.y) < 13.0;
 	var zp = z;
 	if reflect {
 		zp = vec2(1.0, 0.0) - z;
@@ -308,13 +344,18 @@ fn coloring_standard(z: vec2f) -> vec3f {
 		return vec3f(0.5, 0.5, 0.5);
 	}
 
-	let mag_sq = dot(z, z);
+	let mag = vlength(z);
-	if mag_sq > 3.40282347E+38 {
+	if mag > 3.40282347E+38 {
 		return vec3f(1.0, 1.0, 1.0);
 	}
-	let mag = sqrt(mag_sq);
+	if uniforms.shading_intensity > 0.0 && mag > 1.8446E+19 {
+		return vec3f(1.0, 1.0, 1.0);
+	}
+	if uniforms.shading_intensity == 0.0 && mag < 1.0E-38 {
+		return vec3f(0.0, 0.0, 0.0);
+	}
 
-	let arg = atan2(z.y, z.x);
+	let arg = c_arg(z).x;
 
 	let hsv = vec3f(arg / TAU + 1.0, shademap(1.0/mag), shademap(mag));
 	return hsv2rgb(hsv);
@@ -328,13 +369,18 @@ fn coloring_uniform(z: vec2f) -> vec3f {
 		return vec3f(0.5, 0.5, 0.5);
 	}
 
-	let mag_sq = dot(z, z);
+	let mag = vlength(z);
-	if mag_sq > 3.40282347E+38 {
+	if mag > 3.40282347E+38 {
 		return vec3f(1.0, 1.0, 1.0);
 	}
-	let mag = sqrt(mag_sq);
+	if uniforms.shading_intensity > 0.0 && mag > 1.8446E+19 {
+		return vec3f(1.0, 1.0, 1.0);
+	}
+	if uniforms.shading_intensity == 0.0 && mag < 1.0E-38 {
+		return vec3f(0.0, 0.0, 0.0);
+	}
 
-	let arg = atan2(z.y, z.x);
+	let arg = c_arg(z).x;
 
 	let r = cos(arg - 0.0*TAU/3.0)*0.5 + 0.5;
 	let g = cos(arg - 1.0*TAU/3.0)*0.5 + 0.5;
@@ -358,7 +404,7 @@ fn decoration_contour_im(z: vec2f) -> f32 {
 }
 
 fn decoration_contour_arg(z: vec2f) -> f32 {
-	let arg = atan2(z.y, z.x);
+	let arg = c_arg(z).x;
 	return round(correct_mod(arg + TAU, TAU/8.0) * 8.0/TAU) * 2.0 - 1.0;
 }
 
@@ -370,7 +416,7 @@ fn decoration_contour_mag(z: vec2f) -> f32 {
 @fragment
 fn main(@builtin(position) in: vec4f) -> @location(0) vec4f {
 	let pos = vec2(in.x, f32(uniforms.resolution.y) - in.y);
-	let w = remap(pos, vec2(0.0), vec2f(uniforms.resolution), uniforms.bounds_min, uniforms.bounds_max);
+	let w = remap(pos, vec2(0.0, 0.0), vec2f(uniforms.resolution), uniforms.bounds_min, uniforms.bounds_max);
 
 	let z = func_plot(w);