docs: baked a lot of API docs

docs/API/math.md

@@ -6,4 +6,478 @@ references:
 
 The `math` namespace contains Lua-compatible numeric functions plus Space Lua's `cosineSimilarity` helper.
 
-${spacelua.renderApiDocumentation("math")}
+<!--#lua spacelua.renderApiDocumentation("math") -->
+## math.abs
+
+`math.abs(x)`
+
+Returns the absolute value of `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.acos
+
+`math.acos(x)`
+
+Returns the arc cosine of `x` in radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.asin
+
+`math.asin(x)`
+
+Returns the arc sine of `x` in radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.atan
+
+`math.atan(y, x?)`
+
+Returns the arc tangent of `y/x` in radians, using `1` for omitted `x`.
+
+**Parameters:**
+
+- `y` (`number`)
+- `x?` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.ceil
+
+`math.ceil(x)`
+
+Returns the smallest integer greater than or equal to `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `integer`
+
+## math.cos
+
+`math.cos(x)`
+
+Returns the cosine of `x` radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.cosh
+
+`math.cosh(x)`
+
+> **Deprecated:** Retained for compatibility with older Lua versions.
+
+Returns the hyperbolic cosine of `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.cosineSimilarity
+
+`math.cosineSimilarity(vecA, vecB)`
+
+Returns the cosine similarity between two equal-length numeric vectors.
+
+**Parameters:**
+
+- `vecA` (`table`)
+- `vecB` (`table`)
+
+**Returns:**
+
+- `number` — Cosine similarity.
+
+**Example:**
+
+```lua
+print(math.cosineSimilarity({1, 2, 3}, {4, 5, 6}))
+```
+
+## math.deg
+
+`math.deg(x)`
+
+Converts an angle from radians to degrees.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+**Example:**
+
+```lua
+print(math.deg(math.pi)) -- 180
+```
+
+## math.exp
+
+`math.exp(x)`
+
+Returns `e` raised to `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.floor
+
+`math.floor(x)`
+
+Returns the largest integer less than or equal to `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `integer`
+
+## math.fmod
+
+`math.fmod(x, y)`
+
+Returns the remainder of `x / y` with the quotient rounded toward zero.
+
+**Parameters:**
+
+- `x` (`number`)
+- `y` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.frexp
+
+`math.frexp(x)`
+
+Decomposes `x` into a normalized fraction and a power-of-two exponent.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number` — Fraction.
+- `integer` — Exponent.
+
+## math.ldexp
+
+`math.ldexp(m, e)`
+
+Returns `m * 2^e`, the inverse of `math.frexp`.
+
+**Parameters:**
+
+- `m` (`number`)
+- `e` (`integer`)
+
+**Returns:**
+
+- `number`
+
+## math.log
+
+`math.log(x, base?)`
+
+Returns the logarithm of `x`, using the natural base unless another base is supplied.
+
+**Parameters:**
+
+- `x` (`number`)
+- `base?` (`number`)
+
+**Returns:**
+
+- `number`
+
+**Example:**
+
+```lua
+print(math.log(100, 10)) -- 2
+```
+
+## math.max
+
+`math.max(x, ...): number`
+
+Returns the greatest of its arguments.
+
+**Returns:**
+
+- `number`
+
+## math.min
+
+`math.min(x, ...): number`
+
+Returns the least of its arguments.
+
+**Returns:**
+
+- `number`
+
+## math.modf
+
+`math.modf(x)`
+
+Splits `x` into its integral and fractional parts.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `integer` — Integral part.
+- `float` — Fractional part.
+
+**Example:**
+
+```lua
+local integer, fraction = math.modf(3.14)
+```
+
+## math.pow
+
+`math.pow(x, y)`
+
+> **Deprecated:** Use the `^` operator instead.
+
+Returns `x` raised to the power `y`.
+
+**Parameters:**
+
+- `x` (`number`)
+- `y` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.rad
+
+`math.rad(x)`
+
+Converts an angle from degrees to radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.random
+
+`math.random(): number`
+`math.random(n): integer`
+`math.random(m, n): integer`
+
+Returns a pseudo-random float or an integer in a requested inclusive range.
+
+**Parameters:**
+
+- `m?` (`integer`)
+- `n?` (`integer`)
+
+**Returns:**
+
+- `number` — Pseudo-random result.
+
+**Example:**
+
+```lua
+print(math.random())
+print(math.random(10))
+print(math.random(5, 10))
+```
+
+## math.randomseed
+
+`math.randomseed(): integer, integer`
+`math.randomseed(x, y): integer, integer`
+
+Seeds the pseudo-random generator and returns the two seeds used.
+
+**Parameters:**
+
+- `x?` (`integer`)
+- `y?` (`integer`)
+
+**Returns:**
+
+- `integer` — First seed.
+- `integer` — Second seed.
+
+## math.sin
+
+`math.sin(x)`
+
+Returns the sine of `x` radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.sinh
+
+`math.sinh(x)`
+
+> **Deprecated:** Retained for compatibility with older Lua versions.
+
+Returns the hyperbolic sine of `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.sqrt
+
+`math.sqrt(x)`
+
+Returns the square root of `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.tan
+
+`math.tan(x)`
+
+Returns the tangent of `x` radians.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.tanh
+
+`math.tanh(x)`
+
+> **Deprecated:** Retained for compatibility with older Lua versions.
+
+Returns the hyperbolic tangent of `x`.
+
+**Parameters:**
+
+- `x` (`number`)
+
+**Returns:**
+
+- `number`
+
+## math.tointeger
+
+`math.tointeger(x)`
+
+Converts a value to an integer when it has an exact finite integral representation.
+
+**Parameters:**
+
+- `x` — Value to convert.
+
+**Returns:**
+
+- `integer|nil` — Converted integer or `nil`.
+
+## math.type
+
+`math.type(x)`
+
+Returns `integer` or `float` for a number, or `nil` for other values.
+
+**Parameters:**
+
+- `x` — Value to inspect.
+
+**Returns:**
+
+- `string|nil` — Numeric subtype or `nil`.
+
+## math.ult
+
+`math.ult(m, n)`
+
+Compares two integers as unsigned 32-bit values.
+
+**Parameters:**
+
+- `m` (`integer`)
+- `n` (`integer`)
+
+**Returns:**
+
+- `boolean`
+
+**Example:**
+
+```lua
+print(math.ult(2, 3)) -- true
+```
+<!--/lua-->
+