added complext number support

docs/Complex.md

@@ -0,0 +1,82 @@
+# Complex Numbers (`lyng.complex`)
+
+`lyng.complex` adds a pure-Lyng `Complex` type backed by `Real` components.
+
+Import it when you want ordinary complex arithmetic:
+
+```lyng
+import lyng.complex
+```
+
+## Construction
+
+Use any of these:
+
+```lyng
+import lyng.complex
+
+val a = Complex(1.0, 2.0)
+val b = complex(1.0, 2.0)
+val c = 2.i
+val d = 3.re
+
+assertEquals(Complex(1.0, 2.0), 1 + 2.i)
+```
+
+Convenience extensions:
+
+- `Int.re`, `Real.re`: embed a real value into the complex plane
+- `Int.i`, `Real.i`: create a pure imaginary value
+- `cis(angle)`: shorthand for `cos(angle) + i sin(angle)`
+
+## Core Operations
+
+`Complex` supports:
+
+- `+`
+- `-`
+- `*`
+- `/`
+- unary `-`
+- `conjugate`
+- `magnitude`
+- `phase`
+
+Mixed arithmetic with `Int` and `Real` is enabled through `lyng.operators`, so both sides work naturally:
+
+```lyng
+import lyng.complex
+
+assertEquals(Complex(1.0, 2.0), 1 + 2.i)
+assertEquals(Complex(1.5, 2.0), 1.5 + 2.i)
+assertEquals(Complex(2.0, 2.0), 2.i + 2)
+```
+
+Mixed equality with built-in numeric types is intentionally not promised yet. Keep equality checks in the `Complex` domain for now.
+
+## Transcendental Functions
+
+For now, use member-style calls:
+
+```lyng
+import lyng.complex
+
+val z = 1 + π.i
+val w = z.exp()
+val s = z.sin()
+val r = z.sqrt()
+```
+
+This is deliberate. Lyng already has built-in top-level real-valued functions such as `exp(x)` and `sin(x)`, and imported modules do not currently replace those root bindings. So plain `exp(z)` is not yet the right extension mechanism for complex math.
+
+## Design Scope
+
+This module intentionally uses `Complex` with `Real` parts, not `Complex<T>`.
+
+Reasons:
+
+- the existing math runtime is `Real`-centric
+- the operator interop registry works with concrete runtime classes
+- transcendental functions (`exp`, `sin`, `ln`, `sqrt`) are defined over the `Real` math backend here
+
+If Lyng later gets a more general numeric-trait or callable-overload registry, a generic algebraic `Complex<T>` can be revisited on firmer ground.

docs/ai_stdlib_reference.md

@@ -56,6 +56,8 @@ Sources: `lynglib/src/commonMain/kotlin/net/sergeych/lyng/Script.kt`, `lynglib/s
 ## 5. Additional Built-in Modules (import explicitly)
 - `import lyng.observable`
   - `Observable`, `Subscription`, `ObservableList`, `ListChange` and change subtypes, `ChangeRejectionException`.
+- `import lyng.complex`
+  - `Complex`, `complex(re, im)`, `cis(angle)`, and numeric embedding extensions such as `2.i` / `3.re`.
 - `import lyng.buffer`
   - `Buffer`, `MutableBuffer`.
 - `import lyng.serialization`

lynglib/build.gradle.kts

@@ -149,6 +149,9 @@ abstract class GenerateLyngStdlib : DefaultTask() {
         val outBase = outputDir.get().asFile
         val targetDir = outBase.resolve(pkgPath)
         targetDir.mkdirs()
+        targetDir.listFiles()
+            ?.filter { it.isFile && it.name.endsWith(".generated.kt") }
+            ?.forEach { it.delete() }
 
         val srcDir = sourceDir.get().asFile
         val files = srcDir.walkTopDown()
@@ -156,34 +159,38 @@ abstract class GenerateLyngStdlib : DefaultTask() {
             .sortedBy { it.name }
             .toList()
 
-        val content = if (files.isEmpty()) "" else buildString {
-            files.forEachIndexed { idx, f ->
-                val text = f.readText()
-                if (idx > 0) append("\n\n")
-                append(text)
-            }
-        }
-
         fun escapeForQuoted(s: String): String = buildString {
             for (ch in s) when (ch) {
                 '\\' -> append("\\\\")
                 '"' -> append("\\\"")
+                '$' -> append("\\$")
                 '\n' -> append("\\n")
                 '\r' -> {}
                 '\t' -> append("\\t")
                 else -> append(ch)
             }
         }
-        val body = escapeForQuoted(content)
 
+        fun constantName(baseName: String): String {
+            val parts = baseName.split(Regex("[^A-Za-z0-9]+")).filter { it.isNotEmpty() }
+            if (parts.isEmpty()) return "moduleLyng"
+            val head = parts.first().replaceFirstChar { it.lowercase() }
+            val tail = parts.drop(1).joinToString("") { part ->
+                part.replaceFirstChar { it.uppercase() }
+            }
+            return "${head}${tail}Lyng"
+        }
+
+        for (file in files) {
+            val body = escapeForQuoted(file.readText())
             val sb = StringBuilder()
             sb.append("package ").append(targetPkg).append("\n\n")
             sb.append("@Suppress(\"Unused\", \"MemberVisibilityCanBePrivate\")\n")
-        sb.append("internal val rootLyng = \"")
+            sb.append("internal val ").append(constantName(file.nameWithoutExtension)).append(" = \"")
             sb.append(body)
             sb.append("\"\n")
-
-        targetDir.resolve("root_lyng.generated.kt").writeText(sb.toString())
+            targetDir.resolve("${file.nameWithoutExtension}_lyng.generated.kt").writeText(sb.toString())
+        }
     }
 }
 

lynglib/src/commonMain/kotlin/net/sergeych/lyng/Script.kt

@@ -27,6 +27,7 @@ import net.sergeych.lyng.bytecode.CmdVm
 import net.sergeych.lyng.miniast.*
 import net.sergeych.lyng.obj.*
 import net.sergeych.lyng.pacman.ImportManager
+import net.sergeych.lyng.stdlib_included.complexLyng
 import net.sergeych.lyng.stdlib_included.decimalLyng
 import net.sergeych.lyng.stdlib_included.observableLyng
 import net.sergeych.lyng.stdlib_included.operatorsLyng
@@ -615,12 +616,91 @@ class Script(
                 type = type("lyng.Real")
             )
             getOrCreateNamespace("Math").apply {
+                fun ensureFn(name: String, fn: suspend ScopeFacade.() -> Obj) {
+                    if (members.containsKey(name)) return
+                    addFn(name, code = fn)
+                }
                 addConstDoc(
                     name = "PI",
                     value = pi,
                     doc = "The mathematical constant pi (π) in the Math namespace.",
                     type = type("lyng.Real")
                 )
+                ensureFn("floor") {
+                    val x = args.firstAndOnly()
+                    if (x is ObjInt) x else ObjReal(floor(x.toDouble()))
+                }
+                ensureFn("ceil") {
+                    val x = args.firstAndOnly()
+                    if (x is ObjInt) x else ObjReal(ceil(x.toDouble()))
+                }
+                ensureFn("round") {
+                    val x = args.firstAndOnly()
+                    if (x is ObjInt) x else ObjReal(round(x.toDouble()))
+                }
+                ensureFn("sin") {
+                    ObjReal(sin(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("cos") {
+                    ObjReal(cos(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("tan") {
+                    ObjReal(tan(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("asin") {
+                    ObjReal(asin(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("acos") {
+                    ObjReal(acos(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("atan") {
+                    ObjReal(atan(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("sinh") {
+                    ObjReal(sinh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("cosh") {
+                    ObjReal(cosh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("tanh") {
+                    ObjReal(tanh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("asinh") {
+                    ObjReal(asinh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("acosh") {
+                    ObjReal(acosh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("atanh") {
+                    ObjReal(atanh(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("exp") {
+                    ObjReal(exp(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("ln") {
+                    ObjReal(ln(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("log10") {
+                    ObjReal(log10(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("log2") {
+                    ObjReal(log2(args.firstAndOnly().toDouble()))
+                }
+                ensureFn("pow") {
+                    requireExactCount(2)
+                    ObjReal(
+                        (args[0].toDouble()).pow(args[1].toDouble())
+                    )
+                }
+                ensureFn("sqrt") {
+                    ObjReal(
+                        sqrt(args.firstAndOnly().toDouble())
+                    )
+                }
+                ensureFn("abs") {
+                    val x = args.firstAndOnly()
+                    if (x is ObjInt) ObjInt(x.value.absoluteValue) else ObjReal(x.toDouble().absoluteValue)
+                }
             }
         }
 
@@ -759,6 +839,9 @@ class Script(
                     module.eval(Source("lyng.decimal", decimalLyng))
                     ObjBigDecimalSupport.bindTo(module)
                 }
+                addPackage("lyng.complex") { module ->
+                    module.eval(Source("lyng.complex", complexLyng))
+                }
                 addPackage("lyng.buffer") {
                     it.addConstDoc(
                         name = "Buffer",

lynglib/src/commonTest/kotlin/net/sergeych/lyng/ComplexModuleTest.kt

@@ -0,0 +1,76 @@
+/*
+ * Copyright 2026 Sergey S. Chernov real.sergeych@gmail.com
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ */
+
+package net.sergeych.lyng
+
+import kotlinx.coroutines.test.runTest
+import kotlin.test.Test
+
+class ComplexModuleTest {
+    @Test
+    fun testComplexArithmeticAndInterop() = runTest {
+        val scope = Script.newScope()
+        scope.eval(
+            """
+            import lyng.complex
+
+            assertEquals(Complex(0.0, 2.0), 2.i)
+            assertEquals(Complex(2.0, 0.0), 2.re)
+            assertEquals(Complex(1.0, 2.0), 1 + 2.i)
+            assertEquals(Complex(1.5, 2.0), 1.5 + 2.i)
+            assertEquals(Complex(3.0, 2.0), 1 + Complex(2.0, 2.0))
+            val product: Complex = Complex(1.0, 2.0) * Complex(3.0, -1.0)
+            assertEquals(5.0, product.re)
+            assertEquals(5.0, product.im)
+            val quotient: Complex = Complex(5.0, 5.0) / Complex(3.0, -1.0)
+            assertEquals(1.0, quotient.re)
+            assertEquals(2.0, quotient.im)
+            assertEquals(Complex(1.0, -2.0), Complex(1.0, 2.0).conjugate)
+            """.trimIndent()
+        )
+    }
+
+    @Test
+    fun testComplexMemberMathFunctions() = runTest {
+        val scope = Script.newScope()
+        scope.eval(
+            """
+            import lyng.complex
+
+            val eps = 1e-9
+
+            val eipi = Complex.imaginary(π).exp()
+            assert(abs(eipi.re + 1.0) < eps)
+            assert(abs(eipi.im) < eps)
+
+            val iy: Complex = 2.i
+            val sinIy = iy.sin()
+            assert(abs(sinIy.re) < eps)
+            assert(abs(sinIy.im - sinh(2.0)) < eps)
+
+            val minusOne: Complex = (-1).re
+            val root = minusOne.sqrt()
+            assert(abs(root.re) < eps)
+            assert(abs(root.im - 1.0) < eps)
+
+            val unitLeft: Complex = cis(π)
+            assert(abs(unitLeft.re + 1.0) < eps)
+            assert(abs(unitLeft.im) < eps)
+            """.trimIndent()
+        )
+    }
+}

lynglib/stdlib/lyng/complex.lyng

@@ -0,0 +1,158 @@
+package lyng.complex
+
+import lyng.operators
+
+/*
+Complex number backed by `Real` components.
+
+This module intentionally keeps the storage model simple:
+- `re`: real part
+- `im`: imaginary part
+
+The algebra is implemented in pure Lyng and interoperates with `Int` and `Real`
+through `lyng.operators`, so expressions like `1 + 2.i` and `0.5 * (1 + 2.i)` work.
+
+For transcendental functions, use the member-style API for now:
+- `z.exp()`
+- `z.ln()`
+- `z.sin()`
+- `z.cos()`
+- `z.tan()`
+- `z.sqrt()`
+
+This avoids collisions with the built-in real-valued top-level math functions
+such as `exp(x)` and `sin(x)`.
+*/
+class Complex(val real: Real, val imag: Real = 0.0) {
+    val re get() = real
+    val im get() = imag
+
+    fun plus(other: Complex): Complex {
+        val ar = real
+        val ai = imag
+        val br = other.real
+        val bi = other.imag
+        val realPart = ar + br
+        val imagPart = ai + bi
+        Complex(realPart, imagPart)
+    }
+
+    fun minus(other: Complex): Complex {
+        val ar = real
+        val ai = imag
+        val br = other.real
+        val bi = other.imag
+        val realPart = ar - br
+        val imagPart = ai - bi
+        Complex(realPart, imagPart)
+    }
+
+    fun mul(other: Complex): Complex {
+        val ar = real
+        val ai = imag
+        val br = other.real
+        val bi = other.imag
+        val realPart = ar * br - ai * bi
+        val imagPart = ar * bi + ai * br
+        Complex(realPart, imagPart)
+    }
+
+    fun div(other: Complex): Complex {
+        val ar = real
+        val ai = imag
+        val br = other.real
+        val bi = other.imag
+        val denominator = br * br + bi * bi
+        val realPart = (ar * br + ai * bi) / denominator
+        val imagPart = (ai * br - ar * bi) / denominator
+        Complex(realPart, imagPart)
+    }
+
+    fun negate(): Complex = Complex(-real, -imag)
+
+    val conjugate get() = Complex(real, -imag)
+    val magnitude2 get() = real * real + imag * imag
+    val magnitude get() = Math.sqrt(magnitude2)
+
+    val phase: Real
+        get() = if (real > 0.0) {
+            Math.atan(imag / real)
+        } else if (real < 0.0 && imag >= 0.0) {
+            Math.atan(imag / real) + π
+        } else if (real < 0.0 && imag < 0.0) {
+            Math.atan(imag / real) - π
+        } else if (real == 0.0 && imag > 0.0) {
+            π / 2.0
+        } else if (real == 0.0 && imag < 0.0) {
+            -π / 2.0
+        } else {
+            0.0
+        }
+
+    fun exp(): Complex {
+        val scale = Math.exp(real)
+        Complex(scale * Math.cos(imag), scale * Math.sin(imag))
+    }
+
+    fun ln(): Complex = Complex(Math.ln(magnitude), phase)
+
+    fun sin(): Complex =
+        Complex(
+            Math.sin(real) * Math.cosh(imag),
+            Math.cos(real) * Math.sinh(imag)
+        )
+
+    fun cos(): Complex =
+        Complex(
+            Math.cos(real) * Math.cosh(imag),
+            -Math.sin(real) * Math.sinh(imag)
+        )
+
+    fun tan(): Complex = sin() / cos()
+
+    fun sqrt(): Complex = if (imag == 0.0 && real >= 0.0) {
+        Complex(Math.sqrt(real), 0.0)
+    } else {
+        val radius = magnitude
+        val realPart = Math.sqrt((radius + real) / 2.0)
+        val imagPart = Math.sqrt((radius - real) / 2.0)
+        Complex(realPart, if (imag < 0.0) -imagPart else imagPart)
+    }
+
+    override fun toString() =
+        real.toString() +
+        (if (imag < 0.0) imag.toString() else "+" + imag.toString()) +
+        "i"
+
+    static fun fromInt(value: Int): Complex = Complex(value + 0.0, 0.0)
+    static fun fromReal(value: Real): Complex = Complex(value, 0.0)
+    static fun imaginary(value: Real): Complex = Complex(0.0, value)
+    static fun fromPolar(radius: Real, angle: Real): Complex =
+        Complex(radius * Math.cos(angle), radius * Math.sin(angle))
+}
+
+fun complex(re: Real, im: Real = 0.0): Complex = Complex(re, im)
+fun cis(angle: Real): Complex = Complex.fromPolar(1.0, angle)
+
+val Int.re: Complex get() = Complex.fromInt(this)
+val Real.re: Complex get() = Complex.fromReal(this)
+val Int.i: Complex get() = Complex.imaginary(this + 0.0)
+val Real.i: Complex get() = Complex.imaginary(this)
+
+OperatorInterop.register(
+    Int,
+    Complex,
+    Complex,
+    [BinaryOperator.Plus, BinaryOperator.Minus, BinaryOperator.Mul, BinaryOperator.Div],
+    { x: Int -> Complex.fromInt(x) },
+    { x: Complex -> x }
+)
+
+OperatorInterop.register(
+    Real,
+    Complex,
+    Complex,
+    [BinaryOperator.Plus, BinaryOperator.Minus, BinaryOperator.Mul, BinaryOperator.Div],
+    { x: Real -> Complex.fromReal(x) },
+    { x: Complex -> x }
+)