Base level translator: it could compile primitive functions with arithmetic operations:

note: operations are hardcoded e.g. operato plus resolved in corresponding instruction.

fun sum(a:Int, b:Int) = a + b

produces following code:
target datalayout = "e-m:o-i64:64-f80:128-n8:16:32:64-S128"
target triple = "x86_64-apple-macosx10.12.0"

define i32 @"kfun:sum"(i32, i32) {
entry:
  %a = alloca i32
  store i32 %0, i32* %a
  %b = alloca i32
  store i32 %1, i32* %b
  %tmp1 = load i32, i32* %a
  %tmp2 = load i32, i32* %b
  %tmp0 = add i32 %tmp1, %tmp2
  ret i32 %tmp0
}

Note: this code is optimizable with -mem2reg
> opt-mp-3.8 -mem2reg sum.BCkt -o - | llvm-dis-mp-3.8 -o -
; ModuleID = '<stdin>'
target datalayout = "e-m:o-i64:64-f80:128-n8:16:32:64-S128"
target triple = "x86_64-apple-macosx10.12.0"

define i32 @"kfun:sum"(i32, i32) {
entry:
  %tmp0 = add i32 %0, %1
  ret i32 %tmp0
}

backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/native/llvm/CodeGenerator.kt

@@ -0,0 +1,67 @@
+package org.jetbrains.kotlin.backend.native.llvm
+
+import llvm.*
+import org.jetbrains.kotlin.descriptors.FunctionDescriptor
+import org.jetbrains.kotlin.ir.declarations.IrFunction
+import org.jetbrains.kotlin.types.KotlinType
+import java.util.*
+
+
+/**
+ *
+ * Created by minamoto on 07/10/2016.
+ */
+
+internal class CodeGenerator(override val context:Context) : ContextUtils {
+    var currentFunction:FunctionDescriptor? = null
+
+    fun function(declaration: IrFunction) {
+        index = 0
+        currentFunction = declaration.descriptor
+        val fn = LLVMAddFunction(context.llvmModule, declaration.descriptor.symbolName, getLlvmFunctionType(declaration.descriptor))
+        val block = LLVMAppendBasicBlock(fn, "entry")
+        LLVMPositionBuilderAtEnd(context.llvmBuilder, block)
+        function2variables.put(declaration.descriptor, mutableMapOf())
+        declaration.descriptor.valueParameters.forEachIndexed { i, descriptor ->
+            val name = descriptor.name.asString()
+            val type = descriptor.type
+            val v = alloca(type, name)
+            store(LLVMGetParam(fn, i)!!, v)
+            currentFunction!!.registerVariable(name, v)
+        }
+
+    }
+
+    fun tmpVariable():String = currentFunction!!.tmpVariable()
+
+    val variablesGlobal = mapOf<String, LLVMOpaqueValue?>()
+    fun variable(varName:String):LLVMOpaqueValue? = currentFunction!!.variable(varName)
+
+    fun FunctionDescriptor.param(num:Int):LLVMOpaqueValue? = LLVMGetParam(llvmFunction.getLlvmValue(), num)
+
+    var index:Int = 0
+    private var FunctionDescriptor.tmpVariableIndex: Int
+        get() = index
+        set(i:Int){ index = i}
+
+    fun FunctionDescriptor.tmpVariable():String = "tmp${tmpVariableIndex++}"
+
+    fun registerVariable(varName: String, value:LLVMOpaqueValue) = currentFunction!!.registerVariable(varName, value)
+
+    val function2variables = mutableMapOf<FunctionDescriptor, MutableMap<String, LLVMOpaqueValue?>>()
+
+
+    val FunctionDescriptor.variables: MutableMap<String, LLVMOpaqueValue?>
+        get() = this@CodeGenerator.function2variables[this]!!
+
+
+    fun FunctionDescriptor.registerVariable(varName: String, value:LLVMOpaqueValue?) = variables.put(varName, value)
+    private fun FunctionDescriptor.variable(varName: String): LLVMOpaqueValue? = variables[varName]
+
+    fun plus(arg0:LLVMOpaqueValue, arg1:LLVMOpaqueValue, result:String):LLVMOpaqueValue = LLVMBuildAdd(context.llvmBuilder, arg0, arg1, result)!!
+    fun alloca(type: KotlinType, varName: String):LLVMOpaqueValue = LLVMBuildAlloca(context.llvmBuilder, getLLVMType(type), varName)!!
+    fun load(value:LLVMOpaqueValue, varName: String):LLVMOpaqueValue = LLVMBuildLoad(context.llvmBuilder, value, varName)!!
+    fun store(value:LLVMOpaqueValue, ptr:LLVMOpaqueValue):LLVMOpaqueValue = LLVMBuildStore(context.llvmBuilder, value, ptr)!!
+}
+
+

backend.native/compiler/ir/backend.native/src/org/jetbrains/kotlin/backend/native/llvm/IrToBitcode.kt

@@ -3,7 +3,10 @@ package org.jetbrains.kotlin.backend.native.llvm
 import llvm.*
 import org.jetbrains.kotlin.ir.IrElement
 import org.jetbrains.kotlin.ir.declarations.IrClass
+import org.jetbrains.kotlin.ir.declarations.IrFunction
 import org.jetbrains.kotlin.ir.declarations.IrModuleFragment
+import org.jetbrains.kotlin.ir.declarations.IrVariable
+import org.jetbrains.kotlin.ir.expressions.*
 import org.jetbrains.kotlin.ir.visitors.IrElementVisitorVoid
 import org.jetbrains.kotlin.ir.visitors.acceptChildrenVoid
 
@@ -16,6 +19,7 @@ fun emitLLVM(module: IrModuleFragment, runtimeFile: String, outFile: String) {
     val context = Context(module, runtime, llvmModule) // TODO: dispose
 
     module.accept(RTTIGeneratorVisitor(context), null)
+    module.accept(CodeGeneratorVisitor(context), null)
     LLVMWriteBitcodeToFile(llvmModule, outFile)
 }
 
@@ -31,4 +35,71 @@ internal class RTTIGeneratorVisitor(context: Context) : IrElementVisitorVoid {
         generator.generate(declaration.descriptor)
     }
 
-}
+}
+
+/**
+ * TODO: split CodeGeneratorVisitor on Visitor and Generator :)
+ */
+internal class CodeGeneratorVisitor(val context: Context) : IrElementVisitorVoid {
+    val generator = CodeGenerator(context)
+    override fun visitFunction(declaration: IrFunction) {
+        generator.function(declaration)
+        declaration.acceptChildrenVoid(this)
+    }
+
+    override fun visitElement(element: IrElement) {
+        element.acceptChildrenVoid(this)
+    }
+
+    override fun visitSetVariable(expression: IrSetVariable) {
+        val value = evaluateExpression(generator.tmpVariable(), expression.value)
+        generator.store(value!!, generator.variable(expression.descriptor.name.asString())!!)
+    }
+
+    private fun evaluateExpression(tmpVariableName: String, value: IrExpression?): LLVMOpaqueValue? {
+        when (value) {
+            is IrCall -> return evaluateCall(tmpVariableName, value)
+            is IrGetValue -> return generator.load(generator.variable(value.descriptor.name.asString())!!, tmpVariableName)
+            null -> return null
+            else -> {
+                TODO()
+            }
+        }
+    }
+
+    private fun evaluateCall(tmpVariableName: String, value: IrCall?): LLVMOpaqueValue? {
+        /* TODO: should we count on receiver?
+         * val tmp = tmpVar()
+         * val lhs = evaluateExpression(tmp, value.dispatchReceiver!!)
+         */
+        val args = mutableListOf<LLVMOpaqueValue?>()
+        value!!.acceptChildrenVoid(object:IrElementVisitorVoid{
+            override fun visitElement(element: IrElement) {
+                val tmp = generator.tmpVariable()
+                args.add(evaluateExpression(tmp, element as IrExpression))
+            }
+        })
+        when (value!!.origin) {
+            IrStatementOrigin.PLUS -> return generator.plus(args[0]!!, args[1]!!, tmpVariableName)
+            else -> {
+                TODO()
+            }
+        }
+        TODO()
+    }
+
+    override fun visitVariable(declaration: IrVariable) {
+        val variableName = declaration.descriptor.name.asString()
+        val variableType = declaration.descriptor.type
+        generator.registerVariable(variableName, generator.alloca(variableType, variableName))
+
+        evaluateExpression(variableName, declaration.initializer)
+    }
+
+    override fun visitReturn(expression: IrReturn) {
+        val tmpVarName = generator.tmpVariable()
+        val value:LLVMOpaqueValue?
+        value = evaluateExpression(tmpVarName, expression.value)
+        LLVMBuildRet(context.llvmBuilder, value)
+    }
+}

sum.c

@@ -0,0 +1,5 @@
+int foo(int a, int b){
+  int c;
+  c = a + b;
+  return c;
+}

sum.kt

@@ -0,0 +1 @@
+fun sum(a:Int, b:Int) = a + b

sum_func.c

@@ -0,0 +1,3 @@
+int foo() { return 1; }
+int bar() {return 2;}
+int sum() {return foo() + bar();}

sum_func.kt

@@ -0,0 +1,3 @@
+fun foo():Int = 1
+//fun bar():Int = 2
+//fun sum():Int = foo() + bar()

sum_silly.kt

@@ -0,0 +1,5 @@
+fun sum(a:Int, b:Int):Int {
+ var c:Int
+ c = a + b
+ return c
+}