macでc/c++をコンパイルできない。

macで下記C/C++のコードを書きましたが、下記エラーでコンパイルできません。

intarray.cpp

#include<stddef.h>
#include<stdlib.h>
#include<stdio.h>


struct IntArray {
  int *elems;
  size_t numElems;
};

void IA_init(IntArray *object);
void IA_cleanup(IntArray *object);
void IA_setSize(IntArray *object, size_t value);
size_t IA_getSize(IntArray *object);
void IA_setElem(IntArray *object, size_t index, int value);
int IA_getElem(IntArray *object, size_t index);


void IA_init(IntArray *object, size_t value){
  object->numElems = 0;
  object->elems = 0;
}

void IA_cleanup(IntArray *object){
  free(object->elems);
}

void IA_setSize(IntArray *object, size_t value){
  if(object->elems != 0) free(object->elems);
  object->numElems = value;
  object->elems = (int *)malloc(value * sizeof(int));
}

void IA_setElem(IntArray *object, size_t value, int index){
  if(index >= object->numElems) {
    printf("bad index");
    return;
  }
  object->elems[index] = value;
}

int IA_getElem(IntArray *object, size_t index){
  if(index >= object->numElems){
    printf("bad index");
    return 0;
  }
  return object->elems[index];
}

int main(){
  IntArray powersOf2;
  IA_init(&powersOf2);
  IA_setSize(&powersOf2, 8);
  IA_setElem(&powersOf2, 0, 1);
  int i;
  for(i=1; i<8; i++){
    IA_setElem(&powersOf2, i, 2 * IA_getElem(&powersOf2, i-1));
  }
  IA_cleanup(&powersOf2);

  return 0;
}

コマンド

g++ -v intarray.cpp -o intarray

エラー

Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.2.0
Thread model: posix
 "/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/clang" -cc1 -triple x86_64-apple-macosx10.11.0 -Wdeprecated-objc-isa-usage -Werror=deprecated-objc-isa-usage -emit-obj -mrelax-all -disable-free -disable-llvm-verifier -main-file-name intarray.cpp -mrelocation-model pic -pic-level 2 -mthread-model posix -mdisable-fp-elim -masm-verbose -munwind-tables -target-cpu core2 -target-linker-version 253.9 -v -dwarf-column-info -resource-dir /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2 -stdlib=libc++ -fdeprecated-macro -fdebug-compilation-dir /Users/username/workspaces/c_plus_plus_workspace/class -ferror-limit 19 -fmessage-length 144 -stack-protector 1 -mstackrealign -fblocks -fobjc-runtime=macosx-10.11.0 -fencode-extended-block-signature -fcxx-exceptions -fexceptions -fmax-type-align=16 -fdiagnostics-show-option -fcolor-diagnostics -o /var/folders/2z/x8jb59gs1lz7n1hhbhk_st8c0000gn/T/intarray-f42434.o -x c++ intarray.cpp
clang -cc1 version 7.0.2 based upon LLVM 3.7.0svn default target x86_64-apple-darwin15.2.0
ignoring nonexistent directory "/usr/include/c++/v1"
#include "..." search starts here:
#include <...> search starts here:
 /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../include/c++/v1
 /usr/local/include
 /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/include
 /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include
 /usr/include
 /System/Library/Frameworks (framework directory)
 /Library/Frameworks (framework directory)
End of search list.
 "/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/ld" -demangle -dynamic -arch x86_64 -macosx_version_min 10.11.0 -o intarray /var/folders/2z/x8jb59gs1lz7n1hhbhk_st8c0000gn/T/intarray-f42434.o -lc++ -lSystem /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/lib/darwin/libclang_rt.osx.a
Undefined symbols for architecture x86_64:
  "IA_init(IntArray*)", referenced from:
      _main in intarray-f42434.o
     (maybe you meant: __Z7IA_initP8IntArraym)
ld: symbol(s) not found for architecture x86_64
clang: error: linker command failed with exit code 1 (use -v to see invocation)

検索すると幾つか同じエラーになっているという報告を見られましたが、解決方法を試しても解決しませんでした。

しかし、下記コードはコンパイルできました。

hello.cpp

#include<stdio.h>

int main(){
  printf("Hello, world");
  return 0;
}

hello.cpp

#include<iostream>

int main(){
  std::cout << "Hello, world" << "\n";
  return 0;
}

なぜ上記のコードはコンパイルできないのでしょうか。

実行環境

Mac El Captan bash

追記

ちなみに下記コードでもエラーが出ました。

intarray2.h

#include<stddef.h>
#include<stdio.h>
#include<stdlib.h>

class IntArray{
  public:
    void init();
    void cleanup();
    void setSize(size_t value);
    size_t getSize();
    void setElem(size_t index, int value);
    int getElem(size_t index);

  private:
    int *elems;
    size_t numElems;
};

intarray2.cpp

#include<stddef.h>
#include<stdio.h>
#include<stdlib.h>

class IntArray{
  void IntArray::init(){
    this->numElems = 0;
    this->elems = 0;
  }

  void IntArray::cleanup(){
    this->numElems = 0;
    free(this->elems);
  }

  void setSize(size_t, value){
   if(this->elems != 0) free(this->elems);
   this->numElems = value;
   this->elems = (int *) malloc(value * sizeof(int));
  }

  void IntArray::setElem(size_t valuem, int index){
    if(index >= this->numElems){
      printf("bad index");
      return;
    }
    this->elems[index] = value;
  }

  int IntArray::getElem(size_t index){
    if(index >= this->numElems){
      printf("bad index");
      return 1;
    }
    return this->elems[index];
  }
}

main.cpp

#include "IntArray2.h"

int main(){
  IntArray powerOf2;
  powerOf2.init();
  powerOf2.setSize(8);
  int i;
  for(i=0;i<8;i++){
    powerOf2.setElem(i, 2 * powerOf2.getElem(i-1));
  }
  powerOf2.cleanup();
  return 0;
}

エラー

Undefined symbols for architecture x86_64:
  "IntArray::init()", referenced from:
      _main in main-d429d9.o
  "IntArray::cleanup()", referenced from:
      _main in main-d429d9.o
  "IntArray::getElem(unsigned long)", referenced from:
      _main in main-d429d9.o
  "IntArray::setElem(unsigned long, int)", referenced from:
      _main in main-d429d9.o
  "IntArray::setSize(unsigned long)", referenced from:
      _main in main-d429d9.o
ld: symbol(s) not found for architecture x86_64
clang: error: linker command failed with exit code 1 (use -v to see invocation)