diff --git a/defs.h b/defs.h
index 43f35d2..8ea46d6 100644
--- a/defs.h
+++ b/defs.h
@@ -161,11 +161,11 @@ int             allocuvm(pde_t*, uint, uint);
 int             deallocuvm(pde_t*, uint, uint);
 void            freevm(pde_t*);
 void            inituvm(pde_t*, char*, uint);
-int             loaduvm(pde_t*, char*, struct inode *, uint, uint);
-pde_t*          copyuvm(pde_t*,uint);
+int             loaduvm(pde_t*, char*, struct inode*, uint, uint);
+pde_t*          copyuvm(pde_t*, uint);
 void            switchuvm(struct proc*);
 void            switchkvm(void);
-int             copyout(pde_t *pgdir, uint va, void *buf, uint len);
+int             copyout(pde_t*, uint, void*, uint);
 
 // number of elements in fixed-size array
 #define NELEM(x) (sizeof(x)/sizeof((x)[0]))
diff --git a/kalloc.c b/kalloc.c
index e31d71d..bf1616a 100644
--- a/kalloc.c
+++ b/kalloc.c
@@ -27,7 +27,7 @@ kinit(void)
 
   initlock(&kmem.lock, "kmem");
   p = (char*)PGROUNDUP((uint)end);
-  for(; p + PGSIZE - 1 < (char*)PHYSTOP; p += PGSIZE)
+  for(; p + PGSIZE <= (char*)PHYSTOP; p += PGSIZE)
     kfree(p);
 }
 
diff --git a/vm.c b/vm.c
index 940cc2f..bfc0845 100644
--- a/vm.c
+++ b/vm.c
@@ -250,16 +250,16 @@ loaduvm(pde_t *pgdir, char *addr, struct inode *ip, uint offset, uint sz)
 int
 allocuvm(pde_t *pgdir, uint oldsz, uint newsz)
 {
-  char *a, *last, *mem;
+  char *mem;
+  uint a;
 
   if(newsz > USERTOP)
     return 0;
   if(newsz < oldsz)
     return oldsz;
 
-  a = (char*)PGROUNDUP(oldsz);
-  last = PGROUNDDOWN(newsz - 1);
-  for(; a <= last; a += PGSIZE){
+  a = PGROUNDUP(oldsz);
+  for(; a < newsz; a += PGSIZE){
     mem = kalloc();
     if(mem == 0){
       cprintf("allocuvm out of memory\n");
@@ -267,7 +267,7 @@ allocuvm(pde_t *pgdir, uint oldsz, uint newsz)
       return 0;
     }
     memset(mem, 0, PGSIZE);
-    mappages(pgdir, a, PGSIZE, PADDR(mem), PTE_W|PTE_U);
+    mappages(pgdir, (char*)a, PGSIZE, PADDR(mem), PTE_W|PTE_U);
   }
   return newsz;
 }
@@ -279,17 +279,15 @@ allocuvm(pde_t *pgdir, uint oldsz, uint newsz)
 int
 deallocuvm(pde_t *pgdir, uint oldsz, uint newsz)
 {
-  char *a, *last;
   pte_t *pte;
-  uint pa;
+  uint a, pa;
 
   if(newsz >= oldsz)
     return oldsz;
 
-  a = (char*)PGROUNDUP(newsz);
-  last = PGROUNDDOWN(oldsz - 1);
-  for(; a <= last; a += PGSIZE){
-    pte = walkpgdir(pgdir, a, 0);
+  a = PGROUNDUP(newsz);
+  for(; a  < oldsz; a += PGSIZE){
+    pte = walkpgdir(pgdir, (char*)a, 0);
     if(pte && (*pte & PTE_P) != 0){
       pa = PTE_ADDR(*pte);
       if(pa == 0)
@@ -351,7 +349,6 @@ bad:
 
 // copy some data to user address va in page table pgdir.
 // most useful when pgdir is not the current page table.
-// returns 1 if everthing OK, 0 on error.
 // uva2ka ensures this only works for PTE_U pages.
 int
 copyout(pde_t *pgdir, uint va, void *xbuf, uint len)