diff --git a/entry.S b/entry.S
index 18947b0..5f4e124 100644
--- a/entry.S
+++ b/entry.S
@@ -36,7 +36,7 @@ multiboot_header:
 .globl _start
 _start = V2P_WO(entry)
 
-# Entering xv6 on boot processor.  Machine is mostly set up.
+# Entering xv6 on boot processor, with paging off.
 .globl entry
 entry:
   # Turn on page size extension for 4Mbyte pages
diff --git a/memlayout.h b/memlayout.h
index cd4433d..6a62cd7 100644
--- a/memlayout.h
+++ b/memlayout.h
@@ -10,13 +10,13 @@
 
 #ifndef __ASSEMBLER__
 
-static inline uint v2p(void *a) { return (uint) a  - KERNBASE; }
-static inline void *p2v(uint a) { return (void *) a + KERNBASE; }
+static inline uint v2p(void *a) { return ((uint) (a))  - KERNBASE; }
+static inline void *p2v(uint a) { return (void *) ((a) + KERNBASE); }
 
 #endif
 
-#define V2P(a) ((uint) a - KERNBASE)
-#define P2V(a) ((void *) a + KERNBASE)
+#define V2P(a) (((uint) (a)) - KERNBASE)
+#define P2V(a) (((void *) (a)) + KERNBASE)
 
 #define V2P_WO(x) ((x) - KERNBASE)    // same as V2P, but without casts
 #define P2V_WO(x) ((x) + KERNBASE)    // same as V2P, but without casts
diff --git a/vm.c b/vm.c
index 75fbc59..a41bfa1 100644
--- a/vm.c
+++ b/vm.c
@@ -90,36 +90,39 @@ mappages(pde_t *pgdir, void *va, uint size, uint pa,
   return 0;
 }
 
-// The mappings from logical to virtual are one to one (i.e.,
-// segmentation doesn't do anything). There is one page table per
-// process, plus one that's used when a CPU is not running any process
-// (kpgdir). A user process uses the same page table as the kernel; the
-// page protection bits prevent it from accessing kernel memory.
+// There is one page table per process, plus one that's used when
+// a CPU is not running any process (kpgdir). The kernel uses the
+// current process's page table during system calls and interrupts;
+// page protection bits prevent user code from using the kernel's
+// mappings.
 // 
 // setupkvm() and exec() set up every page table like this:
-//   0..KERNBASE: user memory (text+data+stack+heap), mapped to some free
-//                phys memory
+//
+//   0..KERNBASE: user memory (text+data+stack+heap), mapped to
+//                phys memory allocated by the kernel
 //   KERNBASE..KERNBASE+EXTMEM: mapped to 0..EXTMEM (for I/O space)
-//   KERNBASE+EXTMEM..KERNBASE+end: mapped to EXTMEM..end  kernel,
-//                                  w. no write permission
-//   KERNBASE+end..KERBASE+PHYSTOP: mapped to end..PHYSTOP, 
-//                                  rw data + free memory
+//   KERNBASE+EXTMEM..data: mapped to EXTMEM..V2P(data)
+//                for the kernel's instructions and r/o data
+//   data..KERNBASE+PHYSTOP: mapped to V2P(data)..PHYSTOP, 
+//                                  rw data + free physical memory
 //   0xfe000000..0: mapped direct (devices such as ioapic)
 //
-// The kernel allocates memory for its heap and for user memory
-// between KERNBASE+end and the end of physical memory (PHYSTOP).
-// The user program sits in the bottom of the address space, and the
-// kernel at the top at KERNBASE.
+// The kernel allocates physical memory for its heap and for user memory
+// between V2P(end) and the end of physical memory (PHYSTOP)
+// (directly addressable from end..P2V(PHYSTOP)).
+
+// This table defines the kernel's mappings, which are present in
+// every process's page table.
 static struct kmap {
   void *virt;
   uint phys_start;
   uint phys_end;
   int perm;
 } kmap[] = {
-  { P2V(0), 0, 1024*1024, PTE_W},  // I/O space
-  { (void*)KERNLINK, V2P(KERNLINK), V2P(data),  0}, // kernel text+rodata
-  { data, V2P(data), PHYSTOP,  PTE_W},  // kernel data, memory
-  { (void*)DEVSPACE, DEVSPACE, 0, PTE_W},  // more devices
+  { (void*) KERNBASE, 0,             EXTMEM,    PTE_W},  // I/O space
+  { (void*) KERNLINK, V2P(KERNLINK), V2P(data), 0}, // kernel text+rodata
+  { (void*) data,     V2P(data),     PHYSTOP,   PTE_W},  // kernel data, memory
+  { (void*) DEVSPACE, DEVSPACE,      0,         PTE_W},  // more devices
 };
 
 // Set up kernel part of a page table.