diff --git a/minzip/SysUtil.c b/minzip/SysUtil.c
index 1858cd5..0ac1fa9 100644
--- a/minzip/SysUtil.c
+++ b/minzip/SysUtil.c
@@ -19,9 +19,9 @@
 #include "Log.h"
 #include "SysUtil.h"
 
-static int getFileStartAndLength(int fd, off_t *start_, size_t *length_)
+static int getFileStartAndLength(int fd, loff_t *start_, size_t *length_)
 {
-    off_t start, end;
+    loff_t start, end;
     size_t length;
 
     assert(start_ != NULL);
@@ -29,11 +29,11 @@
 
     // TODO: isn't start always 0 for the single call site? just use fstat instead?
 
-    start = TEMP_FAILURE_RETRY(lseek(fd, 0L, SEEK_CUR));
-    end = TEMP_FAILURE_RETRY(lseek(fd, 0L, SEEK_END));
+    start = TEMP_FAILURE_RETRY(lseek64(fd, 0L, SEEK_CUR));
+    end = TEMP_FAILURE_RETRY(lseek64(fd, 0L, SEEK_END));
 
-    if (TEMP_FAILURE_RETRY(lseek(fd, start, SEEK_SET)) == -1 ||
-                start == (off_t) -1 || end == (off_t) -1) {
+    if (TEMP_FAILURE_RETRY(lseek64(fd, start, SEEK_SET)) == -1 ||
+                start == (loff_t) -1 || end == (loff_t) -1) {
         LOGE("could not determine length of file\n");
         return -1;
     }
@@ -59,7 +59,7 @@
  */
 static int sysMapFD(int fd, MemMapping* pMap)
 {
-    off_t start;
+    loff_t start;
     size_t length;
     void* memPtr;
 
@@ -68,7 +68,12 @@
     if (getFileStartAndLength(fd, &start, &length) < 0)
         return -1;
 
+#if (PLATFORM_SDK_VERSION >= 21)
+    memPtr = mmap64(NULL, length, PROT_READ, MAP_PRIVATE, fd, start);
+#else
+    // Older versions of Android do not have mmap64 so we will just use mmap instead
     memPtr = mmap(NULL, length, PROT_READ, MAP_PRIVATE, fd, start);
+#endif
     if (memPtr == MAP_FAILED) {
         LOGW("mmap(%d, R, PRIVATE, %d, %d) failed: %s\n", (int) length,
             fd, (int) start, strerror(errno));
diff --git a/minzip/Zip.c b/minzip/Zip.c
index 1f035ad..f47a480 100644
--- a/minzip/Zip.c
+++ b/minzip/Zip.c
@@ -366,7 +366,7 @@
         }
         pEntry->offset = localHdrOffset + LOCHDR
             + get2LE(localHdr + LOCNAM) + get2LE(localHdr + LOCEXT);
-        if (!safe_add(NULL, pEntry->offset, pEntry->compLen)) {
+        if (!safe_add(NULL, pEntry->offset, (typeof(pEntry->offset))pEntry->compLen)) {
             LOGW("Integer overflow adding in parseZipArchive\n");
             goto bail;
         }
diff --git a/minzip/Zip.h b/minzip/Zip.h
index 86d8db5..0a03451 100644
--- a/minzip/Zip.h
+++ b/minzip/Zip.h
@@ -32,7 +32,7 @@
 typedef struct ZipEntry {
     unsigned int fileNameLen;
     const char*  fileName;       // not null-terminated
-    long         offset;
+    loff_t       offset;
     long         compLen;
     long         uncompLen;
     int          compression;
@@ -85,7 +85,7 @@
 const ZipEntry* mzFindZipEntry(const ZipArchive* pArchive,
         const char* entryName);
 
-INLINE long mzGetZipEntryOffset(const ZipEntry* pEntry) {
+INLINE loff_t mzGetZipEntryOffset(const ZipEntry* pEntry) {
     return pEntry->offset;
 }
 INLINE long mzGetZipEntryUncompLen(const ZipEntry* pEntry) {