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And about mmap(2):
import os,sys,time,mmap
MP0 = ((2**30)-1)
MP1 = ((2**31)-1)
MP2 = ((2**32)-1)
MPV = (2**20) * 100
SIZES = (MP0-MPV, MP0, MP0+MPV,
 MP1-MPV, MP1, MP1+MPV,
 MP2-MPV, MP2, MP2+MPV)
FILE = 'test.dat'
print('Start:', time.gmtime())
for i in SIZES:
 print('Testing file size ', i, ': ', sep='', end='')
 sys.stdout.flush()
 with open(FILE, "wb+") as f:
 f.seek(i)
 f.write(b'asdf')
 f.flush()
 sb = os.stat(FILE) 
 if sb.st_size != i+4:
 print('size failure:', sb.st_size, ' != ', i, sep='', end='')
 sys.stdout.flush()
 mem = mmap.mmap(f.fileno(), 0, access=mmap.ACCESS_READ)
 if mem[0] != ord('0円'):
 print('offset 0 failed: ', ord(mem[0]), ' ', end='', sep='')
 else:
 print('offset 0 ok ', end='', sep='')
 sys.stdout.flush()
 if mem[i] != ord('a'):
 print('offset i failed: ', ord(mem[i]), ' ', end='', sep='')
 else:
 print('offset i ok ', end='', sep='')
 print()
 sys.stdout.flush()
 os.unlink(FILE)
print('End:', time.gmtime())
...
Start: time.struct_time(tm_year=2011, tm_mon=4, tm_mday=14, tm_hour=17, tm_min=27, tm_sec=30, tm_wday=3, tm_yday=104, tm_isdst=0)
Testing file size 968884223: offset 0 ok offset i ok 
Testing file size 1073741823: offset 0 ok offset i ok 
Testing file size 1178599423: offset 0 ok offset i ok 
Testing file size 2042626047: offset 0 ok offset i ok 
Testing file size 2147483647: offset 0 ok offset i ok 
Testing file size 2252341247: offset 0 ok offset i ok 
Testing file size 4190109695: offset 0 ok offset i ok 
Testing file size 4294967295: offset 0 ok offset i ok 
Testing file size 4399824895: offset 0 ok offset i ok 
End: time.struct_time(tm_year=2011, tm_mon=4, tm_mday=14, tm_hour=17, tm_min=27, tm_sec=30, tm_wday=3, tm_yday=104, tm_isdst=0)
Now i think that can't be any faster.
Changing to
 MP0 = ((2**30)-0)
 MP1 = ((2**31)-0)
 MP2 = ((2**32)-0)
results in
Start: time.struct_time(tm_year=2011, tm_mon=4, tm_mday=14, tm_hour=17, tm_min=27, tm_sec=55, tm_wday=3, tm_yday=104, tm_isdst=0)
Testing file size 968884224: offset 0 ok offset i ok 
Testing file size 1073741824: offset 0 ok offset i ok 
Testing file size 1178599424: offset 0 ok offset i ok 
Testing file size 2042626048: offset 0 ok offset i ok 
Testing file size 2147483648: offset 0 ok offset i ok 
Testing file size 2252341248: offset 0 ok offset i ok 
Testing file size 4190109696: offset 0 ok offset i ok 
Testing file size 4294967296: <- EOF here
Manually adjusted SIZES:
Testing file size 4294967295: offset 0 ok offset i ok 
Testing file size 4296015872: offset 0 ok offset i ok (MP2+1024*1024)
Testing file size 4295491584: offset 0 ok offset i ok (MP2+1024*512)
Testing file size 4295229440: offset 0 ok offset i ok (MP2+1024*256)
...
Testing file size 4294971392: offset 0 ok offset i ok (MP2+1024*4)
Testing file size 4294969344: <- EOF here (MP2+1024*2)
Pagesize = 4096.
I think the state machine can be easier than i thought.