Ubuntu 12.04 won't install due to odd partitioning

[D. Hugh Redelmeier]

I have a notebook on which I previously installed Ubuntu 8.04 and
10.04 and I want to install 12.04 (over 8.04).  See a pattern?  I want
the latest LTS and the one before.

When I try to install 12.04, and ask to configure the partitions, the
installer sees none.  And gives no explanation!

I exited the installer (this is a live DVD of Ubuntu 12.04 for AMD64)
and run parted from the console, it prints a terse message to stderr:
    ======================
    libparted : 2.3
    ======================
    Can't have a partition outside the disk!

A hint.  But not too explicit: it doesn't say what partition.

Here what fdisk says (decorated with labels from the partitions):

    Disk /dev/sda: 120.0 GB, 120034123776 bytes
    255 heads, 63 sectors/track, 14593 cylinders
    Units = cylinders of 16065 * 512 = 8225280 bytes
    Sector size (logical/physical): 512 bytes / 512 bytes
    I/O size (minimum/optimal): 512 bytes / 512 bytes
    Disk identifier: 0x17a417a4
     Device Boot      Start         End      Blocks   Id  System
    /dev/sda1               1        1020     8193116   27  Unknown
    Partition 1 does not end on cylinder boundary.
    /dev/sda2   *        1021        6368    42957804+   7  HPFS/NTFS
    /dev/sda3            6369        7388     8193148   83  Linux: Ubuntu8.04
    /dev/sda4            7389       14594    57882195    f  W95 Ext'd (LBA)
    /dev/sda5            7389        8153     6144820   82  Linux swap / Solaris
    /dev/sda6            8154       13573    43536116   83  Linux: /home
    /dev/sda7           13574       14594     8195072   83  Linux: Ubuntu10.04

It all looks good: all the cylinder numbers make sense.

But it turns out that
(120034123776 bytes/disk) / (8225280 bytes/cylinder)
  = 14593.31764705882352941176 cylinders/disk
NOT 14593 as fdisk reported.

So: the extended partition sda4 and the last partion within it, sda7
extend into this fractional final partition.  Any block past
(8225280 bytes/cylinder) * (14593 cylinders/disk) / (512 bytes/block)
  = 234436545 blocks
is in the fractional extra cylinder.

You can see this with "sfdisk -u S" output:

    Disk /dev/sda: 14593 cylinders, 255 heads, 63 sectors/track
    Units = sectors of 512 bytes, counting from 0

       Device Boot    Start       End   #sectors  Id  System
    /dev/sda1            63  16386294   16386232  27  Hidden NTFS WinRE
    /dev/sda2   *  16386300 102301908   85915609   7  HPFS/NTFS/exFAT
    /dev/sda3     102301920 118688215   16386296  83  Linux
    /dev/sda4     118688220 234452609  115764390   f  W95 Ext'd (LBA)
    /dev/sda5     118688283 130977922   12289640  82  Linux swap / Solaris
    /dev/sda6     130978008 218050239   87072232  83  Linux
    /dev/sda7     218050560 234440703   16390144  83  Linux
    Warning: partition 4 extends past end of disk

Interestingly, there is a bit of unused space after sda7 still within
sda4.  But I still would have expected a warning about sda7 going past
the end of the disk.

If I use "sfdisk" without flags, I get a lot of cylinder numbers
decorated with + and - suffixes that indicate rounding.


    Disk /dev/sda: 14593 cylinders, 255 heads, 63 sectors/track
    Units = cylinders of 8225280 bytes, blocks of 1024 bytes, counting from 0

       Device Boot Start     End   #cyls    #blocks   Id  System
    /dev/sda1          0+   1019-   1020-   8193116   27  Hidden NTFS WinRE
    /dev/sda2   *   1020    6367-   5348-  42957804+   7  HPFS/NTFS/exFAT
    /dev/sda3       6368    7387-   1020-   8193148   83  Linux
    /dev/sda4       7388   14593    7206   57882195    f  W95 Ext'd (LBA)
    /dev/sda5       7388+   8152-    765-   6144820   82  Linux swap / Solaris
    /dev/sda6       8153+  13572-   5420-  43536116   83  Linux
    /dev/sda7      13573+  14593-   1021-   8195072   83  Linux
    Warning: partition 4 extends past end of disk

Cylinder numbers seem to be off quite often.

What can I do to fix this, at least to the point where gparted and
friends will look at it?  I want to keep the contents of my current
partitions (other than sda3).

Can I somehow get the rather arbitrary geometry of the disk changed so
that the partitions don't look screwy?

BTW, I would guess that this partitioning was created by Ubuntu 
something-or-other.
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