How to read the mode field of git-ls-tree's output

From the Git index-format.txt file, regarding the mode:

32-bit mode, split into (high to low bits)

    4-bit object type
      valid values in binary are 1000 (regular file), 1010 (symbolic link)
      and 1110 (gitlink)

    3-bit unused

    9-bit unix permission. Only 0755 and 0644 are valid for regular files.
    Symbolic links and gitlinks have value 0 in this field.

Also, a directory object type (binary 0100) and group-writeable (0664 permissions) regular file are allowed as indicated by the fsck.c fsck_tree method. The regular non-executable group-writeable file is a non-standard mode that was supported in earlier versions of Git.

This makes valid modes (as binary and octal):

• 0100000000000000 (040000): Directory
• 1000000110100100 (100644): Regular non-executable file
• 1000000110110100 (100664): Regular non-executable group-writeable file
• 1000000111101101 (100755): Regular executable file
• 1010000000000000 (120000): Symbolic link
• 1110000000000000 (160000): Gitlink

The 6 digits show the file mode using the classical UNIX notations. First two digits show file type, the third one is about set-uid/set-gid/sticky bits, and you know the last three.

Here is how man 2 stat documents it on my GNU/Linux system:

   The following flags are defined for the st_mode field:

       S_IFMT     0170000   bit mask for the file type bit fields
       S_IFSOCK   0140000   socket
       S_IFLNK    0120000   symbolic link
       S_IFREG    0100000   regular file
       S_IFBLK    0060000   block device
       S_IFDIR    0040000   directory
       S_IFCHR    0020000   character device
       S_IFIFO    0010000   FIFO
       S_ISUID    0004000   set UID bit
       S_ISGID    0002000   set-group-ID bit (see below)
       S_ISVTX    0001000   sticky bit (see below)
       S_IRWXU    00700     mask for file owner permissions
       S_IRUSR    00400     owner has read permission
       S_IWUSR    00200     owner has write permission
       S_IXUSR    00100     owner has execute permission
       S_IRWXG    00070     mask for group permissions
       S_IRGRP    00040     group has read permission
       S_IWGRP    00020     group has write permission
       S_IXGRP    00010     group has execute permission
       S_IRWXO    00007     mask for permissions for others (not in group)
       S_IROTH    00004     others have read permission           
       S_IWOTH    00002     others have write permission
       S_IXOTH    00001     others have execute permission