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It's very difficult for me to understand GDT (Global Descriptor Table) in JOS (xv6-rev7)

For example 

.word (((lim) >> 12) & 0xffff), ((base) & 0xffff);

Why shift right 12? Why AND 0xffff?
What do these number mean?
What does the formula mean?

Can anyone give me some resources or tutorials or hints?

Here, It's two parts of snippet code as following for my problem.

1st Part

0654 #define SEG_NULLASM \
0655 .word 0, 0; \
0656 .byte 0, 0, 0, 0
0657
0658 // The 0xC0 means the limit is in 4096−byte units
0659 // and (for executable segments) 32−bit mode.
0660 #define SEG_ASM(type,base,lim) \
0661 .word (((lim) >> 12) & 0xffff), ((base) & 0xffff); \
0662 .byte (((base) >> 16) & 0xff), (0x90 | (type)), \
0663 (0xC0 | (((lim) >> 28) & 0xf)), (((base) >> 24) & 0xff)
0664
0665 #define STA_X 0x8 // Executable segment
0666 #define STA_E 0x4 // Expand down (non−executable segments)
0667 #define STA_C 0x4 // Conforming code segment (executable only)
0668 #define STA_W 0x2 // Writeable (non−executable segments)
0669 #define STA_R 0x2 // Readable (executable segments)
0670 #define STA_A 0x1 // Accessed

2nd Part

8480 # Bootstrap GDT
8481 .p2align 2 # force 4 byte alignment
8482 gdt:
8483 SEG_NULLASM # null seg
8484 SEG_ASM(STA_X|STA_R, 0x0, 0xffffffff) # code seg
8485 SEG_ASM(STA_W, 0x0, 0xffffffff) # data seg
8486
8487 gdtdesc:
8488 .word (gdtdesc − gdt − 1) # sizeof(gdt) − 1
8489 .long gdt # address gdt

The complete part: http://pdos.csail.mit.edu/6.828/2012/xv6/xv6-rev7.pdf

Gapry
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2 Answers2

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Well, it isn't a real formula at all. Limit is shifted twelve bits to right, what's equivalent to division by 2^12, what is 4096, and that is granularity of GDT entry base, when G bit is set (in your code G bit is encoded in constants you use in your macro). Whenever address is to be accessed using correnspondig selector, only higher 20 bits are compared with limit and if they're greater, #GP is thrown. Also note that standard pages are 4KB in size, so any number greater than limit by less than 4 kilobytes is handled by page corresponding selector limit. Landing is there partly for suppressing compiler warnings about number overflow, as the operand 0xFFFF is maximal value for single word (16 bits).

Same applies for other shifts and AND, where in other expressions numbers can be shifted more to get another parts.

user35443
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GDT descriptor

The structure of GDT descriptor sees above.

((lim) >> 12) & 0xffff) corresponding to Segment Limit(Bit 0-15). Shift right means minimal unit is 2^12 byte(granularity of GDT entry base); && 0xffff means we need the lower 16 bits of lim) >> 12, which fits to lowest part of 16 bits of GDT descriptor.

The rest of the 'formula' is the same.

here is a good material for learning GTD descriptor.

xinnjie
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