Error in fatgen103

There is an error in the FAT Volume Initialization algorithm (on page 21) to calculate the number of sectors in a FAT32
File Allocation Table. Even though the document is over 10 years old it's still the most current.

fatgen103, page 21 wrote:

Do not spend too much time trying to figure out why this math works. The basis for the computation is complicated;

It's actually quite simple. Start with the total sectors, subtract the reserved sectors and the sectors used for both FATs.
Then add two clusters to account for the first two FAT entries. The total data sectors of the volume must be less or equal
to 4GB-1 for FAT32 and the MBR table. These sectors are not managed by the FAT. This leaves the total data sectors,
divide by the sectors per cluster for the total data clusters. Divide the total data clusters by the sector size divided by 4
to get the total FAT sectors. Any fractional remainder will require one extra FAT sector.

Code:

  FATSz = DskSize - BPB_ResvdSecCnt - (2 * FATSz) + (2 * BPB_SecPerClus)/ BPB_SecPerClus * (BPB_BytsPerSec / 4)

Multiply both sides by (BPB_SecPerClus * (BPB_BytsPerSec / 4))

Code:

    FATSz * (BPB_SecPerClus * (BPB_BytsPerSec / 4)) = DskSize - BPB_ResvdSecCnt - (2 * FATSz) + (2 * BPB_SecPerClus)

Add (2 * FATSz) to both sides

Code:

   (FATSz * (BPB_SecPerClus * (BPB_BytsPerSec / 4))) + (2 * FATSz) = DskSize - BPB_ResvdSecCnt + (2 * BPB_SecPerClus)

Combine the FATSz

Code:

    FATSz * ((BPB_SecPerClus * (BPB_BytsPerSec / 4)) + 2) = DskSize - BPB_ResvdSecCnt + (2 * BPB_SecPerClus)

Finally divide both sides by ((BPB_SecPerClus * (BPB_BytsPerSec / 4)) + 2) to get FATSz. Round up any fractional remainder.

Code:

    FATSz = (DskSize - BPB_ResvdSecCnt + (2 * BPB_SecPerClus)) / ((BPB_SecPerClus * (BPB_BytsPerSec / 4)) + 2)

This is different (and much simpler) than the MS version:

fatgen103, page 21 wrote:

Code:

RootDirSectors = ((BPB_RootEntCnt * 32) + (BPB_BytsPerSec - 1)) / BPB_BytsPerSec;
TmpVal1 = DskSize - (BPB_ResvdSecCnt + RootDirSectors);
TmpVal2 = (256 * BPB_SecPerClus) + BPB_NumFATs;
If(FATType == FAT32)
TmpVal2 = TmpVal2 / 2;
FATSz = (TMPVal1 + (TmpVal2 - 1)) / TmpVal2;

fatgen103, page 13 wrote:

Note that on a FAT32 volume the BPB_RootEntCnt value is always 0, so on a FAT32 volume RootDirSectors is always 0.

Here's the FASM code which works as either use16 or use32. Note edx:eax is the 64 bit total bytes size.

Code:

  shrd eax, edx, cl             ; ecx is BPB_BytsPerSec exponent, 512=9, 2048=11, 4096=12
  shr edx, cl                   ; divide size by 512 for DskSize
  movzx ebx, WORD [BPB_ResvdSecCnt]
  sub eax, ebx
  sbb edx, 0                    ; DskSize - BPB_ResvdSecCnt
  movzx ebx, BYTE [BPB_SecPerClus]
  add eax, ebx
  add eax, ebx                  ; + (2 * BPB_SecPerClus)
  jnc .1
  mov eax, -1                   ; max size 4GB-1
.1:
  sub ecx, 2
  shl ebx, cl
  add ebx, 2                    ; (BPB_SecPerClus * (BPB_BytsPerSec / 4)) + 2
  xor edx, edx
  div ebx                       ; (DskSize - BPB_ResvdSecCnt) / ((BPB_SecPerClus * (BPB_BytsPerSec / 4)) + 2)
  cmp edx, 0
  adc eax, 0                    ; need one extra sector if any remainder

Format any size USB flash drive FAT32. Using a disk editor like HxD the following variables are located at the following offsets from the start of the first volume sector.

Code:

BPB_SecPerClus                    equ 13 ; BYTE
BPB_ResvdSecCnt                   equ 14 ; WORD
BPB_NumFATs                       equ 16 ; BYTE
DskSize                           equ 32 ; DWORD
FATSz                             equ 36 ; DWORD

Do the math and check the FATSz as actually formatted.

Edit: Added correction to code by revolution
Edit: Added size of sector calculation and compensation for first two FAT entries.