Re: [ft-devel] Question about TTF

[Werner LEMBERG]

>      I am a grad student of University of Waterloo.  We have a
>      project about TTF. We are trying to translate TTF bytecode to
>      some kind of 3-addr-code, and optimize the 3-addr-code, then
>      convert it back to bytecode.

Nice!  I think I've already read about this (or a similar) project a
few years ago.

>      We tested our program on arial.ttf, and found that there is a
>      CALL instruction in some fpgm, which calls an uncertain fixed
>      point value (bytecode attached below).
>
>      As you can see, the callee is the result of a series of
>      arithmetic operations, (4096 DIV MIN(MAX(0, 64 SUB F26Dot6),
>      192) ADD 44), where 192 not even divides 4096.

You are misinterpreting the code.  Rewriting the code with normal
decimal numbers we get

  min(max(round(x) - 1.0, 0), 3) + 44

Remarks:

  * The `4096 DIV' bytecode converts an F26Dot6 number to a plain
    integer (i.e., a division by 64) – it thus disappears in the
    decimal formula.

  * Value 44 is the function offset; possible function numbers are
    obviously 44-47, since the above code uses `min' and `max' to
    limit the value accordingly.

>      So, I wonder how do you deal with such a call instruction, do
>      you just throw an exception?

Why should we do that?  The arithmetic code is fully valid!  Depending
on the input code (some scaled CVT value, I guess) it either calls
function 44, 45, 46, or 47.


    Werner


======================================================================


      PUSH[ ]
      17
      FDEF[ ]   /* FunctionDefinition */
      DUP[ ]    /* DuplicateTopStack */
      ROUND[01] /* Round */
      PUSHB[ ]  /* 1 value pushed */
      64
      SUB[ ]    /* Subtract */
      PUSHB[ ]  /* 1 value pushed */
      0
      MAX[ ]    /* Maximum */
      DUP[ ]    /* DuplicateTopStack */
      PUSHB[ ]  /* 2 values pushed */
      44  192
      ROLL[ ]   /* RollTopThreeStack */
      MIN[ ]    /* Minimum */
      PUSHW[ ]  /* 1 value pushed */
      4096      /* word */
      DIV[ ]    /* Divide */
      ADD[ ]    /* Add */
      CALL[ ]   /* CallFunction */
      GPV[ ]    /* GetPVector */
      ABS[ ]    /* Absolute */
      SWAP[ ]   /* SwapTopStack */
      ABS[ ]    /* Absolute */
      SUB[ ]    /* Subtract */
      NOT[ ]    /* LogicalNot */
      IF[ ]     /* If */
      PUSHB[ ]  /* 1 value pushed */
      3
      SUB[ ]    /* Subtract */
      EIF[ ]    /* EndIf */
      ENDF[ ]   /* EndFunctionDefinition */