3.17 Flags and Comparisons ¶

In a false-flag all bits are clear (0 when interpreted as integer). In a canonical true-flag all bits are set (-1 as a twos-complement signed integer); in many contexts (e.g., if) any non-zero value is treated as true flag.

false .
true .
true hex u. decimal

Comparison words produce canonical flags:

1 1 = .
1 0= .
0 1 < .
0 0 < .
-1 1 u< . \ type error, u< interprets -1 as large unsigned number
-1 1 < .

Gforth supports all combinations of the prefixes 0 u d d0 du f f0 (or none) and the comparisons = <> < > <= >=. Only a part of these combinations are standard (for details see the standard, Numeric comparison, Floating Point or Word Index).

You can use and or xor invert as operations on canonical flags. Actually they are bitwise operations:

1 2 and .
1 2 or .
1 3 xor .
1 invert .

You can convert a zero/non-zero flag into a canonical flag with 0<> (and complement it on the way with 0=; indeed, it is more common to use 0= instead of invert for canonical flags).

1 0= .
1 0<> .

While you can use if without 0<> to test for zero/non-zero, you sometimes need to use 0<> when combining zero/non-zero values with and or xor because of their bitwise nature. The simplest, least error-prone, and probably clearest way is to use 0<> in all these cases, but in some cases you can use fewer 0<>s. Here are some stack effects, where fc represents a canonical flag, and fz represents zero/non-zero (every fc also works as fz):

or  ( fz1 fz2 -- fz3 )
and ( fz1 fc  -- fz2 )
and ( fc  fz1 -- fz2 )

So, if you see code like this:

( n1 n2 ) 0<> and if

This tests whether n1 and n2 are non-zero and if yes, performs the code after if; it treats n1 as zero/non-zero and uses 0<> to convert n2 into a canonical flag; the and then produces an fz, which is consumed by the if.

You can use the all-bits-set feature of canonical flags and the bitwise operation of the Boolean operations to avoid ifs:

: foo ( n1 -- n2 )
  0= if
    14
  else
    0
  endif ;
0 foo .
1 foo .

: foo ( n1 -- n2 )
  0= 14 and ;
0 foo .
1 foo .

Assignment: Write min without if.

For reference, see Boolean Flags, Numeric comparison, and Bitwise operations.