#### 6.5.6 Bitwise operations ¶

````and` ( w1 w2 – w ) core “and”
```
````or` ( w1 w2 – w ) core “or”
```
````xor` ( w1 w2 – w ) core “x-or”
```
````invert` ( w1 – w2 ) core “invert”
```
````mux` ( u1 u2 u3 – u ) gforth-1.0 “mux”
```

Multiplex: For every bit in u3: for a 1 bit, select the corresponding bit from u1, otherwise the corresponding bit from u2. E.g., `%0011 %1100 %1010 mux` gives `%0110`

````lshift` ( u1 u – u2 ) core “l-shift”
```

Shift u1 left by u bits.

````rshift` ( u1 u – u2 ) core “r-shift”
```

Shift u1 (cell) right by u bits, filling the shifted-in bits with zero (logical/unsigned shift).

````arshift` ( n1 u – n2 ) gforth-1.0 “ar-shift”
```

Shift n1 (cell) right by u bits, filling the shifted-in bits from the sign bit of n1 (arithmetic shift).

````dlshift` ( ud1 u – ud2 ) gforth-1.0 “dlshift”
```

Shift ud1 (double-cell) left by u bits.

````drshift` ( ud1 u – ud2 ) gforth-1.0 “drshift”
```

Shift ud1 (double-cell) right by u bits, filling the shifted-in bits with zero (logical/unsigned shift).

````darshift` ( d1 u – d2 ) gforth-1.0 “darshift”
```

Shift d1 (double-cell) right by u bits, filling the shifted-in bits from the sign bit of d1 (arithmetic shift).

````2*` ( n1 – n2 ) core “two-star”
```

Shift left by 1; also works on unsigned numbers

````2/` ( n1 – n2 ) core “two-slash”
```

Arithmetic shift right by 1. For signed numbers this is a floored division by 2 (note that `/` not necessarily floors).

````d2*` ( d1 – d2 ) double “d-two-star”
```

Shift double-cell left by 1; also works on unsigned numbers

````d2/` ( d1 – d2 ) double “d-two-slash”
```

Arithmetic shift right by 1. For signed numbers this is a floored division by 2.

````>pow2` ( u1 – u2 ) gforth-1.0 “to-pow2”
```

u2 is the lowest power-of-2 number with u2>=u1.

````log2` ( u – n ) gforth-1.0 “log2”
```

N is the rounded-down binary logarithm of u, i.e., the index of the first set bit; if u=0, n=-1.

````pow2?` ( u – f  ) gforth-1.0 “pow-two-query”
```

f is true iff u is a power of two, i.e., there is exactly one bit set in u.

````ctz` ( x – u  ) gforth-1.0 “c-t-z”
```

count trailing zeros in binary representation of x

Unlike most other operations, rotation of narrower units cannot easily be synthesized from rotation of wider units, so using cell-wide and double-wide rotation operations means that the results depend on the cell width. For published algorithms or cell-width-independent results, you usually need to use a fixed-width rotation operation.

````wrol` ( u1 u – u2 ) gforth-1.0 “wrol”
```

Rotate the least significant 16 bits of u1 left by u bits, set the other bits to 0.

````wror` ( u1 u – u2 ) gforth-1.0 “wror”
```

Rotate the least significant 16 bits of u1 right by u bits, set the other bits to 0.

````lrol` ( u1 u – u2 ) gforth-1.0 “lrol”
```

Rotate the least significant 32 bits of u1 left by u bits, set the other bits to 0.

````lror` ( u1 u – u2 ) gforth-1.0 “lror”
```

Rotate the least significant 32 bits of u1 right by u bits, set the other bits to 0.

````rol` ( u1 u – u2 ) gforth-1.0 “rol”
```

Rotate all bits of u1 left by u bits.

````ror` ( u1 u – u2 ) gforth-1.0 “ror”
```

Rotate all bits of u1 right by u bits.

````drol` ( ud1 u – ud2 ) gforth-1.0 “drol”
```

Rotate all bits of ud1 (double-cell) left by u bits.

````dror` ( ud1 u – ud2 ) gforth-1.0 “dror”
```

Rotate all bits of ud1 (double-cell) right by u bits.