# Leo Operators


|Leo Syntax | Aleo Instruction | Description |
| --------------------------------- |--------------------------------- | ----------------------------------|
|`.abs()` | `abs`   | Absolute value operation           |
| `.abs_wrapped()`| `abs.w`                  | Wrapping absolute value operation  |
| `+`, `+=`, `.add(..)` | `add`                      | Addition operation                 |
|`.add_wrapped(..)`| `add.w`                   | Wrapping add operation             |
|`&`, `&=`, `.and(..)`| `and`                       | Bitwise AND operation              |
|`&&`, `&&=`, `.and(..)` | `and`                       | Logical AND operation              |
|`BHP256::commit(..)`| `commit.bhp256`   | 256-bit input BHP commitment       |
| `BHP512::commit(..)`| `commit.bhp512`   | 512-bit input BHP commitment       |
| `BHP768::commit(..)`| `commit.bhp768`   | 768-bit input BHP commitment       |
| `BHP1024::commit(..)`| `commit.bhp1024` | 1024-bit input BHP commitment      |
| `/`, `/=`, `.div(..)` | `div`                     | Division operation                 |
| `.div_wrapped(..)`| `div.w`                | Wrapping division operation        |
| `.double(..)`| `double`               | Double operation                   |
| `>`, `.gt(..)`| `gt`                        | Greater than comparison            |
| `>=`, `.gte(..)`| `gte`                       | Greater than or equal to comparison|
|`BHP256::hash(..)`| `hash.bhp256`      | 256-bit input BHP hash             |
| `BHP512::hash(..)`| `hash.bhp512`       | 512-bit input BHP hash             |
| `BHP768::hash(..)`| `hash.bhp768`      | 768-bit input BHP hash             |
| `BHP1024::hash(..)`| `hash.bhp1024`     | 1024-bit input BHP hash            |
| `Pedersen64::hash(..)`| `hash.ped64`         | 64-bit input Pedersen hash         |
| `Pedersen128::hash(..)`| `hash.ped128`       | 128-bit input Pedersen hash        |
| `Poseidon2::hash(..)`| `hash.psd2`          | Poseidon hash with input rate 2    |
| `Poseidon4::hash(..)`| `hash.psd4`           | Poseidon hash with input rate 4    |
| `Poseidon8::hash(..)`| `hash.psd8`           | Poseidon hash with input rate 8    |
| `.inv(..)` | `inv`                       | Multiplicative inverse operation   |
| `==`, `.eq(..)`| `is.eq`                   | Equality comparison                |
|`!=`, `.neq(..)`| `is.neq`                 | Not equal comparison               |
| `<`, `.lt(..)`| `lt`                         | Less than comparison               |
| `<=`, `.lte(..)`| `lte`                       | Less than or equal to comparison   |
| `.mod(..)` | `mod`                       | Arithmetic modulo operation        |
| `*`, `*=`, `.mul(..)`| `mul`                       | Multiplication operation           |
| `.mul_wrapped(..)`| `mul.w`                  | Wrapping multiplication operation  |
| `.nand(..)` | `nand`                    | `Boolean` NAND operation           |
| `-`, `.neg()`| `neg`                       | Additive inverse operation         |
| `.nor(..)`| `nor`                      | `Boolean` NOR operation            |
| `!`, `.not()`| `not`                      | NOT operation              |
| `\|`, `\|=`, `.or(..)` | `or`                   | Bitwise OR Operation               |
|  `\|\|`, `\|\|=`, `.or(..)` | `or`                        | Logical OR Operation               |
| `**`, `**=`, `.pow(..)`| `pow`                       | Exponentiation operation           |
|`.pow_wrapped(..)`| `pow.w`                  | Wrapping exponentiation operation  |
| `%`, `%=`, `.rem(..)`| `rem`                      | Remainder operation                |
| `.rem_wrapped(..)`| `rem.w`                  | Wrapping remainder operation       |
| `<<`, `<<=`, `.shl(..)`| `shl`                       | Shift left operation               |
| `.shl_wrapped(..)`| `shl.w`                  | Wrapping Shift left operation      |
| `>>`, `>>=`, `.shr(..)`| `shr`                      | Shift right operation              |
| `.shr_wrapped(..)`| `shr.w`                  | Wrapping Shift right operation     |
| `.sqrt()`| `sqrt`                    | Square root operation              |
|`-`, `-=`, `.sub(..)`| `sub`                      | Subtraction operation              |
|`.sub_wrapped(..)`| `sub.w`                   | Wrapping Subtraction operation     |
|`.square()`| `square`                | Square operation                   |
|`condition ? first : second`| `ternary`               | Ternary select operation           |
|`^`, `^=`, `.xor(..)` | `xor`                       | XOR operation              |