Opcodes

The following lists show the standard and cryptographic opcodes supported by Beo instructions.

Table of Standard Opcodes​

Name	Description
abs	Absolute value operation
abs.w	Wrapping absolute value operation
add	Addition operation
add.w	Wrapping addition operation
and	AND operation
assert.eq	Assert equality
assert.neq	Assert non-equality
branch.eq	Branches to a position if the arguments are equal
branch.neq	Branches to a position if the arguments are not equal
cast	Cast between literals
cast.lossy	Cast between literals with lossy truncation
div	Division operation
div.w	Wrapping division operation
double	Double operation
gt	Greater than comparison
gte	Greater than or equal to comparison
inv	Multiplicative inverse operation
is.eq	Equality comparison
is.neq	Not equal comparison
lt	Less than comparison
lte	Less than or equal to comparison
mod	Arithmetic modulo operation
mul	Multiplication operation
mul.w	Wrapping multiplication operation
nand	Boolean NAND operation
neg	Additive inverse operation
nor	Boolean NOR operation
not	NOT operation
or	OR Operation
position	The position command
pow	Exponentiation operation
pow.w	Wrapping exponentiation operation
rand.chacha	Generates a random value within the finalize scope.
rem	Remainder operation
rem.w	Wrapping remainder operation
shl	Shift left operation
shl.w	Wrapping shift left operation
shr	Shift right operation
shr.w	Wrapping shift right operation
sqrt	Square root operation
square	Square operation
sub	Subtraction operation
sub.w	Wrapping subtraction operation
ternary	Ternary select operation
xor	XOR operation

Table of Cryptographic Opcodes​

Name	Description
commit.bhp256	256-bit input BHP commitment
commit.bhp512	512-bit input BHP commitment
commit.bhp768	768-bit input BHP commitment
commit.bhp1024	1024-bit input BHP commitment
commit.ped64	64-bit input Pedersen commitment
commit.ped128	128-bit input Pedersen commitment
hash.bhp256	256-bit input BHP hash
hash.bhp512	512-bit input BHP hash
hash.bhp768	768-bit input BHP hash
hash.bhp1024	1024-bit input BHP hash
hash.keccak256	256-bit input Keccak hash
hash.keccak384	384-bit input Keccak hash
hash.keccak512	512-bit input Keccak hash
hash.ped64	64-bit input Pedersen hash
hash.ped128	128-bit input Pedersen hash
hash.psd2	Poseidon hash with input rate 2
hash.psd4	Poseidon hash with input rate 4
hash.psd8	Poseidon hash with input rate 8
hash.sha3_256	256-bit input SHA3 hash
hash.sha3_384	384-bit input SHA3 hash
hash.sha3_512	512-bit input SHA3 hash
sign.verify	Verify a Schnorr signature

Specification​

The following is the specification for each opcode in the Beo Virtual Machine (BVM).

abs​

Back to Top

Description​

Computes the absolute value of the input, checking for overflow, storing the result in the destination register.

For integer types, a constraint is added to check for underflow. For cases where wrapping semantics are needed, see the abs.w instruction. This underflow happens when the input is the minimum value of a signed integer type. For example, abs -128i8 would result in underflow, since 128 cannot be represented as an i8.

Supported Types​

Input	Destination
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128

---

abs.w​

Back to Top

Description​

Compute the absolute value of the input, wrapping around at the boundary of the type, and storing the result in the destination register.

Supported Types​

Input	Destination
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128

---

add​

Back to Top

Description​

Adds first with second, storing the outcome in destination.

For integer types, a constraint is added to check for overflow. For cases where wrapping semantics are needed for integer types, see the add.w instruction.

Supported Types​

First	Second	Destination
Field	Field	Field
Group	Group	Group
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128
Scalar	Scalar	Scalar

---

add.w​

Back to Top

Description​

Adds first with second, wrapping around at the boundary of the type, and storing the outcome in destination.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

and​

Back to Top

Description​

Performs an AND operation on integer (bitwise) or boolean first and second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Boolean	Boolean	Boolean
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

assert.eq​

Back to Top

Description​

Checks whether first and second are equal, halting if they are not equal.

Supported Types​

First	Second
Address	Address
Boolean	Boolean
Field	Field
Group	Group
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128
U8	U8
U16	U16
U32	U32
U64	U64
U128	U128
Scalar	Scalar
Signature	Signature
Struct	Struct
Record	Record

---

assert.neq​

Back to Top

Description​

Checks whether first and second are not equal, halting if they are equal.

Supported Types​

First	Second
Address	Address
Boolean	Boolean
Field	Field
Group	Group
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128
U8	U8
U16	U16
U32	U32
U64	U64
U128	U128
Scalar	Scalar
Signature	Signature
Struct	Struct
Record	Record

---

branch.eq​

Back to Top

Description​

The command branch.eq <first> <second> to <destination> branches execution to the position indicated by destination if first and second are equal. This command is restricted to the finalize scope, and the destination must follow the command. Backward branches are not currently supported.

First	Second	Destination
Address	Address	Position
Boolean	Boolean	Position
Field	Field	Position
Group	Group	Position
I8	I8	Position
I16	I16	Position
I32	I32	Position
I64	I64	Position
I128	I128	Position
U8	U8	Position
U16	U16	Position
U32	U32	Position
U64	U64	Position
U128	U128	Position
Scalar	Scalar	Position
Struct	Struct	Position
Record	Record	Position

---

branch.neq​

Back to Top

Description​

The command branch.neq <first> <second> to <destination> branches execution to the position indicated by destination if first and second are not equal. This command is restricted to the finalize scope, and the destination must follow the command. Backward branches are not currently supported.

First	Second	Destination
Address	Address	Position
Boolean	Boolean	Position
Field	Field	Position
Group	Group	Position
I8	I8	Position
I16	I16	Position
I32	I32	Position
I64	I64	Position
I128	I128	Position
U8	U8	Position
U16	U16	Position
U32	U32	Position
U64	U64	Position
U128	U128	Position
Scalar	Scalar	Position
Struct	Struct	Position
Record	Record	Position

---

cast​

Back to Top

Description​

Enables casting between different literals.

Example Usage​

input r0 as field.private;
cast r0 into r1 as group;
cast r0 into r2 as u8;
cast r3 r4 r5 r6 into r7 as [boolean; 4u32];
cast r7 into r8 as [[boolean; 4u32]; 1u32];

Supported Types​

First	Second
Address	Address
Array	Array
Boolean	Boolean
Field	Field
Group	Group
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128
U8	U8
U16	U16
U32	U32
U64	U64
U128	U128
Scalar	Scalar

---

cast.lossy​

Back to Top

Description​

Perform casting with lossy truncation.

Example Usage​

input r0 as field.private;
cast r0 into r1 as group;
cast r0 into r2 as u8;
cast.lossy r0 into r3 as u8; // The bottom 8 bits of the r0 are extracted into a u8 and placed into r3

Supported Types​

First	Second
Address	Address
Boolean	Boolean
Field	Field
Group	Group
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128
U8	U8
U16	U16
U32	U32
U64	U64
U128	U128
Scalar	Scalar

---

commit.bhp256​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen commitment on inputs of 256-bit chunks in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment will always be an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 129 bits.

Supported Types​

First	Second	Destination
Address	Scalar	Address, Field, Group
Boolean	Scalar	Address, Field, Group
Field	Scalar	Address, Field, Group
Group	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
I64	Scalar	Address, Field, Group
I128	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
U64	Scalar	Address, Field, Group
U128	Scalar	Address, Field, Group
Scalar	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

commit.bhp512​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen commitment on inputs of 512-bit chunks in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment will always be an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 171 bits.

Supported Types​

First	Second	Destination
Address	Scalar	Address, Field, Group
Boolean	Scalar	Address, Field, Group
Field	Scalar	Address, Field, Group
Group	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
I64	Scalar	Address, Field, Group
I128	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
U64	Scalar	Address, Field, Group
U128	Scalar	Address, Field, Group
Scalar	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

commit.bhp768​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen commitment on inputs of 768-bit chunks in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment will always be an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 129 bits.

Supported Types​

First	Second	Destination
Address	Scalar	Address, Field, Group
Boolean	Scalar	Address, Field, Group
Field	Scalar	Address, Field, Group
Group	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
I64	Scalar	Address, Field, Group
I128	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
U64	Scalar	Address, Field, Group
U128	Scalar	Address, Field, Group
Scalar	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

commit.bhp1024​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen commitment on inputs of 1024-bit chunks in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment will always be an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 171 bits.

Supported Types​

First	Second	Destination
Address	Scalar	Address, Field, Group
Boolean	Scalar	Address, Field, Group
Field	Scalar	Address, Field, Group
Group	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
I64	Scalar	Address, Field, Group
I128	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
U64	Scalar	Address, Field, Group
U128	Scalar	Address, Field, Group
Scalar	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

commit.ped64​

Back to Top

Description​

Computes a Pedersen commitment up to a 64-bit input in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment is an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given Struct value exceeds the 64-bit limit.

Supported Types​

First	Second	Destination
Boolean	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

commit.ped128​

Back to Top

Description​

Computes a Pedersen commitment up to a 128-bit input in first, and some randomness in second, storing the commitment in destination. Randomness should always be a Scalar value, and the produced commitment is an Address, Field, or Group value, as specified via as at the end of the instruction.

The instruction will halt if the given Struct value exceeds the 128-bit limit.

Supported Types​

First	Second	Destination
Boolean	Scalar	Address, Field, Group
I8	Scalar	Address, Field, Group
I16	Scalar	Address, Field, Group
I32	Scalar	Address, Field, Group
I64	Scalar	Address, Field, Group
U8	Scalar	Address, Field, Group
U16	Scalar	Address, Field, Group
U32	Scalar	Address, Field, Group
U64	Scalar	Address, Field, Group
Struct	Scalar	Address, Field, Group

---

div​

Back to Top

Description​

Divides first by second, storing the outcome in destination. Halts on division by zero.

For integer types, this operation performs truncated division. Furthermore, a constraint is added to check for underflow. This underflow happens when dividing the minimum value of a signed integer type by -1. For example, div -128i8 -1i8 would result in underflow, since 128 cannot be represented as an i8.

For cases where wrapping semantics are needed for integer types, see the div.w instruction.

Supported Types​

First	Second	Destination
Field	Field	Field
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

div.w​

Back to Top

Description​

Divides first by second, wrapping around at the boundary of the type, and storing the outcome in destination.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

double​

Back to Top

Description​

Doubles the input, storing the outcome in destination.

Supported Types​

Input	Destination
Field	Field
Group	Group

---

gt​

Back to Top

Description​

Checks if first is greater than second, storing the result in destination.

Supported Types​

First	Second	Destination
Field	Field	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean

---

gte​

Back to Top

Description​

Checks if first is greater than or equal to second, storing the result in destination.

Supported Types​

First	Second	Destination
Field	Field	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean

---

hash.bhp256​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen hash on inputs of 256-bit chunks in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 129 bits.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.bhp512​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen hash on inputs of 512-bit chunks in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 171 bits.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.bhp768​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen hash on inputs of 768-bit chunks in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 129 bits.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.bhp1024​

Back to Top

Description​

Computes a Bowe-Hopwood-Pedersen hash on inputs of 1024-bit chunks in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given input is smaller than 171 bits.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.keccak256​

Back to Top

Description​

Performs a Keccak hash on first, storing a 256-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.keccak384​

Back to Top

Description​

Performs a Keccak hash on first, storing a 384-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.keccak512​

Back to Top

Description​

Performs a Keccak hash on first, storing a 512-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.ped64​

Back to Top

Description​

Computes a Pedersen hash up to a 64-bit input in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given Struct value exceeds the 64-bit limit.

Supported Types​

First	Destination
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.ped128​

Back to Top

Description​

Computes a Pedersen hash up to a 128-bit input in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

The instruction will halt if the given Struct value exceeds the 128-bit limit.

Supported Types​

First	Destination
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.psd2​

Back to Top

Description​

Calculates a Poseidon hash with an input rate of 2, from an input in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.psd4​

Back to Top

Description​

Calculates a Poseidon hash with an input rate of 4, from an input in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.psd8​

Description​

Calculates a Poseidon hash with an input rate of 8, from an input in first, storing the hash in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.sha3_256​

Description​

Calculates a SHA3-256 hash, from an input in first, storing the 256-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.sha3_384​

Back to Top

Description​

Calculates a SHA3-384 hash, from an input in first, storing the 384-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

hash.sha3_512​

Back to Top

Description​

Calculates a SHA3-512 hash, from an input in first, storing the 512-bit digest in destination. The produced hash will always be an arithmetic (U8, U16, U32, U64, U128, I8, I16, I32,I64,I128, Field, Group, or Scalar) or Address value, as specified via as at the end of the instruction.

Supported Types​

First	Destination
Address	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Boolean	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Field	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Group	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
I128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U8	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U16	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U32	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U64	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
U128	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Scalar	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128
Struct	Address, Field, Group, Scalar, I8, I16, I32,I64,I128, U8, U16, U32, U64, U128

---

inv​

Back to Top

Description​

Computes the multiplicative inverse of the input, storing the outcome in destination.

Supported Types​

Input	Destination
Field	Field

---

is.eq​

Back to Top

Description​

Compares first and second, storing the result in destination.

Supported Types​

First	Second	Destination
Address	Address	Boolean
Boolean	Boolean	Boolean
Field	Field	Boolean
Group	Group	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean
Signature	Signature	Boolean
Struct	Struct	Boolean
Record	Record	Boolean

---

is.neq​

Back to Top

Description​

Returns true if first is not equal to second, storing the result in destination.

Supported Types​

First	Second	Destination
Address	Address	Boolean
Boolean	Boolean	Boolean
Field	Field	Boolean
Group	Group	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean
Signature	Signature	Boolean
Struct	Struct	Boolean
Record	Record	Boolean

---

lt​

Back to Top

Description​

Checks if first is less than second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Field	Field	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean

---

lte​

Back to Top

Description​

Checks if first is less than or equal to second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Field	Field	Boolean
I8	I8	Boolean
I16	I16	Boolean
I32	I32	Boolean
I64	I64	Boolean
I128	I128	Boolean
U8	U8	Boolean
U16	U16	Boolean
U32	U32	Boolean
U64	U64	Boolean
U128	U128	Boolean
Scalar	Scalar	Boolean

---

mod​

Back to Top

Description​

Takes the modulus of first with respect to second, storing the outcome in destination. Halts if second is zero.

The semantics of this operation are consistent with the mathematical definition of modulo operation.

Supported Types​

First	Second	Destination
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

mul​

Back to Top

Description​

Multiplies first with second, storing the outcome in destination.

For integer types, a constraint is added to check for overflow/underflow. For cases where wrapping semantics are needed for integer types, see the mul.w instruction.

Supported Types​

First	Second	Destination
Field	Field	Field
Group	Scalar	Group
Scalar	Group	Group
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

mul.w​

Back to Top

Description​

Multiplies first with second, wrapping around at the boundary of the type, and storing the outcome in destination.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

nand​

Back to Top

Description​

Returns false only if first and second are true, storing the outcome in destination.

Supported Types​

First	Second	Destination
Boolean	Boolean	Boolean

---

neg​

Back to Top

Description​

Negates first, storing the outcome in destination.

For signed integer types, calling neg on the minimum value is an invalid operation. For example, the input -128i8 would not be valid since 128 cannot be represented as an i8.

Supported Types​

Input	Destination
Field	Field
Group	Group
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128

---

nor​

Back to Top

Description​

Returns true when neither first nor second is true, storing the outcome in destination.

Supported Type​

First	Second	Destination
Boolean	Boolean	Boolean

---

not​

Back to Top

Description​

Perform a NOT operation on an integer (bitwise) or boolean input, storing the outcome in destination.

Supported Types​

Input	Destination
Boolean	Boolean
I8	I8
I16	I16
I32	I32
I64	I64
I128	I128
U8	U8
U16	U16
U32	U32
U64	U64
U128	U128

---

or​

Back to Top

Description​

Performs an OR operation on integer (bitwise) or boolean first and second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Boolean	Boolean	Boolean
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

position​

Back to Top

Description​

The position declaration, e.g. position <name>, which indicates a location name in the program to branch execution to. Positions must be a lowercase alphanumeric string.

---

pow​

Back to Top

Description​

Raises first to the power of second, storing the outcome in destination.

For integer types, a constraint is added to check for overflow/underflow. For cases where wrapping semantics are needed for integer types, see the pow.w instruction.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
Field	Field	Field
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

pow.w​

Back to Top

Description​

Raises first to the power of second, wrapping around at the boundary of the type, storing the outcome in destination.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

rand.chacha​

Description​

The rand.chacha opcode is used to generate random values within the finalize scope. It supports a wide range of types for the random value.

Example Usage​

rand.chacha into r0 as field;
rand.chacha r0 into r1 as field;
rand.chacha r0 r1 into r2 as field;
rand.chacha 1u8 2i16 into r27 as u32;

Supported Types​

Single can be any of the following types Address, Boolean, Field, Group, I8, I16, I32, I64, I128, U8, U16, U32, U64, U128, or Scalar. Composite data types such as structs and mappings are not allowed.

First	Second	Destination
Single	Single	Single

---

rem​

Back to Top

Description​

Computes the truncated remainder of first divided by second, storing the outcome in destination. Halts on division by zero.

A constraint is added to check for underflow. This underflow happens when the associated division operation, div, underflows.

For cases where wrapping semantics are needed for integer types, see the rem.w instruction.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

rem.w​

Back to Top

Description​

Computes the truncated remainder of first divided by second, wrapping around at the boundary of the type, and storing the outcome in destination.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

sign.verify​

Back to Top

Description​

Verifies the signature first against the address public key second and the message third, storing the outcome in destination.

Example Usage​

sign.verify r0 r1 r2 into r3;

Supported Types​

First	Second	Third	Destination
Signature	Address	Message	Boolean

---

shl​

Back to Top

Description​

Shifts first left by second bits, storing the outcome in destination.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

shl.w​

Back to Top

Description​

Shifts first left by second bits, wrapping around at the boundary of the type, storing the outcome in destination.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

shr​

Back to Top

Description​

Shifts first right by second bits, storing the outcome in destination.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

shr.w​

Back to Top

Description​

Shifts first right by second bits, wrapping around at the boundary of the type, storing the outcome in destination.

Supported Types​

Magnitude can be a U8, U16, or U32.

First	Second	Destination
I8	Magnitude	I8
I16	Magnitude	I16
I32	Magnitude	I32
I64	Magnitude	I64
I128	Magnitude	I128
U8	Magnitude	U8
U16	Magnitude	U16
U32	Magnitude	U32
U64	Magnitude	U64
U128	Magnitude	U128

---

square​

Back to Top

Description​

Squares the input, storing the outcome in destination.

Supported Types​

Input	Destination
Field	Field

---

sqrt​

Back to Top

Description​

Computes the square root of the input, storing the outcome in destination.

Supported Types​

Input	Destination
Field	Field

---

sub​

Back to Top

Description​

Computes first - second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Field	Field	Field
Group	Group	Group
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

sub.w​

Back to Top

Description​

Computes first - second, wrapping around at the boundary of the type, and storing the outcome in destination.

Supported Types​

First	Second	Destination
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128

---

ternary​

Back to Top

Description​

Selects first, if condition is true, otherwise selects second, storing the result in destination.

Example: ternary r0 r1 r2 into r3, where r0 is the condition, r1 is first, r2 is second, and r3 is the destination.

Supported Types​

Condition	First	Second	Destination
Boolean	Boolean	Boolean	Boolean
Boolean	Field	Field	Field
Boolean	Group	Group	Group
Boolean	I8	I8	I8
Boolean	I16	I16	I16
Boolean	I32	I32	I32
Boolean	I64	I64	I64
Boolean	I128	I128	I128
Boolean	U8	U8	U8
Boolean	U16	U16	U16
Boolean	U32	U32	U32
Boolean	U64	U64	U64
Boolean	U128	U128	U128
Boolean	Scalar	Scalar	Scalar
Boolean	Signature	Signature	Signature

---

xor​

Back to Top

Description​

Performs a XOR operation on integer (bitwise) or boolean first and second, storing the outcome in destination.

Supported Types​

First	Second	Destination
Boolean	Boolean	Boolean
I8	I8	I8
I16	I16	I16
I32	I32	I32
I64	I64	I64
I128	I128	I128
U8	U8	U8
U16	U16	U16
U32	U32	U32
U64	U64	U64
U128	U128	U128