u32 Operations

Miden assembly provides a set of instructions which can perform operations on regular two-complement 32-bit integers. These instructions are described in the tables below.

For instructions where one or more operands can be provided as immediate parameters (e.g., u32wrapping_add and u32wrapping_add.b), we provide stack transition diagrams only for the non-immediate version. For the immediate version, it can be assumed that the operand with the specified name is not present on the stack.

In all the table below, the number of cycles it takes for the VM to execute each instruction is listed beneath the instruction.

Conversions and tests

Instruction	Stack input	Stack output	Notes
u32test - (5 cycles)	[a, ...]	[b, a, ...]	$b \leftarrow {1, 0, if a < 2^{32} otherwise$
u32testw - (23 cycles)	[A, ...]	[b, A, ...]	$b \leftarrow {1, 0, if \forall i \in {0, 1, 2, 3} a_{i} < 2^{32} otherwise$
u32assert - (3 cycles)	[a, ...]	[a, ...]	Fails if $a \geq 2^{32}$
u32assert2 - (1 cycle)	[b, a,...]	[b, a,...]	Fails if $a \geq 2^{32}$ or $b \geq 2^{32}$
u32assertw - (6 cycles)	[A, ...]	[A, ...]	Fails if $\exists i \in {0, 1, 2, 3} : a_{i} \geq 2^{32}$
u32cast - (2 cycles)	[a, ...]	[b, ...]	$b \leftarrow a mod 2^{32}$
u32split - (1 cycle)	[a, ...]	[c, b, ...]	$b \leftarrow a mod 2^{32}$ , $c \leftarrow ⌊ a / 2^{32} ⌋$

The instructions u32assert, u32assert2 and u32assertw can also be parametrized with an error code which can be any 32-bit value specified either directly or via a named constant. For example:

u32assert.err=123
u32assert.err=MY_CONSTANT

If the error code is omitted, the default value of $0$ is assumed.

Arithmetic operations

Instruction	Stack input	Stack output	Notes
u32overflowing_add - (1 cycle) u32overflowing_add.b - (2-3 cycles)	[b, a, ...]	[d, c, ...]	$c \leftarrow (a + b) mod 2^{32}$ $d \leftarrow {1, 0, if (a + b) \geq 2^{32} otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32wrapping_add - (2 cycles) u32wrapping_add.b - (3-4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow (a + b) mod 2^{32}$ Undefined if $ma x (a, b) \geq 2^{32}$
u32overflowing_add3 - (1 cycle)	[c, b, a, ...]	[e, d, ...]	$d \leftarrow (a + b + c) mod 2^{32}$ , $e \leftarrow ⌊(a + b + c) / 2^{32} ⌋$ Undefined if $ma x (a, b, c) \geq 2^{32}$
u32wrapping_add3 - (2 cycles)	[c, b, a, ...]	[d, ...]	$d \leftarrow (a + b + c) mod 2^{32}$ , Undefined if $ma x (a, b, c) \geq 2^{32}$
u32overflowing_sub - (1 cycle) u32overflowing_sub.b - (2-3 cycles)	[b, a, ...]	[d, c, ...]	$c \leftarrow (a - b) mod 2^{32}$ $d \leftarrow {1, 0, if a < b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32wrapping_sub - (2 cycles) u32wrapping_sub.b - (3-4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow (a - b) mod 2^{32}$ Undefined if $ma x (a, b) \geq 2^{32}$
u32overflowing_mul - (1 cycle) u32overflowing_mul.b - (2-3 cycles)	[b, a, ...]	[d, c, ...]	$c \leftarrow (a \cdot b) mod 2^{32}$ $d \leftarrow ⌊(a \cdot b) / 2^{32} ⌋$ Undefined if $ma x (a, b) \geq 2^{32}$
u32wrapping_mul - (2 cycles) u32wrapping_mul.b - (3-4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow (a \cdot b) mod 2^{32}$ Undefined if $ma x (a, b) \geq 2^{32}$
u32overflowing_madd - (1 cycle)	[b, a, c, ...]	[e, d, ...]	$d \leftarrow (a \cdot b + c) mod 2^{32}$ $e \leftarrow ⌊(a \cdot b + c) / 2^{32} ⌋$ Undefined if $ma x (a, b, c) \geq 2^{32}$
u32wrapping_madd - (2 cycles)	[b, a, c, ...]	[d, ...]	$d \leftarrow (a \cdot b + c) mod 2^{32}$ Undefined if $ma x (a, b, c) \geq 2^{32}$
u32div - (2 cycles) u32div.b - (3-4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow ⌊ a / b ⌋$ Fails if $b = 0$ Undefined if $ma x (a, b) \geq 2^{32}$
u32mod - (3 cycles) u32mod.b - (4-5 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow a mod b$ Fails if $b = 0$ Undefined if $ma x (a, b) \geq 2^{32}$
u32divmod - (1 cycle) u32divmod.b - (2-3 cycles)	[b, a, ...]	[d, c, ...]	$c \leftarrow ⌊ a / b ⌋$ $d \leftarrow a mod b$ Fails if $b = 0$ Undefined if $ma x (a, b) \geq 2^{32}$

Bitwise operations

Instruction	Stack input	Stack output	Notes
u32and - (1 cycle)	[b, a, ...]	[c, ...]	Computes $c$ as a bitwise `AND` of binary representations of $a$ and $b$ . Fails if $ma x (a, b) \geq 2^{32}$
u32or - (6 cycle)s	[b, a, ...]	[c, ...]	Computes $c$ as a bitwise `OR` of binary representations of $a$ and $b$ . Fails if $ma x (a, b) \geq 2^{32}$
u32xor - (1 cycle)	[b, a, ...]	[c, ...]	Computes $c$ as a bitwise `XOR` of binary representations of $a$ and $b$ . Fails if $ma x (a, b) \geq 2^{32}$
u32not - (5 cycles)	[a, ...]	[b, ...]	Computes $b$ as a bitwise `NOT` of binary representation of $a$ . Fails if $a \geq 2^{32}$
u32shl - (18 cycles) u32shl.b - (3 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow (a \cdot 2^{b}) mod 2^{32}$ Undefined if $a \geq 2^{32}$ or $b > 31$
u32shr - (18 cycles) u32shr.b - (3 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow ⌊ a / 2^{b} ⌋$ Undefined if $a \geq 2^{32}$ or $b > 31$
u32rotl - (18 cycles) u32rotl.b - (3 cycles)	[b, a, ...]	[c, ...]	Computes $c$ by rotating a 32-bit representation of $a$ to the left by $b$ bits. Undefined if $a \geq 2^{32}$ or $b > 31$
u32rotr - (22 cycles) u32rotr.b - (3 cycles)	[b, a, ...]	[c, ...]	Computes $c$ by rotating a 32-bit representation of $a$ to the right by $b$ bits. Undefined if $a \geq 2^{32}$ or $b > 31$
u32popcnt - (33 cycles)	[a, ...]	[b, ...]	Computes $b$ by counting the number of set bits in $a$ (hamming weight of $a$ ). Undefined if $a \geq 2^{32}$
u32clz - (37 cycles)	[a, ...]	[b, ...]	Computes $b$ as a number of leading zeros of $a$ . Undefined if $a \geq 2^{32}$
u32ctz - (34 cycles)	[a, ...]	[b, ...]	Computes $b$ as a number of trailing zeros of $a$ . Undefined if $a \geq 2^{32}$
u32clo - (36 cycles)	[a, ...]	[b, ...]	Computes $b$ as a number of leading ones of $a$ . Undefined if $a \geq 2^{32}$
u32cto - (33 cycles)	[a, ...]	[b, ...]	Computes $b$ as a number of trailing ones of $a$ . Undefined if $a \geq 2^{32}$

Comparison operations

Instruction	Stack input	Stack output	Notes
u32lt - (3 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {1, 0, if a < b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32lte - (5 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {1, 0, if a \leq b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32gt - (4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {1, 0, if a > b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32gte - (4 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {1, 0, if a \geq b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32min - (8 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {a, b, if a < b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$
u32max - (9 cycles)	[b, a, ...]	[c, ...]	$c \leftarrow {a, b, if a > b otherwise$ Undefined if $ma x (a, b) \geq 2^{32}$