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Miden VM Instruction Reference

This page provides a comprehensive reference for Miden Assembly instructions.

Field Operations

Comparison Operations

InstructionStack InputStack OutputCyclesNotes
lte
lte.b
[b, a, ...][c, ...]15
16
lt
lt.b
[b, a, ...][c, ...]14
15
gte
gte.b
[b, a, ...][c, ...]16
17
gt
gt.b
[b, a, ...][c, ...]15
16
eq
eq.b
[b, a, ...][c, ...]1
1-2
neq
neq.b
[b, a, ...][c, ...]2
2-3
eqw[A, B, ...][c, A, B, ...]15
is_odd[a, ...][b, ...]5

Assertions and Tests

InstructionStack InputStack OutputCyclesNotes
assert[a, ...][...]1Removes if . Fails if .
assertz[a, ...][...]2Removes if . Fails if .
assert_eq[b, a, ...][...]2Removes if . Fails if .
assert_eqw[B, A, ...][...]11Removes if . Fails if .

Note: Assertions can be parameterized with an error message (e.g., assert.err="Division by 0").

Arithmetic and Boolean Operations

InstructionStack InputStack OutputCyclesNotes
add
add.b
[b, a, ...][c, ...]1
1-2
sub
sub.b
[b, a, ...][c, ...]2
2
mul
mul.b
[b, a, ...][c, ...]1
2
div
div.b
[b, a, ...][c, ...]2
2
. Fails if .
neg[a, ...][b, ...]1
inv[a, ...][b, ...]1. Fails if .
pow2[a, ...][b, ...]16. Fails if .
exp.uxx
exp.b
[b, a, ...][c, ...]9+xx
9+log2(b)
. Fails if is outside . exp is exp.u64 (73 cycles).
ilog2[a, ...][b, ...]44. Fails if .
not[a, ...][b, ...]1. Fails if .
and[b, a, ...][c, ...]1. Fails if .
or[b, a, ...][c, ...]1. Fails if .
xor[b, a, ...][c, ...]7. Fails if .

Extension Field Operations

InstructionStack InputStack OutputCyclesNotes
ext2add[b1, b0, a1, a0, ...][c1, c0, ...]5
ext2sub[b1, b0, a1, a0, ...][c1, c0, ...]7
ext2mul[b1, b0, a1, a0, ...][c1, c0, ...]3
ext2neg[a1, a0, ...][a1', a0', ...]4
ext2inv[a1, a0, ...][a1', a0', ...]8. Fails if .
ext2div[b1, b0, a1, a0, ...][c1, c0, ...]11. Fails if . Multiplication and inversion are as defined previously.

U32 Operations

Operations on 32-bit integers. Most instructions will fail or have undefined behavior if inputs are not valid u32 values.

Conversions and Tests

InstructionStack InputStack OutputCyclesNotes
u32test[a, ...][b, a, ...]5
u32testw[A, ...][b, A, ...]23
u32assert[a, ...][a, ...]3Fails if .
u32assert2[b, a,...][b, a,...]1Fails if or .
u32assertw[A, ...][A, ...]6Fails if any element of is .
u32cast[a, ...][b, ...]2
u32split[a, ...][c, b, ...]1,

Note: Assertions can be parameterized with an error message (e.g., assert.err="Division by 0").

Arithmetic Operations

InstructionStack InputStack OutputCyclesNotes
u32overflowing_add
u32overflowing_add.b
[b, a, ...][d, c, ...]1
2-3
, . Undefined if .
u32wrapping_add
u32wrapping_add.b
[b, a, ...][c, ...]2
3-4
. Undefined if .
u32overflowing_add3[c, b, a, ...][e, d, ...]1, . Undefined if .
u32wrapping_add3[c, b, a, ...][d, ...]2. Undefined if .
u32overflowing_sub
u32overflowing_sub.b
[b, a, ...][d, c, ...]1
2-3
, . Undefined if .
u32wrapping_sub
u32wrapping_sub.b
[b, a, ...][c, ...]2
3-4
. Undefined if .
u32overflowing_mul
u32overflowing_mul.b
[b, a, ...][d, c, ...]1
2-3
, . Undefined if .
u32wrapping_mul
u32wrapping_mul.b
[b, a, ...][c, ...]2
3-4
. Undefined if .
u32overflowing_madd[b, a, c, ...][e, d, ...]1, . Undefined if .
u32wrapping_madd[b, a, c, ...][d, ...]2. Undefined if .
u32div
u32div.b
[b, a, ...][c, ...]2
3-4
. Fails if . Undefined if .
u32mod
u32mod.b
[b, a, ...][c, ...]3
4-5
. Fails if . Undefined if .
u32divmod
u32divmod.b
[b, a, ...][d, c, ...]1
2-3
, . Fails if . Undefined if .

Bitwise Operations

InstructionStack InputStack OutputCyclesNotes
u32and
u32and.b
[b, a, ...][c, ...]1
2
Bitwise AND. Fails if .
u32or
u32or.b
[b, a, ...][c, ...]6
7
Bitwise OR. Fails if .
u32xor
u32xor.b
[b, a, ...][c, ...]1
2
Bitwise XOR. Fails if .
u32not
u32not.a
[a, ...][b, ...]5
6
Bitwise NOT. Fails if .
u32shl
u32shl.b
[b, a, ...][c, ...]18
3
. Undefined if or .
u32shr
u32shr.b
[b, a, ...][c, ...]18
3
. Undefined if or .
u32rotl
u32rotl.b
[b, a, ...][c, ...]18
3
Rotate left. Undefined if or .
u32rotr
u32rotr.b
[b, a, ...][c, ...]23
3
Rotate right. Undefined if or .
u32popcnt[a, ...][b, ...]33Population count (Hamming weight). Undefined if .
u32clz[a, ...][b, ...]42Count leading zeros. Undefined if .
u32ctz[a, ...][b, ...]34Count trailing zeros. Undefined if .
u32clo[a, ...][b, ...]41Count leading ones. Undefined if .
u32cto[a, ...][b, ...]33Count trailing ones. Undefined if .

Comparison Operations

InstructionStack InputStack OutputCyclesNotes
u32lt
u32lt.b
[b, a, ...][c, ...]3
4
. Undefined if .
u32lte
u32lte.b
[b, a, ...][c, ...]5
6
. Undefined if .
u32gt
u32gt.b
[b, a, ...][c, ...]4
5
. Undefined if .
u32gte
u32gte.b
[b, a, ...][c, ...]4
5
. Undefined if .
u32min
u32min.b
[b, a, ...][c, ...]8
9
. Undefined if .
u32max
u32max.b
[b, a, ...][c, ...]9
10
. Undefined if .

Stack Manipulation

Instructions for directly manipulating the operand stack. Only the top 16 elements are directly accessible.

InstructionStack InputStack OutputCyclesNotes
drop[a, ... ][ ... ]1Deletes the top stack item.
dropw[A, ... ][ ... ]4Deletes a word (4 elements) from the top of the stack.
padw[ ... ][0,0,0,0, ... ]4Pushes four 0 values onto the stack.
dup.n[ ..., a, ... ][a, ..., a, ... ]1-3Pushes a copy of the nth stack item (0-indexed) onto the stack. dup is dup.0. Valid for n in 0..=15.
dupw.n[ ..., A, ... ][A, ..., A, ... ]4Pushes a copy of the nth stack word (0-indexed) onto the stack. dupw is dupw.0. Valid for n in 0..=3.
swap.n[a, ..., b, ... ][b, ..., a, ... ]1-6Swaps the top stack item with the nth stack item (1-indexed). swap is swap.1. Valid for n in 1..=15.
swapw.n[A, ..., B, ... ][B, ..., A, ... ]1Swaps the top stack word with the nth stack word (1-indexed). swapw is swapw.1. Valid for n in 1..=3.
swapdw[D,C,B,A, ... ][B,A,D,C ... ]1Swaps words: 1st with 3rd, 2nd with 4th.
movup.n[ ..., a, ... ][a, ... ]1-4Moves the nth stack item (2-indexed) to the top. Valid for n in 2..=15.
movupw.n[ ..., A, ... ][A, ... ]2-3Moves the nth stack word (2-indexed) to the top. Valid for n in 2..=3.
movdn.n[a, ... ][ ..., a, ... ]1-4Moves the top stack item to the nth position (2-indexed). Valid for n in 2..=15.
movdnw.n[A, ... ][ ..., A, ... ]2-3Moves the top stack word to the nth word position (2-indexed). Valid for n in 2..=3.

Conditional Manipulation

InstructionStack InputStack OutputCyclesNotes
cswap[c, b, a, ... ][e, d, ... ]1If c = 1, d=b, e=a. If c = 0, d=a, e=b. Fails if c > 1.
cswapw[c, B, A, ... ][E, D, ... ]1If c = 1, D=B, E=A. If c = 0, D=A, E=B. Fails if c > 1.
cdrop[c, b, a, ... ][d, ... ]2If c = 1, d=b. If c = 0, d=a. Fails if c > 1.
cdropw[c, B, A, ... ][D, ... ]5If c = 1, D=B. If c = 0, D=A. Fails if c > 1.

Input/Output Operations

Instructions for moving data between the stack and other sources like program code, environment, advice provider, and memory.

Constant Inputs

InstructionStack InputStack OutputCyclesNotes
push.a...[ ... ][c, b, a, ...]1-2Pushes up to 16 field elements (decimal or hex) onto the stack. Hex words (32 bytes) are little-endian; short hex values are big-endian. Example: push.0x1234.0x5678 or push.0x34120000...78560000...

Environment Inputs

InstructionStack InputStack OutputCyclesNotes
clk[ ... ][t, ... ]1Pushes current clock cycle t.
sdepth[ ... ][d, ... ]1Pushes current stack depth d.
caller[A, b,...][H, b,...]1Overwrites top 4 stack items with hash H of the function that initiated the current SYSCALL. Fails if not in SYSCALL.
locaddr.i[ ... ][a, ... ]2Pushes absolute memory address a of local memory at index i.
procref.name[ ... ][A, ... ]4Pushes MAST root A of procedure name.

Nondeterministic Inputs (Advice Provider)

Reading from Advice Stack

InstructionStack InputStack OutputCyclesNotes
adv_push.n[ ... ][a, ...]nPops n values from advice stack to operand stack (1st popped is deepest). Valid n in 1..=16. Fails if advice stack has < n values.
adv_loadw[0,0,0,0, ...][A, ...]1Pops word A (4 elements) from advice stack, overwrites top word of operand stack. Fails if advice stack has < 4 values.
adv_pipe[C,B,A,a,...][E,D,A,a',...]1Pops 2 words [D,E] from advice stack. Overwrites top 2 words of operand stack. Writes [D,E] to memory at a and a+1. a' <- a+2. Fails if advice stack has < 8 values.

Injecting into Advice Provider (System Events - 0 cycles)

Push to Advice Stack:

InstructionStack InputStack OutputNotes
adv.push_mapval[K, ... ][K, ... ]Pushes values from advice_map[K] to advice stack.
adv.push_mapvaln[K, ... ][K, ... ]Pushes [n, ele1, ele2, ...] from advice_map[K] to advice stack, where n is element count.
adv.push_mtnode[d, i, R, ... ][d, i, R, ... ]Pushes Merkle tree node (root R, depth d, index i) from Merkle store to advice stack.
adv.push_u64div[b1, b0, a1, a0, ...][b1, b0, a1, a0, ...]Pushes quotient and remainder of u64 division a/b (represented by 32-bit limbs) to advice stack.
adv.push_ext2intt[osize,isize,iptr,...][osize,isize,iptr,...]Interpolates polynomial evaluations (from memory at iptr, isize evals) and pushes coefficients (osize) to advice stack.
adv.push_smtpeek[K, R, ...][K, R, ...]Pushes value for key K in Sparse Merkle Tree with root R to advice stack.

Insert into Advice Map:

InstructionStack InputStack OutputNotes
adv.insert_mem[K, a, b, ... ][K, a, b, ... ]advice_map[K] <- mem[a..b].
adv.insert_hdword[B, A, ... ][B, A, ... ]K <- hash(A || B, domain=0). advice_map[K] <- [A,B].
adv.insert_hdword_d[B, A, d, ... ][B, A, d, ... ]K <- hash(A || B, domain=d). advice_map[K] <- [A,B].
adv.insert_hperm[B, A, C, ...][B, A, C, ...]K <- permute(C,A,B).digest. advice_map[K] <- [A,B].

Random Access Memory

Memory is 0-initialized. Addresses are absolute [0, 2^32). Locals are stored at offset 2^30.

Absolute Addressing

InstructionStack InputStack OutputCyclesNotes
mem_load
mem_load.a
[a, ... ][v, ... ]1
2
v <- mem[a]. Pushes element from mem[a]. If a on stack, it's popped. Fails if a >= 2^32.
mem_loadw
mem_loadw.a
[a, 0,0,0,0,...][A, ... ]1
2
A <- mem[a..a+3] (word). Overwrites top 4 stack elements (mem[a+3] is top). If a on stack, it's popped. Fails if a >= 2^32 or a not multiple of 4.
mem_store
mem_store.a
[a, v, ... ][ ... ]2
3-4
mem[a] <- v. Pops v to mem[a]. If a on stack, it's popped. Fails if a >= 2^32.
mem_storew
mem_storew.a
[a, A, ... ][A, ... ]1
2-3
mem[a..a+3] <- A. Stores word A (top stack element at mem[a+3]). If a on stack, it's popped. Fails if a >= 2^32 or a not multiple of 4.
mem_stream[C, B, A, a, ... ][E,D,A,a',...]1[E,D] <- [mem[a..a+3], mem[a+4..a+7]]. a' <- a+8. Reads 2 sequential words from memory to top of stack.

Procedure Locals (Context-Specific)

Locals are not 0-initialized. Max locals per procedure, total. Rounded up to multiple of 4.

InstructionStack InputStack OutputCyclesNotes
loc_load.i[ ... ][v, ... ]3-4v <- local[i]. Pushes element from local memory at index i.
loc_loadw.i[0,0,0,0, ...][A, ... ]3-4A <- local[i..i+3]. Reads word, local[i+3] is top of stack. Fails if i not multiple of 4.
loc_store.i[v, ... ][ ... ]4-5local[i] <- v. Pops v to local memory at index i.
loc_storew.i[A, ... ][A, ... ]3-4local[i..i+3] <- A. Stores word, top stack element at local[i+3].

Cryptographic Operations

Common cryptographic operations, including hashing and Merkle tree manipulations using Rescue Prime Optimized.

Hashing and Merkle Trees

InstructionStack InputStack OutputCyclesNotes
hash[A, ...][B, ...]20B <- hash(A). 1-to-1 Rescue Prime Optimized hash.
hperm[B, A, C, ...][F, E, D, ...]1D,E,F <- permute(C,A,B). Rescue Prime Optimized permutation. C=capacity, A,B=rate, E=digest.
hmerge[B, A, ...][C, ...]16C <- hash(A,B). 2-to-1 Rescue Prime Optimized hash.
mtree_get[d, i, R, ...][V, R, ...]9Verifies Merkle path for node V at depth d, index i for tree R (from advice provider), returns V.
mtree_set[d, i, R, V', ...][V, R', ...]29Updates node in tree R at d,i to V'. Returns old value V and new root R'. Both trees in advice provider.
mtree_merge[R, L, ...][M, ...]16Merges Merkle trees with roots L (left) and R (right) into new tree M. Input trees retained.
mtree_verify[V, d, i, R, ...][V,d,i,R,...]1Verifies Merkle path for node V at depth d, index i for tree R (from advice provider).
Can be parameterized with err code (e.g., mtree_verify.err=123). Default error code is 0.

Flow Control Operations

High-level constructs for controlling the execution flow.

Conditional Execution: if.true ... else ... end / if.false ... else ... end

  • Syntax:
    if.true
      # instructions for true branch
    else
      # instructions for false branch
    end
    
    Or with if.false (condition inverted). The else block is optional.
  • Stack Input: [cond, ...] (where cond is 0 or 1)
  • Cycles: Incurs a small overhead. For simple conditionals, cdrop might be more efficient if side-effects can be managed.
  • Notes:
    • Pops cond from the stack. Fails if not boolean.
    • if.true: Executes first block if cond = 1, second (else) block if cond = 0.
    • if.false: Executes first block if cond = 0, second (else) block if cond = 1.
    • Empty or elided branches are treated as a nop.
    • Ensure stack consistency at join points if modifications persist beyond a branch.

Counter-Controlled Loops: repeat.count ... end

  • Syntax:
    repeat.COUNT
      # instructions to repeat
    end
    
  • Cycles: No additional cost for counting; the block is unrolled COUNT times during compilation.
  • Notes:
    • COUNT must be an integer or a named constant greater than 0.
    • Instructions inside can include nested control structures.

Condition-Controlled Loops: while.true ... end

  • Syntax:
    while.true
      # instructions for loop body
    end
    
  • Stack Input (for each iteration check): [cond, ...] (where cond is 0 or 1)
  • Cycles: Overhead per iteration for condition check.
  • Notes:
    1. Pops cond from the stack. If 0, skips loop. Fails if not boolean.
    2. If cond = 1, executes loop body.
    3. After body execution, pops a new cond. If 1, repeats body. If 0, exits loop. Fails if not boolean.

No-Operation: nop

  • Syntax: nop
  • Cycles: 1
  • Notes:
    • Increments the cycle counter with no other effects.
    • Useful for empty blocks or explicitly advancing cycles.
    • Assembler automatically inserts nop for empty/elided branches in if statements.

Debugging Operations

Instructions for inspecting VM state during execution. These do not affect VM state or program hash and are only active when the assembler is in debug mode.

debug

  • Syntax & Parameters:
    • debug.stack: Prints entire stack.
    • debug.stack.N: Prints top N stack items (0 < N < 256).
    • debug.mem: Prints entire RAM.
    • debug.mem.A: Prints memory at address A.
    • debug.mem.A.M: Prints memory from address A to M (inclusive, M >= A).
    • debug.local: Prints entire local memory of the current procedure.
    • debug.local.I: Prints local memory at index I (0 <= I < 65536).
    • debug.local.I.M: Prints local memory from index I to M (inclusive, M >= I, 0 <= I, M < 65536).
  • Cycles: 0 (does not consume VM cycles).
  • Notes:
    • Prints the specified part of the VM state.
    • Ignored if assembler is not in debug mode.