Miden Assembly (MASM)

Miden assembly is a low-level language for Miden VM, a stack-based zero-knowledge virtual machine.

Key Concepts

Stack Machine

• Operand stack holds field elements (prime field p = 2^64 - 2^32 + 1)
• Top 16 elements directly accessible
• A word = 4 field elements
• Stack grows upward;

  push

  adds to top, operations consume from top

Stack Notation

• [a, b, ...]

  means

  a

  is on top,

  b

  below
• Operations consume inputs and push outputs
• Example:

  add

  with

  [3, 5, ...]

  produces

  [8, ...]

Quick Reference

Basic Operations

# Arithmetic (field elements)
push.5 push.3 add    # [8, ...]
push.10 push.2 sub   # [8, ...]
push.4 push.3 mul    # [12, ...]

# Stack manipulation
dup.0                # Duplicate top
swap                 # Swap top two
drop                 # Remove top
movup.2              # Move 3rd item to top

# Memory
push.42 mem_store.100        # mem[100] = 42
push.100 mem_load            # push mem[100]

# Control flow
push.1
if.true
    push.10
else
    push.20
end

push.5
dup.0 neq.0
while.true
    push.1 sub
    dup.0 neq.0
end
drop

Program Structure

# Import from core library
use miden::core::math::u64

# Constants
const ADDR = 100
const LIMIT = 1000

# Private procedure with locals
@locals(4)
proc helper
    loc_store.0    # Store to local
    loc_load.0     # Load from local
end

# Public procedure (exported)
pub proc api_function
    exec.helper
end

# Program entry point
begin
    push.42
    exec.api_function
end

Reference Files

Load these as needed for detailed information:

• instruction_reference.md: Complete instruction set with stack effects and cycle counts
• code_organization.md: Procedures, modules, constants, types, execution contexts
• core_library.md: Standard library modules (u64, hashes, memory, etc.)

Common Patterns

U32 Operations

# u32 values must be < 2^32
push.100 push.50 u32wrapping_add   # 150
push.100 push.50 u32lt             # 0 (100 < 50 is false)
push.0xFF push.0x0F u32and         # 0x0F

U64 Operations (via core library)

use miden::core::math::u64

# u64 = [hi, lo] on stack, with lo deeper (push lo first, then hi)
push.100.0 push.50.0    # Two u64s: 100, 50
exec.u64::wrapping_add  # Result: [0, 150]

Conditional Selection

# cdrop: select based on condition
push.10 push.20 push.1 cdrop   # [20, ...] (cond=1 selects b)
push.10 push.20 push.0 cdrop   # [10, ...] (cond=0 selects a)

Loop with Counter

# repeat.N - compile-time unrolled
repeat.5
    push.1 add
end

# while.true - runtime condition
push.1
while.true
    # loop body
    # must push 0 or 1 for next iteration check
    push.0   # exit after one iteration
end

Memory Words

# Store/load 4 elements as word
padw                        # [0, 0, 0, 0, ...]
push.1.2.3.4               # [4, 3, 2, 1, 0, 0, 0, 0, ...]
push.100 mem_storew_be     # Store word at addr 100
dropw padw                 # Clear and prepare
push.100 mem_loadw_be      # Load word from addr 100

Procedure Locals

@locals(8)
proc with_locals
    push.42 loc_store.0     # Store to local[0]
    loc_load.0              # Load from local[0]

    # Word loads (loc_loadw_*) require indices divisible by 4
    padw loc_storew_be.4    # Store word at local[4..7]
end

Hashing

# Single word hash
push.1.2.3.4 hash          # [digest_word, ...]

# Merge two words
push.1.2.3.4 push.5.6.7.8 hmerge  # [digest_word, ...]

Debugging

# Only active in debug mode
debug.stack        # Print entire stack
debug.stack.8      # Print top 8 items
debug.mem.100      # Print memory at address 100
debug.local        # Print procedure locals

# Tracing (requires -t flag)
trace.1            # Emit trace event

Best Practices

1. Validate inputs: Use

   u32assert

   ,

   assert

   before operations with preconditions
2. Track stack state: Comment stack layout at key points
3. Minimize cycles: Check cycle counts for hot paths
4. Use locals sparingly: They have overhead vs. stack manipulation
5. Word-align memory: Load/store words at addresses divisible by 4
6. Return correctly:

   call

   /

   dyncall

   /

   syscall

   require stack depth = 16 on return

Error Patterns

# Division by zero
push.10 push.0 div      # FAILS

# Boolean required
push.2
if.true                 # FAILS: 2 is not boolean
end

# u32 range check
push.0x100000000 u32assert  # FAILS: value >= 2^32