#################
Solidity Assembly
#################

.. index:: ! assembly, ! asm, ! evmasm

Solidity defines an assembly language that you can use without Solidity and also
as "inline assembly" inside Solidity source code. This guide starts with describing
how to use inline assembly, how it differs from standalone assembly, and
specifies assembly itself.

.. _inline-assembly:

Inline Assembly
===============

You can interleave Solidity statements with inline assembly in a language close
to the one of the virtual machine. This gives you more fine-grained control,
especially when you are enhancing the language by writing libraries.

As the EVM is a stack machine, it is often hard to address the correct stack slot
and provide arguments to opcodes at the correct point on the stack. Solidity's inline
assembly helps you do this, and with other issues that arise when writing manual assembly.

Inline assembly has the following features:

* functional-style opcodes: ``mul(1, add(2, 3))``
* assembly-local variables: ``let x := add(2, 3)  let y := mload(0x40)  x := add(x, y)``
* access to external variables: ``function f(uint x) public { assembly { x := sub(x, 1) } }``
* loops: ``for { let i := 0 } lt(i, x) { i := add(i, 1) } { y := mul(2, y) }``
* if statements: ``if slt(x, 0) { x := sub(0, x) }``
* switch statements: ``switch x case 0 { y := mul(x, 2) } default { y := 0 }``
* function calls: ``function f(x) -> y { switch x case 0 { y := 1 } default { y := mul(x, f(sub(x, 1))) }   }``

.. warning::
    Inline assembly is a way to access the Ethereum Virtual Machine
    at a low level. This bypasses several important safety
    features and checks of Solidity. You should only use it for
    tasks that need it, and only if you are confident with using it.

Syntax
------

Assembly parses comments, literals and identifiers in the same way as Solidity, so you can use the
usual ``//`` and ``/* */`` comments. Inline assembly is marked by ``assembly { ... }`` and inside
these curly braces, you can use the following (see the later sections for more details):

 - literals, i.e. ``0x123``, ``42`` or ``"abc"`` (strings up to 32 characters)
 - opcodes in functional style, e.g. ``add(1, mlod(0))``
 - variable declarations, e.g. ``let x := 7``, ``let x := add(y, 3)`` or ``let x`` (initial value of empty (0) is assigned)
 - identifiers (assembly-local variables and externals if used as inline assembly), e.g. ``add(3, x)``, ``sstore(x_slot, 2)``
 - assignments, e.g. ``x := add(y, 3)``
 - blocks where local variables are scoped inside, e.g. ``{ let x := 3 { let y := add(x, 1) } }``

The following features are only available for standalone assembly:

 - direct stack control via ``dup1``, ``swap1``, ...
 - direct stack assignments (in "instruction style"), e.g. ``3 =: x``
 - labels, e.g. ``name:``
 - jump opcodes

.. note::
  Standalone assembly is supported for backwards compatibility but is not documented
  here anymore.

At the end of the ``assembly { ... }`` block, the stack must be balanced,
unless you require it otherwise. If it is not balanced, the compiler generates
a warning.

Example
-------

The following example provides library code to access the code of another contract and
load it into a ``bytes`` variable. This is not possible with "plain Solidity" and the
idea is that assembly libraries will be used to enhance the Solidity language.

.. code::

    pragma solidity >=0.4.0 <0.6.0;

    library GetCode {
        function at(address _addr) public view returns (bytes memory o_code) {
            assembly {
                // retrieve the size of the code, this needs assembly
                let size := extcodesize(_addr)
                // allocate output byte array - this could also be done without assembly
                // by using o_code = new bytes(size)
                o_code := mload(0x40)
                // new "memory end" including padding
                mstore(0x40, add(o_code, and(add(add(size, 0x20), 0x1f), not(0x1f))))
                // store length in memory
                mstore(o_code, size)
                // actually retrieve the code, this needs assembly
                extcodecopy(_addr, add(o_code, 0x20), 0, size)
            }
        }
    }

Inline assembly is also beneficial in cases where the optimizer fails to produce
efficient code, for example:

.. code::

    pragma solidity >=0.4.16 <0.6.0;

    library VectorSum {
        // This function is less efficient because the optimizer currently fails to
        // remove the bounds checks in array access.
        function sumSolidity(uint[] memory _data) public pure returns (uint o_sum) {
            for (uint i = 0; i < _data.length; ++i)
                o_sum += _data[i];
        }

        // We know that we only access the array in bounds, so we can avoid the check.
        // 0x20 needs to be added to an array because the first slot contains the
        // array length.
        function sumAsm(uint[] memory _data) public pure returns (uint o_sum) {
            for (uint i = 0; i < _data.length; ++i) {
                assembly {
                    o_sum := add(o_sum, mload(add(add(_data, 0x20), mul(i, 0x20))))
                }
            }
        }

        // Same as above, but accomplish the entire code within inline assembly.
        function sumPureAsm(uint[] memory _data) public pure returns (uint o_sum) {
            assembly {
               // Load the length (first 32 bytes)
               let len := mload(_data)

               // Skip over the length field.
               //
               // Keep temporary variable so it can be incremented in place.
               //
               // NOTE: incrementing _data would result in an unusable
               //       _data variable after this assembly block
               let data := add(_data, 0x20)

               // Iterate until the bound is not met.
               for
                   { let end := add(data, mul(len, 0x20)) }
                   lt(data, end)
                   { data := add(data, 0x20) }
               {
                   o_sum := add(o_sum, mload(data))
               }
            }
        }
    }


.. _opcodes:

Opcodes
-------

This document does not want to be a full description of the Ethereum virtual machine, but the
following list can be used as a reference of its opcodes.

If an opcode takes arguments (always from the top of the stack), they are given in parentheses.
Note that the order of arguments can be seen to be reversed in non-functional style (explained below).
Opcodes marked with ``-`` do not push an item onto the stack, those marked with ``*`` are
special and all others push exactly one item onto the stack.
Opcodes marked with ``F``, ``H``, ``B`` or ``C`` are present since Frontier, Homestead, Byzantium or Constantinople, respectively.
Constantinople is still in planning and all instructions marked as such will result in an invalid instruction exception.

In the following, ``mem[a...b)`` signifies the bytes of memory starting at position ``a`` up to
but not including position ``b`` and ``storage[p]`` signifies the storage contents at position ``p``.

The opcodes ``pushi`` and ``jumpdest`` cannot be used directly.

In the grammar, opcodes are represented as pre-defined identifiers.

+-------------------------+-----+---+-----------------------------------------------------------------+
| Instruction             |     |   | Explanation                                                     |
+=========================+=====+===+=================================================================+
| stop                    + `-` | F | stop execution, identical to return(0,0)                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| add(x, y)               |     | F | x + y                                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sub(x, y)               |     | F | x - y                                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mul(x, y)               |     | F | x * y                                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| div(x, y)               |     | F | x / y                                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sdiv(x, y)              |     | F | x / y, for signed numbers in two's complement                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mod(x, y)               |     | F | x % y                                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| smod(x, y)              |     | F | x % y, for signed numbers in two's complement                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| exp(x, y)               |     | F | x to the power of y                                             |
+-------------------------+-----+---+-----------------------------------------------------------------+
| not(x)                  |     | F | ~x, every bit of x is negated                                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| lt(x, y)                |     | F | 1 if x < y, 0 otherwise                                         |
+-------------------------+-----+---+-----------------------------------------------------------------+
| gt(x, y)                |     | F | 1 if x > y, 0 otherwise                                         |
+-------------------------+-----+---+-----------------------------------------------------------------+
| slt(x, y)               |     | F | 1 if x < y, 0 otherwise, for signed numbers in two's complement |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sgt(x, y)               |     | F | 1 if x > y, 0 otherwise, for signed numbers in two's complement |
+-------------------------+-----+---+-----------------------------------------------------------------+
| eq(x, y)                |     | F | 1 if x == y, 0 otherwise                                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| iszero(x)               |     | F | 1 if x == 0, 0 otherwise                                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| and(x, y)               |     | F | bitwise and of x and y                                          |
+-------------------------+-----+---+-----------------------------------------------------------------+
| or(x, y)                |     | F | bitwise or of x and y                                           |
+-------------------------+-----+---+-----------------------------------------------------------------+
| xor(x, y)               |     | F | bitwise xor of x and y                                          |
+-------------------------+-----+---+-----------------------------------------------------------------+
| byte(n, x)              |     | F | nth byte of x, where the most significant byte is the 0th byte  |
+-------------------------+-----+---+-----------------------------------------------------------------+
| shl(x, y)               |     | C | logical shift left y by x bits                                  |
+-------------------------+-----+---+-----------------------------------------------------------------+
| shr(x, y)               |     | C | logical shift right y by x bits                                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sar(x, y)               |     | C | arithmetic shift right y by x bits                              |
+-------------------------+-----+---+-----------------------------------------------------------------+
| addmod(x, y, m)         |     | F | (x + y) % m with arbitrary precision arithmetic                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mulmod(x, y, m)         |     | F | (x * y) % m with arbitrary precision arithmetic                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| signextend(i, x)        |     | F | sign extend from (i*8+7)th bit counting from least significant  |
+-------------------------+-----+---+-----------------------------------------------------------------+
| keccak256(p, n)         |     | F | keccak(mem[p...(p+n)))                                          |
+-------------------------+-----+---+-----------------------------------------------------------------+
| jump(label)             | `-` | F | jump to label / code position                                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| jumpi(label, cond)      | `-` | F | jump to label if cond is nonzero                                |
+-------------------------+-----+---+-----------------------------------------------------------------+
| pc                      |     | F | current position in code                                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| pop(x)                  | `-` | F | remove the element pushed by x                                  |
+-------------------------+-----+---+-----------------------------------------------------------------+
| dup1 ... dup16          |     | F | copy nth stack slot to the top (counting from top)              |
+-------------------------+-----+---+-----------------------------------------------------------------+
| swap1 ... swap16        | `*` | F | swap topmost and nth stack slot below it                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mload(p)                |     | F | mem[p...(p+32))                                                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mstore(p, v)            | `-` | F | mem[p...(p+32)) := v                                            |
+-------------------------+-----+---+-----------------------------------------------------------------+
| mstore8(p, v)           | `-` | F | mem[p] := v & 0xff (only modifies a single byte)                |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sload(p)                |     | F | storage[p]                                                      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| sstore(p, v)            | `-` | F | storage[p] := v                                                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| msize                   |     | F | size of memory, i.e. largest accessed memory index              |
+-------------------------+-----+---+-----------------------------------------------------------------+
| gas                     |     | F | gas still available to execution                                |
+-------------------------+-----+---+-----------------------------------------------------------------+
| address                 |     | F | address of the current contract / execution context             |
+-------------------------+-----+---+-----------------------------------------------------------------+
| balance(a)              |     | F | wei balance at address a                                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| caller                  |     | F | call sender (excluding ``delegatecall``)                        |
+-------------------------+-----+---+-----------------------------------------------------------------+
| callvalue               |     | F | wei sent together with the current call                         |
+-------------------------+-----+---+-----------------------------------------------------------------+
| calldataload(p)         |     | F | call data starting from position p (32 bytes)                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| calldatasize            |     | F | size of call data in bytes                                      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| calldatacopy(t, f, s)   | `-` | F | copy s bytes from calldata at position f to mem at position t   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| codesize                |     | F | size of the code of the current contract / execution context    |
+-------------------------+-----+---+-----------------------------------------------------------------+
| codecopy(t, f, s)       | `-` | F | copy s bytes from code at position f to mem at position t       |
+-------------------------+-----+---+-----------------------------------------------------------------+
| extcodesize(a)          |     | F | size of the code at address a                                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| extcodecopy(a, t, f, s) | `-` | F | like codecopy(t, f, s) but take code at address a               |
+-------------------------+-----+---+-----------------------------------------------------------------+
| returndatasize          |     | B | size of the last returndata                                     |
+-------------------------+-----+---+-----------------------------------------------------------------+
| returndatacopy(t, f, s) | `-` | B | copy s bytes from returndata at position f to mem at position t |
+-------------------------+-----+---+-----------------------------------------------------------------+
| extcodehash(a)          |     | C | code hash of address a                                          |
+-------------------------+-----+---+-----------------------------------------------------------------+
| create(v, p, s)         |     | F | create new contract with code mem[p...(p+s)) and send v wei     |
|                         |     |   | and return the new address                                      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| create2(v, n, p, s)     |     | C | create new contract with code mem[p...(p+s)) at address         |
|                         |     |   | keccak256(0xff . self . n . keccak256(mem[p...(p+s)))           |
|                         |     |   | and send v wei and return the new address, where ``0xff`` is a  |
|                         |     |   | 8 byte value, ``self`` is the current contract's address        |
|                         |     |   | as a 20 byte value and ``n`` is a big-endian 256-bit value      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| call(g, a, v, in,       |     | F | call contract at address a with input mem[in...(in+insize))     |
| insize, out, outsize)   |     |   | providing g gas and v wei and output area                       |
|                         |     |   | mem[out...(out+outsize)) returning 0 on error (eg. out of gas)  |
|                         |     |   | and 1 on success                                                |
+-------------------------+-----+---+-----------------------------------------------------------------+
| callcode(g, a, v, in,   |     | F | identical to ``call`` but only use the code from a and stay     |
| insize, out, outsize)   |     |   | in the context of the current contract otherwise                |
+-------------------------+-----+---+-----------------------------------------------------------------+
| delegatecall(g, a, in,  |     | H | identical to ``callcode`` but also keep ``caller``              |
| insize, out, outsize)   |     |   | and ``callvalue``                                               |
+-------------------------+-----+---+-----------------------------------------------------------------+
| staticcall(g, a, in,    |     | B | identical to ``call(g, a, 0, in, insize, out, outsize)`` but do |
| insize, out, outsize)   |     |   | not allow state modifications                                   |
+-------------------------+-----+---+-----------------------------------------------------------------+
| return(p, s)            | `-` | F | end execution, return data mem[p...(p+s))                       |
+-------------------------+-----+---+-----------------------------------------------------------------+
| revert(p, s)            | `-` | B | end execution, revert state changes, return data mem[p...(p+s)) |
+-------------------------+-----+---+-----------------------------------------------------------------+
| selfdestruct(a)         | `-` | F | end execution, destroy current contract and send funds to a     |
+-------------------------+-----+---+-----------------------------------------------------------------+
| invalid                 | `-` | F | end execution with invalid instruction                          |
+-------------------------+-----+---+-----------------------------------------------------------------+
| log0(p, s)              | `-` | F | log without topics and data mem[p...(p+s))                      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| log1(p, s, t1)          | `-` | F | log with topic t1 and data mem[p...(p+s))                       |
+-------------------------+-----+---+-----------------------------------------------------------------+
| log2(p, s, t1, t2)      | `-` | F | log with topics t1, t2 and data mem[p...(p+s))                  |
+-------------------------+-----+---+-----------------------------------------------------------------+
| log3(p, s, t1, t2, t3)  | `-` | F | log with topics t1, t2, t3 and data mem[p...(p+s))              |
+-------------------------+-----+---+-----------------------------------------------------------------+
| log4(p, s, t1, t2, t3,  | `-` | F | log with topics t1, t2, t3, t4 and data mem[p...(p+s))          |
| t4)                     |     |   |                                                                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| origin                  |     | F | transaction sender                                              |
+-------------------------+-----+---+-----------------------------------------------------------------+
| gasprice                |     | F | gas price of the transaction                                    |
+-------------------------+-----+---+-----------------------------------------------------------------+
| blockhash(b)            |     | F | hash of block nr b - only for last 256 blocks excluding current |
+-------------------------+-----+---+-----------------------------------------------------------------+
| coinbase                |     | F | current mining beneficiary                                      |
+-------------------------+-----+---+-----------------------------------------------------------------+
| timestamp               |     | F | timestamp of the current block in seconds since the epoch       |
+-------------------------+-----+---+-----------------------------------------------------------------+
| number                  |     | F | current block number                                            |
+-------------------------+-----+---+-----------------------------------------------------------------+
| difficulty              |     | F | difficulty of the current block                                 |
+-------------------------+-----+---+-----------------------------------------------------------------+
| gaslimit                |     | F | block gas limit of the current block                            |
+-------------------------+-----+---+-----------------------------------------------------------------+

Literals
--------

You can use integer constants by typing them in decimal or hexadecimal notation and an
appropriate ``PUSHi`` instruction will automatically be generated. The following creates code
to add 2 and 3 resulting in 5 and then computes the bitwise and with the string "abc".
The final value is assigned to a local variable called ``x``.
Strings are stored left-aligned and cannot be longer than 32 bytes.

.. code::

    assembly { let x := and("abc", add(3, 2)) }


Functional Style
-----------------

For a sequence of opcodes, it is often hard to see what the actual
arguments for certain opcodes are. In the following example,
``3`` is added to the contents in memory at position ``0x80``.

.. code::

    3 0x80 mload add 0x80 mstore

Solidity inline assembly has a "functional style" notation where the same code
would be written as follows:

.. code::

    mstore(0x80, add(mload(0x80), 3))

If you read the code from right to left, you end up with exactly the same
sequence of constants and opcodes, but it is much clearer where the
values end up.

If you care about the exact stack layout, just note that the
syntactically first argument for a function or opcode will be put at the
top of the stack.

Access to External Variables, Functions and Libraries
-----------------------------------------------------

You can access Solidity variables and other identifiers by using their name.
For variables stored in the memory data location, this pushes the address, and not the value
onto the stack. Variables stored in the storage data location are different, as they might not
occupy a full storage slot, so their "address" is composed of a slot and a byte-offset
inside that slot. To retrieve the slot pointed to by the variable ``x``, you
use ``x_slot``, and to retrieve the byte-offset you use ``x_offset``.

Local Solidity variables are available for assignments, for example:

.. code::

    pragma solidity >=0.4.11 <0.6.0;

    contract C {
        uint b;
        function f(uint x) public view returns (uint r) {
            assembly {
                r := mul(x, sload(b_slot)) // ignore the offset, we know it is zero
            }
        }
    }

.. warning::
    If you access variables of a type that spans less than 256 bits
    (for example ``uint64``, ``address``, ``bytes16`` or ``byte``),
    you cannot make any assumptions about bits not part of the
    encoding of the type. Especially, do not assume them to be zero.
    To be safe, always clear the data properly before you use it
    in a context where this is important:
    ``uint32 x = f(); assembly { x := and(x, 0xffffffff) /* now use x */ }``
    To clean signed types, you can use the ``signextend`` opcode.

Labels
------

Support for labels has been removed in version 0.5.0 of Solidity.
Please use functions, loops, if or switch statements instead.

Declaring Assembly-Local Variables
----------------------------------

You can use the ``let`` keyword to declare variables that are only visible in
inline assembly and actually only in the current ``{...}``-block. What happens
is that the ``let`` instruction will create a new stack slot that is reserved
for the variable and automatically removed again when the end of the block
is reached. You need to provide an initial value for the variable which can
be just ``0``, but it can also be a complex functional-style expression.

.. code::

    pragma solidity >=0.4.16 <0.6.0;

    contract C {
        function f(uint x) public view returns (uint b) {
            assembly {
                let v := add(x, 1)
                mstore(0x80, v)
                {
                    let y := add(sload(v), 1)
                    b := y
                } // y is "deallocated" here
                b := add(b, v)
            } // v is "deallocated" here
        }
    }


Assignments
-----------

Assignments are possible to assembly-local variables and to function-local
variables. Take care that when you assign to variables that point to
memory or storage, you will only change the pointer and not the data.

Variables can only be assigned expressions that result in exactly one value.
If you want to assign the values returned from a function that has
multiple return parameters, you have to provide multiple variables.

.. code::

    {
        let v := 0
        let g := add(v, 2)
        function f() -> a, b { }
        let c, d := f()
    }

If
--

The if statement can be used for conditionally executing code.
There is no "else" part, consider using "switch" (see below) if
you need multiple alternatives.

.. code::

    {
        if eq(value, 0) { revert(0, 0) }
    }

The curly braces for the body are required.

Switch
------

You can use a switch statement as a very basic version of "if/else".
It takes the value of an expression and compares it to several constants.
The branch corresponding to the matching constant is taken. Contrary to the
error-prone behaviour of some programming languages, control flow does
not continue from one case to the next. There can be a fallback or default
case called ``default``.

.. code::

    {
        let x := 0
        switch calldataload(4)
        case 0 {
            x := calldataload(0x24)
        }
        default {
            x := calldataload(0x44)
        }
        sstore(0, div(x, 2))
    }

The list of cases does not require curly braces, but the body of a
case does require them.

Loops
-----

Assembly supports a simple for-style loop. For-style loops have
a header containing an initializing part, a condition and a post-iteration
part. The condition has to be a functional-style expression, while
the other two are blocks. If the initializing part
declares any variables, the scope of these variables is extended into the
body (including the condition and the post-iteration part).

The following example computes the sum of an area in memory.

.. code::

    {
        let x := 0
        for { let i := 0 } lt(i, 0x100) { i := add(i, 0x20) } {
            x := add(x, mload(i))
        }
    }

For loops can also be written so that they behave like while loops:
Simply leave the initialization and post-iteration parts empty.

.. code::

    {
        let x := 0
        let i := 0
        for { } lt(i, 0x100) { } {     // while(i < 0x100)
            x := add(x, mload(i))
            i := add(i, 0x20)
        }
    }

Functions
---------

Assembly allows the definition of low-level functions. These take their
arguments (and a return PC) from the stack and also put the results onto the
stack. Calling a function looks the same way as executing a functional-style
opcode.

Functions can be defined anywhere and are visible in the block they are
declared in. Inside a function, you cannot access local variables
defined outside of that function. There is no explicit ``return``
statement.

If you call a function that returns multiple values, you have to assign
them to a tuple using ``a, b := f(x)`` or ``let a, b := f(x)``.

The following example implements the power function by square-and-multiply.

.. code::

    {
        function power(base, exponent) -> result {
            switch exponent
            case 0 { result := 1 }
            case 1 { result := base }
            default {
                result := power(mul(base, base), div(exponent, 2))
                switch mod(exponent, 2)
                    case 1 { result := mul(base, result) }
            }
        }
    }

Things to Avoid
---------------

Inline assembly might have a quite high-level look, but it actually is extremely
low-level. Function calls, loops, ifs and switches are converted by simple
rewriting rules and after that, the only thing the assembler does for you is re-arranging
functional-style opcodes, counting stack height for
variable access and removing stack slots for assembly-local variables when the end
of their block is reached.

Conventions in Solidity
-----------------------

In contrast to EVM assembly, Solidity knows types which are narrower than 256 bits,
e.g. ``uint24``. In order to make them more efficient, most arithmetic operations just
treat them as 256-bit numbers and the higher-order bits are only cleaned at the
point where it is necessary, i.e. just shortly before they are written to memory
or before comparisons are performed. This means that if you access such a variable
from within inline assembly, you might have to manually clean the higher order bits
first.

Solidity manages memory in a very simple way: There is a "free memory pointer"
at position ``0x40`` in memory. If you want to allocate memory, just use the memory
starting from where this pointer points at and update it accordingly.
There is no guarantee that the memory has not been used before and thus
you cannot assume that its contents are zero bytes.
There is no built-in mechanism to release or free allocated memory.
Here is an assembly snippet that can be used for allocating memory::

    function allocate(length) -> pos {
      pos := mload(0x40)
      mstore(0x40, add(pos, length))
    }

The first 64 bytes of memory can be used as "scratch space" for short-term
allocation. The 32 bytes after the free memory pointer (i.e. starting at ``0x60``)
is meant to be zero permanently and is used as the initial value for
empty dynamic memory arrays.
This means that the allocatable memory starts at ``0x80``, which is the initial value
of the free memory pointer.

Elements in memory arrays in Solidity always occupy multiples of 32 bytes (yes, this is
even true for ``byte[]``, but not for ``bytes`` and ``string``). Multi-dimensional memory
arrays are pointers to memory arrays. The length of a dynamic array is stored at the
first slot of the array and followed by the array elements.

.. warning::
    Statically-sized memory arrays do not have a length field, but it might be added later
    to allow better convertibility between statically- and dynamically-sized arrays, so
    please do not rely on that.


Standalone Assembly
===================

The assembly language described as inline assembly above can also be used
standalone and in fact, the plan is to use it as an intermediate language
for the Solidity compiler. In this form, it tries to achieve several goals:

1. Programs written in it should be readable, even if the code is generated by a compiler from Solidity.
2. The translation from assembly to bytecode should contain as few "surprises" as possible.
3. Control flow should be easy to detect to help in formal verification and optimization.

In order to achieve the first and last goal, assembly provides high-level constructs
like ``for`` loops, ``if`` and ``switch`` statements and function calls. It should be possible
to write assembly programs that do not make use of explicit ``SWAP``, ``DUP``,
``JUMP`` and ``JUMPI`` statements, because the first two obfuscate the data flow
and the last two obfuscate control flow. Furthermore, functional statements of
the form ``mul(add(x, y), 7)`` are preferred over pure opcode statements like
``7 y x add mul`` because in the first form, it is much easier to see which
operand is used for which opcode.

The second goal is achieved by compiling the
higher level constructs to bytecode in a very regular way.
The only non-local operation performed
by the assembler is name lookup of user-defined identifiers (functions, variables, ...),
which follow very simple and regular scoping rules and cleanup of local variables from the stack.

Scoping: An identifier that is declared (label, variable, function, assembly)
is only visible in the block where it was declared (including nested blocks
inside the current block). It is not legal to access local variables across
function borders, even if they would be in scope. Shadowing is not allowed.
Local variables cannot be accessed before they were declared, but
functions and assemblies can. Assemblies are special blocks that are used
for e.g. returning runtime code or creating contracts. No identifier from an
outer assembly is visible in a sub-assembly.

If control flow passes over the end of a block, pop instructions are inserted
that match the number of local variables declared in that block.
Whenever a local variable is referenced, the code generator needs
to know its current relative position in the stack and thus it needs to
keep track of the current so-called stack height. Since all local variables
are removed at the end of a block, the stack height before and after the block
should be the same. If this is not the case, compilation fails.

Using ``switch``, ``for`` and functions, it should be possible to write
complex code without using ``jump`` or ``jumpi`` manually. This makes it much
easier to analyze the control flow, which allows for improved formal
verification and optimization.

Furthermore, if manual jumps are allowed, computing the stack height is rather complicated.
The position of all local variables on the stack needs to be known, otherwise
neither references to local variables nor removing local variables automatically
from the stack at the end of a block will work properly.

Example:

We will follow an example compilation from Solidity to assembly.
We consider the runtime bytecode of the following Solidity program::

    pragma solidity >=0.4.16 <0.6.0;

    contract C {
      function f(uint x) public pure returns (uint y) {
        y = 1;
        for (uint i = 0; i < x; i++)
          y = 2 * y;
      }
    }

The following assembly will be generated::

    {
      mstore(0x40, 0x80) // store the "free memory pointer"
      // function dispatcher
      switch div(calldataload(0), exp(2, 226))
      case 0xb3de648b {
        let r := f(calldataload(4))
        let ret := $allocate(0x20)
        mstore(ret, r)
        return(ret, 0x20)
      }
      default { revert(0, 0) }
      // memory allocator
      function $allocate(size) -> pos {
        pos := mload(0x40)
        mstore(0x40, add(pos, size))
      }
      // the contract function
      function f(x) -> y {
        y := 1
        for { let i := 0 } lt(i, x) { i := add(i, 1) } {
          y := mul(2, y)
        }
      }
    }


Assembly Grammar
----------------

The tasks of the parser are the following:

- Turn the byte stream into a token stream, discarding C++-style comments
  (a special comment exists for source references, but we will not explain it here).
- Turn the token stream into an AST according to the grammar below
- Register identifiers with the block they are defined in (annotation to the
  AST node) and note from which point on, variables can be accessed.

The assembly lexer follows the one defined by Solidity itself.

Whitespace is used to delimit tokens and it consists of the characters
Space, Tab and Linefeed. Comments are regular JavaScript/C++ comments and
are interpreted in the same way as Whitespace.

Grammar::

    AssemblyBlock = '{' AssemblyItem* '}'
    AssemblyItem =
        Identifier |
        AssemblyBlock |
        AssemblyExpression |
        AssemblyLocalDefinition |
        AssemblyAssignment |
        AssemblyStackAssignment |
        LabelDefinition |
        AssemblyIf |
        AssemblySwitch |
        AssemblyFunctionDefinition |
        AssemblyFor |
        'break' |
        'continue' |
        SubAssembly
    AssemblyExpression = AssemblyCall | Identifier | AssemblyLiteral
    AssemblyLiteral = NumberLiteral | StringLiteral | HexLiteral
    Identifier = [a-zA-Z_$] [a-zA-Z_0-9]*
    AssemblyCall = Identifier '(' ( AssemblyExpression ( ',' AssemblyExpression )* )? ')'
    AssemblyLocalDefinition = 'let' IdentifierOrList ( ':=' AssemblyExpression )?
    AssemblyAssignment = IdentifierOrList ':=' AssemblyExpression
    IdentifierOrList = Identifier | '(' IdentifierList ')'
    IdentifierList = Identifier ( ',' Identifier)*
    AssemblyStackAssignment = '=:' Identifier
    LabelDefinition = Identifier ':'
    AssemblyIf = 'if' AssemblyExpression AssemblyBlock
    AssemblySwitch = 'switch' AssemblyExpression AssemblyCase*
        ( 'default' AssemblyBlock )?
    AssemblyCase = 'case' AssemblyExpression AssemblyBlock
    AssemblyFunctionDefinition = 'function' Identifier '(' IdentifierList? ')'
        ( '->' '(' IdentifierList ')' )? AssemblyBlock
    AssemblyFor = 'for' ( AssemblyBlock | AssemblyExpression )
        AssemblyExpression ( AssemblyBlock | AssemblyExpression ) AssemblyBlock
    SubAssembly = 'assembly' Identifier AssemblyBlock
    NumberLiteral = HexNumber | DecimalNumber
    HexLiteral = 'hex' ('"' ([0-9a-fA-F]{2})* '"' | '\'' ([0-9a-fA-F]{2})* '\'')
    StringLiteral = '"' ([^"\r\n\\] | '\\' .)* '"'
    HexNumber = '0x' [0-9a-fA-F]+
    DecimalNumber = [0-9]+