EIPs/EIPS/eip-2315.md

eip	title	status	type	category	author	discussions-to	created
2315	Simple Subroutines for the EVM	Draft	Standards Track	Core	Greg Colvin <greg@colvin.org>, Martin Holst Swende (@holiman)	https://ethereum-magicians.org/t/eip-2315-simple-subroutines-for-the-evm/3941	2019-10-17

Simple Summary

A small change to the EVM that provides native subroutines.

Abstract

This proposal introduces three opcodes to support subroutines: BEGINSUB, JUMPSUB and RETURNSUB. It deprecates JUMP and JUMPI.

Substantial gains in efficiency and reduced gas costs are achieved.

Safety properties equivalent to EIP-615 — including valid jump destinations — are ensured by following a few simple rules, which are validated at contract creation time — not runtime — by the provided algorithm, and without imposing syntactic constraints.

Motivation

The EVM does not provide subroutines as a primitive. Instead, calls can be synthesized by fetching and pushing the current program counter on the data stack and jumping to the subroutine address; returns can be synthesized by getting the return address to the top of the stack and jumping back to it. These conventions are more costly than necessary, and impede static analysis of EVM code, especially rapid validation of some important safety properties.

Facilities to directly support subroutines are provided by all but one of the real and virtual machines programmed by the lead author, including the Burroughs 5000, CDC 7600, IBM 360, DEC PDP 11 and VAX, Motorola 68000, a few generations of Intel silicon, Sun SPARC, UCSD p-Machine, Sun JVM, Wasm, and the sole exception — the EVM. In whatever form, these operations provide for

• capturing the current context of execution,
• transferring control to a new context, and
• returning to the original context
• • after possible further transfers of control
• • to some arbitrary depth.

The concept goes back to Turing (1946):

We also wish to be able to arrange for the splitting up of operations into subsidiary operations. This should be done in such a way that once we have written down how an operation is done we can use it as a subsidiary to any other operation. ... When we wish to start on a subsidiary operation we need only make a note of where we left off the major operation and then apply the first instruction of the subsidiary. When the subsidiary is over we look up the note and continue with the major operation. Each subsidiary operation can end with instructions for this recovery of the note. How is the burying and disinterring of the note to be done? There are of course many ways. One is to keep a list of these notes in one or more standard size delay lines, (1024) with the most recent last. The position of the most recent of these will be kept in a fixed TS, and this reference will be modified every time a subsidiary is started or finished...

We propose to use Turing's simple mechanism, long known to work well for virtual stack machines, as specified below. Note that this specification is entirely semantic. It constrains only stack usage and control flow and imposes no syntax on code beyond being a sequence of bytes to be executed.

Specification

We introduce one more stack into the EVM in addition to the existing data stack, known as the return stack. The return stack is limited to 1024 items. This stack supports three new instructions for subroutines.

BEGINSUB

Marks an entry point to a subroutine. Execution of a BEGINSUB is a no-op.

JUMPSUB location

Transfers control to a subroutine.

1. Decode the location from the immediate data. The data is encoded as two bytes, MSB-first.
2. If the opcode at location is not a BEGINSUB abort.
3. If the return stack already has 1024 items abort.
4. Push the current PC + 1 to the return stack.
5. Set PC to location.

• pops one item off the data stack
• pushes one item on the return stack

RETURNSUB

Returns control to the caller of a subroutine.

1. If the return stack is empty abort.
2. Pop PC off the return stack.

• pops one item off the return stack

Notes:

• If a resulting PC to be executed is beyond the last instruction then the opcode is implicitly a STOP, which is not an error.
• Values popped off the return stack do not need to be validated, since they are alterable only by JUMPSUB and RETURNSUB.
• The description above lays out the semantics of this feature in terms of a return stack. But the actual state of the return stack is not observable by EVM code or consensus-critical to the protocol. (For example, a node implementor may code JUMPSUB to unobservably push PC on the return stack rather than PC + 1, which is allowed so long as RETURNSUB observably returns control to the PC + 1 location.)
• The `return stack is the functional equivalent of Turing's "delay line" of "where we left off".

Dependencies

We need EVM Object Format (EOF) to allow for immediate arguments without special encoding.

We need EOF Static Relative Jumps or the equivalent to define and validate the rules for contract safety. These jumps — RJUMP offset and RJUMPI offset — transfer control to a location in the bytecode at a fixed offset relative to the current PC.

Rationale

We modeled this design on the proven, archetypal Forth virtual machine of 1970. It is a two-stack design — the data stack is supplemented with a return stack to support jumping into and returning from subroutines, as specified above. The return address (Turing's "note") is pushed onto the return stack when calling, and the stack is popped into the PC when returning.

The alternative design is to push the return address and the destination address on the data stack before jumping, and to pop the data stack and jump back to the popped PC to return. We prefer the separate return stack because it ensures that the return address cannot be overwritten or mislaid, uses fewer data stack slots, and obviates any need to swap the return address past the arguments or return values on the stack. Crucially, a dynamic jump is not needed to implement subroutine returns, allowing for deprecation of JUMP and JUMPI.

(JUMPSUB and RETURNSUB are also defined in terms of a return stack in EIP-615).

Backwards and Forwards Compatibility

These changes affect the semantics of existing EVM code. The EVM Object Format is required to allow for immediate data.

These changes are compatible with using EIP-3337 to provide stack frames, by associating a frame with each subroutine, as sketched out in the Appendix below.

Implementations

Three clients have implemented this (or an earlier version of this) proposal:

• geth,
• besu, and
• openethereum.

Costs and Codes

We suggest that the cost of

• BEGINSUB be jumpdest (1)
• JUMPSUB be low (5)
• RETURNSUB be verylow (3)

The low cost of JUMPSUB is justified by needing only about six Go operations, pushing the return address on the return stack, and decoding the two byte destination to the PC. The verylow cost of RETURNSUB is justified by needing only about three Go operations to pop the return stack into the PC. No 256-bit arithmetic or checking for valid destinations is needed.

Benchmarking might be needed to tell if the costs are well-balanced.

We suggest the following opcodes:

0x5c BEGINSUB
0x5d RETURNSUB
0x5e JUMPSUB

Efficiency

These opcodes increase the efficiency and reduce the gas costs of both ordinary subroutine calls and low-level optimizations.

Subroutine Call

Consider this example of calling a minimal subroutine using JUMPDEF

TEST_DIV:
    beginsub        ; 1 gas
    0x02            ; 3 gas
    0x03            ; 3 gas
    jumpsub DIVIDE  ; 5 gas
    returnsub       ; 3 gas

DIVIDE:
    beginsub        ; 1 gas
    div             ; 5 gas
    returnsub       ; 3 gas

Total 24 gas.

The same code, using JUMP.

TEST_DIV:
   jumpdest         ; 1 gas
   RTN_DIV          ; 3 gas
   0x02             ; 3 gas
   0x03             ; 3 gas
   DIVIDE           ; 3 gas
   jump             ; 8 gas
RTN_DIV:
   jumpdest         ; 1 gas
   swap1            ; 3 gas
   jump             ; 8 gas

DIVIDE:
   jumpdest         ; 1 gas
   div              ; 5 gas
   swap1            ; 3 gas
   jump             ; 8 gas

Total: 50 gas

Using JUMP uses 50 - 24 = 26 more gas than using JUMPSUB.

Tail Call Optimization

Of course in cases like this one we can optimize the tail call, so that the final jump in DIVIDE actually returns from TEST_DIV.

TEST_DIV:
    beginsub        ; 1 gas
    0x02            ; 3 gas
    0x03            ; 3 gas
    rjump DIVIDE    ; 3 gas

DIVIDE:
    beginsub        ; 1 gas
    div             ; 5 gas
    returnsub       ; 3 gas

Total: 22 gas

Or the same code, using JUMP

TEST_DIV:
   jumpdest         ; 1 gas
   0x02             ; 3 gas
   0x03             ; 3 gas
   DIVIDE           ; 3 gas
   jump             ; 8 gas

DIVIDE:
   jumpdest         ; 1 gas
   div              ; 5 gas
   swap1            ; 3 gas
   jump             ; 8 gas

Total: 35 gas

Using JUMP cost 35 - 22 = 13 more gas than using JUMPSUB.

Tail Call Elimination

We can even take advantage of DIVIDE just happening to directly follow TEST_DIV and just fall through rather than jump at all.

TEST_DIV:
    beginsub        ; 1 gas
    0x02            ; 3 gas
    0x03            ; 3 gas
DIVIDE:
    beginsub        ; 1 gas
    div             ; 5 gas
    returnsub       ; 3 gas

Total 16 gas.

The same code, using JUMP.

TEST_DIV:
   jumpdest         ; 1 gas
   0x02             ; 3 gas
   0x03             ; 3 gas
DIVIDE:
   jumpdest         ; 1 gas
   div              ; 5 gas
   swap1            ; 3 gas
   jump             ; 8 gas

Total: 24 gas

Using JUMP costs 24 - 16 = 8 more gas than using JUMPSUB.

Security Considerations

These changes do introduce new flow control instructions, so any software which does static/dynamic analysis of EVM code needs to be modified accordingly. The JUMPSUB semantics are similar to JUMP (but jumping to a BEGINSUB), whereas the RETURNSUB instruction is different, since it can 'land' on any opcode (but the possible destinations can be statically inferred).

Safety and amenability to static analysis of valid programs are comparable to EIP-615, but without imposing syntactic constraints, and thus with improved low-level optimizations (as shown above.) Validity can ensured by following the rules given in the next section, and programs can be validated with the provided algorithm. The validation algorithm is simple and bounded by the size of the code, allowing for validation at creation time. And compilers can easily follow the rules.

Validity

We define safety here as avoiding exceptional halting states.

Exceptional Halting States

Execution is as defined in the Yellow Paper — a sequence of changes to the EVM state. The conditions on valid code are preserved by state changes. At runtime, if execution of an instruction would violate a condition the execution is in an exceptional halting state. The Yellow Paper defines five such states.

1. Insufficient gas
2. More than 1024 stack items
3. Insufficient stack items
4. Invalid jump destination
5. Invalid instruction

We would like to consider EVM code valid iff no execution of the program can lead to an exceptional halting state, but we must be able to validate code in linear time to avoid denial of service attacks. So in practice, we can only partially meet these requirements. Our validation algorithm does not consider the code’s data and computations, only its control flow and stack use. This means we will reject programs with any invalid code paths, even if those paths are not reachable at runtime. Further, conditions 1 and 2 — Insufficient gas and stack overflow — must in general be checked at runtime. Conditions 3, 4, and 5 cannot occur if the code conforms to the following rules.

The Rules

0. JUMP and JUMPI are deprecated.
1. RJUMP and RJUMPI address only valid JUMPDEST instructions.
2. JUMPSUB addresses only valid BEGINSUB instructions.
3. For each instruction in the code the stack depth is always the same.
4. The stack depth is always positive and at most 1024.

Rule 0, deprecating JUMP and JUMPI, forbids dynamic jumps. Absent dynamic jumps another mechanism is needed for subroutine returns, as provided here.

Jump destinations are currently checked at runtime. Static jumps allow them to be validated at creation time, per rule 1 and rule 2. Note: Valid instructions are not part of immediate data.

For rule 3 and rule 4 we need to define stack depth. The Yellow Paper has the stack pointer or SP pointing just past the top item on the data stack. We define the stack base as where the SP pointed before the most recent JUMPSUB, or 0 on program entry. So we can define the stack depth as the number of stack elements between the current SP and the current stack base.

Given our definition of stack depth, rule 3 ensures that control flows which return to the same place with a different stack depth are invalid. These can be caused by irreducible paths like jumping into loops and subroutines, and calling subroutines with different numbers of arguments. Taken together, these rules allow for code to be validated by following the control-flow graph, traversing each edge only once.

Finally, rule 4 catches all stack underflows. It also catches stack overflows in programs that overflow without (or before) recursion.

Validation

The following is a pseudo-Go implementation of an algorithm for enforcing program validity – being a symbolic execution that recursively traverses the bytecode, following its control flow and stack use and checking for violations of the rules above.

This algorithm runs in time equal to O(vertices + edges) in the program's control-flow graph, where vertices represent control-flow instructions and the edges represent basic blocks – thus the algorithm takes time proportional to the size of the bytecode.

(For simplicity we assume an advance_pc() routine to skip immediate data and removed_items() and added_items() functions that return the effect of each instruction on the stack. We also don't specify JUMPTABLE — which amounts to a loop over RJUMP.)

   var bytecode []byte
   var stack_depth []int
   var SP := 0

   func validate(PC :=0) boolean {
      // traverse code sequentially
      // recurse for subroutines and conditional jumps
      while true {
         instruction = bytecode[PC]
         if is_invalid(instruction) {
            return false;
         }

         // stack depth must be the same
         if SP != stack_depth[PC] {
               return false
         }
         // if stack depth non-zero we have been here before 
         // return true to break cycle in control flow graph
         if stack_depth[PC] != 0 { 
            return true
         }
         stack_depth[PC] = SP

         // effect of instruction on stack
         SP -= removed_items(instruction)
         SP += added_items(instruction)
         if SP < 0 || 1024 < SP {
             return false
         }

         // successful validation of path
         if instruction == STOP, RETURN, or SUICIDE {
             return true
         }

         if instruction == RJUMP {

             // check for valid destination
             jumpdest = *PC, PC++, jumpdest << 8, jumpdest = *PC
             if bytecode[jumpdest] != JUMPDEST {
                 return false
             }

             // reset PC to destination of jump 
             PC = jumpdest
             continue
         }
         if instruction == RJUMPI {

             // check for valid destination
             jumpdest = *PC, PC++, jumpdest << 8, jumpdest = *PC
             if bytecode[jumpdest] != JUMPDEST {
                 return false
             }

             // reset PC to destination of jump 
             PC = jumpdest

             // recurse to jump to code to validate 
             if !validate(stack[SP])) {
                 return false
             }
             continue 
         }
         if instruction == JUMPSUB {

             // check for valid destination
             jumpdest = *PC, PC++, jumpdest << 8
             if bytecode[jumpdest] != BEGINSUB {
                 return false
             }

             // recurse to jump to code to validate
             prevSP = SP
             depth = SP - prevSP
             SP = depth
             if  !validate(stack[SP]+1)) {
                 return false
             }
             SP = prevSP - depth + SP
             PC = prevPC
             continue
         }
         if instruction == RETURNSUB {
             PC = prevPC
             return true
         }

         // advance PC according to instruction
         PC = advance_pc(PC, instruction)
      }    
   }

Test Cases

Simple routine

This should jump into a subroutine, back out and stop.

Bytecode: 0x60045e005c5d (PUSH1 0x04, JUMPSUB, STOP, BEGINSUB, RETURNSUB)

Pc	Op	Cost	Stack	RStack
0	JUMPSUB	5	[]	[]
3	RETURNSUB	5	[]	[0]
4	STOP	0	[]	[]

Output: 0x Consumed gas: 10

Two levels of subroutines

This should execute fine, going into one two depths of subroutines

Bytecode: 0x6800000000000000000c5e005c60115e5d5c5d (PUSH9 0x00000000000000000c, JUMPSUB, STOP, BEGINSUB, PUSH1 0x11, JUMPSUB, RETURNSUB, BEGINSUB, RETURNSUB)

Pc	Op	Cost	Stack	RStack
0	JUMPSUB	5	[]	[]
3	JUMPSUB	5	[]	[0]
4	RETURNSUB	5	[]	[0,3]
5	RETURNSUB	5	[]	[3]
6	STOP	0	[]	[]

Consumed gas: 20

Failure 1: invalid jump

This should fail, since the given location is outside of the code-range. The code is the same as previous example, except that the pushed location is 0x01000000000000000c instead of 0x0c.

Bytecode: (PUSH9 0x01000000000000000c, JUMPSUB, 0x6801000000000000000c5e005c60115e5d5c5d, STOP, BEGINSUB, PUSH1 0x11, JUMPSUB, RETURNSUB, BEGINSUB, RETURNSUB)

Pc	Op	Cost	Stack	RStack
0	JUMPSUB	10	[18446744073709551628]	[]

Error: at pc=10, op=JUMPSUB: invalid jump destination

Failure 2: shallow return stack

This should fail at first opcode, due to shallow return_stack

Bytecode: 0x5d5858 (RETURNSUB, PC, PC)

Pc	Op	Cost	Stack	RStack
0	RETURNSUB	5	[]	[]

Error: at pc=0, op=RETURNSUB: invalid retsub

Subroutine at end of code

In this example. the JUMPSUB is on the last byte of code. When the subroutine returns, it should hit the 'virtual stop' after the bytecode, and not exit with error

Bytecode: 0x6005565c5d5b60035e (PUSH1 0x05, JUMP, BEGINSUB, RETURNSUB, JUMPDEST, PUSH1 0x03, JUMPSUB)

Pc	Op	Cost	Stack	RStack
0	PUSH1	3	[]	[]
2	JUMP	8	[5]	[]
5	JUMPDEST	1	[]	[]
6	JUMPSUB	5	[]	[]
2	RETURNSUB	5	[]	[2]
7	STOP	0	[]	[]

Consumed gas: 30

Appendix: Stack Frames

Given EIP-3337 — which introduces a frame pointer register FP relative to which which memory can be addressed , we can create a frame stack — a list of data frames in memory for arguments and local variables. Two conventions are typical — either create the frame before calling the subroutine, or create the frame after the BEGINSUB. Adding these two instructions to EIP-3337 would ease the way. They are modeled on the corresponding Intel opcodes.

ENTER frame_size

Write the current FP to memory as with MSTOREF at FP - frame_size, then set FP to FP - frame size. This a shorthand for

MSTOREF
GETFP
PUSH frame_size
SUB
SETFP

This should be placed either before a JUMPSUB operation or after a BEGINSUB, depending on the calling convention. Repeated calls to ENTER create a stack of frames, linked by their previous FP field. The stack grows towards lower addresses in memory, as is the common, efficient practice.

LEAVE

Restores FP to the value which was stored at offset FP in memory by the most recent ENTER, thus popping a frame off of the stack of frames. This a shorthand for

MLOADF
SETFP

This should be placed after the JUMPSUB operation or before the RETURNSUB – depending on the calling convention – to pop the most recent frame from the call stack.

These operations would be especially useful if the gas formula for memory was reinterpreted so that writes from the top of memory down (equivalently, from -1 down, twos-complement) are charged the same gas as writes from the bottom of memory up.

The total cost to expand the memory to size a words is

Cmem(a) = 3 * a + floor(a ** 2 / 512)

If the memory is already b words long, the incremental cost is

Cmem(a) - Cmem(b)

If a, b and memory offsets in general are allowed to be negative the formula gives the desired results – stack memory can grow from the top down, and heap memory can be allocated from the bottom up, without address conflicts or excessive gas charges.

References

A.M. Turing, Proposals for the development in the Mathematics Division of an Automatic Computing Engine (ACE) Report E882, Executive Committee, NPL 1946

Alex Beregszaszi, Paweł Bylica, Andrei Maiboroda, EVM Object Format (EOF) v1 2021

Andrei Maiboroda, EOF static relative jumps

Gavin Wood, Ethereum: A Secure Decentralized Generalized Transaction Ledger, 2014-2021

Greg Colvin, Brooklyn Zelenka, Paweł Bylica, Christian Reitwiessner, EIP-615: Subroutines and Static Jumps for the EVM, 2016-2019

Nick Johnson, EIP-3337: Frame pointer support for memory load and store operations, 2021

Copyright

Copyright and related rights waived via CC0.