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-rw-r--r--data/transactions/logic/TEAL_opcodes_v6.md118
1 files changed, 59 insertions, 59 deletions
diff --git a/data/transactions/logic/TEAL_opcodes_v6.md b/data/transactions/logic/TEAL_opcodes_v6.md
index eab29a84c..bacca46d4 100644
--- a/data/transactions/logic/TEAL_opcodes_v6.md
+++ b/data/transactions/logic/TEAL_opcodes_v6.md
@@ -41,9 +41,9 @@ The 32 byte public key is the last element on the stack, preceded by the 64 byte
## ecdsa_verify
-- Syntax: `ecdsa_verify V` ∋ V: [ECDSA](#field-group-ecdsa)
+- Syntax: `ecdsa_verify V` where V: [ECDSA](#field-group-ecdsa)
- Bytecode: 0x05 {uint8}
-- Stack: ..., A: [32]byte, B: []byte, C: []byte, D: []byte, E: []byte → ..., bool
+- Stack: ..., A: [32]byte, B: [32]byte, C: [32]byte, D: [32]byte, E: [32]byte → ..., bool
- for (data A, signature B, C and pubkey D, E) verify the signature of the data against the pubkey => {0 or 1}
- **Cost**: Secp256k1=1700
- Availability: v5
@@ -61,9 +61,9 @@ The 32 byte Y-component of a public key is the last element on the stack, preced
## ecdsa_pk_decompress
-- Syntax: `ecdsa_pk_decompress V` ∋ V: [ECDSA](#field-group-ecdsa)
+- Syntax: `ecdsa_pk_decompress V` where V: [ECDSA](#field-group-ecdsa)
- Bytecode: 0x06 {uint8}
-- Stack: ..., A: []byte → ..., X: []byte, Y: []byte
+- Stack: ..., A: [33]byte → ..., X: [32]byte, Y: [32]byte
- decompress pubkey A into components X, Y
- **Cost**: Secp256k1=650
- Availability: v5
@@ -72,9 +72,9 @@ The 33 byte public key in a compressed form to be decompressed into X and Y (top
## ecdsa_pk_recover
-- Syntax: `ecdsa_pk_recover V` ∋ V: [ECDSA](#field-group-ecdsa)
+- Syntax: `ecdsa_pk_recover V` where V: [ECDSA](#field-group-ecdsa)
- Bytecode: 0x07 {uint8}
-- Stack: ..., A: [32]byte, B: uint64, C: [32]byte, D: [32]byte → ..., X: []byte, Y: []byte
+- Stack: ..., A: [32]byte, B: uint64, C: [32]byte, D: [32]byte → ..., X: [32]byte, Y: [32]byte
- for (data A, recovery id B, signature C, D) recover a public key
- **Cost**: 2000
- Availability: v5
@@ -174,7 +174,7 @@ Overflow is an error condition which halts execution and fails the transaction.
## itob
- Bytecode: 0x16
-- Stack: ..., A: uint64 → ..., []byte
+- Stack: ..., A: uint64 → ..., [8]byte
- converts uint64 A to big-endian byte array, always of length 8
## btoi
@@ -240,7 +240,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## intcblock
-- Syntax: `intcblock UINT ...` ∋ UINT ...: a block of int constant values
+- Syntax: `intcblock UINT ...` where UINT ...: a block of int constant values
- Bytecode: 0x20 {varuint count, [varuint ...]}
- Stack: ... → ...
- prepare block of uint64 constants for use by intc
@@ -249,7 +249,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## intc
-- Syntax: `intc I` ∋ I: an index in the intcblock
+- Syntax: `intc I` where I: an index in the intcblock
- Bytecode: 0x21 {uint8}
- Stack: ... → ..., uint64
- Ith constant from intcblock
@@ -280,7 +280,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## bytecblock
-- Syntax: `bytecblock BYTES ...` ∋ BYTES ...: a block of byte constant values
+- Syntax: `bytecblock BYTES ...` where BYTES ...: a block of byte constant values
- Bytecode: 0x26 {varuint count, [varuint length, bytes ...]}
- Stack: ... → ...
- prepare block of byte-array constants for use by bytec
@@ -289,7 +289,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## bytec
-- Syntax: `bytec I` ∋ I: an index in the bytecblock
+- Syntax: `bytec I` where I: an index in the bytecblock
- Bytecode: 0x27 {uint8}
- Stack: ... → ..., []byte
- Ith constant from bytecblock
@@ -320,7 +320,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## arg
-- Syntax: `arg N` ∋ N: an arg index
+- Syntax: `arg N` where N: an arg index
- Bytecode: 0x2c {uint8}
- Stack: ... → ..., []byte
- Nth LogicSig argument
@@ -356,7 +356,7 @@ The notation J,K indicates that two uint64 values J and K are interpreted as a u
## txn
-- Syntax: `txn F` ∋ F: [txn](#field-group-txn)
+- Syntax: `txn F` where F: [txn](#field-group-txn)
- Bytecode: 0x31 {uint8}
- Stack: ... → ..., any
- field F of current transaction
@@ -429,7 +429,7 @@ Fields (see [transaction reference](https://developer.algorand.org/docs/referenc
## global
-- Syntax: `global F` ∋ F: [global](#field-group-global)
+- Syntax: `global F` where F: [global](#field-group-global)
- Bytecode: 0x32 {uint8}
- Stack: ... → ..., any
- global field F
@@ -459,7 +459,7 @@ Fields
## gtxn
-- Syntax: `gtxn T F` ∋ T: transaction group index, F: [txn](#field-group-txn)
+- Syntax: `gtxn T F` where T: transaction group index, F: [txn](#field-group-txn)
- Bytecode: 0x33 {uint8}, {uint8}
- Stack: ... → ..., any
- field F of the Tth transaction in the current group
@@ -468,21 +468,21 @@ for notes on transaction fields available, see `txn`. If this transaction is _i_
## load
-- Syntax: `load I` ∋ I: position in scratch space to load from
+- Syntax: `load I` where I: position in scratch space to load from
- Bytecode: 0x34 {uint8}
- Stack: ... → ..., any
- Ith scratch space value. All scratch spaces are 0 at program start.
## store
-- Syntax: `store I` ∋ I: position in scratch space to store to
+- Syntax: `store I` where I: position in scratch space to store to
- Bytecode: 0x35 {uint8}
- Stack: ..., A → ...
- store A to the Ith scratch space
## txna
-- Syntax: `txna F I` ∋ F: [txna](#field-group-txna), I: transaction field array index
+- Syntax: `txna F I` where F: [txna](#field-group-txna), I: transaction field array index
- Bytecode: 0x36 {uint8}, {uint8}
- Stack: ... → ..., any
- Ith value of the array field F of the current transaction<br />`txna` can be called using `txn` with 2 immediates.
@@ -503,7 +503,7 @@ Fields (see [transaction reference](https://developer.algorand.org/docs/referenc
## gtxna
-- Syntax: `gtxna T F I` ∋ T: transaction group index, F: [txna](#field-group-txna), I: transaction field array index
+- Syntax: `gtxna T F I` where T: transaction group index, F: [txna](#field-group-txna), I: transaction field array index
- Bytecode: 0x37 {uint8}, {uint8}, {uint8}
- Stack: ... &rarr; ..., any
- Ith value of the array field F from the Tth transaction in the current group<br />`gtxna` can be called using `gtxn` with 3 immediates.
@@ -511,7 +511,7 @@ Fields (see [transaction reference](https://developer.algorand.org/docs/referenc
## gtxns
-- Syntax: `gtxns F` ∋ F: [txn](#field-group-txn)
+- Syntax: `gtxns F` where F: [txn](#field-group-txn)
- Bytecode: 0x38 {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- field F of the Ath transaction in the current group
@@ -521,7 +521,7 @@ for notes on transaction fields available, see `txn`. If top of stack is _i_, `g
## gtxnsa
-- Syntax: `gtxnsa F I` ∋ F: [txna](#field-group-txna), I: transaction field array index
+- Syntax: `gtxnsa F I` where F: [txna](#field-group-txna), I: transaction field array index
- Bytecode: 0x39 {uint8}, {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ith value of the array field F from the Ath transaction in the current group<br />`gtxnsa` can be called using `gtxns` with 2 immediates.
@@ -529,7 +529,7 @@ for notes on transaction fields available, see `txn`. If top of stack is _i_, `g
## gload
-- Syntax: `gload T I` ∋ T: transaction group index, I: position in scratch space to load from
+- Syntax: `gload T I` where T: transaction group index, I: position in scratch space to load from
- Bytecode: 0x3a {uint8}, {uint8}
- Stack: ... &rarr; ..., any
- Ith scratch space value of the Tth transaction in the current group
@@ -540,7 +540,7 @@ for notes on transaction fields available, see `txn`. If top of stack is _i_, `g
## gloads
-- Syntax: `gloads I` ∋ I: position in scratch space to load from
+- Syntax: `gloads I` where I: position in scratch space to load from
- Bytecode: 0x3b {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ith scratch space value of the Ath transaction in the current group
@@ -551,7 +551,7 @@ for notes on transaction fields available, see `txn`. If top of stack is _i_, `g
## gaid
-- Syntax: `gaid T` ∋ T: transaction group index
+- Syntax: `gaid T` where T: transaction group index
- Bytecode: 0x3c {uint8}
- Stack: ... &rarr; ..., uint64
- ID of the asset or application created in the Tth transaction of the current group
@@ -586,7 +586,7 @@ for notes on transaction fields available, see `txn`. If top of stack is _i_, `g
## bnz
-- Syntax: `bnz TARGET` ∋ TARGET: branch offset
+- Syntax: `bnz TARGET` where TARGET: branch offset
- Bytecode: 0x40 {int16 (big-endian)}
- Stack: ..., A: uint64 &rarr; ...
- branch to TARGET if value A is not zero
@@ -597,7 +597,7 @@ At v2 it became allowed to branch to the end of the program exactly after the la
## bz
-- Syntax: `bz TARGET` ∋ TARGET: branch offset
+- Syntax: `bz TARGET` where TARGET: branch offset
- Bytecode: 0x41 {int16 (big-endian)}
- Stack: ..., A: uint64 &rarr; ...
- branch to TARGET if value A is zero
@@ -607,7 +607,7 @@ See `bnz` for details on how branches work. `bz` inverts the behavior of `bnz`.
## b
-- Syntax: `b TARGET` ∋ TARGET: branch offset
+- Syntax: `b TARGET` where TARGET: branch offset
- Bytecode: 0x42 {int16 (big-endian)}
- Stack: ... &rarr; ...
- branch unconditionally to TARGET
@@ -650,7 +650,7 @@ See `bnz` for details on how branches work. `b` always jumps to the offset.
## dig
-- Syntax: `dig N` ∋ N: depth
+- Syntax: `dig N` where N: depth
- Bytecode: 0x4b {uint8}
- Stack: ..., A, [N items] &rarr; ..., A, [N items], A
- Nth value from the top of the stack. dig 0 is equivalent to dup
@@ -672,7 +672,7 @@ See `bnz` for details on how branches work. `b` always jumps to the offset.
## cover
-- Syntax: `cover N` ∋ N: depth
+- Syntax: `cover N` where N: depth
- Bytecode: 0x4e {uint8}
- Stack: ..., [N items], A &rarr; ..., A, [N items]
- remove top of stack, and place it deeper in the stack such that N elements are above it. Fails if stack depth <= N.
@@ -680,7 +680,7 @@ See `bnz` for details on how branches work. `b` always jumps to the offset.
## uncover
-- Syntax: `uncover N` ∋ N: depth
+- Syntax: `uncover N` where N: depth
- Bytecode: 0x4f {uint8}
- Stack: ..., A, [N items] &rarr; ..., [N items], A
- remove the value at depth N in the stack and shift above items down so the Nth deep value is on top of the stack. Fails if stack depth <= N.
@@ -697,7 +697,7 @@ See `bnz` for details on how branches work. `b` always jumps to the offset.
## substring
-- Syntax: `substring S E` ∋ S: start position, E: end position
+- Syntax: `substring S E` where S: start position, E: end position
- Bytecode: 0x51 {uint8}, {uint8}
- Stack: ..., A: []byte &rarr; ..., []byte
- A range of bytes from A starting at S up to but not including E. If E < S, or either is larger than the array length, the program fails
@@ -744,7 +744,7 @@ When A is a uint64, index 0 is the least significant bit. Setting bit 3 to 1 on
## extract
-- Syntax: `extract S L` ∋ S: start position, L: length
+- Syntax: `extract S L` where S: start position, L: length
- Bytecode: 0x57 {uint8}, {uint8}
- Stack: ..., A: []byte &rarr; ..., []byte
- A range of bytes from A starting at S up to but not including S+L. If L is 0, then extract to the end of the string. If S or S+L is larger than the array length, the program fails
@@ -801,7 +801,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), _ava
## app_local_get
- Bytecode: 0x62
-- Stack: ..., A, B: []byte &rarr; ..., any
+- Stack: ..., A, B: stateKey &rarr; ..., any
- local state of the key B in the current application in account A
- Availability: v2
- Mode: Application
@@ -811,7 +811,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), stat
## app_local_get_ex
- Bytecode: 0x63
-- Stack: ..., A, B: uint64, C: []byte &rarr; ..., X: any, Y: bool
+- Stack: ..., A, B: uint64, C: stateKey &rarr; ..., X: any, Y: bool
- X is the local state of application B, key C in account A. Y is 1 if key existed, else 0
- Availability: v2
- Mode: Application
@@ -821,7 +821,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), _ava
## app_global_get
- Bytecode: 0x64
-- Stack: ..., A: []byte &rarr; ..., any
+- Stack: ..., A: stateKey &rarr; ..., any
- global state of the key A in the current application
- Availability: v2
- Mode: Application
@@ -831,7 +831,7 @@ params: state key. Return: value. The value is zero (of type uint64) if the key
## app_global_get_ex
- Bytecode: 0x65
-- Stack: ..., A: uint64, B: []byte &rarr; ..., X: any, Y: bool
+- Stack: ..., A: uint64, B: stateKey &rarr; ..., X: any, Y: bool
- X is the global state of application A, key B. Y is 1 if key existed, else 0
- Availability: v2
- Mode: Application
@@ -841,7 +841,7 @@ params: Txn.ForeignApps offset (or, since v4, an _available_ application id), st
## app_local_put
- Bytecode: 0x66
-- Stack: ..., A, B: []byte, C &rarr; ...
+- Stack: ..., A, B: stateKey, C &rarr; ...
- write C to key B in account A's local state of the current application
- Availability: v2
- Mode: Application
@@ -851,7 +851,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), stat
## app_global_put
- Bytecode: 0x67
-- Stack: ..., A: []byte, B &rarr; ...
+- Stack: ..., A: stateKey, B &rarr; ...
- write B to key A in the global state of the current application
- Availability: v2
- Mode: Application
@@ -859,7 +859,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), stat
## app_local_del
- Bytecode: 0x68
-- Stack: ..., A, B: []byte &rarr; ...
+- Stack: ..., A, B: stateKey &rarr; ...
- delete key B from account A's local state of the current application
- Availability: v2
- Mode: Application
@@ -871,7 +871,7 @@ Deleting a key which is already absent has no effect on the application local st
## app_global_del
- Bytecode: 0x69
-- Stack: ..., A: []byte &rarr; ...
+- Stack: ..., A: stateKey &rarr; ...
- delete key A from the global state of the current application
- Availability: v2
- Mode: Application
@@ -882,7 +882,7 @@ Deleting a key which is already absent has no effect on the application global s
## asset_holding_get
-- Syntax: `asset_holding_get F` ∋ F: [asset_holding](#field-group-asset_holding)
+- Syntax: `asset_holding_get F` where F: [asset_holding](#field-group-asset_holding)
- Bytecode: 0x70 {uint8}
- Stack: ..., A, B: uint64 &rarr; ..., X: any, Y: bool
- X is field F from account A's holding of asset B. Y is 1 if A is opted into B, else 0
@@ -903,7 +903,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ address), asset id (or
## asset_params_get
-- Syntax: `asset_params_get F` ∋ F: [asset_params](#field-group-asset_params)
+- Syntax: `asset_params_get F` where F: [asset_params](#field-group-asset_params)
- Bytecode: 0x71 {uint8}
- Stack: ..., A: uint64 &rarr; ..., X: any, Y: bool
- X is field F from asset A. Y is 1 if A exists, else 0
@@ -934,7 +934,7 @@ params: Txn.ForeignAssets offset (or, since v4, an _available_ asset id. Return:
## app_params_get
-- Syntax: `app_params_get F` ∋ F: [app_params](#field-group-app_params)
+- Syntax: `app_params_get F` where F: [app_params](#field-group-app_params)
- Bytecode: 0x72 {uint8}
- Stack: ..., A: uint64 &rarr; ..., X: any, Y: bool
- X is field F from app A. Y is 1 if A exists, else 0
@@ -962,7 +962,7 @@ params: Txn.ForeignApps offset or an _available_ app id. Return: did_exist flag
## acct_params_get
-- Syntax: `acct_params_get F` ∋ F: [acct_params](#field-group-acct_params)
+- Syntax: `acct_params_get F` where F: [acct_params](#field-group-acct_params)
- Bytecode: 0x73 {uint8}
- Stack: ..., A &rarr; ..., X: any, Y: bool
- X is field F from account A. Y is 1 if A owns positive algos, else 0
@@ -992,7 +992,7 @@ params: Txn.Accounts offset (or, since v4, an _available_ account address), _ava
## pushbytes
-- Syntax: `pushbytes BYTES` ∋ BYTES: a byte constant
+- Syntax: `pushbytes BYTES` where BYTES: a byte constant
- Bytecode: 0x80 {varuint length, bytes}
- Stack: ... &rarr; ..., []byte
- immediate BYTES
@@ -1002,7 +1002,7 @@ pushbytes args are not added to the bytecblock during assembly processes
## pushint
-- Syntax: `pushint UINT` ∋ UINT: an int constant
+- Syntax: `pushint UINT` where UINT: an int constant
- Bytecode: 0x81 {varuint}
- Stack: ... &rarr; ..., uint64
- immediate UINT
@@ -1012,7 +1012,7 @@ pushint args are not added to the intcblock during assembly processes
## callsub
-- Syntax: `callsub TARGET` ∋ TARGET: branch offset
+- Syntax: `callsub TARGET` where TARGET: branch offset
- Bytecode: 0x88 {int16 (big-endian)}
- Stack: ... &rarr; ...
- branch unconditionally to TARGET, saving the next instruction on the call stack
@@ -1078,7 +1078,7 @@ bitlen interprets arrays as big-endian integers, unlike setbit/getbit
## bsqrt
- Bytecode: 0x96
-- Stack: ..., A: []byte &rarr; ..., []byte
+- Stack: ..., A: bigint &rarr; ..., bigint
- The largest integer I such that I^2 <= A. A and I are interpreted as big-endian unsigned integers
- **Cost**: 40
- Availability: v6
@@ -1169,7 +1169,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## b%
- Bytecode: 0xaa
-- Stack: ..., A: []byte, B: []byte &rarr; ..., []byte
+- Stack: ..., A: bigint, B: bigint &rarr; ..., bigint
- A modulo B. A and B are interpreted as big-endian unsigned integers. Fail if B is zero.
- **Cost**: 20
- Availability: v4
@@ -1235,7 +1235,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## itxn_field
-- Syntax: `itxn_field F` ∋ F: [txn](#field-group-txn)
+- Syntax: `itxn_field F` where F: [txn](#field-group-txn)
- Bytecode: 0xb2 {uint8}
- Stack: ..., A &rarr; ...
- set field F of the current inner transaction to A
@@ -1256,7 +1256,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## itxn
-- Syntax: `itxn F` ∋ F: [txn](#field-group-txn)
+- Syntax: `itxn F` where F: [txn](#field-group-txn)
- Bytecode: 0xb4 {uint8}
- Stack: ... &rarr; ..., any
- field F of the last inner transaction
@@ -1265,7 +1265,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## itxna
-- Syntax: `itxna F I` ∋ F: [txna](#field-group-txna), I: a transaction field array index
+- Syntax: `itxna F I` where F: [txna](#field-group-txna), I: a transaction field array index
- Bytecode: 0xb5 {uint8}, {uint8}
- Stack: ... &rarr; ..., any
- Ith value of the array field F of the last inner transaction
@@ -1284,7 +1284,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## gitxn
-- Syntax: `gitxn T F` ∋ T: transaction group index, F: [txn](#field-group-txn)
+- Syntax: `gitxn T F` where T: transaction group index, F: [txn](#field-group-txn)
- Bytecode: 0xb7 {uint8}, {uint8}
- Stack: ... &rarr; ..., any
- field F of the Tth transaction in the last inner group submitted
@@ -1293,7 +1293,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## gitxna
-- Syntax: `gitxna T F I` ∋ T: transaction group index, F: [txna](#field-group-txna), I: transaction field array index
+- Syntax: `gitxna T F I` where T: transaction group index, F: [txna](#field-group-txna), I: transaction field array index
- Bytecode: 0xb8 {uint8}, {uint8}, {uint8}
- Stack: ... &rarr; ..., any
- Ith value of the array field F from the Tth transaction in the last inner group submitted
@@ -1302,7 +1302,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## txnas
-- Syntax: `txnas F` ∋ F: [txna](#field-group-txna)
+- Syntax: `txnas F` where F: [txna](#field-group-txna)
- Bytecode: 0xc0 {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ath value of the array field F of the current transaction
@@ -1310,7 +1310,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## gtxnas
-- Syntax: `gtxnas T F` ∋ T: transaction group index, F: [txna](#field-group-txna)
+- Syntax: `gtxnas T F` where T: transaction group index, F: [txna](#field-group-txna)
- Bytecode: 0xc1 {uint8}, {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ath value of the array field F from the Tth transaction in the current group
@@ -1318,7 +1318,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## gtxnsas
-- Syntax: `gtxnsas F` ∋ F: [txna](#field-group-txna)
+- Syntax: `gtxnsas F` where F: [txna](#field-group-txna)
- Bytecode: 0xc2 {uint8}
- Stack: ..., A: uint64, B: uint64 &rarr; ..., any
- Bth value of the array field F from the Ath transaction in the current group
@@ -1342,7 +1342,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## itxnas
-- Syntax: `itxnas F` ∋ F: [txna](#field-group-txna)
+- Syntax: `itxnas F` where F: [txna](#field-group-txna)
- Bytecode: 0xc5 {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ath value of the array field F of the last inner transaction
@@ -1351,7 +1351,7 @@ The notation A,B indicates that A and B are interpreted as a uint128 value, with
## gitxnas
-- Syntax: `gitxnas T F` ∋ T: transaction group index, F: [txna](#field-group-txna)
+- Syntax: `gitxnas T F` where T: transaction group index, F: [txna](#field-group-txna)
- Bytecode: 0xc6 {uint8}, {uint8}
- Stack: ..., A: uint64 &rarr; ..., any
- Ath value of the array field F from the Tth transaction in the last inner group submitted