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Semantics64

Exec64-jalr

Semantics of the JALR instruction [ISA:2.5.1].

Signature
(exec64-jalr rd rs1 imm pc stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte12p imm).; pc — Guard (ubyte64p pc).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

We read an unsigned 64-bit integer from rs1. We sign-extend the 12-bit immediate to 64 bits, obtaining an unsigned 64-bit offset. We add the offset to the integer from the register, and set the least significant bit to 0; this is the jump target. We write the address of the instruction just after this to rd; since instructions are 32-bit long, the address of the next instruction is obtained by adding 4 to pc, which is the address of this instruction, passed as input to this function. We write the jump target to the program counter.

Definitions and Theorems

Function: exec64-jalr

(defun exec64-jalr (rd rs1 imm pc stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte12p imm)
                              (ubyte64p pc)
                              (state64p stat))))
  (let ((__function__ 'exec64-jalr))
    (declare (ignorable __function__))
    (b* ((base (read64-xreg-unsigned rs1 stat))
         (offset (loghead 64 (logext 12 (ubyte12-fix imm))))
         (target-pc (logand 18446744073709551614 (+ base offset)))
         (next-pc (+ (ubyte64-fix pc) 4))
         (stat (write64-xreg rd next-pc stat))
         (stat (write64-pc target-pc stat)))
      stat)))

Theorem: state64p-of-exec64-jalr

(defthm state64p-of-exec64-jalr
  (b* ((new-stat (exec64-jalr rd rs1 imm pc stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: exec64-jalr-of-ubyte5-fix-rd

(defthm exec64-jalr-of-ubyte5-fix-rd
  (equal (exec64-jalr (ubyte5-fix rd)
                      rs1 imm pc stat)
         (exec64-jalr rd rs1 imm pc stat)))

Theorem: exec64-jalr-ubyte5-equiv-congruence-on-rd

(defthm exec64-jalr-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec64-jalr rd rs1 imm pc stat)
                  (exec64-jalr rd-equiv rs1 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec64-jalr-of-ubyte5-fix-rs1

(defthm exec64-jalr-of-ubyte5-fix-rs1
  (equal (exec64-jalr rd (ubyte5-fix rs1)
                      imm pc stat)
         (exec64-jalr rd rs1 imm pc stat)))

Theorem: exec64-jalr-ubyte5-equiv-congruence-on-rs1

(defthm exec64-jalr-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec64-jalr rd rs1 imm pc stat)
                  (exec64-jalr rd rs1-equiv imm pc stat)))
  :rule-classes :congruence)

Theorem: exec64-jalr-of-ubyte12-fix-imm

(defthm exec64-jalr-of-ubyte12-fix-imm
  (equal (exec64-jalr rd rs1 (ubyte12-fix imm)
                      pc stat)
         (exec64-jalr rd rs1 imm pc stat)))

Theorem: exec64-jalr-ubyte12-equiv-congruence-on-imm

(defthm exec64-jalr-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec64-jalr rd rs1 imm pc stat)
                  (exec64-jalr rd rs1 imm-equiv pc stat)))
  :rule-classes :congruence)

Theorem: exec64-jalr-of-ubyte64-fix-pc

(defthm exec64-jalr-of-ubyte64-fix-pc
  (equal (exec64-jalr rd rs1 imm (ubyte64-fix pc)
                      stat)
         (exec64-jalr rd rs1 imm pc stat)))

Theorem: exec64-jalr-ubyte64-equiv-congruence-on-pc

(defthm exec64-jalr-ubyte64-equiv-congruence-on-pc
  (implies (acl2::ubyte64-equiv pc pc-equiv)
           (equal (exec64-jalr rd rs1 imm pc stat)
                  (exec64-jalr rd rs1 imm pc-equiv stat)))
  :rule-classes :congruence)

Theorem: exec64-jalr-of-state64-fix-stat

(defthm exec64-jalr-of-state64-fix-stat
  (equal (exec64-jalr rd rs1 imm pc (state64-fix stat))
         (exec64-jalr rd rs1 imm pc stat)))

Theorem: exec64-jalr-state64-equiv-congruence-on-stat

(defthm exec64-jalr-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (exec64-jalr rd rs1 imm pc stat)
                  (exec64-jalr rd rs1 imm pc stat-equiv)))
  :rule-classes :congruence)