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Semantics32

Exec32-jalr

Semantics of the JALR instruction [ISA:2.5.1].

Signature
(exec32-jalr rd rs1 imm pc stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte12p imm).; pc — Guard (ubyte32p pc).; stat — Guard (state32p stat).
Returns: new-stat — Type (state32p new-stat).

We read an unsigned 32-bit integer from rs1. We sign-extend the 12-bit immediate to 32 bits, obtaining an unsigned 32-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: exec32-jalr

(defun exec32-jalr (rd rs1 imm pc stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte12p imm)
                              (ubyte32p pc)
                              (state32p stat))))
  (let ((__function__ 'exec32-jalr))
    (declare (ignorable __function__))
    (b* ((base (read32-xreg-unsigned rs1 stat))
         (offset (loghead 32 (logext 12 (ubyte12-fix imm))))
         (target-pc (logand 4294967294 (+ base offset)))
         (next-pc (+ (ubyte32-fix pc) 4))
         (stat (write32-xreg rd next-pc stat))
         (stat (write32-pc target-pc stat)))
      stat)))

Theorem: state32p-of-exec32-jalr

(defthm state32p-of-exec32-jalr
  (b* ((new-stat (exec32-jalr rd rs1 imm pc stat)))
    (state32p new-stat))
  :rule-classes :rewrite)

Theorem: exec32-jalr-of-ubyte5-fix-rd

(defthm exec32-jalr-of-ubyte5-fix-rd
  (equal (exec32-jalr (ubyte5-fix rd)
                      rs1 imm pc stat)
         (exec32-jalr rd rs1 imm pc stat)))

Theorem: exec32-jalr-ubyte5-equiv-congruence-on-rd

(defthm exec32-jalr-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec32-jalr rd rs1 imm pc stat)
                  (exec32-jalr rd-equiv rs1 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-jalr-of-ubyte5-fix-rs1

(defthm exec32-jalr-of-ubyte5-fix-rs1
  (equal (exec32-jalr rd (ubyte5-fix rs1)
                      imm pc stat)
         (exec32-jalr rd rs1 imm pc stat)))

Theorem: exec32-jalr-ubyte5-equiv-congruence-on-rs1

(defthm exec32-jalr-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec32-jalr rd rs1 imm pc stat)
                  (exec32-jalr rd rs1-equiv imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-jalr-of-ubyte12-fix-imm

(defthm exec32-jalr-of-ubyte12-fix-imm
  (equal (exec32-jalr rd rs1 (ubyte12-fix imm)
                      pc stat)
         (exec32-jalr rd rs1 imm pc stat)))

Theorem: exec32-jalr-ubyte12-equiv-congruence-on-imm

(defthm exec32-jalr-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec32-jalr rd rs1 imm pc stat)
                  (exec32-jalr rd rs1 imm-equiv pc stat)))
  :rule-classes :congruence)

Theorem: exec32-jalr-of-ubyte32-fix-pc

(defthm exec32-jalr-of-ubyte32-fix-pc
  (equal (exec32-jalr rd rs1 imm (ubyte32-fix pc)
                      stat)
         (exec32-jalr rd rs1 imm pc stat)))

Theorem: exec32-jalr-ubyte32-equiv-congruence-on-pc

(defthm exec32-jalr-ubyte32-equiv-congruence-on-pc
  (implies (acl2::ubyte32-equiv pc pc-equiv)
           (equal (exec32-jalr rd rs1 imm pc stat)
                  (exec32-jalr rd rs1 imm pc-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-jalr-of-state32-fix-stat

(defthm exec32-jalr-of-state32-fix-stat
  (equal (exec32-jalr rd rs1 imm pc (state32-fix stat))
         (exec32-jalr rd rs1 imm pc stat)))

Theorem: exec32-jalr-state32-equiv-congruence-on-stat

(defthm exec32-jalr-state32-equiv-congruence-on-stat
  (implies (state32-equiv stat stat-equiv)
           (equal (exec32-jalr rd rs1 imm pc stat)
                  (exec32-jalr rd rs1 imm pc stat-equiv)))
  :rule-classes :congruence)