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Semantics32

Exec32-jal

Semantics of the JAL instruction [ISA:2.5.1].

Signature
(exec32-jal rd imm pc stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; imm — Guard (ubyte20p imm).; pc — Guard (ubyte32p pc).; stat — Guard (stat32ip stat).
Returns: new-stat — Type (stat32ip new-stat).

We use the 20 bits of the immediate as the high bits of an unsigned 21-bit integer, whose low bit is 0 (i.e. the immediate measures multiples of 2); the unsigned 21-bit integer is sign-extended to 32 bits, obtaining an offset. We add the offset to the address of the instruction, which is passed as the pc input to this function; 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. We write the jump target to the program counter.

Definitions and Theorems

Function: exec32-jal

(defun exec32-jal (rd imm pc stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte20p imm)
                              (ubyte32p pc)
                              (stat32ip stat))))
  (let ((__function__ 'exec32-jal))
    (declare (ignorable __function__))
    (b* ((offset (loghead 32
                          (logext 21 (ash (ubyte20-fix imm) 1))))
         (pc (ubyte32-fix pc))
         (target-pc (+ pc offset))
         (next-pc (+ pc 4))
         (stat (write32-xreg rd next-pc stat))
         (stat (write32-pc target-pc stat)))
      stat)))

Theorem: stat32ip-of-exec32-jal

(defthm stat32ip-of-exec32-jal
  (b* ((new-stat (exec32-jal rd imm pc stat)))
    (stat32ip new-stat))
  :rule-classes :rewrite)

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

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

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

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

Theorem: exec32-jal-of-ubyte20-fix-imm

(defthm exec32-jal-of-ubyte20-fix-imm
  (equal (exec32-jal rd (ubyte20-fix imm)
                     pc stat)
         (exec32-jal rd imm pc stat)))

Theorem: exec32-jal-ubyte20-equiv-congruence-on-imm

(defthm exec32-jal-ubyte20-equiv-congruence-on-imm
  (implies (acl2::ubyte20-equiv imm imm-equiv)
           (equal (exec32-jal rd imm pc stat)
                  (exec32-jal rd imm-equiv pc stat)))
  :rule-classes :congruence)

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

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

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

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

Theorem: exec32-jal-of-stat32i-fix-stat

(defthm exec32-jal-of-stat32i-fix-stat
  (equal (exec32-jal rd imm pc (stat32i-fix stat))
         (exec32-jal rd imm pc stat)))

Theorem: exec32-jal-stat32i-equiv-congruence-on-stat

(defthm exec32-jal-stat32i-equiv-congruence-on-stat
  (implies (stat32i-equiv stat stat-equiv)
           (equal (exec32-jal rd imm pc stat)
                  (exec32-jal rd imm pc stat-equiv)))
  :rule-classes :congruence)